4. The model file¶
4.1. Conventions¶
A model file contains a list of commands and of blocks. Each command
and each element of a block is terminated by a semicolon (;). Blocks
are terminated by end;
.
Most Dynare commands have arguments and several accept options, indicated in parentheses after the command keyword. Several options are separated by commas.
In the description of Dynare commands, the following conventions are observed:
 Optional arguments or options are indicated between square brackets: ‘[]’;
 Repeated arguments are indicated by ellipses: “…”;
 Mutually exclusive arguments are separated by vertical bars: ‘’;
 INTEGER indicates an integer number;
 INTEGER_VECTOR indicates a vector of integer numbers separated by spaces, enclosed by square brackets;
 DOUBLE indicates a double precision number. The following syntaxes
are valid:
1.1e3
,1.1E3
,1.1d3
,1.1D3
. In some places, infinite ValuesInf
andInf
are also allowed;  NUMERICAL_VECTOR indicates a vector of numbers separated by spaces, enclosed by square brackets;
 EXPRESSION indicates a mathematical expression valid outside the model description (see Expressions);
 MODEL_EXPRESSION (sometimes MODEL_EXP) indicates a mathematical expression valid in the model description (see Expressions and Model declaration);
 MACRO_EXPRESSION designates an expression of the macroprocessor (see Macro expressions);
 VARIABLE_NAME (sometimes VAR_NAME) indicates a variable name starting with an alphabetical character and can’t contain: ‘()+*/^=!;:@#.’ or accentuated characters;
 PARAMETER_NAME (sometimes PARAM_NAME) indicates a parameter name starting with an alphabetical character and can’t contain: ‘()+*/^=!;:@#.’ or accentuated characters;
 LATEX_NAME (sometimes TEX_NAME) indicates a valid LaTeX expression in math mode (not including the dollar signs);
 FUNCTION_NAME indicates a valid MATLAB function name;
 FILENAME indicates a filename valid in the underlying operating system; it is necessary to put it between quotes when specifying the extension or if the filename contains a nonalphanumeric character;
4.2. Variable declarations¶
While Dynare allows the user to choose their own variable names, there
are some restrictions to be kept in mind. First, variables and
parameters must not have the same name as Dynare commands or builtin
functions. In this respect, Dynare is not casesensitive. For example,
do not use Ln
or Sigma_e
to name your variable. Not conforming
to this rule might yield hardtodebug error messages or
crashes. Second, to minimize interference with MATLAB or Octave
functions that may be called by Dynare or userdefined steady state
files, it is recommended to avoid using the name of MATLAB
functions. In particular when working with steady state files, do not
use correctlyspelled greek names like alpha, because there are
Matlab functions of the same name. Rather go for alppha
or
alph
. Lastly, please do not name a variable or parameter
i
. This may interfere with the imaginary number i and the index in
many loops. Rather, name investment invest
. Using inv
is also
not recommended as it already denotes the inverse operator. Commands
for declaring variables and parameters are described below.

Command:
var
VAR_NAME [$TEX_NAME$] [(long_name=QUOTED_STRNAME=QUOTED_STR)]...;
¶ 
Command:
var
(deflator=MODEL_EXPR) VAR_NAME (... same options apply)

Command:
var
(log_deflator=MODEL_EXPR) VAR_NAME (... same options apply)
This required command declares the endogenous variables in the model. See Conventions for the syntax of VAR_NAME and MODEL_EXPR. Optionally it is possible to give a LaTeX name to the variable or, if it is nonstationary, provide information regarding its deflator.var
commands can appear several times in the file and Dynare will concatenate them. Dynare stores the list of declared parameters, in the order of declaration, in a column cell arrayM_.endo_names
.Options
If the model is nonstationary and is to be written as such in the
model
block, Dynare will need the trend deflator for the appropriate endogenous variables in order to stationarize the model. The trend deflator must be provided alongside the variables that follow this trend.
deflator = MODEL_EXPR
¶ The expression used to detrend an endogenous variable. All trend variables, endogenous variables and parameters referenced in MODEL_EXPR must already have been declared by the
trend_var, log_trend_var, var
andparameters
commands. The deflator is assumed to be multiplicative; for an additive deflator, uselog_deflator
.

log_deflator = MODEL_EXPR
¶ Same as
deflator
, except that the deflator is assumed to be additive instead of multiplicative (or, to put it otherwise, the declared variable is equal to the log of a variable with a multiplicative trend).

long_name = QUOTED_STR
¶ This is the long version of the variable name. Its value is stored in
M_.endo_names_long
(a column cell array, in the same order asM_.endo_names
). In case multiplelong_name
options are provided, the last one will be used. Default:VAR_NAME
.

NAME = QUOTED_STR
¶ This is used to create a partitioning of variables. It results in the direct output in the
.m
file analogous to:M_.endo_partitions.NAME = QUOTED_STR
;.
Example (variable partitioning)
var c gnp cva (country=`US', state=`VA') cca (country=`US', state=`CA', long_name=`Consumption CA'); var(deflator=A) i b; var c $C$ (long_name=`Consumption');


Command:
varexo
VAR_NAME [$TEX_NAME$] [(long_name=QUOTED_STRNAME=QUOTED_STR)...];
¶
This optional command declares the exogenous variables in the model. See Conventions for the syntax ofVAR_NAME
. Optionally it is possible to give a LaTeX name to the variable. Exogenous variables are required if the user wants to be able to apply shocks to her model.varexo
commands can appear several times in the file and Dynare will concatenate them.Options

NAME = QUOTED_STRING
¶ Like partitioning but QUOTED_STRING stored in
M_.exo_partitions.NAME
.
Example
varexo m gov;
Remarks
An exogenous variable is an innovation, in the sense that this variable cannot be predicted from the knowledge of the current state of the economy. For instance, if logged TFP is a first order autoregressive process:
\[a_t = \rho a_{t1} + \varepsilon_t\]then logged TFP \(a_t\) is an endogenous variable to be declared with
var
, its best prediction is \(\rho a_{t1}\), while the innovation \(\varepsilon_t\) is to be declared withvarexo
.

Command:
varexo_det
VAR_NAME [$TEX_NAME$] [(long_name=QUOTED_STRNAME=QUOTED_STR)...];
¶
This optional command declares exogenous deterministic variables in a stochastic model. See Conventions for the syntax of VARIABLE_NAME. Optionally it is possible to give a LaTeX name to the variable.varexo_det
commands can appear several times in the file and Dynare will concatenate them.It is possible to mix deterministic and stochastic shocks to build models where agents know from the start of the simulation about future exogenous changes. In that case
stoch_simul
will compute the rational expectation solution adding future information to the state space (nothing is shown in the output ofstoch_simul
) and forecast will compute a simulation conditional on initial conditions and future information.Options

long_name = QUOTED_STRING
Like long_name but value stored in
M_.exo_det_names_long
.

NAME = QUOTED_STRING
Like partitioning but QUOTED_STRING stored in
M_.exo_det_partitions.NAME
.
Example
varexo m gov; varexo_det tau;


Command:
parameters
PARAM_NAME [$TEX_NAME$] [(long_name=QUOTED_STRNAME=QUOTED_STR)...];
¶
This command declares parameters used in the model, in variable initialization or in shocks declarations. See Conventions for the syntax ofPARAM_NAME
. Optionally it is possible to give a LaTeX name to the parameter.The parameters must subsequently be assigned values (see Parameter initialization).
parameters
commands can appear several times in the file and Dynare will concatenate them.Options

long_name = QUOTED_STRING
Like long_name but value stored in
M_.param_names_long
.

NAME = QUOTED_STRING
Like partitioning but QUOTED_STRING stored in
M_.param_partitions.NAME
.
Example
parameters alpha, bet;


Command:
change_type
(varvarexovarexo_detparameters) VAR_NAME  PARAM_NAME...;
¶ Changes the types of the specified variables/parameters to another type: endogenous, exogenous, exogenous deterministic or parameter. It is important to understand that this command has a global effect on the
.mod
file: the type change is effective after, but also before, thechange_type
command. This command is typically used when flipping some variables for steady state calibration: typically a separate model file is used for calibration, which includes the list of variable declarations with the macroprocessor, and flips some variable.Example
var y, w; parameters alpha, beta; ... change_type(var) alpha, beta; change_type(parameters) y, w;
Here, in the whole model file,
alpha
andbeta
will be endogenous andy
andw
will be parameters.

Command:
predetermined_variables
VAR_NAME...;
¶
In Dynare, the default convention is that the timing of a variable reflects when this variable is decided. The typical example is for capital stock: since the capital stock used at current period is actually decided at the previous period, then the capital stock entering the production function isk(1)
, and the law of motion of capital must be written:k = i + (1delta)*k(1)
Put another way, for stock variables, the default in Dynare is to use a “stock at the end of the period” concept, instead of a “stock at the beginning of the period” convention.
The
predetermined_variables
is used to change that convention. The endogenous variables declared as predetermined variables are supposed to be decided one period ahead of all other endogenous variables. For stock variables, they are supposed to follow a “stock at the beginning of the period” convention.Note that Dynare internally always uses the “stock at the end of the period” concept, even when the model has been entered using the
predetermined_variables
command. Thus, when plotting, computing or simulating variables, Dynare will follow the convention to use variables that are decided in the current period. For example, when generating impulse response functions for capital, Dynare will plotk
, which is the capital stock decided upon by investment today (and which will be used in tomorrow’s production function). This is the reason that capital is shown to be moving on impact, because it isk
and not the predeterminedk(1)
that is displayed. It is important to remember that this also affects simulated time series and output from smoother routines for predetermined variables. Compared to nonpredetermined variables they might otherwise appear to be falsely shifted to the future by one period.Example
The following two program snippets are strictly equivalent.
Using default Dynare timing convention:
var y, k, i; ... model; y = k(1)^alpha; k = i + (1delta)*k(1); ... end;
Using the alternative timing convention:
var y, k, i; predetermined_variables k; ... model; y = k^alpha; k(+1) = i + (1delta)*k; ... end;

Command:
trend_var
(growth_factor = MODEL_EXPR) VAR_NAME [$LATEX_NAME$]...;
¶
This optional command declares the trend variables in the model. See ref:conv for the syntax of MODEL_EXPR and VAR_NAME. Optionally it is possible to give a LaTeX name to the variable.The variable is assumed to have a multiplicative growth trend. For an additive growth trend, use
log_trend_var
instead.Trend variables are required if the user wants to be able to write a nonstationary model in the
model
block. Thetrend_var
command must appear before the var command that references the trend variable.trend_var
commands can appear several times in the file and Dynare will concatenate them.If the model is nonstationary and is to be written as such in the
model
block, Dynare will need the growth factor of every trend variable in order to stationarize the model. The growth factor must be provided within the declaration of the trend variable, using thegrowth_factor
keyword. All endogenous variables and parameters referenced in MODEL_EXPR must already have been declared by the var and parameters commands.Example
trend_var (growth_factor=gA) A;

Command:
log_trend_var
(log_growth_factor = MODEL_EXPR) VAR_NAME [$LATEX_NAME$]...;
¶
Same astrend_var
, except that the variable is supposed to have an additive trend (or, to put it otherwise, to be equal to the log of a variable with a multiplicative trend).

Command:
model_local_variable
VARIABLE_NAME [LATEX_NAME]... ;
¶
This optional command declares a model local variable. See Conventions for the syntax of VARIABLE_NAME. As you can create model local variables on the fly in the model block (see Model declaration), the interest of this command is primarily to assign a LATEX_NAME to the model local variable.Example
model_local_variable GDP_US $GDPUS$;
4.3. Expressions¶
Dynare distinguishes between two types of mathematical expressions: those that are used to describe the model, and those that are used outside the model block (e.g. for initializing parameters or variables, or as command options). In this manual, those two types of expressions are respectively denoted by MODEL_EXPRESSION and EXPRESSION.
Unlike MATLAB or Octave expressions, Dynare expressions are necessarily scalar ones: they cannot contain matrices or evaluate to matrices [1].
Expressions can be constructed using integers (INTEGER), floating point numbers (DOUBLE), parameter names (PARAMETER_NAME), variable names (VARIABLE_NAME), operators and functions.
The following special constants are also accepted in some contexts:

Constant:
inf
¶ Represents infinity.

Constant:
nan
¶ “Not a number”: represents an undefined or unrepresentable value.
4.3.1. Parameters and variables¶
Parameters and variables can be introduced in expressions by simply typing their names. The semantics of parameters and variables is quite different whether they are used inside or outside the model block.
4.3.1.1. Inside the model¶
Parameters used inside the model refer to the value given through
parameter initialization (see Parameter initialization) or homotopy_setup
when doing a simulation, or are the estimated variables when doing an
estimation.
Variables used in a MODEL_EXPRESSION denote current period values when
neither a lead or a lag is given. A lead or a lag can be given by
enclosing an integer between parenthesis just after the variable name:
a positive integer means a lead, a negative one means a lag. Leads or
lags of more than one period are allowed. For example, if c
is an
endogenous variable, then c(+1)
is the variable one period ahead,
and c(2)
is the variable two periods before.
When specifying the leads and lags of endogenous variables, it is important to respect the following convention: in Dynare, the timing of a variable reflects when that variable is decided. A control variable — which by definition is decided in the current period — must have no lead. A predetermined variable — which by definition has been decided in a previous period — must have a lag. A consequence of this is that all stock variables must use the “stock at the end of the period” convention.
Leads and lags are primarily used for endogenous variables, but can be used for exogenous variables. They have no effect on parameters and are forbidden for local model variables (see Model declaration).
4.3.1.2. Outside the model¶
When used in an expression outside the model block, a parameter or a
variable simply refers to the last value given to that variable. More
precisely, for a parameter it refers to the value given in the
corresponding parameter initialization (see Parameter initialization); for an
endogenous or exogenous variable, it refers to the value given in the
most recent initval
or endval
block.
4.3.2. Operators¶
The following operators are allowed in both MODEL_EXPRESSION and EXPRESSION:
 Binary arithmetic operators:
+
,
,*
,/
,^
 Unary arithmetic operators:
+
,
 Binary comparison operators (which evaluate to either 0 or 1):
<
,>
,<=
,>=
,==
,!=
Note the binary comparison operators are differentiable everywhere except on a line of the 2dimensional real plane. However for facilitating convergence of Newtontype methods, Dynare assumes that, at the points of nondifferentiability, the partial derivatives of these operators with respect to both arguments is equal to 0 (since this is the value of the partial derivatives everywhere else).
The following special operators are accepted in MODEL_EXPRESSION (but not in EXPRESSION):

Operator:
STEADY_STATE (MODEL_EXPRESSION)
¶ This operator is used to take the value of the enclosed expression at the steady state. A typical usage is in the Taylor rule, where you may want to use the value of GDP at steady state to compute the output gap.

Operator:
EXPECTATION (INTEGER) (MODEL_EXPRESSION)
¶ This operator is used to take the expectation of some expression using a different information set than the information available at current period. For example,
EXPECTATION(1)(x(+1))
is equal to the expected value of variable x at next period, using the information set available at the previous period. See Auxiliary variables for an explanation of how this operator is handled internally and how this affects the output.
4.3.3. Functions¶
4.3.3.1. Builtin functions¶
The following standard functions are supported internally for both MODEL_EXPRESSION and EXPRESSION:

Function:
exp
(x)
¶ Natural exponential.

Function:
log
(x)
¶

Function:
ln
(x)
¶ Natural logarithm.

Function:
log10
(x)
¶ Base 10 logarithm.

Function:
sqrt
(x)
¶ Square root.

Function:
sign
(x)
¶ Signum function, defined as:
\[\begin{split}\textrm{sign}(x) = \begin{cases} 1 &\quad\text{if }x<0\\ 0 &\quad\text{if }x=0\\ 1 &\quad\text{if }x>0 \end{cases}\end{split}\]Note that this function is not continuous, hence not differentiable, at \(x=0\). However, for facilitating convergence of Newtontype methods, Dynare assumes that the derivative at \(x=0\) is equal to \(0\). This assumption comes from the observation that both the right and leftderivatives at this point exist and are equal to \(0\), so we can remove the singularity by postulating that the derivative at \(x=0\) is \(0\).

Function:
abs
(x)
¶ Absolute value.
Note that this continuous function is not differentiable at \(x=0\). However, for facilitating convergence of Newtontype methods, Dynare assumes that the derivative at \(x=0\) is equal to \(0\) (even if the derivative does not exist). The rational for this mathematically unfounded definition, rely on the observation that the derivative of \(\mathrm{abs}(x)\) is equal to \(\mathrm{sign}(x)\) for any \(x\neq 0\) in \(\mathbb R\) and from the convention for the value of \(\mathrm{sign}(x)\) at \(x=0\)).

Function:
sin
(x)
¶

Function:
cos
(x)
¶

Function:
tan
(x)
¶

Function:
asin
(x)
¶

Function:
acos
(x)
¶

Function:
atan
(x)
¶ Trigonometric functions.

Function:
max
(a, b)
¶

Function:
min
(a, b)
¶ Maximum and minimum of two reals.
Note that these functions are differentiable everywhere except on a line of the 2dimensional real plane defined by \(a=b\). However for facilitating convergence of Newtontype methods, Dynare assumes that, at the points of nondifferentiability, the partial derivative of these functions with respect to the first (resp. the second) argument is equal to \(1\) (resp. to \(0\)) (i.e. the derivatives at the kink are equal to the derivatives observed on the halfplane where the function is equal to its first argument).

Function:
normcdf
(x)
¶ 
Function:
normcdf
(x, mu, sigma)
Gaussian cumulative density function, with mean mu and standard deviation sigma. Note that
normcdf(x)
is equivalent tonormcdf(x,0,1)
.

Function:
normpdf
(x)
¶ 
Function:
normpdf
(x, mu, sigma)
Gaussian probability density function, with mean mu and standard deviation sigma. Note that
normpdf(x)
is equivalent tonormpdf(x,0,1)
.

Function:
erf
(x)
¶ Gauss error function.
4.3.3.2. External functions¶
Any other userdefined (or builtin) MATLAB or Octave function may be used in both a MODEL_EXPRESSION and an EXPRESSION, provided that this function has a scalar argument as a return value.
To use an external function in a MODEL_EXPRESSION, one must declare
the function using the external_function
statement. This is not
required for external functions used in an EXPRESSION outside of a
model
block or steady_state_model
block.

Command:
external_function
(OPTIONS...);
¶ This command declares the external functions used in the model block. It is required for every unique function used in the model block.
external_function
commands can appear several times in the file and must come before the model block.Options

name = NAME
¶ The name of the function, which must also be the name of the M/MEX file implementing it. This option is mandatory.

nargs = INTEGER
¶ The number of arguments of the function. If this option is not provided, Dynare assumes
nargs = 1
.

first_deriv_provided [= NAME]
¶ If NAME is provided, this tells Dynare that the Jacobian is provided as the only output of the M/MEX file given as the option argument. If NAME is not provided, this tells Dynare that the M/MEX file specified by the argument passed to NAME returns the Jacobian as its second output argument.

second_deriv_provided [= NAME]
¶ If NAME is provided, this tells Dynare that the Hessian is provided as the only output of the M/MEX file given as the option argument. If NAME is not provided, this tells Dynare that the M/MEX file specified by the argument passed to NAME returns the Hessian as its third output argument. NB: This option can only be used if the
first_deriv_provided
option is used in the sameexternal_function
command.
Example
external_function(name = funcname); external_function(name = otherfuncname, nargs = 2, first_deriv_provided, second_deriv_provided); external_function(name = yetotherfuncname, nargs = 3, first_deriv_provided = funcname_deriv);

4.3.4. A few words of warning in stochastic context¶
The use of the following functions and operators is strongly
discouraged in a stochastic context: max
, min
, abs
,
sign
, <
, >
, <=
, >=
, ==
, !=
.
The reason is that the local approximation used by stoch_simul
or
estimation
will by nature ignore the nonlinearities introduced by
these functions if the steady state is away from the kink. And, if the
steady state is exactly at the kink, then the approximation will be
bogus because the derivative of these functions at the kink is bogus
(as explained in the respective documentations of these functions and
operators).
Note that extended_path
is not affected by this problem, because
it does not rely on a local approximation of the mode.
4.4. Parameter initialization¶
When using Dynare for computing simulations, it is necessary to calibrate the parameters of the model. This is done through parameter initialization.
The syntax is the following:
PARAMETER_NAME = EXPRESSION;
Here is an example of calibration:
parameters alpha, beta;
beta = 0.99;
alpha = 0.36;
A = 1alpha*beta;
Internally, the parameter values are stored in M_.params
:

MATLAB/Octave variable:
M_.params
¶ Contains the values of model parameters. The parameters are in the order that was used in the parameters command, hence oredered as in
M_.param_names
.
4.5. Model declaration¶
The model is declared inside a model
block:

Block:
model
;
¶ 
Block:
model
(OPTIONS...);
The equations of the model are written in a block delimited bymodel
andend
keywords.There must be as many equations as there are endogenous variables in the model, except when computing the unconstrained optimal policy with
ramsey_model
,ramsey_policy
ordiscretionary_policy
.The syntax of equations must follow the conventions for MODEL_EXPRESSION as described in Expressions. Each equation must be terminated by a semicolon (‘;’). A normal equation looks like:
MODEL_EXPRESSION = MODEL_EXPRESSION;
When the equations are written in homogenous form, it is possible to omit the ‘=0’ part and write only the left hand side of the equation. A homogenous equation looks like:MODEL_EXPRESSION;
Inside the model block, Dynare allows the creation of modellocal variables, which constitute a simple way to share a common expression between several equations. The syntax consists of a pound sign (#) followed by the name of the new model local variable (which must not be declared as in Variable declarations, but may have been declared bymodel_local_variable
), an equal sign, and the expression for which this new variable will stand. Later on, every time this variable appears in the model, Dynare will substitute it by the expression assigned to the variable. Note that the scope of this variable is restricted to the model block; it cannot be used outside. To assign a LaTeX name to the model local variable, use the declaration syntax outlined bymodel_local_variable
. A model local variable declaration looks like:#VARIABLE_NAME = MODEL_EXPRESSION;
It is possible to tag equations written in the model block. A tag can serve different purposes by allowing the user to attach arbitrary informations to each equation and to recover them at runtime. For instance, it is possible to name the equations with aname
tag, using a syntax like:model; [name = 'Budget constraint']; c + k = k^theta*A; end;
Here,
name
is the keyword indicating that the tag names the equation. If an equation of the model is tagged with a name, theresid
command will display the name of the equations (which may be more informative than the equation numbers) in addition to the equation number. Several tags for one equation can be separated using a comma:model; [name='Taylor rule',mcp = 'r > 1.94478'] r = rho*r(1) + (1rho)*(gpi*Infl+gy*YGap) + e; end;
More information on tags is available on the Dynare wiki.
Options

linear
¶ Declares the model as being linear. It spares oneself from having to declare initial values for computing the steady state of a stationary linear model. This option can’t be used with nonlinear models, it will NOT trigger linearization of the model.

use_dll
¶ Instructs the preprocessor to create dynamic loadable libraries (DLL) containing the model equations and derivatives, instead of writing those in Mfiles. You need a working compilation environment, i.e. a working
mex
command (see Compiler installation for more details). On MATLAB for Windows, you will need to also pass the compiler name at the command line. Using this option can result in faster simulations or estimations, at the expense of some initial compilation time. [2]

block
¶ Perform the block decomposition of the model, and exploit it in computations (steadystate, deterministic simulation, stochastic simulation with first order approximation and estimation). See Dynare wiki for details on the algorithms used in deterministic simulation and steadystate computation.

bytecode
¶ Instead of Mfiles, use a bytecode representation of the model, i.e. a binary file containing a compact representation of all the equations.

cutoff = DOUBLE
¶ Threshold under which a jacobian element is considered as null during the model normalization. Only available with option
block
. Default:1e15

mfs = INTEGER
¶ Controls the handling of minimum feedback set of endogenous variables. Only available with option
block
. Possible values:0
All the endogenous variables are considered as feedback variables (Default).1
The endogenous variables assigned to equation naturally normalized (i.e. of the form \(x=f(Y)\) where \(x\) does not appear in \(Y\)) are potentially recursive variables. All the other variables are forced to belong to the set of feedback variables.2
In addition of variables withmfs = 1
the endogenous variables related to linear equations which could be normalized are potential recursive variables. All the other variables are forced to belong to the set of feedback variables.3
In addition of variables withmfs = 2
the endogenous variables related to nonlinear equations which could be normalized are potential recursive variables. All the other variables are forced to belong to the set of feedback variables.

no_static
¶ Don’t create the static model file. This can be useful for models which don’t have a steady state.

differentiate_forward_vars differentiate_forward_vars = ( VARIABLE_NAME [VARIABLE_NAME ...] )
¶ Tells Dynare to create a new auxiliary variable for each endogenous variable that appears with a lead, such that the new variable is the time differentiate of the original one. More precisely, if the model contains
x(+1)
, then a variableAUX_DIFF_VAR
will be created such thatAUX_DIFF_VAR=xx(1)
, andx(+1)
will be replaced withx+AUX_DIFF_VAR(+1)
.The transformation is applied to all endogenous variables with a lead if the option is given without a list of variables. If there is a list, the transformation is restricted to endogenous with a lead that also appear in the list.
This option can useful for some deterministic simulations where convergence is hard to obtain. Bad values for terminal conditions in the case of very persistent dynamics or permanent shocks can hinder correct solutions or any convergence. The new differentiated variables have obvious zero terminal conditions (if the terminal condition is a steady state) and this in many cases helps convergence of simulations.

parallel_local_files = ( FILENAME [, FILENAME]... )
¶ Declares a list of extra files that should be transferred to slave nodes when doing a parallel computation (see Parallel Configuration).
Example (Elementary RBC model)
var c k; varexo x; parameters aa alph bet delt gam; model; c =  k + aa*x*k(1)^alph + (1delt)*k(1); c^(gam) = (aa*alph*x(+1)*k^(alph1) + 1  delt)*c(+1)^(gam)/(1+bet); end;
Example (Use of model local variables)
The following program:
model; # gamma = 1  1/sigma; u1 = c1^gamma/gamma; u2 = c2^gamma/gamma; end;
…is formally equivalent to:
model; u1 = c1^(11/sigma)/(11/sigma); u2 = c2^(11/sigma)/(11/sigma); end;
Example (A linear model)
model(linear); x = a*x(1)+b*y(+1)+e_x; y = d*y(1)+e_y; end;

Dynare has the ability to output the original list of model equations
to a LaTeX file, using the write_latex_original_model
command, the list of transformed model equations using the
write_latex_dynamic_model command
, and the list of static model
equations using the write_latex_static_model
command.

Command:
write_latex_original_model
(OPTIONS);
¶
This command creates two LaTeX files: one containing the model as defined in the model block and one containing the LaTeX document header information.If your
.mod
file isFILENAME.mod
, then Dynare will create a file calledFILENAME_original.tex
, which includes a file calledFILENAME_original_content.tex
(also created by Dynare) containing the list of all the original model equations.If LaTeX names were given for variables and parameters (see Variable declarations), then those will be used; otherwise, the plain text names will be used.
Time subscripts (
t
,t+1
,t1
, …) will be appended to the variable names, as LaTeX subscripts.Compiling the TeX file requires the following LaTeX packages:
geometry, fullpage, breqn
.Options
Write the equation tags in the LaTeX output. The equation tags will be interpreted with LaTeX markups.

Command:
write_latex_dynamic_model
;
¶ 
Command:
write_latex_dynamic_model
(OPTIONS);
This command creates two LaTeX files: one containing the dynamic model and one containing the LaTeX document header information.If your
.mod
file isFILENAME.mod
, then Dynare will create a file calledFILENAME_dynamic.tex
, which includes a file calledFILENAME_dynamic_content.tex
(also created by Dynare) containing the list of all the dynamic model equations.If LaTeX names were given for variables and parameters (see Variable declarations), then those will be used; otherwise, the plain text names will be used.
Time subscripts (
t
,t+1
,t1
, …) will be appended to the variable names, as LaTeX subscripts.Note that the model written in the TeX file will differ from the model declared by the user in the following dimensions:
 The timing convention of predetermined variables (see
predetermined_variables
) will have been changed to the default Dynare timing convention; in other words, variables declared as predetermined will be lagged on period back,  The expectation operators (see
expectation
) will have been removed, replaced by auxiliary variables and new equations as explained in the documentation of the operator,  Endogenous variables with leads or lags greater or equal than two will have been removed, replaced by new auxiliary variables and equations,
 F_or a stochastic model, exogenous variables with leads or lags will also have been replaced by new auxiliary variables and equations.
For the required LaTeX packages, see
write_latex_original_model
.Options

write_equation_tags
 The timing convention of predetermined variables (see

Command:
write_latex_static_model
(OPTIONS);
¶
This command creates two LaTeX files: one containing the static model and one containing the LaTeX document header information.If your
.mod
file isFILENAME.mod
, then Dynare will create a file calledFILENAME_static.tex
, which includes a file calledFILENAME_static_content.tex
(also created by Dynare) containing the list of all the steady state model equations.If LaTeX names were given for variables and parameters (see Variable declarations), then those will be used; otherwise, the plain text names will be used.
Note that the model written in the TeX file will differ from the model declared by the user in the some dimensions (see
write_latex_dynamic_model
for details).Also note that this command will not output the contents of the optional
steady_state_model
block (seesteady_state_model
); it will rather output a static version (i.e. without leads and lags) of the dynamicmodel
declared in the model block. To write the LaTeX contents of thesteady_state_model
seewrite_latex_steady_state_model
.For the required LaTeX packages, see
write_latex_original_model
.Options

write_equation_tags
See
write_equation_tags
.


Command:
write_latex_steady_state_model
()¶
This command creates two LaTeX files: one containing the steady state model and one containing the LaTeX document header information.If your
.mod
file isFILENAME.mod
, then Dynare will create a file calledFILENAME_steady_state.tex
, which includes a file calledFILENAME_steady_state_content.tex
(also created by Dynare) containing the list of all the steady state model equations.If LaTeX names were given for variables and parameters (see Variable declarations), then those will be used; otherwise, the plain text names will be used.
Note that the model written in the
.tex
file will differ from the model declared by the user in some dimensions (seewrite_latex_dynamic_model
for details).For the required LaTeX packages, see
write_latex_original_model
.
4.6. Auxiliary variables¶
The model which is solved internally by Dynare is not exactly the model declared by the user. In some cases, Dynare will introduce auxiliary endogenous variables—along with corresponding auxiliary equations—which will appear in the final output.
The main transformation concerns leads and lags. Dynare will perform a transformation of the model so that there is only one lead and one lag on endogenous variables and, in the case of a stochastic model, no leads/lags on exogenous variables.
This transformation is achieved by the creation of auxiliary variables
and corresponding equations. For example, if x(+2)
exists in the
model, Dynare will create one auxiliary variable AUX_ENDO_LEAD =
x(+1)
, and replace x(+2)
by AUX_ENDO_LEAD(+1)
.
A similar transformation is done for lags greater than 2 on endogenous
(auxiliary variables will have a name beginning with
AUX_ENDO_LAG
), and for exogenous with leads and lags (auxiliary
variables will have a name beginning with AUX_EXO_LEAD
or
AUX_EXO_LAG
respectively).
Another transformation is done for the EXPECTATION
operator. For
each occurrence of this operator, Dynare creates an auxiliary variable
defined by a new equation, and replaces the expectation operator by a
reference to the new auxiliary variable. For example, the expression
EXPECTATION(1)(x(+1))
is replaced by AUX_EXPECT_LAG_1(1)
,
and the new auxiliary variable is declared as AUX_EXPECT_LAG_1 =
x(+2)
.
Auxiliary variables are also introduced by the preprocessor for the
ramsey_model
and ramsey_policy
commands. In this case, they
are used to represent the Lagrange multipliers when first order
conditions of the Ramsey problem are computed. The new variables take
the form MULT_i
, where i represents the constraint with which
the multiplier is associated (counted from the order of declaration in
the model block).
The last type of auxiliary variables is introduced by the
differentiate_forward_vars
option of the model block. The new
variables take the form AUX_DIFF_FWRD_i
, and are equal to
xx(1)
for some endogenous variable x
.
Once created, all auxiliary variables are included in the set of endogenous variables. The output of decision rules (see below) is such that auxiliary variable names are replaced by the original variables they refer to.
The number of endogenous variables before the creation of auxiliary
variables is stored in M_.orig_endo_nbr
, and the number of
endogenous variables after the creation of auxiliary variables is
stored in M_.endo_nbr
.
See Dynare wiki for more technical details on auxiliary variables.
4.7. Initial and terminal conditions¶
For most simulation exercises, it is necessary to provide initial (and possibly terminal) conditions. It is also necessary to provide initial guess values for nonlinear solvers. This section describes the statements used for those purposes.
In many contexts (deterministic or stochastic), it is necessary to
compute the steady state of a nonlinear model: initval
then
specifies numerical initial values for the nonlinear solver. The
command resid
can be used to compute the equation residuals for
the given initial values.
Used in perfect foresight mode, the types of forwardlooking models for which Dynare was designed require both initial and terminal conditions. Most often these initial and terminal conditions are static equilibria, but not necessarily.
One typical application is to consider an economy at the equilibrium
at time 0, trigger a shock in first period, and study the trajectory
of return to the initial equilibrium. To do that, one needs
initval
and shocks
(see Shocks on exogenous variables).
Another one is to study how an economy, starting from arbitrary
initial conditions at time 0 converges towards equilibrium. In this
case models, the command histval
permits to specify different
historical initial values for variables with lags for the periods
before the beginning of the simulation. Due to the design of Dynare,
in this case initval
is used to specify the terminal conditions.

Block:
initval
;
¶ 
Block:
initval
(OPTIONS...);
Theinitval
block has two main purposes: providing guess values for nonlinear solvers in the context of perfect foresight simulations and providing guess values for steady state computations in both perfect foresight and stochastic simulations. Depending on the presence ofhistval
andendval
blocks it is also used for declaring the initial and terminal conditions in a perfect foresight simulation exercise. Because of this interaction of the meaning of aninitval
block with the presence ofhistval
andendval
blocks in perfect foresight simulations, it is strongly recommended to check that the constructedoo_.endo_simul
andoo_.exo_simul
variables contain the desired values after runningperfect_foresight_setup
and before runningperfect_foresight_solver
. In the presence of leads and lags, these subfields of the results structure will store the historical values for the lags in the first column/row and the terminal values for the leads in the last column/row.The
initval
block is terminated byend;
and contains lines of the form:VARIABLE_NAME = EXPRESSION;
In a deterministic (i.e. perfect foresight) modelFirst, it will fill both the
oo_.endo_simul
andoo_.exo_simul
variables storing the endogenous and exogenous variables with the values provided by this block. If there are no other blocks present, it will therefore provide the initial and terminal conditions for all the endogenous and exogenous variables, because it will also fill the last column/row of these matrices. For the intermediate simulation periods it thereby provides the starting values for the solver. In the presence of ahistval
block (and therefore absence of anendval
block), thishistval
block will provide/overwrite the historical values for the state variables (lags) by setting the first column/row ofoo_.endo_simul
andoo_.exo_simul
. This implies that theinitval
block in the presence ofhistval
only sets the terminal values for the variables with leads and provides initial values for the perfect foresight solver.Because of these various functions of
initval
it is often necessary to provide values for all the endogenous variables in aninitval
block. Initial and terminal conditions are strictly necessary for lagged/leaded variables, while feasible starting values are required for the solver. It is important to be aware that if some variables, endogenous or exogenous, are not mentioned in theinitval
block, a zero value is assumed. It is particularly important to keep this in mind when specifying exogenous variables usingvarexo
that are not allowed to take on the value of zero, like e.g. TFP.Note that if the
initval
block is immediately followed by asteady
command, its semantics are slightly changed. Thesteady
command will compute the steady state of the model for all the endogenous variables, assuming that exogenous variables are kept constant at the value declared in theinitval
block. These steady state values conditional on the declared exogenous variables are then written intooo_.endo_simul
and take up the potential roles as historical and terminal conditions as well as starting values for the solver. Aninitval
block followed bysteady
is therefore formally equivalent to aninitval
block with the specified values for the exogenous variables, and the endogenous variables set to the associated steady state values conditional on the exogenous variables.
In a stochastic modelThe main purpose of
initval
is to provide initial guess values for the nonlinear solver in the steady state computation. Note that if theinitval
block is not followed bysteady
, the steady state computation will still be triggered by subsequent commands (stoch_simul
,estimation
…).It is not necessary to declare 0 as initial value for exogenous stochastic variables, since it is the only possible value.
The subsequently computed steady state (not the initial values, use histval for this) will be used as the initial condition at all the periods preceeding the first simulation period for the three possible types of simulations in stochastic mode:
stoch_simul
, if theperiods
option is specified.forecast
as the initial point at which the forecasts are computed.conditional_forecast
as the initial point at which the conditional forecasts are computed.
To start simulations at a particular set of starting values that are not a computed steady state, use
histval
.Options

all_values_required
¶ Issues an error and stops processing the .mod file if there is at least one endogenous or exogenous variable that has not been set in the initval block.
 Example
initval; c = 1.2; k = 12; x = 1; end; steady;

Block:
endval
;
¶ 
Block:
endval
(OPTIONS...);
This block is terminated byend;
and contains lines of the form:VARIABLE_NAME = EXPRESSION;
Theendval
block makes only sense in a deterministic model and cannot be used together withhistval
. Similar to theinitval
command, it will fill both theoo_.endo_simul
andoo_.exo_simul
variables storing the endogenous and exogenous variables with the values provided by this block. If noinitval
block is present, it will fill the whole matrices, therefore providing the initial and terminal conditions for all the endogenous and exogenous variables, because it will also fill the first and last column/row of these matrices. Due to also filling the intermediate simulation periods it will provide the starting values for the solver as well.If an
initval
block is present,initval
will provide the historical values for the variables (if there are states/lags), whileendval
will fill the remainder of the matrices, thereby still providing i) the terminal conditions for variables entering the model with a lead and ii) the initial guess values for all endogenous variables at all the simulation dates for the perfect foresight solver.Note that if some variables, endogenous or exogenous, are NOT mentioned in the
endval
block, the value assumed is that of the lastinitval
block orsteady
command (if present). Therefore, in contrast toinitval
, omitted variables are not automatically assumed to be 0 in this case. Again, it is strongly recommended to check the constructedoo_.endo_simul
andoo_.exo_simul
variables after runningperfect_foresight_setup
and before runningperfect_foresight_solver
to see whether the desired outcome has been achieved.Like
initval
, if theendval
block is immediately followed by asteady
command, its semantics are slightly changed. Thesteady
command will compute the steady state of the model for all the endogenous variables, assuming that exogenous variables are kept constant to the value declared in theendval
block. These steady state values conditional on the declared exogenous variables are then written intooo_.endo_simul
and therefore take up the potential roles as historical and terminal conditions as well as starting values for the solver. Anendval
block followed bysteady
is therefore formally equivalent to anendval
block with the specified values for the exogenous variables, and the endogenous variables set to the associated steady state values.Options

all_values_required
See
all_values_required
.
Example
var c k; varexo x; initval; c = 1.2; k = 12; x = 1; end; steady; endval; c = 2; k = 20; x = 2; end; steady;
The initial equilibrium is computed by
steady
conditional onx=1
, and the terminal one conditional onx=2
. Theinitval
block sets the initial condition fork
, while theendval
block sets the terminal condition forc
. The starting values for the perfect foresight solver are given by theendval
block. A detailed explanation follows below the next example.Example
var c k; varexo x; model; c + k  aa*x*k(1)^alph  (1delt)*k(1); c^(gam)  (1+bet)^(1)*(aa*alph*x(+1)*k^(alph1) + 1  delt)*c(+1)^(gam); end; initval; k = 12; end; endval; c = 2; x = 1.1; end; simul(periods=200);
In this example, the problem is finding the optimal path for consumption and capital for the periods \(t=1\) to \(T=200\), given the path of the exogenous technology level
x
.c
is a forwardlooking variable and the exogenous variablex
appears with a lead in the expected return of physical capital, so we need terminal conditions for them, whilek
is a purely backwardlooking (state) variable, so we need an initial condition for it.Setting
x=1.1
in theendval
block without ashocks
block implies that technology is at \(1.1\) in \(t=1\) and stays there forever, becauseendval
is filling all entries ofoo_.endo_simul
andoo_.exo_simul
except for the very first one, which stores the initial conditions and was set to \(0\) by theinitval
block when not explicitly specifying a value for it.Because the law of motion for capital is backwardlooking, we need an initial condition for
k
at time \(0\). Due to the presence ofendval
, this cannot be done via ahistval
block, but rather must be specified in theinitval
block. Similarly, because the Euler equation is forwardlooking, we need a terminal condition forc
at \(t=201\), which is specified in theendval
block.As can be seen, it is not necessary to specify
c
andx
in theinitval
block andk
in theendval
block, because they have no impact on the results. Due to the optimization problem in the first period being to choosec,k
at \(t=1\) given the predetermined capital stockk
inherited from \(t=0\) as well as the current and future values for technologyx
, the values forc
andx
at time \(t=0\) play no role. The same applies to the choice ofc,k
at time \(t=200\), which does not depend onk
at \(t=201\). As the Euler equation shows, that choice only depends on current capital as well as future consumptionc
and technologyx
, but not on future capitalk
. The intuitive reason is that those variables are the consequence of optimization problems taking place in at periods \(t=0\) and \(t=201\), respectively, which are not modeled here.Example
initval; c = 1.2; k = 12; x = 1; end; endval; c = 2; k = 20; x = 1.1; end;
In this example, initial conditions for the forwardlooking variables
x
andc
are provided, together with a terminal condition for the backwardlooking variablek
. As shown in the previous example, these values will not affect the simulation results. Dynare simply takes them as given and basically assumes that there were realizations of exogenous variables and states that make those choices equilibrium values (basically initial/terminal conditions at the unspecified time periods \(t<0\) and \(t>201\)).The above example suggests another way of looking at the use of
steady
afterinitval
andendval
. Instead of saying that the implicit unspecified conditions before and after the simulation range have to fit the initial/terminal conditions of the endogenous variables in those blocks, steady specifies that those conditions at \(t<0\) and \(t>201\) are equal to being at the steady state given the exogenous variables in theinitval
andendval
blocks. The endogenous variables at \(t=0\) and \(t=201\) are then set to the corresponding steady state equilibrium values.The fact that
c
at \(t=0\) andk
at \(t=201\) specified ininitval
and``endval
are taken as given has an important implication for plotting the simulated vector for the endogenous variables, i.e. the rows ofoo_.endo_simul
: this vector will also contain the initial and terminal conditions and thus is 202 periods long in the example. When you specify arbitrary values for the initial and terminal conditions for forward and backwardlooking variables, respectively, these values can be very far away from the endogenously determined values at \(t=1\) and \(t=200\). While the values at \(t=0\) and \(t=201\) are unrelated to the dynamics for \(0<t<201\), they may result in strangelooking large jumps. In the example above, consumption will display a large jump from \(t=0\) to \(t=1\) and capital will jump from \(t=200\) to \(t=201\) when usingrplot
or manually plottingoo_.endo_val
.

Block:
histval
;
¶ 
Block:
histval
(OPTIONS...);
In a deterministic perfect foresight contextIn models with lags on more than one period, the
histval
block permits to specify different historical initial values for different periods of the state variables. In this case, theinitval
block takes over the role of specifying terminal conditions and starting values for the solver. Note that thehistval
block does not take nonstate variables.This block is terminated by
end;
and contains lines of the form:VARIABLE_NAME(INTEGER) = EXPRESSION;
EXPRESSION is any valid expression returning a numerical value and can contain already initialized variable names.By convention in Dynare, period 1 is the first period of the simulation. Going backward in time, the first period before the start of the simulation is period 0, then period 1, and so on.
State variables not initialized in the
histval
block are assumed to have a value of zero at period 0 and before. Note thathistval
cannot be followed bysteady
.Example
model; x=1.5*x(1)0.6*x(2)+epsilon; log(c)=0.5*x+0.5*log(c(+1)); end; histval; x(0)=1; x(1)=0.2; end; initval; c=1; x=1; end;
In this example,
histval
is used to set the historical conditions for the two lags of the endogenous variablex
, stored in the first column ofoo_.endo_simul
. Theinitval
block is used to set the terminal condition for the forward looking variablec
, stored in the last column ofoo_.endo_simul
. Moreover, theinitval
block defines the starting values for the perfect foresight solver for both endogenous variablesc
andx
.In a stochastic simulation context
In the context of stochastic simulations,
histval
allows setting the starting point of those simulations in the state space. As for the case of perfect foresight simulations, all not explicitly specified variables are set to 0. Moreover, as only states enter the recursive policy functions, all values specified for control variables will be ignored. This can be used In
stoch_simul
, if theperiods
option is specified. Note that this only affects the starting point for the simulation, but not for the impulse response functions. When using the loglinear option, thehistval
block nevertheless takes the unlogged starting values.  In
forecast
as the initial point at which the forecasts are computed. When using the loglinear option, thehistval
block nevertheless takes the unlogged starting values.  In
conditional_forecast
for a calibrated model as the initial point at which the conditional forecasts are computed. When using the loglinear option, the histvalblock nevertheless takes the unlogged starting values.  In
Ramsey policy
, where it also specifies the values of the endogenous states at which the objective function of the planner is computed. Note that the initial values of the Lagrange multipliers associated with the planner’s problem cannot be set (see planner_objective_value).
Options

all_values_required
See
all_values_required
.
Example
var x y; varexo e; model; x = y(1)^alpha*y(2)^(1alpha)+e; end; initval; x = 1; y = 1; e = 0.5; end; steady; histval; y(0) = 1.1; y(1) = 0.9; end; stoch_simul(periods=100);
 In

Command:
resid
;
¶
This command will display the residuals of the static equations of the model, using the values given for the endogenous in the lastinitval
orendval
block (or the steady state file if you provided one, see Steady state).

Command:
initval_file
(filename = FILENAME);
¶
In a deterministic setup, this command is used to specify a path for all endogenous and exogenous variables. The length of these paths must be equal to the number of simulation periods, plus the number of leads and the number of lags of the model (for example, with 50 simulation periods, in a model with 2 lags and 1 lead, the paths must have a length of 53). Note that these paths cover two different things: The constraints of the problem, which are given by the path for exogenous and the initial and terminal values for endogenous
 The initial guess for the nonlinear solver, which is given by the path for endogenous variables for the simulation periods (excluding initial and terminal conditions)
The command accepts three file formats:
 Mfile (extension
.m
): for each endogenous and exogenous variable, the file must contain a row or column vector of the same name. Their length must beperiods + M_.maximum_lag + M_.maximum_lead
 MATfile (extension
.mat
): same as for Mfiles.  Excel file (extension
.xls
or.xlsx
): for each endogenous and exogenous, the file must contain a column of the same name. NB: Octave only supports the.xlsx
file extension and must have the io package installed (easily done via octave by typing ‘pkg install forge io
’).
Warning
The extension must be omitted in the command argument. Dynare will automatically figure out the extension and select the appropriate file type.

Command:
histval_file
(filename = FILENAME);
¶
This command is equivalent tohistval
, except that it reads its input from a file, and is typically used in conjunction withsmoother2histval
.
4.8. Shocks on exogenous variables¶
In a deterministic context, when one wants to study the transition of
one equilibrium position to another, it is equivalent to analyze the
consequences of a permanent shock and this in done in Dynare through
the proper use of initval
and endval
.
Another typical experiment is to study the effects of a temporary
shock after which the system goes back to the original equilibrium (if
the model is stable…). A temporary shock is a temporary change of
value of one or several exogenous variables in the model. Temporary
shocks are specified with the command shocks
.
In a stochastic framework, the exogenous variables take random values
in each period. In Dynare, these random values follow a normal
distribution with zero mean, but it belongs to the user to specify the
variability of these shocks. The nonzero elements of the matrix of
variancecovariance of the shocks can be entered with the shocks
command. Or, the entire matrix can be directly entered with
Sigma_e
(this use is however deprecated).
If the variance of an exogenous variable is set to zero, this variable will appear in the report on policy and transition functions, but isn’t used in the computation of moments and of Impulse Response Functions. Setting a variance to zero is an easy way of removing an exogenous shock.
Note that, by default, if there are several shocks
or mshocks
blocks in the same .mod
file, then they are cumulative: all the
shocks declared in all the blocks are considered; however, if a
shocks
or mshocks
block is declared with the overwrite
option, then it replaces all the previous shocks
and mshocks
blocks.

Block:
shocks
;
¶ 
Block:
shocks
(overwrite);
See above for the meaning of theoverwrite
option.In deterministic context
For deterministic simulations, the
shocks
block specifies temporary changes in the value of exogenous variables. For permanent shocks, use anendval
block.The block should contain one or more occurrences of the following group of three lines:
var VARIABLE_NAME; periods INTEGER[:INTEGER] [[,] INTEGER[:INTEGER]]...; values DOUBLE  (EXPRESSION) [[,] DOUBLE  (EXPRESSION) ]...;
It is possible to specify shocks which last several periods and which can vary over time. The
periods
keyword accepts a list of several dates or date ranges, which must be matched by as many shock values in thevalues
keyword. Note that a range in theperiods
keyword can be matched by only one value in thevalues
keyword. Ifvalues
represents a scalar, the same value applies to the whole range. Ifvalues
represents a vector, it must have as many elements as there are periods in the range.Note that shock values are not restricted to numerical constants: arbitrary expressions are also allowed, but you have to enclose them inside parentheses.
Example (with scalar values)
shocks; var e; periods 1; values 0.5; var u; periods 4:5; values 0; var v; periods 4:5 6 7:9; values 1 1.1 0.9; var w; periods 1 2; values (1+p) (exp(z)); end;
Example (with vector values)
xx = [1.2; 1.3; 1]; shocks; var e; periods 1:3; values (xx); end;
In stochastic contextFor stochastic simulations, the
shocks
block specifies the non zero elements of the covariance matrix of the shocks of exogenous variables.You can use the following types of entries in the block:
Specification of the standard error of an exogenous variable.
var VARIABLE_NAME; stderr EXPRESSION;
Specification of the variance of an exogenous variable.
var VARIABLE_NAME = EXPRESSION;
Specification the covariance of two exogenous variables.
var VARIABLE_NAME, VARIABLE_NAME = EXPRESSION;
Specification of the correlation of two exogenous variables.
corr VARIABLE_NAME, VARIABLE_NAME = EXPRESSION;
In an estimation context, it is also possible to specify variances and covariances on endogenous variables: in that case, these values are interpreted as the calibration of the measurement errors on these variables. This requires the
varobs
command to be specified before theshocks
block.Example
shocks; var e = 0.000081; var u; stderr 0.009; corr e, u = 0.8; var v, w = 2; end;
Mixing deterministic and stochastic shocks
It is possible to mix deterministic and stochastic shocks to build models where agents know from the start of the simulation about future exogenous changes. In that case
stoch_simul
will compute the rational expectation solution adding future information to the state space (nothing is shown in the output ofstoch_simul
) andforecast
will compute a simulation conditional on initial conditions and future information.Example
varexo_det tau; varexo e; ... shocks; var e; stderr 0.01; var tau; periods 1:9; values 0.15; end; stoch_simul(irf=0); forecast;

Block:
mshocks
;
¶ 
Block:
mshocks
(overwrite);
The purpose of this block is similar to that of theshocks
block for deterministic shocks, except that the numeric values given will be interpreted in a multiplicative way. For example, if a value of1.05
is given as shock value for some exogenous at some date, it means 5% above its steady state value (as given by the lastinitval
orendval
block).The syntax is the same than
shocks
in a deterministic context.This command is only meaningful in two situations:
 on exogenous variables with a nonzero steady state, in a deterministic setup,
 on deterministic exogenous variables with a nonzero steady state, in a stochastic setup.
See above for the meaning of the
overwrite
option.

Special variable:
Sigma_e
¶
This special variable specifies directly the covariance matrix of the stochastic shocks, as an upper (or lower) triangular matrix. Dynare builds the corresponding symmetric matrix. Each row of the triangular matrix, except the last one, must be terminated by a semicolon ;. For a given element, an arbitrary EXPRESSION is allowed (instead of a simple constant), but in that case you need to enclose the expression in parentheses. The order of the covariances in the matrix is the same as the one used in thevarexo
declaration.Example
varexo u, e; Sigma_e = [ 0.81 (phi*0.9*0.009); 0.000081];
This sets the variance of
u
to 0.81, the variance ofe
to 0.000081, and the correlation betweene
andu
tophi
.Warning
The use of this special variable is deprecated and is strongly discouraged. You should use a
shocks
block instead.
4.9. Other general declarations¶

Command:
dsample
INTEGER [INTEGER];
¶
Reduces the number of periods considered in subsequent output commands.

Command:
periods
INTEGER
¶
This command is now deprecated (but will still work for older model files). It is not necessary when no simulation is performed and is replaced by an optionperiods
inperfect_foresight_setup
,simul
andstoch_simul
.This command sets the number of periods in the simulation. The periods are numbered from 1 to INTEGER. In perfect foresight simulations, it is assumed that all future events are perfectly known at the beginning of period 1.
Example
periods 100;
4.10. Steady state¶
There are two ways of computing the steady state (i.e. the static equilibrium) of a model. The first way is to let Dynare compute the steady state using a nonlinear Newtontype solver; this should work for most models, and is relatively simple to use. The second way is to give more guidance to Dynare, using your knowledge of the model, by providing it with a method to compute the steady state, either using a steady_state_model block or writing matlab routine.
4.10.1. Finding the steady state with Dynare nonlinear solver¶

Command:
steady
;
¶ 
Command:
steady
(OPTIONS...);
This command computes the steady state of a model using a nonlinear Newtontype solver and displays it. When a steady state file is usedsteady
displays the steady state and checks that it is a solution of the static model.More precisely, it computes the equilibrium value of the endogenous variables for the value of the exogenous variables specified in the previous
initval
orendval
block.steady
uses an iterative procedure and takes as initial guess the value of the endogenous variables set in the previousinitval
orendval
block.For complicated models, finding good numerical initial values for the endogenous variables is the trickiest part of finding the equilibrium of that model. Often, it is better to start with a smaller model and add new variables one by one.
Options

maxit = INTEGER
¶ Determines the maximum number of iterations used in the nonlinear solver. The default value of
maxit
is 50.

tolf = DOUBLE
¶ Convergence criterion for termination based on the function value. Iteration will cease when the residuals are smaller than
tolf
. Default:eps^(1/3)

solve_algo = INTEGER
¶ Determines the nonlinear solver to use. Possible values for the option are:
0
Usefsolve
(under MATLAB, only available if you have the Optimization Toolbox; always available under Octave).1
Use Dynare’s own nonlinear equation solver (a Newtonlike algorithm with linesearch).2
Splits the model into recursive blocks and solves each block in turn using the same solver as value 1.3
Use Chris Sims’ solver.4
Splits the model into recursive blocks and solves each block in turn using a trustregion solver with autoscaling.5
Newton algorithm with a sparse Gaussian elimination (SPE) (requiresbytecode
option, see Model declaration).6
Newton algorithm with a sparse LU solver at each iteration (requiresbytecode
and/orblock
option, see Model declaration).7
Newton algorithm with a Generalized Minimal Residual (GMRES) solver at each iteration (requiresbytecode
and/orblock
option, see Model declaration; not available under Octave).8
Newton algorithm with a Stabilized BiConjugate Gradient (BICGSTAB) solver at each iteration (requires bytecode and/or block option, see Model declaration).9
Trustregion algorithm on the entire model.10
LevenbergMarquardt mixed complementarity problem (LMMCP) solver (Kanzow and Petra (2004)).11
PATH mixed complementarity problem solver of Ferris and Munson (1999). The complementarity conditions are specified with anmcp
equation tag, seelmmcp
. Dynare only provides the interface for using the solver. Due to licence restrictions, you have to download the solver’s most current version yourself from http://pages.cs.wisc.edu/~ferris/path.html and place it in Matlab’s search path.
Default value is4
.

homotopy_mode = INTEGER
¶ Use a homotopy (or divideandconquer) technique to solve for the steady state. If you use this option, you must specify a
homotopy_setup
block. This option can take three possible values:1
In this mode, all the parameters are changed simultaneously, and the distance between the boundaries for each parameter is divided in as many intervals as there are steps (as defined by thehomotopy_steps
option); the problem is solves as many times as there are steps.2
Same as mode1
, except that only one parameter is changed at a time; the problem is solved as many times as steps times number of parameters.3
Dynare tries first the most extreme values. If it fails to compute the steady state, the interval between initial and desired values is divided by two for all parameters. Every time that it is impossible to find a steady state, the previous interval is divided by two. When it succeeds to find a steady state, the previous interval is multiplied by two. In that last casehomotopy_steps
contains the maximum number of computations attempted before giving up.

homotopy_steps = INTEGER
¶ Defines the number of steps when performing a homotopy. See
homotopy_mode
option for more details.

homotopy_force_continue = INTEGER
¶ This option controls what happens when homotopy fails.
0
steady
fails with an error message1
steady
keeps the values of the last homotopy step that was successful and continues. BE CAREFUL: parameters and/or exogenous variables are NOT at the value expected by the user
Default is0
.

nocheck
¶ Don’t check the steady state values when they are provided explicitly either by a steady state file or a
steady_state_model
block. This is useful for models with unit roots as, in this case, the steady state is not unique or doesn’t exist.

markowitz = DOUBLE
¶ Value of the Markowitz criterion, used to select the pivot. Only used when
solve_algo = 5
. Default: 0.5.
Example

After computation, the steady state is available in the following variable:

MATLAB/Octave variable:
oo_.steady_state
¶ Contains the computed steady state. Endogenous variables are ordered in order of declaration used in the
var
command (which is also the order used inM_.endo_names
).

Block:
homotopy_setup
;
¶ This block is used to declare initial and final values when using a homotopy method. It is used in conjunction with the option
homotopy_mode
of the steady command.The idea of homotopy (also called divideandconquer by some authors) is to subdivide the problem of finding the steady state into smaller problems. It assumes that you know how to compute the steady state for a given set of parameters, and it helps you finding the steady state for another set of parameters, by incrementally moving from one to another set of parameters.
The purpose of the
homotopy_setup
block is to declare the final (and possibly also the initial) values for the parameters or exogenous that will be changed during the homotopy. It should contain lines of the form:VARIABLE_NAME, EXPRESSION, EXPRESSION;
This syntax specifies the initial and final values of a given parameter/exogenous.
There is an alternative syntax:
VARIABLE_NAME, EXPRESSION;
Here only the final value is specified for a given parameter/exogenous; the initial value is taken from the preceeding
initval
block.A necessary condition for a successful homotopy is that Dynare must be able to solve the steady state for the initial parameters/exogenous without additional help (using the guess values given in the
initval
block).If the homotopy fails, a possible solution is to increase the number of steps (given in
homotopy_steps
option ofsteady
).Example
In the following example, Dynare will first compute the steady state for the initial values (
gam=0.5
andx=1
), and then subdivide the problem into 50 smaller problems to find the steady state for the final values (gam=2
andx=2
):var c k; varexo x; parameters alph gam delt bet aa; alph=0.5; delt=0.02; aa=0.5; bet=0.05; model; c + k  aa*x*k(1)^alph  (1delt)*k(1); c^(gam)  (1+bet)^(1)*(aa*alph*x(+1)*k^(alph1) + 1  delt)*c(+1)^(gam); end; initval; x = 1; k = ((delt+bet)/(aa*x*alph))^(1/(alph1)); c = aa*x*k^alphdelt*k; end; homotopy_setup; gam, 0.5, 2; x, 2; end; steady(homotopy_mode = 1, homotopy_steps = 50);
4.10.2. Providing the steady state to Dynare¶
If you know how to compute the steady state for your model, you can
provide a MATLAB/Octave function doing the computation instead of
using steady
. Again, there are two options for doing that:
 The easiest way is to write a
steady_state_model
block, which is described below in more details. See alsofs2000.mod
in theexamples
directory for an example. The steady state file generated by Dynare will be called+FILENAME/steadystate.m.
 You can write the corresponding MATLAB function by hand. If your MODfile is called
FILENAME.mod
, the steady state file must be calledFILENAME_steadystate.m
. SeeNK_baseline_steadystate.m
in the examples directory for an example. This option gives a bit more flexibility (loops and conditional structures can be used), at the expense of a heavier programming burden and a lesser efficiency.
Note that both files allow to update parameters in each call of the
function. This allows for example to calibrate a model to a labor
supply of 0.2 in steady state by setting the labor disutility
parameter to a corresponding value (see NK_baseline_steadystate.m
in the examples
directory). They can also be used in estimation
where some parameter may be a function of an estimated parameter and
needs to be updated for every parameter draw. For example, one might
want to set the capital utilization cost parameter as a function of
the discount rate to ensure that capacity utilization is 1 in steady
state. Treating both parameters as independent or not updating one as
a function of the other would lead to wrong results. But this also
means that care is required. Do not accidentally overwrite your
parameters with new values as it will lead to wrong results.

Block:
steady_state_model
;
¶
When the analytical solution of the model is known, this command can be used to help Dynare find the steady state in a more efficient and reliable way, especially during estimation where the steady state has to be recomputed for every point in the parameter space.Each line of this block consists of a variable (either an endogenous, a temporary variable or a parameter) which is assigned an expression (which can contain parameters, exogenous at the steady state, or any endogenous or temporary variable already declared above). Each line therefore looks like:
VARIABLE_NAME = EXPRESSION;
Note that it is also possible to assign several variables at the same time, if the main function in the right hand side is a MATLAB/Octave function returning several arguments:
[ VARIABLE_NAME, VARIABLE_NAME... ] = EXPRESSION;
Dynare will automatically generate a steady state file (of the form
+FILENAME/steadystate.m
) using the information provided in this block.Steady state file for deterministic models
The
steady_state_model
block works also with deterministic models. Aninitval
block and, when necessary, anendval
block, is used to set the value of the exogenous variables. Eachinitval
orendval
block must be followed bysteady
to execute the function created bysteady_state_model
and set the initial, respectively terminal, steady state.Example
var m P c e W R k d n l gy_obs gp_obs y dA; varexo e_a e_m; parameters alp bet gam mst rho psi del; ... // parameter calibration, (dynamic) model declaration, shock calibration... ... steady_state_model; dA = exp(gam); gst = 1/dA; // A temporary variable m = mst; // Three other temporary variables khst = ( (1gst*bet*(1del)) / (alp*gst^alp*bet) )^(1/(alp1)); xist = ( ((khst*gst)^alp  (1gst*(1del))*khst)/mst )^(1); nust = psi*mst^2/( (1alp)*(1psi)*bet*gst^alp*khst^alp ); n = xist/(nust+xist); P = xist + nust; k = khst*n; l = psi*mst*n/( (1psi)*(1n) ); c = mst/P; d = l  mst + 1; y = k^alp*n^(1alp)*gst^alp; R = mst/bet; // You can use MATLAB functions which return several arguments [W, e] = my_function(l, n); gp_obs = m/dA; gy_obs = dA; end; steady;
4.10.3. Replace some equations during steady state computations¶
When there is no steady state file, Dynare computes the steady state
by solving the static model, i.e. the model from the .mod
file
from which leads and lags have been removed.
In some specific cases, one may want to have more control over the way this static model is created. Dynare therefore offers the possibility to explicitly give the form of equations that should be in the static model.
More precisely, if an equation is prepended by a [static]
tag,
then it will appear in the static model used for steady state
computation, but that equation will not be used for other
computations. For every equation tagged in this way, you must tag
another equation with [dynamic]
: that equation will not be used
for steady state computation, but will be used for other computations.
This functionality can be useful on models with a unit root, where
there is an infinity of steady states. An equation (tagged
[dynamic]
) would give the law of motion of the nonstationary
variable (like a random walk). To pin down one specific steady state,
an equation tagged [static]
would affect a constant value to the
nonstationary variable. Another situation where the [static]
tag
can be useful is when one has only a partial closed form solution for
the steady state.
Example
This is a trivial example with two endogenous variables. The second equation takes a different form in the static model:
var c k;
varexo x;
...
model;
c + k  aa*x*k(1)^alph  (1delt)*k(1);
[dynamic] c^(gam)  (1+bet)^(1)*(aa*alph*x(+1)*k^(alph1) + 1  delt)*c(+1)^(gam);
[static] k = ((delt+bet)/(x*aa*alph))^(1/(alph1));
end;
4.11. Getting information about the model¶

Command:
check
;
¶ 
Command:
check
(solve_algo = INTEGER);
Computes the eigenvalues of the model linearized around the values specified by the lastinitval
,endval
orsteady
statement. Generally, the eigenvalues are only meaningful if the linearization is done around a steady state of the model. It is a device for local analysis in the neighborhood of this steady state.A necessary condition for the uniqueness of a stable equilibrium in the neighborhood of the steady state is that there are as many eigenvalues larger than one in modulus as there are forward looking variables in the system. An additional rank condition requires that the square submatrix of the right Schur vectors corresponding to the forward looking variables (jumpers) and to the explosive eigenvalues must have full rank.
Options

solve_algo = INTEGER
See solve_algo, for the possible values and their meaning.

qz_zero_threshold = DOUBLE
¶ Value used to test if a generalized eigenvalue is \(0/0\) in the generalized Schur decomposition (in which case the model does not admit a unique solution). Default:
1e6
.
Output
check
returns the eigenvalues in the global variableoo_.dr.eigval
.

MATLAB/Octave variable:
oo_.dr.eigval
¶ Contains the eigenvalues of the model, as computed by the
check
command.

Command:
model_diagnostics
;
¶
This command performs various sanity checks on the model, and prints a message if a problem is detected (missing variables at current period, invalid steady state, singular Jacobian of static model).

Command:
model_info
;
¶ 
Command:
model_info
(OPTIONS...);
This command provides information about: The normalization of the model: an endogenous variable is attributed to each equation of the model;
 The block structure of the model: for each block
model_info
indicates its type, the equations number and endogenous variables belonging to this block.
This command can only be used in conjunction with the
block
option of themodel
block.There are five different types of blocks depending on the simulation method used:
‘EVALUATE FORWARD’
In this case the block contains only equations where endogenous variable attributed to the equation appears currently on the left hand side and where no forward looking endogenous variables appear. The block has the form: \(y_{j,t} = f_j(y_t, y_{t1}, \ldots, y_{tk})\).
‘EVALUATE BACKWARD’
The block contains only equations where endogenous variable attributed to the equation appears currently on the left hand side and where no backward looking endogenous variables appear. The block has the form: \(y_{j,t} = f_j(y_t, y_{t+1}, \ldots, y_{t+k})\).
‘SOLVE BACKWARD x’
The block contains only equations where endogenous variable attributed to the equation does not appear currently on the left hand side and where no forward looking endogenous variables appear. The block has the form: \(g_j(y_{j,t}, y_t, y_{t1}, \ldots, y_{tk})=0\). x is equal to ‘SIMPLE’ if the block has only one equation. If several equation appears in the block, x is equal to ‘COMPLETE’.
‘SOLVE FORWARD x’
The block contains only equations where endogenous variable attributed to the equation does not appear currently on the left hand side and where no backward looking endogenous variables appear. The block has the form: \(g_j(y_{j,t}, y_t, y_{t+1}, \ldots, y_{t+k})=0\). x is equal to ‘SIMPLE’ if the block has only one equation. If several equation appears in the block, x is equal to ‘COMPLETE’.
‘SOLVE TWO BOUNDARIES x’
The block contains equations depending on both forward and backward variables. The block looks like: \(g_j(y_{j,t}, y_t, y_{t1}, \ldots, y_{tk} ,y_t, y_{t+1}, \ldots, y_{t+k})=0\). x is equal to ‘SIMPLE’ if the block has only one equation. If several equation appears in the block, x is equal to ‘COMPLETE’.
Options

'static'
¶ Prints out the block decomposition of the static model. Without ’static’ option model_info displays the block decomposition of the dynamic model.

'incidence'
¶ Displays the gross incidence matrix and the reordered incidence matrix of the block decomposed model.

Command:
print_bytecode_dynamic_model
;
¶
Prints the equations and the Jacobian matrix of the dynamic model stored in the bytecode binary format file. Can only be used in conjunction with thebytecode
option of themodel
block.

Command:
print_bytecode_static_model
;
¶
Prints the equations and the Jacobian matrix of the static model stored in the bytecode binary format file. Can only be used in conjunction with thebytecode
option of themodel
block.
4.12. Deterministic simulation¶
When the framework is deterministic, Dynare can be used for models
with the assumption of perfect foresight. Typically, the system is
supposed to be in a state of equilibrium before a period ‘1’ when the
news of a contemporaneous or of a future shock is learned by the
agents in the model. The purpose of the simulation is to describe the
reaction in anticipation of, then in reaction to the shock, until the
system returns to the old or to a new state of equilibrium. In most
models, this return to equilibrium is only an asymptotic phenomenon,
which one must approximate by an horizon of simulation far enough in
the future. Another exercise for which Dynare is well suited is to
study the transition path to a new equilibrium following a permanent
shock. For deterministic simulations, the numerical problem consists
of solving a nonlinar system of simultaneous equations in n endogenous
variables in T periods. Dynare offers several algorithms for solving
this problem, which can be chosen via the stack_solve_algo
option. By default (stack_solve_algo=0
), Dynare uses a Newtontype
method to solve the simultaneous equation system. Because the
resulting Jacobian is in the order of n
by T
and hence will be
very large for long simulations with many variables, Dynare makes use
of the sparse matrix capacities of MATLAB/Octave. A slower but
potentially less memory consuming alternative (stack_solve_algo=6
)
is based on a Newtontype algorithm first proposed by Laffargue
(1990) and Boucekkine (1995), which uses relaxation
techniques. Thereby, the algorithm avoids ever storing the full
Jacobian. The details of the algorithm can be found in Juillard
(1996). The third type of algorithms makes use of block decomposition
techniques (divideandconquer methods) that exploit the structure of
the model. The principle is to identify recursive and simultaneous
blocks in the model structure and use this information to aid the
solution process. These solution algorithms can provide a significant
speedup on large models.

Command:
perfect_foresight_setup
;
¶ 
Command:
perfect_foresight_setup
(OPTIONS...);
Prepares a perfect foresight simulation, by extracting the information in theinitval
,endval
andshocks
blocks and converting them into simulation paths for exogenous and endogenous variables.This command must always be called before running the simulation with
perfect_foresight_solver
.Options

periods = INTEGER
¶ Number of periods of the simulation.

datafile = FILENAME
¶ If the variables of the model are not constant over time, their initial values, stored in a text file, could be loaded, using that option, as initial values before a deterministic simulation.
Output
The paths for the exogenous variables are stored into
oo_.exo_simul
.The initial and terminal conditions for the endogenous variables and the initial guess for the path of endogenous variables are stored into
oo_.endo_simul
.

Command:
perfect_foresight_solver
;
¶ 
Command:
perfect_foresight_solver
(OPTIONS...);
Computes the perfect foresight (or deterministic) simulation of the model.Note that
perfect_foresight_setup
must be called before this command, in order to setup the environment for the simulation.Options

maxit = INTEGER
Determines the maximum number of iterations used in the nonlinear solver. The default value of
maxit
is50
.

tolf = DOUBLE
Convergence criterion for termination based on the function value. Iteration will cease when it proves impossible to improve the function value by more than
tolf
. Default:1e5

tolx = DOUBLE
¶ Convergence criterion for termination based on the change in the function argument. Iteration will cease when the solver attempts to take a step that is smaller than
tolx
. Default:1e5

stack_solve_algo = INTEGER
¶ Algorithm used for computing the solution. Possible values are:
0
Newton method to solve simultaneously all the equations for every period, using sparse matrices (Default).1
Use a Newton algorithm with a sparse LU solver at each iteration (requiresbytecode
and/orblock
option, see Model declaration).2
Use a Newton algorithm with a Generalized Minimal Residual (GMRES) solver at each iteration (requiresbytecode
and/orblock
option, see Model declaration; not available under Octave)3
Use a Newton algorithm with a Stabilized BiConjugate Gradient (BICGSTAB) solver at each iteration (requiresbytecode
and/orblock
option, see Model declaration).4
Use a Newton algorithm with a optimal path length at each iteration (requiresbytecode
and/orblock
option, see Model declaration).5
Use a Newton algorithm with a sparse Gaussian elimination (SPE) solver at each iteration (requiresbytecode
option, see Model declaration).6
Use the historical algorithm proposed in Juillard (1996): it is slower thanstack_solve_algo=0
, but may be less memory consuming on big models (not available withbytecode
and/orblock
options).7
Allows the user to solve the perfect foresight model with the solvers available through option
solve_algo
(See solve_algo for a list of possible values, note that values 5, 6, 7 and 8, which requirebytecode
and/orblock
options, are not allowed). For instance, the following commands:perfect_foresight_setup(periods=400); perfect_foresight_solver(stack_solve_algo=7, solve_algo=9)
trigger the computation of the solution with a trust region algorithm.

robust_lin_solve
¶ Triggers the use of a robust linear solver for the default
stack_solve_algo=0
.

solve_algo
¶ See solve_algo. Allows selecting the solver used with
stack_solve_algo=7
.

no_homotopy
¶ By default, the perfect foresight solver uses a homotopy technique if it cannot solve the problem. Concretely, it divides the problem into smaller steps by diminishing the size of shocks and increasing them progressively until the problem converges. This option tells Dynare to disable that behavior. Note that the homotopy is not implemented for purely forward or backward models.

markowitz = DOUBLE
Value of the Markowitz criterion, used to select the pivot. Only used when
stack_solve_algo = 5
. Default:0.5
.

minimal_solving_periods = INTEGER
¶ Specify the minimal number of periods where the model has to be solved, before using a constant set of operations for the remaining periods. Only used when
stack_solve_algo = 5
. Default:1
.

lmmcp
¶ Solves the perfect foresight model with a LevenbergMarquardt mixed complementarity problem (LMMCP) solver (Kanzow and Petra (2004)), which allows to consider inequality constraints on the endogenous variables (such as a ZLB on the nominal interest rate or a model with irreversible investment). This option is equivalent to
stack_solve_algo=7
andsolve_algo=10
. Using the LMMCP solver requires a particular model setup as the goal is to get rid of any min/max operators and complementary slackness conditions that might introduce a singularity into the Jacobian. This is done by attaching an equation tag (see Model declaration) with themcp
keyword to affected equations. This tag states that the equation to which the tag is attached has to hold unless the expression within the tag is binding. For instance, a ZLB on the nominal interest rate would be specified as follows in the model block:model; ... [mcp = 'r > 1.94478'] r = rho*r(1) + (1rho)*(gpi*Infl+gy*YGap) + e; ... end;
where
1.94478
is the steady state level of the nominal interest rate andr
is the nominal interest rate in deviation from the steady state. This construct implies that the Taylor rule is operative, unless the implied interest rater<=1.94478
, in which case ther
is fixed at1.94478
(thereby being equivalent to a complementary slackness condition). By restricting the value ofr
coming out of this equation, themcp
tag also avoids usingmax(r,1.94478)
for other occurrences ofr
in the rest of the model. It is important to keep in mind that, because themcp
tag effectively replaces a complementary slackness condition, it cannot be simply attached to any equation. Rather, it must be attached to the correct affected equation as otherwise the solver will solve a different problem than originally intended.Note that in the current implementation, the content of the
mcp
equation tag is not parsed by the preprocessor. The inequalities must therefore be as simple as possible: an endogenous variable, followed by a relational operator, followed by a number (not a variable, parameter or expression).

endogenous_terminal_period
¶ The number of periods is not constant across Newton iterations when solving the perfect foresight model. The size of the nonlinear system of equations is reduced by removing the portion of the paths (and associated equations) for which the solution has already been identified (up to the tolerance parameter). This strategy can be interpreted as a mix of the shooting and relaxation approaches. Note that round off errors are more important with this mixed strategy (user should check the reported value of the maximum absolute error). Only available with option
stack_solve_algo==0
.

linear_approximation
¶ Solves the linearized version of the perfect foresight model. The model must be stationary. Only available with option
stack_solve_algo==0
.
Output
The simulated endogenous variables are available in global matrix
oo_.endo_simul
.

Command:
simul
;
¶ 
Command:
simul
(OPTIONS...);
Shortform command for triggering the computation of a deterministic simulation of the model. It is strictly equivalent to a call toperfect_foresight_setup
followed by a call toperfect_foresight_solver
.Options
Accepts all the options of
perfect_foresight_setup
andperfect_foresight_solver
.

MATLAB/Octave variable:
oo_.endo_simul
¶
This variable stores the result of a deterministic simulation (computed byperfect_foresight_solver
orsimul
) or of a stochastic simulation (computed bystoch_simul
with the periods option or byextended_path
). The variables are arranged row by row, in order of declaration (as inM_.endo_names
). Note that this variable also contains initial and terminal conditions, so it has more columns than the value ofperiods
option.

MATLAB/Octave variable:
oo_.exo_simul
¶
This variable stores the path of exogenous variables during a simulation (computed byperfect_foresight_solver
,simul
,stoch_simul
orextended_path
). The variables are arranged in columns, in order of declaration (as inM_.exo_names
). Periods are in rows. Note that this convention regarding columns and rows is the opposite of the convention foroo_.endo_simul
!
4.13. Stochastic solution and simulation¶
In a stochastic context, Dynare computes one or several simulations corresponding to a random draw of the shocks.
The main algorithm for solving stochastic models relies on a Taylor
approximation, up to third order, of the expectation functions (see
Judd (1996), Collard and Juillard (2001a), Collard and Juillard
(2001b), and SchmittGrohé and Uríbe (2004)). The details of the
Dynare implementation of the first order solution are given in
Villemot (2011). Such a solution is computed using the
stoch_simul
command.
As an alternative, it is possible to compute a simulation to a
stochastic model using the extended path method presented by Fair
and Taylor (1983). This method is especially useful when there are
strong nonlinearities or binding constraints. Such a solution is
computed using the extended_path
command.
4.13.1. Computing the stochastic solution¶

Command:
stoch_simul
[VARIABLE_NAME...];
¶ 
Command:
stoch_simul
(OPTIONS...) [VARIABLE_NAME...];
Solves a stochastic (i.e. rational expectations) model, using perturbation techniques.More precisely,
stoch_simul
computes a Taylor approximation of the model around the deterministic steady state and solves of the the decision and transition functions for the approximated model. Using this, it computes impulse response functions and various descriptive statistics (moments, variance decomposition, correlation and autocorrelation coefficients). For correlated shocks, the variance decomposition is computed as in the VAR literature through a Cholesky decomposition of the covariance matrix of the exogenous variables. When the shocks are correlated, the variance decomposition depends upon the order of the variables in thevarexo
command.The Taylor approximation is computed around the steady state (see Steady state).
The IRFs are computed as the difference between the trajectory of a variable following a shock at the beginning of period
1
and its steady state value. More details on the computation of IRFs can be found on the Dynare wiki.Variance decomposition, correlation, autocorrelation are only displayed for variables with strictly positive variance. Impulse response functions are only plotted for variables with response larger than \(10^{10}\).
Variance decomposition is computed relative to the sum of the contribution of each shock. Normally, this is of course equal to aggregate variance, but if a model generates very large variances, it may happen that, due to numerical error, the two differ by a significant amount. Dynare issues a warning if the maximum relative difference between the sum of the contribution of each shock and aggregate variance is larger than
0.01%
.The covariance matrix of the shocks is specified with the
shocks
command (see Shocks on exogenous variables).When a list of
VARIABLE_NAME
is specified, results are displayed only for these variables.The
stoch_simul
command with a first order approximation can benefit from the block decomposition of the model (seeblock
).Options

ar = INTEGER
¶ Order of autocorrelation coefficients to compute and to print. Default:
5
.

drop = INTEGER
¶ Number of points (burnin) dropped at the beginning of simulation before computing the summary statistics. Note that this option does not affect the simulated series stored in
oo_.endo_simul
and the workspace. Here, no periods are dropped. Default:100
.

hp_filter = DOUBLE
¶ Uses HP filter with \(\lambda =\)
DOUBLE
before computing moments. If theoretical moments are requested, the spectrum of the model solution is filtered following the approach outlined in Uhlig (2001). Default: no filter.

one_sided_hp_filter = DOUBLE
¶ Uses the onesided HP filter with \(\lambda =\)
DOUBLE
described in Stock and Watson (1999) before computing moments. This option is only available with simulated moments. Default: no filter.

hp_ngrid = INTEGER
¶ Number of points in the grid for the discrete Inverse Fast Fourier Transform used in the HP filter computation. It may be necessary to increase it for highly autocorrelated processes. Default:
512
.

bandpass_filter
¶ Uses a bandpass filter with the default passband before computing moments. If theoretical moments are requested, the spectrum of the model solution is filtered using an ideal bandpass filter. If empirical moments are requested, the Baxter and King (1999) filter is used. Default: no filter.

bandpass_filter = [HIGHEST_PERIODICITY LOWEST_PERIODICITY]
¶ Uses a bandpass filter before computing moments. The passband is set to a periodicity of to LOWEST_PERIODICITY, e.g. \(6\) to \(32\) quarters if the model frequency is quarterly. Default:
[6,32]
.

irf = INTEGER
¶ Number of periods on which to compute the IRFs. Setting
irf=0
suppresses the plotting of IRFs. Default:40
.

irf_shocks = ( VARIABLE_NAME [[,] VARIABLE_NAME ...] )
¶ The exogenous variables for which to compute IRFs. Default: all.

relative_irf
¶ Requests the computation of normalized IRFs. At first order, the normal shock vector of size one standard deviation is divided by the standard deviation of the current shock and multiplied by 100. The impulse responses are hence the responses to a unit shock of size 1 (as opposed to the regular shock size of one standard deviation), multiplied by 100. Thus, for a loglinearized model where the variables are measured in percent, the IRFs have the interpretation of the percent responses to a 100 percent shock. For example, a response of 400 of output to a TFP shock shows that output increases by 400 percent after a 100 percent TFP shock (you will see that TFP increases by 100 on impact). Given linearity at
order=1
, it is straightforward to rescale the IRFs stored inoo_.irfs
to any desired size. At higher order, the interpretation is different. Therelative_irf
option then triggers the generation of IRFs as the response to a 0.01 unit shock (corresponding to 1 percent for shocks measured in percent) and no multiplication with 100 is performed. That is, the normal shock vector of size one standard deviation is divided by the standard deviation of the current shock and divided by 100. For example, a response of 0.04 of log output (thus measured in percent of the steady state output level) to a TFP shock also measured in percent then shows that output increases by 4 percent after a 1 percent TFP shock (you will see that TFP increases by 0.01 on impact).

irf_plot_threshold = DOUBLE
¶ Threshold size for plotting IRFs. All IRFs for a particular variable with a maximum absolute deviation from the steady state smaller than this value are not displayed. Default:
1e10
.

nocorr
¶ Don’t print the correlation matrix (printing them is the default).

nodecomposition
¶ Don’t compute (and don’t print) unconditional variance decomposition.

nofunctions
¶ Don’t print the coefficients of the approximated solution (printing them is the default).

nomoments
¶ Don’t print moments of the endogenous variables (printing them is the default).

nograph
¶ Do not create graphs (which implies that they are not saved to the disk nor displayed). If this option is not used, graphs will be saved to disk (to the format specified by
graph_format
option, except ifgraph_format=none
) and displayed to screen (unlessnodisplay
option is used).

graph
¶ Reenables the generation of graphs previously shut off with
nograph
.

nodisplay
¶ Do not display the graphs, but still save them to disk (unless
nograph
is used).

graph_format = FORMAT
¶ 
graph_format = ( FORMAT, FORMAT... )
¶ Specify the file format(s) for graphs saved to disk. Possible values are
eps
(the default),pdf
,fig
andnone
(under Octave, onlyeps
andnone
are available). If the file format is set equal tonone
, the graphs are displayed but not saved to the disk.

noprint
¶ Don’t print anything. Useful for loops.

print
¶ Print results (opposite of
noprint
).

order = INTEGER
¶ Order of Taylor approximation. Acceptable values are
1
,2
and3
. Note that for third order,k_order_solver
option is implied and only empirical moments are available (you must provide a value forperiods
option). Default:2
(except after anestimation
command, in which case the default is the value used for the estimation).

k_order_solver
¶ Use a korder solver (implemented in C++) instead of the default Dynare solver. This option is not yet compatible with the
bytecode
option (see Model declaration). Default: disabled for order 1 and 2, enabled otherwise.

periods = INTEGER
If different from zero, empirical moments will be computed instead of theoretical moments. The value of the option specifies the number of periods to use in the simulations. Values of the initval block, possibly recomputed by
steady
, will be used as starting point for the simulation. The simulated endogenous variables are made available to the user in a vector for each variable and in the global matrixoo_.endo_simul
(seeoo_.endo_simul
). The simulated exogenous variables are made available inoo_.exo_simul
(seeoo_.exo_simul
). Default:0
.

qz_criterium = DOUBLE
¶ Value used to split stable from unstable eigenvalues in reordering the Generalized Schur decomposition used for solving 1storder problems. Default:
1.000001
(except when estimating withlik_init
option equal to1
: the default is0.999999
in that case; see Estimation).

qz_zero_threshold = DOUBLE
See
qz_zero_threshold
.

replic = INTEGER
¶ Number of simulated series used to compute the IRFs. Default:
1
iforder=1
, and50
otherwise.

simul_replic = INTEGER
¶ Number of series to simulate when empirical moments are requested (i.e.
periods
\(>\) 0). Note that if this option is greater than 1, the additional series will not be used for computing the empirical moments but will simply be saved in binary form to the fileFILENAME_simul
. Default:1
.

solve_algo = INTEGER
See solve_algo, for the possible values and their meaning.

aim_solver
¶ Use the AndersonMoore Algorithm (AIM) to compute the decision

 s:mvar: rules, instead of using Dynare’s default method based on a
 generalized Schur decomposition. This option is only valid for first order approximation. See AIM website for more details on the algorithm.

conditional_variance_decomposition = INTEGER
¶ 
conditional_variance_decomposition = [INTEGER1:INTEGER2]
¶ 
conditional_variance_decomposition = [INTEGER1 INTEGER2 ...]
¶ Computes a conditional variance decomposition for the specified period(s). The periods must be strictly positive. Conditional variances are given by \(var(y_{t+k}\vert t)\). For period 1, the conditional variance decomposition provides the decomposition of the effects of shocks upon impact.
The results are stored in
oo_.conditional_variance_decomposition
(seeoo_.conditional_variance_decomposition
). In the presence of measurement error, theoo_.conditional_variance_decomposition
field will contain the variance contribution after measurement error has been taken out, i.e. the decomposition will be conducted of the actual as opposed to the measured variables. The variance decomposition of the measured variables will be stored inoo_.conditional_variance_decomposition_ME
(seeoo_.conditional_variance_decomposition_ME
). The variance decomposition is only conducted, if theoretical moments are requested, i.e. using theperiods=0
option. In case oforder=2
, Dynare provides a secondorder accurate approximation to the true second moments based on the linear terms of the secondorder solution (see Kim, Kim, Schaumburg and Sims (2008)). Note that the unconditional variance decomposition i.e. at horizon infinity) is automatically conducted if theoretical moments are requested and ifnodecomposition
is not set (seeoo_.variance_decomposition
).

pruning
¶ Discard higher order terms when iteratively computing simulations of the solution. At second order, Dynare uses the algorithm of Kim, Kim, Schaumburg and Sims (2008), while at third order its generalization by Andreasen, FernándezVillaverde and RubioRamírez (2013) is used.

partial_information
¶ Computes the solution of the model under partial information, along the lines of Pearlman, Currie and Levine (1986). Agents are supposed to observe only some variables of the economy. The set of observed variables is declared using the
varobs
command. Note that ifvarobs
is not present or contains all endogenous variables, then this is the full information case and this option has no effect. More references can be found here .

sylvester = OPTION
¶ Determines the algorithm used to solve the Sylvester equation for block decomposed model. Possible values for OPTION are:
default
Uses the default solver for Sylvester equations (gensylv
) based on Ondra Kamenik’s algorithm (see here for more information).fixed_point
Uses a fixed point algorithm to solve the Sylvester equation (gensylv_fp
). This method is faster than the default one for large scale models.
Default value isdefault
.

sylvester_fixed_point_tol = DOUBLE
¶ The convergence criterion used in the fixed point Sylvester solver. Its default value is
1e12
.

dr = OPTION
¶ Determines the method used to compute the decision rule. Possible values for OPTION are:
default
Uses the default method to compute the decision rule based on the generalized Schur decomposition (see Villemot (2011) for more information).cycle_reduction
Uses the cycle reduction algorithm to solve the polynomial equation for retrieving the coefficients associated to the endogenous variables in the decision rule. This method is faster than the default one for large scale models.logarithmic_reduction
Uses the logarithmic reduction algorithm to solve the polynomial equation for retrieving the coefficients associated to the endogenous variables in the decision rule. This method is in general slower than thecycle_reduction
.
Default value isdefault
.

dr_cycle_reduction_tol = DOUBLE
¶ The convergence criterion used in the cycle reduction algorithm. Its default value is
1e7
.

dr_logarithmic_reduction_tol = DOUBLE
¶ The convergence criterion used in the logarithmic reduction algorithm. Its default value is
1e12
.

dr_logarithmic_reduction_maxiter = INTEGER
¶ The maximum number of iterations used in the logarithmic reduction algorithm. Its default value is
100
.

loglinear
¶ See loglinear. Note that ALL variables are logtransformed by using the Jacobian transformation, not only selected ones. Thus, you have to make sure that your variables have strictly positive steady states.
stoch_simul
will display the moments, decision rules, and impulse responses for the loglinearized variables. The decision rules saved inoo_.dr
and the simulated variables will also be the ones for the loglinear variables.

tex
¶ Requests the printing of results and graphs in TeX tables and graphics that can be later directly included in LaTeX files.

dr_display_tol = DOUBLE
¶ Tolerance for the suppression of small terms in the display of decision rules. Rows where all terms are smaller than
dr_display_tol
are not displayed. Default value:1e6
.

contemporaneous_correlation
¶ Saves the contemporaneous correlation between the endogenous variables in
oo_.contemporaneous_correlation
. Requires thenocorr
option not to be set.

spectral_density
¶ Triggers the computation and display of the theoretical spectral density of the (filtered) model variables. Results are stored in ´´oo_.SpectralDensity´´, defined below. Default: do not request spectral density estimates.
Output
This command sets
oo_.dr
,oo_.mean
,oo_.var
andoo_.autocorr
, which are described below.If the
periods
option is present, setsoo_.skewness
,oo_.kurtosis
, andoo_.endo_simul
(seeoo_.endo_simul
), and also saves the simulated variables in MATLAB/Octave vectors of the global workspace with the same name as the endogenous variables.If option
irf
is different from zero, setsoo_.irfs
(see below) and also saves the IRFs in MATLAB/Octave vectors of the global workspace (this latter way of accessing the IRFs is deprecated and will disappear in a future version).If the option
contemporaneous_correlation
is different from0
, setsoo_.contemporaneous_correlation
, which is described below.Example
shocks; var e; stderr 0.0348; end; stoch_simul;
Performs the simulation of the 2ndorder approximation of a model with a single stochastic shock
e
, with a standard error of0.0348
.Example
stoch_simul(irf=60) y k;
Performs the simulation of a model and displays impulse response functions on 60 periods for variables
y
andk
. 

MATLAB/Octave variable:
oo_.mean
¶
After a run ofstoch_simul
, contains the mean of the endogenous variables. Contains theoretical mean if theperiods
option is not present, and simulated mean otherwise. The variables are arranged in declaration order.

MATLAB/Octave variable:
oo_.var
¶
After a run ofstoch_simul
, contains the variancecovariance of the endogenous variables. Contains theoretical variance if theperiods
option is not present (or an approximation thereof fororder=2
), and simulated variance otherwise. The variables are arranged in declaration order.

MATLAB/Octave variable:
oo_.skewness
¶
After a run ofstoch_simul
contains the skewness (standardized third moment) of the simulated variables if theperiods
option is present. The variables are arranged in declaration order.

MATLAB/Octave variable:
oo_.kurtosis
¶
After a run ofstoch_simul
contains the kurtosis (standardized fourth moment) of the simulated variables if theperiods
option is present. The variables are arranged in declaration order.

MATLAB/Octave variable:
oo_.autocorr
¶
After a run ofstoch_simul
, contains a cell array of the autocorrelation matrices of the endogenous variables. The element number of the matrix in the cell array corresponds to the order of autocorrelation. The option ar specifies the number of autocorrelation matrices available. Contains theoretical autocorrelations if theperiods
option is not present (or an approximation thereof fororder=2
), and simulated autocorrelations otherwise. The field is only created if stationary variables are present.The element
oo_.autocorr{i}(k,l)
is equal to the correlation between \(y^k_t\) and \(y^l_{ti}\), where \(y^k\) (resp. \(y^l\)) is the \(k\)th (resp. \(l\)th) endogenous variable in the declaration order.Note that if theoretical moments have been requested,
oo_.autocorr{i}
is the same thanoo_.gamma_y{i+1}
.

MATLAB/Octave variable:
oo_.gamma_y
¶
After a run ofstoch_simul
, if theoretical moments have been requested (i.e. if theperiods
option is not present), this variable contains a cell array with the following values (wherear
is the value of the option of the same name):oo_.gamma{1}
Variance/covariance matrix.oo_.gamma{i+1}
(for i=1:ar)Autocorrelation function. Seeoo_.autocorr
for more details. Beware, this is the autocorrelation function, not the autocovariance function.oo_.gamma{nar+2}
Unconditional variance decomposition, seeoo_.variance_decomposition
.oo_.gamma{nar+3}
If a second order approximation has been requested, contains the vector of the mean correction terms.
In case
order=2
, the theoretical second moments are a second order accurate approximation of the true second moments, see conditional_variance_decomposition.

MATLAB/Octave variable:
oo_.variance_decomposition
¶
After a run ofstoch_simul
when requesting theoretical moments (periods=0
), contains a matrix with the result of the unconditional variance decomposition (i.e. at horizon infinity). The first dimension corresponds to the endogenous variables (in the order of declaration after the command or inM_.endo_names
) and the second dimension corresponds to exogenous variables (in the order of declaration). Numbers are in percent and sum up to 100 across columns. In the presence of measurement error, the field will contain the variance contribution after measurement error has been taken out, i.e. the decomposition will be conducted of the actual as opposed to the measured variables.

MATLAB/Octave variable:
oo_.variance_decomposition_ME
¶
Field set after a run ofstoch_simul
when requesting theoretical moments (periods=0
) if measurement error is present. It is similar tooo_.variance_decomposition
, but the decomposition will be conducted of the measured variables. The field contains a matrix with the result of the unconditional variance decomposition (i.e. at horizon infinity). The first dimension corresponds to the observed endoogenous variables (in the order of declaration after the command) and the second dimension corresponds to exogenous variables (in the order of declaration), with the last column corresponding to the contribution of measurement error. Numbers are in percent and sum up to 100 across columns.

MATLAB/Octave variable:
oo_.conditional_variance_decomposition
¶
After a run ofstoch_simul
with theconditional_variance_decomposition
option, contains a threedimensional array with the result of the decomposition. The first dimension corresponds to forecast horizons (as declared with the option), the second dimension corresponds to endogenous variables (in the order of declaration after the command or inM_.endo_names
if not specified), the third dimension corresponds to exogenous variables (in the order of declaration). In the presence of measurement error, the field will contain the variance contribution after measurement error has been taken out, i.e. the decomposition will be conductedof the actual as opposed to the measured variables.

MATLAB/Octave variable:
oo_.conditional_variance_decomposition_ME
¶
Field set after a run ofstoch_simul
with theconditional_variance_decomposition
option if measurement error is present. It is similar tooo_.conditional_variance_decomposition
, but the decomposition will be conducted of the measured variables. It contains a threedimensional array with the result of the decomposition. The first dimension corresponds to forecast horizons (as declared with the option), the second dimension corresponds to observed endogenous variables (in the order of declaration), the third dimension corresponds to exogenous variables (in the order of declaration), with the last column corresponding to the contribution of the measurement error.

MATLAB/Octave variable:
oo_.contemporaneous_correlation
¶
After a run ofstoch_simul
with thecontemporaneous_correlation option
, contains theoretical contemporaneous correlations if theperiods
option is not present (or an approximation thereof fororder=2
), and simulated contemporaneous correlations otherwise. The variables are arranged in declaration order.

MATLAB/Octave variable:
oo_.SpectralDensity
¶
After a run ofstoch_simul
with optionspectral_density
, contains the spectral density of the model variables. There will be anvars
bynfrequencies
subfieldfreqs
storing the respective frequency grid points ranging from \(0\) to \(2\pi\) and a same sized subfielddensity
storing the corresponding density.

MATLAB/Octave variable:
oo_.irfs
¶
After a run ofstoch_simul
with optionirf
different from zero, contains the impulse responses, with the following naming convention: VARIABLE_NAME_SHOCK_NAME.For example,oo_.irfs.gnp_ea
contains the effect ongnp
of a onestandard deviation shock onea
.
The approximated solution of a model takes the form of a set of
decision rules or transition equations expressing the current value of
the endogenous variables of the model as function of the previous
state of the model and shocks observed at the beginning of the
period. The decision rules are stored in the structure oo_.dr
which is described below.

Command:
extended_path
;
¶ 
Command:
extended_path
(OPTIONS...);
Simulates a stochastic (i.e. rational expectations) model, using the extended path method presented by Fair and Taylor (1983). Time series for the endogenous variables are generated by assuming that the agents believe that there will no more shocks in the following periods.This function first computes a random path for the exogenous variables (stored in
oo_.exo_simul
, seeoo_.exo_simul
) and then computes the corresponding path for endogenous variables, taking the steady state as starting point. The result of the simulation is stored inoo_.endo_simul
(seeoo_.endo_simul
). Note that this simulation approach does not solve for the policy and transition equations but for paths for the endogenous variables.Options

periods = INTEGER
The number of periods for which the simulation is to be computed. No default value, mandatory option.

solver_periods = INTEGER
¶ The number of periods used to compute the solution of the perfect foresight at every iteration of the algorithm. Default:
200
.

order = INTEGER
If order is greater than
0
Dynare uses a gaussian quadrature to take into account the effects of future uncertainty. Iforder
\(=S\) then the time series for the endogenous variables are generated by assuming that the agents believe that there will no more shocks after period \(t+S\). This is an experimental feature and can be quite slow. Default:0
.

hybrid
¶ Use the constant of the second order perturbation reduced form to correct the paths generated by the (stochastic) extended path algorithm.

4.13.2. Typology and ordering of variables¶
Dynare distinguishes four types of endogenous variables:
Purely backward (or purely predetermined) variables
Those that appear only at current and past period in the model, but not at future period (i.e. at \(t\) and \(t1\) but not \(t+1\)). The number of such variables is equal toM_.npred
.
Purely forward variables
Those that appear only at current and future period in the model, but not at past period (i.e. at \(t\) and \(t+1\) but not \(t1\)). The number of such variables is stored inM_.nfwrd
.
Mixed variables
Those that appear at current, past and future period in the model (i.e. at \(t\), \(t+1\) and \(t1\)). The number of such variables is stored inM_.nboth
.
Static variables
Those that appear only at current, not past and future period in the model (i.e. only at \(t\), not at \(t+1\) or \(t1\)). The number of such variables is stored inM_.nstatic
.
Note that all endogenous variables fall into one of these four categories, since after the creation of auxiliary variables (see Auxiliary variables), all endogenous have at most one lead and one lag. We therefore have the following identity:
M_.npred + M_.both + M_.nfwrd + M_.nstatic = M_.endo_nbr
Internally, Dynare uses two orderings of the endogenous variables: the
order of declaration (which is reflected in M_.endo_names
), and an
order based on the four types described above, which we will call the
DRorder (“DR” stands for decision rules). Most of the time, the
declaration order is used, but for elements of the decision rules, the
DRorder is used.
The DRorder is the following: static variables appear first, then purely backward variables, then mixed variables, and finally purely forward variables. Inside each category, variables are arranged according to the declaration order.
Variable oo_.dr.order_var
maps DRorder to declaration order, and
variable oo_.dr.inv_order_var
contains the inverse map. In other
words, the kth variable in the DRorder corresponds to the endogenous
variable numbered oo_.dr_order_var(k)
in declaration
order. Conversely, kth declared variable is numbered
oo_.dr.inv_order_var(k)
in DRorder.
Finally, the state variables of the model are the purely backward
variables and the mixed variables. They are ordered in DRorder when
they appear in decision rules elements. There are M_.nspred =
M_.npred + M_.nboth
such variables. Similarly, one has M_.nsfwrd =
M_.nfwrd + M_.nboth
, and M_.ndynamic = M_.nfwrd + M_.nboth +
M_.npred
.
4.13.3. Firstorder approximation¶
The approximation has the stylized form:
where \(y^s\) is the steady state value of \(y\) and \(y^h_t=y_ty^s\).
The coefficients of the decision rules are stored as follows:
 \(y^s\) is stored in
oo_.dr.ys
. The vector rows correspond to all endogenous in the declaration order.  \(A\) is stored in
oo_.dr.ghx
. The matrix rows correspond to all endogenous in DRorder. The matrix columns correspond to state variables in DRorder.  \(B\) is stored
oo_.dr.ghu
. The matrix rows correspond to all endogenous in DRorder. The matrix columns correspond to exogenous variables in declaration order.
Of course, the shown form of the approximation is only stylized, because it neglects the required different ordering in \(y^s\) and \(y^h_t\). The precise form of the approximation that shows the way Dynare deals with differences between declaration and DRorder, is
where \(\mathrm{k2}\) selects the state variables, \(y_t\) and \(y^s\) are in declaration order and the coefficient matrices are in DRorder. Effectively, all variables on the right hand side are brought into DR order for computations and then assigned to \(y_t\) in declaration order.
4.13.4. Secondorder approximation¶
The approximation has the form:
where \(y^s\) is the steady state value of \(y\), \(y^h_t=y_ty^s\), and \(\Delta^2\) is the shift effect of the variance of future shocks. For the reordering required due to differences in declaration and DR order, see the first order approximation.
The coefficients of the decision rules are stored in the variables described for first order approximation, plus the following variables:
 \(\Delta^2\) is stored in
oo_.dr.ghs2
. The vector rows correspond to all endogenous in DRorder.  \(C\) is stored in
oo_.dr.ghxx
. The matrix rows correspond to all endogenous in DRorder. The matrix columns correspond to the Kronecker product of the vector of state variables in DRorder.  \(D\) is stored in
oo_.dr.ghuu
. The matrix rows correspond to all endogenous in DRorder. The matrix columns correspond to the Kronecker product of exogenous variables in declaration order.  \(E\) is stored in
oo_.dr.ghxu
. The matrix rows correspond to all endogenous in DRorder. The matrix columns correspond to the Kronecker product of the vector of state variables (in DRorder) by the vector of exogenous variables (in declaration order).
4.13.5. Thirdorder approximation¶
The approximation has the form:
where \(y^s\) is the steady state value of \(y\), and
\(z_t\) is a vector consisting of the deviation from the steady
state of the state variables (in DRorder) at date \(t1\)
followed by the exogenous variables at date \(t\) (in declaration
order). The vector \(z_t\) is therefore of size \(n_z\) =
M_.nspred
+ M_.exo_nbr
.
The coefficients of the decision rules are stored as follows:
 \(y^s\) is stored in
oo_.dr.ys
. The vector rows correspond to all endogenous in the declaration order.  \(G_0\) is stored in
oo_.dr.g_0
. The vector rows correspond to all endogenous in DRorder.  \(G_1\) is stored in
oo_.dr.g_1
. The matrix rows correspond to all endogenous in DRorder. The matrix columns correspond to state variables in DRorder, followed by exogenous in declaration order.  \(G_2\) is stored in
oo_.dr.g_2
. The matrix rows correspond to all endogenous in DRorder. The matrix columns correspond to the Kronecker product of state variables (in DRorder), followed by exogenous (in declaration order). Note that the Kronecker product is stored in a folded way, i.e. symmetric elements are stored only once, which implies that the matrix has \(n_z(n_z+1)/2\) columns. More precisely, each column of this matrix corresponds to a pair \((i_1, i_2)\) where each index represents an element of \(z_t\) and is therefore between \(1\) and \(n_z\). Only nondecreasing pairs are stored, i.e. those for which \(i_1 \leq i_2\). The columns are arranged in the lexicographical order of nondecreasing pairs. Also note that for those pairs where \(i_1 \neq i_2\), since the element is stored only once but appears two times in the unfolded \(G_2\) matrix, it must be multiplied by 2 when computing the decision rules.  \(G_3\) is stored in
oo_.dr.g_3
. The matrix rows correspond to all endogenous in DRorder. The matrix columns correspond to the third Kronecker power of state variables (in DRorder), followed by exogenous (in declaration order). Note that the third Kronecker power is stored in a folded way, i.e. symmetric elements are stored only once, which implies that the matrix has \(n_z(n_z+1)(n_z+2)/6\) columns. More precisely, each column of this matrix corresponds to a tuple \((i_1, i_2, i_3)\) where each index represents an element of \(z_t\) and is therefore between \(1\) and \(n_z\). Only nondecreasing tuples are stored, i.e. those for which \(i_1 \leq i_2 \leq i_3\). The columns are arranged in the lexicographical order of nondecreasing tuples. Also note that for tuples that have three distinct indices (i.e. \(i_1 \neq i_2\) and \(i_1 \neq i_3\) and \(i_2 \neq i_3\)), since these elements are stored only once but appears six times in the unfolded \(G_3\) matrix, they must be multiplied by 6 when computing the decision rules. Similarly, for those tuples that have two equal indices (i.e. of the form \((a,a,b)\) or \((a,b,a)\) or \((b,a,a)\)), since these elements are stored only once but appears three times in the unfolded \(G_3\) matrix, they must be multiplied by 3 when computing the decision rules.
4.14. Estimation¶
Provided that you have observations on some endogenous variables, it is possible to use Dynare to estimate some or all parameters. Both maximum likelihood (as in Ireland (2004)) and Bayesian techniques (as in Rabanal and RubioRamirez (2003), Schorfheide (2000) or Smets and Wouters (2003)) are available. Using Bayesian methods, it is possible to estimate DSGE models, VAR models, or a combination of the two techniques called DSGEVAR.
Note that in order to avoid stochastic singularity, you must have at least as many shocks or measurement errors in your model as you have observed variables.
The estimation using a first order approximation can benefit from the
block decomposition of the model (see block
).

Command:
varobs
VARIABLE_NAME...;
¶
This command lists the name of observed endogenous variables for the estimation procedure. These variables must be available in the data file (see estimation_cmd).Alternatively, this command is also used in conjunction with the
partial_information
option ofstoch_simul
, for declaring the set of observed variables when solving the model under partial information.Only one instance of
varobs
is allowed in a model file. If one needs to declare observed variables in a loop, the macroprocessor can be used as shown in the second example below.Example
varobs C y rr;
Declares endogenous variables
C
,y
andrr
as observed variables.Example (with a macroprocessor loop)
varobs @#for co in countries GDP_@{co} @#endfor ;

Block:
observation_trends
;
¶
This block specifies linear trends for observed variables as functions of model parameters. In case theloglinear
option is used, this corresponds to a linear trend in the logged observables, i.e. an exponential trend in the level of the observables.Each line inside of the block should be of the form:
VARIABLE_NAME(EXPRESSION);
In most cases, variables shouldn’t be centered when
observation_trends
is used.Example
observation_trends; Y (eta); P (mu/eta); end;

Block:
estimated_params
;
¶
This block lists all parameters to be estimated and specifies bounds and priors as necessary.Each line corresponds to an estimated parameter.
In a maximum likelihood estimation, each line follows this syntax:
stderr VARIABLE_NAME  corr VARIABLE_NAME_1, VARIABLE_NAME_2  PARAMETER_NAME , INITIAL_VALUE [, LOWER_BOUND, UPPER_BOUND ];
In a Bayesian estimation, each line follows this syntax:
stderr VARIABLE_NAME  corr VARIABLE_NAME_1, VARIABLE_NAME_2  PARAMETER_NAME  DSGE_PRIOR_WEIGHT [, INITIAL_VALUE [, LOWER_BOUND, UPPER_BOUND]], PRIOR_SHAPE, PRIOR_MEAN, PRIOR_STANDARD_ERROR [, PRIOR_3RD_PARAMETER [, PRIOR_4TH_PARAMETER [, SCALE_PARAMETER ] ] ];
The first part of the line consists of one of the four following alternatives:
stderr VARIABLE_NAME
Indicates that the standard error of the exogenous variable VARIABLE_NAME, or of the observation error/measurement errors associated with endogenous observed variable VARIABLE_NAME, is to be estimated.
corr VARIABLE_NAME1, VARIABLE_NAME2
Indicates that the correlation between the exogenous variables VARIABLE_NAME1 and VARIABLE_NAME2, or the correlation of the observation errors/measurement errors associated with endogenous observed variables VARIABLE_NAME1 and VARIABLE_NAME2, is to be estimated. Note that correlations set by previous shocksblocks or estimationcommands are kept at their value set prior to estimation if they are not estimated again subsequently. Thus, the treatment is the same as in the case of deep parameters set during model calibration and not estimated.
PARAMETER_NAME
The name of a model parameter to be estimated
DSGE_PRIOR_WEIGHT
Special name for the weigh of the DSGE model in DSGEVAR model.
The rest of the line consists of the following fields, some of them being optional:

INITIAL_VALUE
¶ Specifies a starting value for the posterior mode optimizer or the maximum likelihood estimation. If unset, defaults to the prior mean.

LOWER_BOUND
¶ Specifies a lower bound for the parameter value in maximum likelihood estimation. In a Bayesian estimation context, sets a lower bound only effective while maximizing the posterior kernel. This lower bound does not modify the shape of the prior density, and is only aimed at helping the optimizer in identifying the posterior mode (no consequences for the MCMC). For some prior densities (namely inverse gamma, gamma, uniform, beta or Weibull) it is possible to shift the support of the prior distributions to the left or the right using
prior_3rd_parameter
. In this case the prior density is effectively modified (note that the truncated Gaussian density is not implemented in Dynare). If unset, defaults to minus infinity (ML) or the natural lower bound of the prior (Bayesian estimation).

UPPER_BOUND
¶ Same as
lower_bound
, but specifying an upper bound instead.

PRIOR_SHAPE
¶ A keyword specifying the shape of the prior density. The possible values are:
beta_pdf
,gamma_pdf
,normal_pdf
,uniform_pdf
,inv_gamma_pdf
,inv_gamma1_pdf
,inv_gamma2_pdf
andweibull_pdf
. Note thatinv_gamma_pdf
is equivalent toinv_gamma1_pdf
.

PRIOR_MEAN
¶ The mean of the prior distribution.

PRIOR_STANDARD_ERROR
¶ The standard error of the prior distribution.

PRIOR_3RD_PARAMETER
¶ A third parameter of the prior used for generalized beta distribution, generalized gamma, generalized Weibull and for the uniform distribution. Default:
0
.

PRIOR_4TH_PARAMETER
¶ A fourth parameter of the prior used for generalized beta distribution and for the uniform distribution. Default:
1
.

SCALE_PARAMETER
¶ A parameter specific scale parameter for the jumping distribution’s covariance matrix of the MetropolisHasting algorithm.
Note that INITIAL_VALUE, LOWER_BOUND, UPPER_BOUND, PRIOR_MEAN, PRIOR_STANDARD_ERROR, PRIOR_3RD_PARAMETER, PRIOR_4TH_PARAMETER and SCALE_PARAMETER can be any valid EXPRESSION. Some of them can be empty, in which Dynare will select a default value depending on the context and the prior shape.
As one uses options more towards the end of the list, all previous options must be filled: for example, if you want to specify SCALE_PARAMETER, you must specify
PRIOR_3RD_PARAMETER
andPRIOR_4TH_PARAMETER
. Use empty values, if these parameters don’t apply.Example
corr eps_1, eps_2, 0.5, , , beta_pdf, 0, 0.3, 1, 1;
Sets a generalized beta prior for the correlation between
eps_1
andeps_2
with mean0
and variance0.3
. By settingPRIOR_3RD_PARAMETER
to1
andPRIOR_4TH_PARAMETER
to1
the standard beta distribution with support[0,1]
is changed to a generalized beta with support[1,1]
. Note that LOWER_BOUND and UPPER_BOUND are left empty and thus default to1
and1
, respectively. The initial value is set to0.5
.Example
corr eps_1, eps_2, 0.5, 0.5, 1, beta_pdf, 0, 0.3, 1, 1;
Sets the same generalized beta distribution as before, but now truncates this distribution to
[0.5,1]
through the use of LOWER_BOUND and UPPER_BOUND. Hence, the prior does not integrate to1
anymore.Parameter transformation
Sometimes, it is desirable to estimate a transformation of a parameter appearing in the model, rather than the parameter itself. It is of course possible to replace the original parameter by a function of the estimated parameter everywhere is the model, but it is often unpractical.
In such a case, it is possible to declare the parameter to be estimated in the parameters statement and to define the transformation, using a pound sign (#) expression (see Model declaration).
Example
parameters bet; model; # sig = 1/bet; c = sig*c(+1)*mpk; end; estimated_params; bet, normal_pdf, 1, 0.05; end;

Block:
estimated_params_init
;
¶ 
Block:
estimated_params_init
(OPTIONS...);
This block declares numerical initial values for the optimizer when these ones are different from the prior mean. It should be specified after theestimated_params
block as otherwise the specified starting values are overwritten by the latter.Each line has the following syntax:
stderr VARIABLE_NAME  corr VARIABLE_NAME_1, VARIABLE_NAME_2  PARAMETER_NAME, INITIAL_VALUE;
Options

use_calibration
¶ For not specifically initialized parameters, use the deep parameters and the elements of the covariance matrix specified in the
shocks
block from calibration as starting values for estimation. For components of theshocks
block that were not explicitly specified during calibration or which violate the prior, the prior mean is used.
See
estimated_params
, for the meaning and syntax of the various components.

Block:
estimated_params_bounds
;
¶
This block declares lower and upper bounds for parameters in maximum likelihood estimation.Each line has the following syntax:
stderr VARIABLE_NAME  corr VARIABLE_NAME_1, VARIABLE_NAME_2  PARAMETER_NAME, LOWER_BOUND, UPPER_BOUND;
See
estimated_params
, for the meaning and syntax of the various components.

Command:
estimation
[VARIABLE_NAME...];

Command:
estimation
(OPTIONS...) [VARIABLE_NAME...];
This command runs Bayesian or maximum likelihood estimation.The following information will be displayed by the command:
 Results from posterior optimization (also for maximum likelihood)
 Marginal log data density
 Posterior mean and highest posterior density interval (shortest credible set) from posterior simulation
 Convergence diagnostic table when only one MCM chain is used or MetropolisHastings convergence graphs documented in Pfeiffer (2014) in case of multiple MCM chains
 Table with numerical inefficiency factors of the MCMC
 Graphs with prior, posterior, and mode
 Graphs of smoothed shocks, smoothed observation errors, smoothed and historical variables
Note that the posterior moments, smoothed variables, kstep ahead filtered variables and forecasts (when requested) will only be computed on the variables listed after the
estimation
command. Alternatively, one can choose to compute these quantities on all endogenous or on all observed variables (seeconsider_all_endogenous
andconsider_only_observed
options below). If no variable is listed after the estimation command, then Dynare will interactively ask which variable set to use.Also, during the MCMC (Bayesian estimation with
mh_replic
\(>0\)) a (graphical or text) waiting bar is displayed showing the progress of the MonteCarlo and the current value of the acceptance ratio. Note that if theload_mh_file
option is used (see below) the reported acceptance ratio does not take into account the draws from the previous MCMC. In the literature there is a general agreement for saying that the acceptance ratio should be close to one third or one quarter. If this not the case, you can stop the MCMC (CtrlC
) and change the value of optionmh_jscale
(see below).Note that by default Dynare generates random numbers using the algorithm
mt199937ar
(i.e. Mersenne Twister method) with a seed set equal to0
. Consequently the MCMCs in Dynare are deterministic: one will get exactly the same results across different Dynare runs (ceteris paribus). For instance, the posterior moments or posterior densities will be exactly the same. This behaviour allows to easily identify the consequences of a change on the model, the priors or the estimation options. But one may also want to check that across multiple runs, with different sequences of proposals, the returned results are almost identical. This should be true if the number of iterations (i.e. the value ofmh_replic
) is important enough to ensure the convergence of the MCMC to its ergodic distribution. In this case the default behaviour of the random number generators in not wanted, and the user should set the seed according to the system clock before the estimation command using the following command:set_dynare_seed('clock');
so that the sequence of proposals will be different across different runs.
Algorithms
The Monte Carlo Markov Chain (MCMC) diagnostics are generated by the estimation command if
mh_replic
is larger than 2000 and if optionnodiagnostic
is not used. Ifmh_nblocks
is equal to one, the convergence diagnostics of Geweke (1992,1999) is computed. It uses a chisquare test to compare the means of the first and last draws specified bygeweke_interval
after discarding the burnin ofmh_drop
. The test is computed using variance estimates under the assumption of no serial correlation as well as using tapering windows specified intaper_steps
. Ifmh_nblocks
is larger than 1, the convergence diagnostics of Brooks and Gelman (1998) are used instead. As described in section 3 of Brooks and Gelman (1998) the univariate convergence diagnostics are based on comparing pooled and within MCMC moments (Dynare displays the second and third order moments, and the length of the Highest Probability Density interval covering 80% of the posterior distribution). Due to computational reasons, the multivariate convergence diagnostic does not follow Brooks and Gelman (1998) strictly, but rather applies their idea for univariate convergence diagnostics to the range of the posterior likelihood function instead of the individual parameters. The posterior kernel is used to aggregate the parameters into a scalar statistic whose convergence is then checked using the Brooks and Gelman (1998) univariate convergence diagnostic.The inefficiency factors are computed as in Giordano et al.(2011) based on Parzen windows as in e.g. Andrews (1991).
Options

datafile = FILENAME
The datafile: a
.m
file, a.mat
file, a.csv
file, or a.xls/.xlsx
file (under Octave, the io package from OctaveForge is required for the.csv
and.xlsx
formats and the.xls
file extension is not supported). Note that the base name (i.e. without extension) of the datafile has to be different from the base name of the model file. If there are several files named FILENAME, but with different file endings, the file name must be included in quoted strings and provide the file ending like:estimation(datafile='../fsdat_simul.mat',...);

dirname = FILENAME
¶ Directory in which to store
estimation
output. To pass a subdirectory of a directory, you must quote the argument. Default:<mod_file>
.

xls_sheet = NAME
¶ The name of the sheet with the data in an Excel file.

xls_range = RANGE
¶ The range with the data in an Excel file. For example,
xls_range=B2:D200
.

nobs = INTEGER
¶ The number of observations following
first_obs
to be used. Default: all observations in the file afterfirst_obs
.

nobs = [INTEGER1:INTEGER2]
¶ Runs a recursive estimation and forecast for samples of size ranging of
INTEGER1
toINTEGER2
. Optionforecast
must also be specified. The forecasts are stored in theRecursiveForecast
field of the results structure (seeRecursiveForecast
). The respective results structuresoo_
are saved inoo_recursive_
(seeoo_recursive_
) and are indexed with the respective sample length.

first_obs = INTEGER
¶ The number of the first observation to be used. In case of estimating a DSGEVAR,
first_obs
needs to be larger than the number of lags. Default:1
.

first_obs = [INTEGER1:INTEGER2]
¶ Runs a rolling window estimation and forecast for samples of fixed size
nobs
starting with the first observation ranging fromINTEGER1
toINTEGER2
. Optionforecast
must also be specified. This option is incompatible with requesting recursive forecasts using an expanding window (seenobs
). The respective results structuresoo_
are saved inoo_recursive_
(seeoo_recursive_
) and are indexed with the respective first observation of the rolling window.

prefilter = INTEGER
¶ A value of 1 means that the estimation procedure will demean each data series by its empirical mean. If the loglinear option without the
logdata
option is requested, the data will first be logged and then demeaned. Default:0
, i.e. no prefiltering.

presample = INTEGER
¶ The number of observations after
first_obs
to be skipped before evaluating the likelihood. These presample observations do not enter the likelihood, but are used as a training sample for starting the Kalman filter iterations. This option is incompatible with estimating a DSGEVAR. Default:0
.

loglinear
Computes a loglinear approximation of the model instead of a linear approximation. As always in the context of estimation, the data must correspond to the definition of the variables used in the model (see Pfeifer (2013) for more details on how to correctly specify observation equations linking model variables and the data). If you specify the loglinear option, Dynare will take the logarithm of both your model variables and of your data as it assumes the data to correspond to the original nonlogged model variables. The displayed posterior results like impulse responses, smoothed variables, and moments will be for the logged variables, not the original unlogged ones. Default: computes a linear approximation.

logdata
¶ Dynare applies the \(log\) transformation to the provided data if a loglinearization of the model is requested (
loglinear
) unlesslogdata
option is used. This option is necessary if the user provides data already in logs, otherwise the \(log\) transformation will be applied twice (this may result in complex data).

plot_priors = INTEGER
¶ Control the plotting of priors.
0
No prior plot.1
Prior density for each estimated parameter is plotted. It is important to check that the actual shape of prior densities matches what you have in mind. Illchosen values for the prior standard density can result in absurd prior densities.
Default value is1
.

nograph
See
nograph
.

posterior_nograph
¶ Suppresses the generation of graphs associated with Bayesian IRFs (
bayesian_irf
), posterior smoothed objects (smoother
), and posterior forecasts (forecast
).

posterior_graph
¶ Reenables the generation of graphs previously shut off with
posterior_nograph
.

nodisplay
See
nodisplay
.

graph_format = FORMAT

graph_format = ( FORMAT, FORMAT... )
See
graph_format
.

lik_init = INTEGER
¶ Type of initialization of Kalman filter:
1
For stationary models, the initial matrix of variance of the error of forecast is set equal to the unconditional variance of the state variables.2
For nonstationary models: a wide prior is used with an initial matrix of variance of the error of forecast diagonal with 10 on the diagonal (follows the suggestion of Harvey and Phillips(1979)).3
For nonstationary models: use a diffuse filter (use rather thediffuse_filter
option).4
The filter is initialized with the fixed point of the Riccati equation.5
Use i) option 2 for the nonstationary elements by setting their initial variance in the forecast error matrix to 10 on the diagonal and all covariances to 0 and ii) option 1 for the stationary elements.
Default value is 1. For advanced use only.

lik_algo = INTEGER
¶ For internal use and testing only.

conf_sig = DOUBLE
¶ Confidence interval used for classical forecasting after estimation. See conf_sig.

mh_conf_sig = DOUBLE
¶ Confidence/HPD interval used for the computation of prior and posterior statistics like: parameter distributions, prior/posterior moments, conditional variance decomposition, impulse response functions, Bayesian forecasting. Default:
0.9
.

mh_replic = INTEGER
¶ Number of replications for MetropolisHastings algorithm. For the time being,
mh_replic
should be larger than 1200. Default:20000
.

sub_draws = INTEGER
¶ Number of draws from the MCMC that are used to compute posterior distribution of various objects (smoothed variable, smoothed shocks, forecast, moments, IRF). The draws used to compute these posterior moments are sampled uniformly in the estimated empirical posterior distribution (i.e. draws of the MCMC).
sub_draws
should be smaller than the total number of MCMC draws available. Default:min(posterior_max_subsample_draws, (Total number of draws)*(number of chains) )
.

posterior_max_subsample_draws = INTEGER
¶ Maximum number of draws from the MCMC used to compute posterior distribution of various objects (smoothed variable, smoothed shocks, forecast, moments, IRF), if not overriden by option
sub_draws
. Default:1200
.

mh_nblocks = INTEGER
¶ Number of parallel chains for MetropolisHastings algorithm. Default:
2
.

mh_drop = DOUBLE
¶ The fraction of initially generated parameter vectors to be dropped as a burnin before using posterior simulations. Default:
0.5
.

mh_jscale = DOUBLE
¶ The scale parameter of the jumping distribution’s covariance matrix (MetropolisHastings or TaRBalgorithm). The default value is rarely satisfactory. This option must be tuned to obtain, ideally, an acceptance ratio of 25%33%. Basically, the idea is to increase the variance of the jumping distribution if the acceptance ratio is too high, and decrease the same variance if the acceptance ratio is too low. In some situations it may help to consider parameterspecific values for this scale parameter. This can be done in the
estimated_params
block.Note that
mode_compute=6
will tune the scale parameter to achieve an acceptance rate of AcceptanceRateTarget. The resulting scale parameter will be saved into a file namedMODEL_FILENAME_mh_scale.mat.
This file can be loaded in subsequent runs via theposterior_sampler_options
option scale_file. Bothmode_compute=6
andscale_file
will overwrite any value specified inestimated_params
with the tuned value. Default:0.2
.

mh_init_scale = DOUBLE
¶ The scale to be used for drawing the initial value of the MetropolisHastings chain. Generally, the starting points should be overdispersed for the Brooks and Gelman (1998) convergence diagnostics to be meaningful. Default:
2*mh_jscale.
It is important to keep in mind that
mh_init_scale
is set at the beginning of Dynare execution, i.e. the default will not take into account potential changes inmh_jscale
introduced by eithermode_compute=6
or theposterior_sampler_options
option scale_file. Ifmh_init_scale
is too wide during initalization of the posterior sampler so that 100 tested draws are inadmissible (e.g. BlanchardKahn conditions are always violated), Dynare will request user input of a newmh_init_scale
value with which the next 100 draws will be drawn and tested. If thenointeractive
option has been invoked, the program will instead automatically decreasemh_init_scale
by 10 percent after 100 futile draws and try another 100 draws. This iterative procedure will take place at most 10 times, at which point Dynare will abort with an error message.

mh_recover
¶ Attempts to recover a MetropolisHastings simulation that crashed prematurely, starting with the last available saved
mh
file. Shouldn’t be used together withload_mh_file
or a differentmh_replic
than in the crashed run. Since Dynare 4.5 the proposal density from the previous run will automatically be loaded. In older versions, to assure a neat continuation of the chain with the same proposal density, you should provide themode_file
used in the previous run or the same userdefinedmcmc_jumping_covariance
when using this option. Note that under Octave, a neat continuation of the crashed chain with the respective last random number generator state is currently not supported.

mh_mode = INTEGER
¶ …

mode_file = FILENAME
¶ Name of the file containing previous value for the mode. When computing the mode, Dynare stores the mode (
xparam1
) and the hessian (hh
, only ifcova_compute=1
) in a file calledMODEL_FILENAME_mode.mat
. After a successful run of the estimation command, themode_file
will be disabled to prevent other function calls from implicitly using an updatedmodefile
. Thus, if the modfile contains subsequentestimation
commands, themode_file
option, if desired, needs to be specified again.

mode_compute = INTEGER  FUNCTION_NAME
¶ Specifies the optimizer for the mode computation:
0
The mode isn’t computed. When the
mode_file
option is specified, the mode is simply read from that file.When
mode_file
option is not specified, Dynare reports the value of the log posterior (log likelihood) evaluated at the initial value of the parameters.When
mode_file
is not specified and there is noestimated_params
block, but thesmoother
option is used, it is a roundabout way to compute the smoothed value of the variables of a model with calibrated parameters.1
Usesfmincon
optimization routine (available under MATLAB if the Optimization Toolbox is installed; not available under Octave).2
Uses the continuous simulated annealing global optimization algorithm described in Corana et al.(1987) and Goffe et al.(1994).3
Usesfminunc
optimization routine (available under MATLAB if the Optimization Toolbox is installed; available under Octave if the optim package from OctaveForge is installed).4
Uses Chris Sims’scsminwel
.5
Uses Marco Ratto’snewrat
. This value is not compatible with non linear filters or DSGEVAR models. This is a slice optimizer: most iterations are a sequence of univariate optimization step, one for each estimated parameter or shock. Usescsminwel
for line search in each step.6
Uses a MonteCarlo based optimization routine (see Dynare wiki for more details).7
Usesfminsearch
, a simplexbased optimization routine (available under MATLAB if the Optimization Toolbox is installed; available under Octave if the optim package from OctaveForge is installed).8
Uses Dynare implementation of the NelderMead simplexbased optimization routine (generally more efficient than the MATLAB or Octave implementation available withmode_compute=7
).9
Uses the CMAES (Covariance Matrix Adaptation Evolution Strategy) algorithm of Hansen and Kern (2004), an evolutionary algorithm for difficult nonlinear nonconvex optimization.10
Uses thesimpsa
algorithm, based on the combination of the nonlinear simplex and simulated annealing algorithms as proposed by Cardoso, Salcedo and Feyo de Azevedo (1996).11
This is not strictly speaking an optimization algorithm. The (estimated) parameters are treated as state variables and estimated jointly with the original state variables of the model using a nonlinear filter. The algorithm implemented in Dynare is described in Liu and West (2001).12
Uses theparticleswarm
optimization routine (available under MATLAB if the Global Optimization Toolbox is installed; not available under Octave).101
Uses the SolveOpt algorithm for local nonlinear optimization problems proposed by Kuntsevich and Kappel (1997).102
Usessimulannealbnd
optimization routine (available under MATLAB if the Global Optimization Toolbox is installed; not available under Octave)FUNCTION_NAME
It is also possible to give a FUNCTION_NAME to this option, instead of an INTEGER. In that case, Dynare takes the return value of that function as the posterior mode.
Default value is4
.

silent_optimizer
¶ Instructs Dynare to run mode computing/optimization silently without displaying results or saving files in between. Useful when running loops.

mcmc_jumping_covariance = OPTION
¶ Tells Dynare which covariance to use for the proposal density of the MCMC sampler. OPTION can be one of the following:
hessian
Uses the Hessian matrix computed at the mode.prior_variance
Uses the prior variances. No infinite prior variances are allowed in this case.identity_matrix
Uses an identity matrix.FILENAME
Loads an arbitrary userspecified covariance matrix fromFILENAME.mat
. The covariance matrix must be saved in a variable namedjumping_covariance
, must be square, positive definite, and have the same dimension as the number of estimated parameters.Note that the covariance matrices are still scaled with
mh_jscale
. Default value ishessian
.

mode_check
¶ Tells Dynare to plot the posterior density for values around the computed mode for each estimated parameter in turn. This is helpful to diagnose problems with the optimizer. Note that for
order>1
the likelihood function resulting from the particle filter is not differentiable anymore due to random chatter introduced by selecting different particles for different parameter values. For this reason, themode_check
plot may look wiggly.

mode_check_neighbourhood_size = DOUBLE
¶ Used in conjunction with option
mode_check
, gives the width of the window around the posterior mode to be displayed on the diagnostic plots. This width is expressed in percentage deviation. TheInf
value is allowed, and will trigger a plot over the entire domain (see alsomode_check_symmetric_plots
). Default:0.5
.

mode_check_symmetric_plots = INTEGER
¶ Used in conjunction with option
mode_check
, if set to1
, tells Dynare to ensure that the check plots are symmetric around the posterior mode. A value of0
allows to have asymmetric plots, which can be useful if the posterior mode is close to a domain boundary, or in conjunction withmode_check_neighbourhood_size = Inf
when the domain in not the entire real line. Default:1
.

mode_check_number_of_points = INTEGER
¶ Number of points around the posterior mode where the posterior kernel is evaluated (for each parameter). Default is
20
.

prior_trunc = DOUBLE
¶ Probability of extreme values of the prior density that is ignored when computing bounds for the parameters. Default:
1e32
.

huge_number = DOUBLE
¶ Value for replacing infinite values in the definition of (prior) bounds when finite values are required for computational reasons. Default:
1e7
.

load_mh_file
¶ Tells Dynare to add to previous MetropolisHastings simulations instead of starting from scratch. Since Dynare 4.5 the proposal density from the previous run will automatically be loaded. In older versions, to assure a neat continuation of the chain with the same proposal density, you should provide the
mode_file
used in the previous run or the same userdefinedmcmc_jumping_covariance
when using this option. Shouldn’t be used together withmh_recover
. Note that under Octave, a neat continuation of the chain with the last random number generator state of the already present draws is currently not supported.

load_results_after_load_mh
¶ This option is available when loading a previous MCMC run without adding additional draws, i.e. when
load_mh_file
is specified withmh_replic=0
. It tells Dynare to load the previously computed convergence diagnostics, marginal data density, and posterior statistics from an existing_results
file instead of recomputing them.

optim = (NAME, VALUE, ...)
¶ A list of NAME and VALUE pairs. Can be used to set options for the optimization routines. The set of available options depends on the selected optimization routine (i.e. on the value of option
mode_compute
):1, 3, 7, 12
Available options are given in the documentation of the MATLAB Optimization Toolbox or in Octave’s documentation.2
Available options are:
'initial_step_length'
Initial step length. Default:1
.'initial_temperature'
Initial temperature. Default:15
.'MaxIter'
Maximum number of function evaluations. Default:100000
.'neps'
Number of final function values used to decide upon termination. Default:10
.'ns'
Number of cycles. Default:10
.'nt'
Number of iterations before temperature reduction. Default:10
.'step_length_c'
Step length adjustment. Default:0.1
.'TolFun'
Stopping criteria. Default:1e8
.'rt'
Temperature reduction factor. Default:0.1
.'verbosity'
Controls verbosity of display during optimization, ranging from0
(silent) to3
(each function evaluation). Default:1
4
Available options are:
'InitialInverseHessian'
Initial approximation for the inverse of the Hessian matrix of the posterior kernel (or likelihood). Obviously this approximation has to be a square, positive definite and symmetric matrix. Default:'1e4*eye(nx)'
, where nx is the number of parameters to be estimated.'MaxIter'
Maximum number of iterations. Default:1000
.'NumgradAlgorithm'
Possible values are2
,3
and5
, respectively, corresponding to the two, three and five points formula used to compute the gradient of the objective function (see Abramowitz and Stegun (1964)). Values13
and15
are more experimental. If perturbations on the right and the left increase the value of the objective function (we minimize this function) then we force the corresponding element of the gradient to be zero. The idea is to temporarily reduce the size of the optimization problem. Default:2
.'NumgradEpsilon'
Size of the perturbation used to compute numerically the gradient of the objective function. Default:1e6
.'TolFun'
Stopping criteria. Default:1e7
.'verbosity'
Controls verbosity of display during optimization. Set to0
to set to silent. Default:1
.'SaveFiles'
Controls saving of intermediate results during optimization. Set to0
to shut off saving. Default:1
.5
Available options are:
'Hessian'
Triggers three types of Hessian computations.0
: outer product gradient;1
: default DYNARE Hessian routine;2
: ’mixed’ outer product gradient, where diagonal elements are obtained using second order derivation formula and outer product is used for correlation structure. Both {0} and {2} options require univariate filters, to ensure using maximum number of individual densities and a positive definite Hessian. Both {0} and {2} are quicker than default DYNARE numeric Hessian, but provide decent starting values for Metropolis for large models (option {2} being more accurate than {0}). Default:1
.'MaxIter'
Maximum number of iterations. Default:1000
.'TolFun'
Stopping criteria. Default:1e5
for numerical derivatives,1e7
for analytic derivatives.'verbosity'
Controls verbosity of display during optimization. Set to0
to set to silent. Default:1
.'SaveFiles'
Controls saving of intermediate results during optimization. Set to0
to shut off saving. Default:1
.6
Available options are:
'AcceptanceRateTarget'
A real number between zero and one. The scale parameter of the jumping distribution is adjusted so that the effective acceptance rate matches the value of option'AcceptanceRateTarget'
. Default:1.0/3.0
.'InitialCovarianceMatrix'
Initial covariance matrix of the jumping distribution. Default is'previous'
if optionmode_file
is used,'prior'
otherwise.'nclimbmh'
Number of iterations in the last MCMC (climbing mode). Default:200000
.'ncovmh'
Number of iterations used for updating the covariance matrix of the jumping distribution. Default:20000
.'nscalemh'
Maximum number of iterations used for adjusting the scale parameter of the jumping distribution. Default:200000
.'NumberOfMh'
Number of MCMC run sequentially. Default:3
.8
Available options are:
'InitialSimplexSize'
Initial size of the simplex, expressed as percentage deviation from the provided initial guess in each direction. Default:.05
.'MaxIter'
Maximum number of iterations. Default:5000
.'MaxFunEvals'
Maximum number of objective function evaluations. No default.'MaxFunvEvalFactor'
SetMaxFunvEvals
equal toMaxFunvEvalFactor
times the number of estimated parameters. Default:500
.'TolFun'
Tolerance parameter (w.r.t the objective function). Default:1e4
.'TolX'
Tolerance parameter (w.r.t the instruments). Default:1e4
.'verbosity'
Controls verbosity of display during optimization. Set to0
to set to silent. Default:1
.9
Available options are:
'CMAESResume'
Resume previous run. Requires thevariablescmaes.mat
from the last run. Set to1
to enable. Default:0
.'MaxIter'
Maximum number of iterations.'MaxFunEvals'
Maximum number of objective function evaluations. Default:Inf
.'TolFun'
Tolerance parameter (w.r.t the objective function). Default:1e7
.'TolX'
Tolerance parameter (w.r.t the instruments). Default:1e7
.'verbosity'
Controls verbosity of display during optimization. Set to0
to set to silent. Default:1
.'SaveFiles'
Controls saving of intermediate results during optimization. Set to0
to shut off saving. Default:1
.10
Available options are:
'EndTemperature'
Terminal condition w.r.t the temperature. When the temperature reachesEndTemperature
, the temperature is set to zero and the algorithm falls back into a standard simplex algorithm. Default:0.1
.'MaxIter'
Maximum number of iterations. Default:5000
.'MaxFunvEvals'
Maximum number of objective function evaluations. No default.'TolFun'
Tolerance parameter (w.r.t the objective function). Default:1e4
.'TolX'
Tolerance parameter (w.r.t the instruments). Default:1e4
.'verbosity'
Controls verbosity of display during optimization. Set to0
to set to silent. Default:1
.101
Available options are:
'LBGradientStep'
Lower bound for the stepsize used for the difference approximation of gradients. Default:1e11
.'MaxIter'
Maximum number of iterations. Default:15000
'SpaceDilation'
Coefficient of space dilation. Default:2.5
.'TolFun'
Tolerance parameter (w.r.t the objective function). Default:1e6
.'TolX'
Tolerance parameter (w.r.t the instruments). Default:1e6
.'verbosity'
Controls verbosity of display during optimization. Set to0
to set to silent. Default:1
.102
Available options are given in the documentation of the MATLAB Global Optimization Toolbox.Example
To change the defaults of
csminwel
(mode_compute=4
):estimation(..., mode_compute=4,optim=('NumgradAlgorithm',3,'TolFun',1e5),...);

nodiagnostic
¶ Does not compute the convergence diagnostics for MetropolisHastings. Default: diagnostics are computed and displayed.

bayesian_irf
¶ Triggers the computation of the posterior distribution of IRFs. The length of the IRFs are controlled by the
irf
option. Results are stored inoo_.PosteriorIRF.dsge
(see below for a description of this variable).

relative_irf
See
relative_irf
.

dsge_var = DOUBLE
¶ Triggers the estimation of a DSGEVAR model, where the weight of the DSGE prior of the VAR model is calibrated to the value passed (see Del Negro and Schorfheide (2004)). It represents the ratio of dummy over actual observations. To assure that the prior is proper, the value must be bigger than \((k+n)/T\), where \(k\) is the number of estimated parameters, \(n\) is the number of observables, and \(T\) is the number of observations.
NB: The previous method of declaringdsge_prior_weight
as a parameter and then calibrating it is now deprecated and will be removed in a future release of Dynare. Some of objects arising during estimation are stored with their values at the mode inoo_.dsge_var.posterior_mode
.

dsge_var
¶ Triggers the estimation of a DSGEVAR model, where the weight of the DSGE prior of the VAR model will be estimated (as in Adjemian et al.(2008)). The prior on the weight of the DSGE prior,
dsge_prior_weight
, must be defined in theestimated_params
section.NB: The previous method of declaring
dsge_prior_weight
as a parameter and then placing it inestimated_params
is now deprecated and will be removed in a future release of Dynare.

dsge_varlag = INTEGER
¶ The number of lags used to estimate a DSGEVAR model. Default:
4
.

posterior_sampling_method = NAME
¶ Selects the sampler used to sample from the posterior distribution during Bayesian estimation. Default:
’random_walk_metropolis_hastings’
.'random_walk_metropolis_hastings'
Instructs Dynare to use the RandomWalk MetropolisHastings. In this algorithm, the proposal density is recentered to the previous draw in every step.'tailored_random_block_metropolis_hastings'
Instructs Dynare to use the Tailored randomized block (TaRB) MetropolisHastings algorithm proposed by Chib and Ramamurthy (2010) instead of the standard RandomWalk MetropolisHastings. In this algorithm, at each iteration the estimated parameters are randomly assigned to different blocks. For each of these blocks a modefinding step is conducted. The inverse Hessian at this mode is then used as the covariance of the proposal density for a RandomWalk MetropolisHastings step. If the numerical Hessian is not positive definite, the generalized Cholesky decomposition of Schnabel and Eskow (1990) is used, but without pivoting. The TaRBMH algorithm massively reduces the autocorrelation in the MH draws and thus reduces the number of draws required to representatively sample from the posterior. However, this comes at a computational cost as the algorithm takes more time to run.'independent_metropolis_hastings'
Use the Independent MetropolisHastings algorithm where the proposal distribution  in contrast to the Random Walk MetropolisHastings algorithm  does not depend on the state of the chain.'slice'
Instructs Dynare to use the Slice sampler of Planas, Ratto, and Rossi (2015). Note that'slice'
is incompatible withprior_trunc=0
.

posterior_sampler_options = (NAME, VALUE, ...)
¶ A list of NAME and VALUE pairs. Can be used to set options for the posterior sampling methods. The set of available options depends on the selected posterior sampling routine (i.e. on the value of option
posterior_sampling_method
):'random_walk_metropolis_hastings'
Available options are:'proposal_distribution'
Specifies the statistical distribution used for the proposal density.'rand_multivariate_normal'
Use a multivariate normal distribution. This is the default.'rand_multivariate_student'
Use a multivariate student distribution.'student_degrees_of_freedom'
Specifies the degrees of freedom to be used with the multivariate student distribution. Default:3
.'use_mh_covariance_matrix'
Indicates to use the covariance matrix of the draws from a previous MCMC run to define the covariance of the proposal distribution. Requires theload_mh_file
option to be specified. Default:0
.'scale_file'
Provides the name of a_mh_scale.mat
file storing the tuned scale factor from a previous run ofmode_compute=6
.'save_tmp_file'
Save the MCMC draws into a_mh_tmp_blck
file at the refresh rate of the status bar instead of just saving the draws when the current_mh*_blck
file is full. Default:0
'independent_metropolis_hastings'
Takes the same options as in the case ofrandom_walk_metropolis_hastings
.'slice'
'rotated'
Triggers rotated slice iterations using a covariance matrix from initial burnin iterations. Requires eitheruse_mh_covariance_matrix
orslice_initialize_with_mode
. Default:0
.'mode_files'
For multimodal posteriors, provide the name of a file containing anparam
bynmodes
variable calledxparams
storing the different modes. This array must have one column vector per mode and the estimated parameters along the row dimension. With this info, the code will automatically trigger therotated
andmode
options. Default:[]
.'slice_initialize_with_mode'
The default for slice is to setmode_compute=0
and start the chain(s) from a random location in the prior space. This option first runs the modefinder and then starts the chain from the mode. Together withrotated
, it will use the inverse Hessian from the mode to perform rotated slice iterations. Default:0
.'initial_step_size'
Sets the initial size of the interval in the steppingout procedure as fraction of the prior support, i.e. the size will beinitial_step_size * (UBLB)
.initial_step_size
must be a real number in the interval[0,1]
. Default:0.8
.'use_mh_covariance_matrix'
'save_tmp_file'
See save_tmp_file. Default:1
.'tailored_random_block_metropolis_hastings'
new_block_probability = DOUBLE
Specifies the probability of the next parameter belonging to a new block when the random blocking in the TaRB MetropolisHastings algorithm is conducted. The higher this number, the smaller is the average block size and the more random blocks are formed during each parameter sweep. Default:0.25
.mode_compute = INTEGER
Specifies the modefinder run in every iteration for every block of the TaRB MetropolisHastings algorithm. Seemode_compute
. Default:4
.optim = (NAME, VALUE,...)
Specifies the options for the modefinder used in the TaRB MetropolisHastings algorithm. Seeoptim
.'scale_file'
See scale_file..'save_tmp_file'
See save_tmp_file. Default:1
.

moments_varendo
¶ Triggers the computation of the posterior distribution of the theoretical moments of the endogenous variables. Results are stored in
oo_.PosteriorTheoreticalMoments
(seeoo_.PosteriorTheoreticalMoments
). The number of lags in the autocorrelation function is controlled by thear
option.

contemporaneous_correlation
See
contemporaneous_correlation
. Results are stored inoo_.PosteriorTheoreticalMoments
. Note that thenocorr
option has no effect.

no_posterior_kernel_density
¶ Shuts off the computation of the kernel density estimator for the posterior objects (see density field).

conditional_variance_decomposition = INTEGER

conditional_variance_decomposition = [INTEGER1:INTEGER2]

conditional_variance_decomposition = [INTEGER1 INTEGER2 ...]
Computes the posterior distribution of the conditional variance decomposition for the specified period(s). The periods must be strictly positive. Conditional variances are given by \(var(y_{t+k}\vert t)\). For period 1, the conditional variance decomposition provides the decomposition of the effects of shocks upon impact. The results are stored in
oo_.PosteriorTheoreticalMoments.dsge.ConditionalVarianceDecomposition
, but currently there is no displayed output. Note that this option requires themoments_varendo
to be specified.

filtered_vars
¶ Triggers the computation of the posterior distribution of filtered endogenous variables/onestep ahead forecasts, i.e. \(E_{t}{y_{t+1}}\). Results are stored in
oo_.FilteredVariables
(see below for a description of this variable)

smoother
¶ Triggers the computation of the posterior distribution of smoothed endogenous variables and shocks, i.e. the expected value of variables and shocks given the information available in all observations up to the final date (\(E_{T}{y_t}\)). Results are stored in
oo_.SmoothedVariables
,oo_.SmoothedShocks
andoo_.SmoothedMeasurementErrors
. Also triggers the computation ofoo_.UpdatedVariables
, which contains the estimation of the expected value of variables given the information available at the current date (\(E_{t}{y_t}\)). See below for a description of all these variables.

forecast = INTEGER
¶ Computes the posterior distribution of a forecast on INTEGER periods after the end of the sample used in estimation. If no MetropolisHastings is computed, the result is stored in variable
oo_.forecast
and corresponds to the forecast at the posterior mode. If a MetropolisHastings is computed, the distribution of forecasts is stored in variablesoo_.PointForecast
andoo_.MeanForecast
. See Forecasting, for a description of these variables.

tex
See
tex
.

kalman_algo = INTEGER
¶ 0
Automatically use the Multivariate Kalman Filter for stationary models and the Multivariate Diffuse Kalman Filter for nonstationary models.1
Use the Multivariate Kalman Filter.2
Use the Univariate Kalman Filter.3
Use the Multivariate Diffuse Kalman Filter.4
Use the Univariate Diffuse Kalman Filter.Default value is
0
. In case of missing observations of single or all series, Dynare treats those missing values as unobserved states and uses the Kalman filter to infer their value (see e.g. Durbin and Koopman (2012), Ch. 4.10) This procedure has the advantage of being capable of dealing with observations where the forecast error variance matrix becomes singular for some variable(s). If this happens, the respective observation enters with a weight of zero in the loglikelihood, i.e. this observation for the respective variable(s) is dropped from the likelihood computations (for details see Durbin and Koopman (2012), Ch. 6.4 and 7.2.5 and Koopman and Durbin (2000)). If the use of a multivariate Kalman filter is specified and a singularity is encountered, Dynare by default automatically switches to the univariate Kalman filter for this parameter draw. This behavior can be changed via theuse_univariate_filters_if_singularity_is_detected
option.

fast_kalman_filter
¶ Select the fast Kalman filter using Chandrasekhar recursions as described by
Herbst (2015)
. This setting is only used withkalman_algo=1
orkalman_algo=3
. In case of using the diffuse Kalman filter (kalman_algo=3/lik_init=3
), the observables must be stationary. This option is not yet compatible withanalytic_derivation
.

kalman_tol = DOUBLE
¶ Numerical tolerance for determining the singularity of the covariance matrix of the prediction errors during the Kalman filter (minimum allowed reciprocal of the matrix condition number). Default value is
1e10
.

diffuse_kalman_tol = DOUBLE
¶ Numerical tolerance for determining the singularity of the covariance matrix of the prediction errors (\(F_{\infty}\)) and the rank of the covariance matrix of the nonstationary state variables (\(P_{\infty}\)) during the Diffuse Kalman filter. Default value is
1e6
.

filter_covariance
¶ Saves the series of one step ahead error of forecast covariance matrices. With Metropolis, they are saved in
oo_.FilterCovariance
, otherwise inoo_.Smoother.Variance
. Saves also kstep ahead error of forecast covariance matrices iffilter_step_ahead
is set.

filter_step_ahead = [INTEGER1:INTEGER2]
¶ 
filter_step_ahead = [INTEGER1 INTEGER2 ...]
¶ Triggers the computation kstep ahead filtered values, i.e. \(E_{t}{y_{t+k}}\). Stores results in
oo_.FilteredVariablesKStepAhead
. Also stores 1step ahead values inoo_.FilteredVariables
.oo_.FilteredVariablesKStepAheadVariances
is stored iffilter_covariance
.

filter_decomposition
¶ Triggers the computation of the shock decomposition of the above kstep ahead filtered values. Stores results in
oo_.FilteredVariablesShockDecomposition
.

smoothed_state_uncertainty
¶ Triggers the computation of the variance of smoothed estimates, i.e. \(var_T(y_t)\). Stores results in
oo_.Smoother.State_uncertainty
.

diffuse_filter
¶ Uses the diffuse Kalman filter (as described in Durbin and Koopman (2012) and Koopman and Durbin (2003) for the multivariate and Koopman and Durbin (2000) for the univariate filter) to estimate models with nonstationary observed variables.
When
diffuse_filter
is used thelik_init
option ofestimation
has no effect.When there are nonstationary exogenous variables in a model, there is no unique deterministic steady state. For instance, if productivity is a pure random walk:
\[a_t = a_{t1} + e_t\]any value of \(\bar a\) of \(a\) is a deterministic steady state for productivity. Consequently, the model admits an infinity of steady states. In this situation, the user must help Dynare in selecting one steady state, except if zero is a trivial model’s steady state, which happens when the
linear
option is used in the model declaration. The user can either provide the steady state to Dynare using asteady_state_model
block (or writing a steady state file) if a closed form solution is available, seesteady_state_model
, or specify some constraints on the steady state, see equation_tag_for_conditional_steady_state, so that Dynare computes the steady state conditionally on some predefined levels for the non stationary variables. In both cases, the idea is to use dummy values for the steady state level of the exogenous non stationary variables.Note that the nonstationary variables in the model must be integrated processes (their first difference or kdifference must be stationary).

selected_variables_only
¶ Only run the classical smoother on the variables listed just after the
estimation
command. This option is incompatible with requesting classical frequentist forecasts and will be overridden in this case. When using Bayesian estimation, the smoother is by default only run on the declared endogenous variables. Default: run the smoother on all the declared endogenous variables.

cova_compute = INTEGER
¶ When
0
, the covariance matrix of estimated parameters is not computed after the computation of posterior mode (or maximum likelihood). This increases speed of computation in large models during development, when this information is not always necessary. Of course, it will break all successive computations that would require this covariance matrix. Otherwise, if this option is equal to1
, the covariance matrix is computed and stored in variablehh
ofMODEL_FILENAME_mode.mat
. Default is1
.

solve_algo = INTEGER
See solve_algo.

order = INTEGER
Order of approximation, either
1
or2
. When equal to2
, the likelihood is evaluated with a particle filter based on a second order approximation of the model (see FernandezVillaverde and RubioRamirez (2005)). Default is1
, i.e. the likelihood of the linearized model is evaluated using a standard Kalman filter.

irf = INTEGER
See
irf
. Only used ifbayesian_irf
is passed.

irf_shocks = ( VARIABLE_NAME [[,] VARIABLE_NAME ...] )
See
irf_shocks
. Only used ifbayesian_irf
is passed.

irf_plot_threshold = DOUBLE
See
irf_plot_threshold
. Only used ifbayesian_irf
is passed.

aim_solver
See
aim_solver
.

sylvester = OPTION
See
sylvester
.

sylvester_fixed_point_tol = DOUBLE
See
sylvester_fixed_point_tol
.

lyapunov = OPTION
¶ Determines the algorithm used to solve the Lyapunov equation to initialized the variancecovariance matrix of the Kalman filter using the steadystate value of state variables. Possible values for OPTION are:
default
Uses the default solver for Lyapunov equations based on BartelsStewart algorithm.fixed_point
Uses a fixed point algorithm to solve the Lyapunov equation. This method is faster than thedefault
one for large scale models, but it could require a large amount of iterations.doubling
Uses a doubling algorithm to solve the Lyapunov equation (disclyap_fast
). This method is faster than the two previous one for large scale models.square_root_solver
Uses a squareroot solver for Lyapunov equations (dlyapchol
). This method is fast for large scale models (available under MATLAB if the Control System Toolbox is installed; available under Octave if the control package from OctaveForge is installed)Default value is
default
.

lyapunov_fixed_point_tol = DOUBLE
¶ This is the convergence criterion used in the fixed point Lyapunov solver. Its default value is
1e10
.

lyapunov_doubling_tol = DOUBLE
¶ This is the convergence criterion used in the doubling algorithm to solve the Lyapunov equation. Its default value is
1e16
.

use_penalized_objective_for_hessian
¶ Use the penalized objective instead of the objective function to compute numerically the hessian matrix at the mode. The penalties decrease the value of the posterior density (or likelihood) when, for some perturbations, Dynare is not able to solve the model (issues with steady state existence, Blanchard and Kahn conditions, …). In pratice, the penalized and original objectives will only differ if the posterior mode is found to be near a region where the model is illbehaved. By default the original objective function is used.

analytic_derivation
¶ Triggers estimation with analytic gradient. The final hessian is also computed analytically. Only works for stationary models without missing observations, i.e. for
kalman_algo<3
.

ar = INTEGER
See
ar
. Only useful in conjunction with optionmoments_varendo
.

endogenous_prior
¶ Use endogenous priors as in Christiano, Trabandt and Walentin (2011). The procedure is motivated by sequential Bayesian learning. Starting from independent initial priors on the parameters, specified in the
estimated_params
block, the standard deviations observed in a “presample”, taken to be the actual sample, are used to update the initial priors. Thus, the product of the initial priors and the presample likelihood of the standard deviations of the observables is used as the new prior (for more information, see the technical appendix of Christiano, Trabandt and Walentin (2011)). This procedure helps in cases where the regular posterior estimates, which minimize insample forecast errors, result in a large overprediction of model variable variances (a statistic that is not explicitly targeted, but often of particular interest to researchers).

use_univariate_filters_if_singularity_is_detected = INTEGER
¶ Decide whether Dynare should automatically switch to univariate filter if a singularity is encountered in the likelihood computation (this is the behaviour if the option is equal to
1
). Alternatively, if the option is equal to0
, Dynare will not automatically change the filter, but rather use a penalty value for the likelihood when such a singularity is encountered. Default:1
.

keep_kalman_algo_if_singularity_is_detected
¶ With the default
use_univariate_filters_if_singularity_is_detected=1
, Dynare will switch to the univariate Kalman filter when it encounters a singular forecast error variance matrix during Kalman filtering. Upon encountering such a singularity for the first time, all subsequent parameter draws and computations will automatically rely on univariate filter, i.e. Dynare will never try the multivariate filter again. Use thekeep_kalman_algo_if_singularity_is_detected
option to have theuse_univariate_filters_if_singularity_is_detected
only affect the behavior for the current draw/computation.

rescale_prediction_error_covariance
¶ Rescales the prediction error covariance in the Kalman filter to avoid badly scaled matrix and reduce the probability of a switch to univariate Kalman filters (which are slower). By default no rescaling is done.

qz_zero_threshold = DOUBLE
See
qz_zero_threshold
.

taper_steps = [INTEGER1 INTEGER2 ...]
¶ Percent tapering used for the spectral window in the Geweke (1992,1999) convergence diagnostics (requires
mh_nblocks=1
). The tapering is used to take the serial correlation of the posterior draws into account. Default:[4 8 15]
.

geweke_interval = [DOUBLE DOUBLE]
¶ Percentage of MCMC draws at the beginning and end of the MCMC chain taken to compute the Geweke (1992,1999) convergence diagnostics (requires
mh_nblocks=1
) after discarding the firstmh_drop = DOUBLE
percent of draws as a burnin. Default: [0.2 0.5].

raftery_lewis_diagnostics
¶ Triggers the computation of the Raftery and Lewis (1992) convergence diagnostics. The goal is deliver the number of draws required to estimate a particular quantile of the CDF
q
with precisionr
with a probabilitys
. Typically, one wants to estimate theq=0.025
percentile (corresponding to a 95 percent HPDI) with a precision of 0.5 percent (r=0.005
) with 95 percent certainty (s=0.95
). The defaults can be changed viaraftery_lewis_qrs
. Based on the theory of first order Markov Chains, the diagnostics will provide a required burnin (M
), the number of draws after the burnin (N
) as well as a thinning factor that would deliver a first order chain (k
). The last line of the table will also deliver the maximum over all parameters for the respective values.

raftery_lewis_qrs = [DOUBLE DOUBLE DOUBLE]
¶ Sets the quantile of the CDF
q
that is estimated with precisionr
with a probabilitys
in the Raftery and Lewis (1992) convergence diagnostics. Default:[0.025 0.005 0.95]
.

consider_all_endogenous
¶ Compute the posterior moments, smoothed variables, kstep ahead filtered variables and forecasts (when requested) on all the endogenous variables. This is equivalent to manually listing all the endogenous variables after the
estimation
command.

consider_only_observed
¶ Compute the posterior moments, smoothed variables, kstep ahead filtered variables and forecasts (when requested) on all the observed variables. This is equivalent to manually listing all the observed variables after the
estimation
command.

number_of_particles = INTEGER
¶ Number of particles used when evaluating the likelihood of a non linear state space model. Default:
1000
.

resampling = OPTION
¶ Determines if resampling of the particles is done. Possible values for OPTION are:
none
No resampling.systematic
Resampling at each iteration, this is the default value.generic
Resampling if and only if the effective sample size is below a certain level defined byresampling_threshold
*number_of_particles
.

resampling_threshold = DOUBLE
¶ A real number between zero and one. The resampling step is triggered as soon as the effective number of particles is less than this number times the total number of particles (as set by
number_of_particles
). This option is effective if and only if optionresampling
has valuegeneric
.

resampling_method = OPTION
¶ Sets the resampling method. Possible values for OPTION are:
kitagawa
,stratified
andsmooth
.

filter_algorithm = OPTION
¶ Sets the particle filter algorithm. Possible values for OPTION are:
sis
Sequential importance sampling algorithm, this is the default value.apf
Auxiliary particle filter.gf
Gaussian filter.gmf
Gaussian mixture filter.cpf
Conditional particle filter.nlkf
Use a standard (linear) Kalman filter algorithm with the nonlinear measurement and state equations.

proposal_approximation = OPTION
¶ Sets the method for approximating the proposal distribution. Possible values for OPTION are:
cubature
,montecarlo
andunscented
. Default value isunscented
.

distribution_approximation = OPTION
¶ Sets the method for approximating the particle distribution. Possible values for OPTION are:
cubature
,montecarlo
andunscented
. Default value isunscented
.

cpf_weights = OPTION
¶ Controls the method used to update the weights in conditional particle filter, possible values are
amisanotristani
(Amisano et al. (2010)) ormurrayjonesparslow
(Murray et al. (2013)). Default value isamisanotristani
.

nonlinear_filter_initialization = INTEGER
¶ Sets the initial condition of the nonlinear filters. By default the nonlinear filters are initialized with the unconditional covariance matrix of the state variables, computed with the reduced form solution of the first order approximation of the model. If
nonlinear_filter_initialization=2
, the nonlinear filter is instead initialized with a covariance matrix estimated with a stochastic simulation of the reduced form solution of the second order approximation of the model. Both these initializations assume that the model is stationary, and cannot be used if the model has unit roots (which can be seen with thecheck
command prior to estimation). If the model has stochastic trends, user must usenonlinear_filter_initialization=3
, the filters are then initialized with an identity matrix for the covariance matrix of the state variables. Default value isnonlinear_filter_initialization=1
(initialization based on the first order approximation of the model).
Note
If no
mh_jscale
parameter is used for a parameter inestimated_params
, the procedure usesmh_jscale
for all parameters. Ifmh_jscale
option isn’t set, the procedure uses0.2
for all parameters. Note that ifmode_compute=6
is used or theposterior_sampler_option
calledscale_file
is specified, the values set inestimated_params
will be overwritten.“Endogenous” prior restrictions
It is also possible to impose implicit “endogenous” priors about IRFs and moments on the model during estimation. For example, one can specify that all valid parameter draws for the model must generate fiscal multipliers that are bigger than 1 by specifying how the IRF to a government spending shock must look like. The prior restrictions can be imposed via
irf_calibration
andmoment_calibration
blocks (see IRF/Moment calibration). The way it works internally is that any parameter draw that is inconsistent with the “calibration” provided in these blocks is discarded, i.e. assigned a prior density of 0. When specifying these blocks, it is important to keep in mind that one won’t be able to easily domodel_comparison
in this case, because the prior density will not integrate to 1.Output
After running estimation, the parameters
M_.params
and the variance matrixM_.Sigma_e
of the shocks are set to the mode for maximum likelihood estimation or posterior mode computation without Metropolis iterations. After estimation with Metropolis iterations (optionmh_replic > 0
or optionload_mh_file
set) the parametersM_.params
and the variance matrixM_.Sigma_e
of the shocks are set to the posterior mean.Depending on the options,
estimation
stores results in various fields of theoo_
structure, described below. In the following variables, we will adopt the following shortcuts for specific field names:MOMENT_NAME
This field can take the following values:
HPDinf
Lower bound of a 90% HPD interval [3].HPDsup
Upper bound of a 90% HPD interval.HPDinf_ME
Lower bound of a 90% HPD interval [4] for observables when taking measurement error into account (see e.g. Christoffel et al. (2010), p.17).HPDsup_ME
Upper bound of a 90% HPD interval for observables when taking measurement error into account.Mean
Mean of the posterior distribution.Median
Median of the posterior distribution.Std
Standard deviation of the posterior distribution.Variance
Variance of the posterior distribution.deciles
Deciles of the distribution.density
Non parametric estimate of the posterior density following the approach outlined in Skoeld and Roberts (2003). First and second columns are respectively abscissa and ordinate coordinates.ESTIMATED_OBJECT
This field can take the following values:
measurement_errors_corr
Correlation between two measurement errors.measurement_errors_std
Standard deviation of measurement errors.parameters
Parameters.shocks_corr
Correlation between two structural shocks.shocks_std
Standard deviation of structural shocks.
MATLAB/Octave variable:
oo_.MarginalDensity.LaplaceApproximation
¶ Variable set by the
estimation
command. Stores the marginal data density based on the Laplace Approximation.

MATLAB/Octave variable:
oo_.MarginalDensity.ModifiedHarmonicMean
¶ Variable set by the
estimation command
, if it is used withmh_replic > 0
orload_mh_file
option. Stores the marginal data density based on Geweke (1999) Modified Harmonic Mean estimator.

MATLAB/Octave variable:
oo_.posterior.optimization
¶ Variable set by the
estimation
command if modefinding is used. Stores the results at the mode. Fields are of the form:oo_.posterior.optimization.OBJECT
where OBJECT is one of the following:
mode
Parameter vector at the mode.Variance
Inverse Hessian matrix at the mode or MCMC jumping covariance matrix when used with theMCMC_jumping_covariance
option.log_density
Log likelihood (ML)/log posterior density (Bayesian) at the mode when used withmode_compute>0
.

MATLAB/Octave variable:
oo_.posterior.metropolis
¶ Variable set by the
estimation
command ifmh_replic>0
is used. Fields are of the form:oo_.posterior.metropolis.OBJECT
where OBJECT is one of the following:
mean
Mean parameter vector from the MCMC.Variance
Covariance matrix of the parameter draws in the MCMC.

MATLAB/Octave variable:
oo_.FilteredVariables
¶ Variable set by the
estimation
command, if it is used with thefiltered_vars
option.After an estimation without Metropolis, fields are of the form:
oo_.FilteredVariables.VARIABLE_NAME
After an estimation with Metropolis, fields are of the form:
oo_.FilteredVariables.MOMENT_NAME.VARIABLE_NAME

MATLAB/Octave variable:
oo_.FilteredVariablesKStepAhead
¶ Variable set by the
estimation
command, if it is used with thefilter_step_ahead
option. The ksteps are stored along the rows while the columns indicate the respective variables. The third dimension of the array provides the observation for which the forecast has been made. For example, iffilter_step_ahead=[1 2 4]
andnobs=200
, the element (3,5,204) stores the four period ahead filtered value of variable 5 computed at time t=200 for time t=204. The periods at the beginning and end of the sample for which no forecasts can be made, e.g. entries (1,5,1) and (1,5,204) in the example, are set to zero. Note that in case of Bayesian estimation the variables will be ordered in the order of declaration after the estimation command (or in general declaration order if no variables are specified here). In case of running the classical smoother, the variables will always be ordered in general declaration order. If theselected_variables_only
option is specified with the classical smoother, nonrequested variables will be simply left out in this order.

MATLAB/Octave variable:
oo_.FilteredVariablesKStepAheadVariances
¶ Variable set by the
estimation
command, if it is used with thefilter_step_ahead option
. It is a 4 dimensional array where the ksteps are stored along the first dimension, while the fourth dimension of the array provides the observation for which the forecast has been made. The second and third dimension provide the respective variables. For example, iffilter_step_ahead=[1 2 4]
andnobs=200
, the element (3,4,5,204) stores the four period ahead forecast error covariance between variable 4 and variable 5, computed at time t=200 for time t=204. Padding with zeros and variable ordering is analogous tooo_.FilteredVariablesKStepAhead
.

MATLAB/Octave variable:
oo_.Filtered_Variables_X_step_ahead
¶ Variable set by the
estimation
command, if it is used with thefilter_step_ahead option
in the context of Bayesian estimation. Fields are of the form:oo_.Filtered_Variables_X_step_ahead.VARIABLE_NAME
The nth entry stores the kstep ahead filtered variable computed at time n for time n+k.

MATLAB/Octave variable:
oo_.FilteredVariablesShockDecomposition
¶ Variable set by the
estimation
command, if it is used with thefilter_step_ahead
option. The ksteps are stored along the rows while the columns indicate the respective variables. The third dimension corresponds to the shocks in declaration order. The fourth dimension of the array provides the observation for which the forecast has been made. For example, iffilter_step_ahead=[1 2 4]
andnobs=200
, the element (3,5,2,204) stores the contribution of the second shock to the four period ahead filtered value of variable 5 (in deviations from the mean) computed at time t=200 for time t=204. The periods at the beginning and end of the sample for which no forecasts can be made, e.g. entries (1,5,1) and (1,5,204) in the example, are set to zero. Padding with zeros and variable ordering is analogous tooo_.FilteredVariablesKStepAhead
.

MATLAB/Octave variable:
oo_.PosteriorIRF.dsge
¶ Variable set by the
estimation
command, if it is used with thebayesian_irf
option. Fields are of the form:oo_.PosteriorIRF.dsge.MOMENT_NAME.VARIABLE_NAME_SHOCK_NAME

MATLAB/Octave variable:
oo_.SmoothedMeasurementErrors
¶ Variable set by the
estimation
command, if it is used with thesmoother
option. Fields are of the form:oo_.SmoothedMeasurementErrors.VARIABLE_NAME

MATLAB/Octave variable:
oo_.SmoothedShocks
¶ Variable set by the
estimation
command (if used with thesmoother
option), or by thecalib_smoother
command.After an estimation without Metropolis, or if computed by
calib_smoother
, fields are of the form:oo_.SmoothedShocks.VARIABLE_NAME
After an estimation with Metropolis, fields are of the form:
oo_.SmoothedShocks.MOMENT_NAME.VARIABLE_NAME

MATLAB/Octave variable:
oo_.SmoothedVariables
¶ Variable set by the
estimation
command (if used with thesmoother
option), or by thecalib_smoother
command.After an estimation without Metropolis, or if computed by
calib_smoother
, fields are of the form:oo_.SmoothedVariables.VARIABLE_NAME
After an estimation with Metropolis, fields are of the form:
oo_.SmoothedVariables.MOMENT_NAME.VARIABLE_NAME

MATLAB/Octave variable:
oo_.UpdatedVariables
¶ Variable set by the
estimation
command (if used with thesmoother
option), or by thecalib_smoother
command. Contains the estimation of the expected value of variables given the information available at the current date.After an estimation without Metropolis, or if computed by
calib_smoother
, fields are of the form:oo_.UpdatedVariables.VARIABLE_NAME
After an estimation with Metropolis, fields are of the form:
oo_.UpdatedVariables.MOMENT_NAME.VARIABLE_NAME

MATLAB/Octave variable:
oo_.FilterCovariance
¶ Threedimensional array set by the
estimation
command if used with thesmoother
and Metropolis, if thefilter_covariance
option has been requested. Contains the series of onestep ahead forecast error covariance matrices from the Kalman smoother. TheM_.endo_nbr
timesM_.endo_nbr
timesT+1
array contains the variables in declaration order along the first two dimensions. The third dimension of the array provides the observation for which the forecast has been made. Fields are of the form:oo_.FilterCovariance.MOMENT_NAME
Note that density estimation is not supported.

MATLAB/Octave variable:
oo_.Smoother.Variance
¶ Threedimensional array set by the
estimation
command (if used with thesmoother
) without Metropolis, or by thecalib_smoother
command, if thefilter_covariance
option has been requested. Contains the series of onestep ahead forecast error covariance matrices from the Kalman smoother. TheM_.endo_nbr
timesM_.endo_nbr
timesT+1
array contains the variables in declaration order along the first two dimensions. The third dimension of the array provides the observation for which the forecast has been made.

MATLAB/Octave variable:
oo_.Smoother.State_uncertainty
¶ Threedimensional array set by the
estimation
command (if used with thesmoother
option) without Metropolis, or by thecalib_smoother
command, if thesmoothed_state_uncertainty
option has been requested. Contains the series of covariance matrices for the state estimate given the full data from the Kalman smoother. TheM_.endo_nbr
timesM_.endo_nbr
timesT
array contains the variables in declaration order along the first two dimensions. The third dimension of the array provides the observation for which the smoothed estimate has been made.

MATLAB/Octave variable:
oo_.Smoother.SteadyState
¶ Variable set by the
estimation
command (if used with thesmoother
) without Metropolis, or by the``calib_smoother
command. Contains the steady state component of the endogenous variables used in the smoother in order of variable declaration.

MATLAB/Octave variable:
oo_.Smoother.TrendCoeffs
¶ Variable set by the
``estimation
command (if used with thesmoother
) without Metropolis, or by thecalib_smoother
command. Contains the trend coefficients of the observed variables used in the smoother in order of declaration of the observed variables.

MATLAB/Octave variable:
oo_.Smoother.Trend
¶ Variable set by the
estimation command
(if used with thesmoother
option), or by the``calib_smoother
command. Contains the trend component of the variables used in the smoother.Fields are of the form:
oo_.Smoother.Trend.VARIABLE_NAME

MATLAB/Octave variable:
oo_.Smoother.Constant
¶ Variable set by the
estimation
command (if used with thesmoother
option), or by thecalib_smoother
command. Contains the constant part of the endogenous variables used in the smoother, accounting e.g. for the data mean when using the prefilter option.Fields are of the form:
oo_.Smoother.Constant.VARIABLE_NAME

MATLAB/Octave variable:
oo_.Smoother.loglinear
¶ Indicator keeping track of whether the smoother was run with the loglinear option and thus whether stored smoothed objects are in logs.

MATLAB/Octave variable:
oo_.PosteriorTheoreticalMoments
¶ Variable set by the
estimation
command, if it is used with themoments_varendo
option. Fields are of the form:oo_.PosteriorTheoreticalMoments.dsge.THEORETICAL_MOMENT.ESTIMATED_OBJECT.MOMENT_NAME.VARIABLE_NAME
where THEORETICAL_MOMENT is one of the following:
covariance
Variancecovariance of endogenous variables.contemporaneous_correlation
Contemporaneous correlation of endogenous variables when thecontemporaneous_correlation
option is specified.correlation
Auto and crosscorrelation of endogenous variables. Fields are vectors with correlations from 1 up to orderoptions_.ar
.VarianceDecomposition
Decomposition of variance (unconditional variance, i.e. at horizon infinity). [5]ConditionalVarianceDecomposition
Only if theconditional_variance_decomposition
option has been specified.

MATLAB/Octave variable:
oo_.posterior_density
¶ Variable set by the
estimation
command, if it is used withmh_replic > 0
orload_mh_file
option. Fields are of the form:oo_.posterior_density.PARAMETER_NAME

MATLAB/Octave variable:
oo_.posterior_hpdinf
¶ Variable set by the
estimation
command, if it is used withmh_replic > 0
orload_mh_file
option. Fields are of the form:oo_.posterior_hpdinf.ESTIMATED_OBJECT.VARIABLE_NAME

MATLAB/Octave variable:
oo_.posterior_hpdsup
¶ Variable set by the
estimation
command, if it is used withmh_replic > 0
orload_mh_file
option. Fields are of the form:oo_.posterior_hpdsup.ESTIMATED_OBJECT.VARIABLE_NAME

MATLAB/Octave variable:
oo_.posterior_mean
¶ Variable set by the
estimation
command, if it is used withmh_replic > 0
orload_mh_file
option. Fields are of the form:oo_.posterior_mean.ESTIMATED_OBJECT.VARIABLE_NAME

MATLAB/Octave variable:
oo_.posterior_mode
¶ Variable set by the
estimation
command during modefinding. Fields are of the form:oo_.posterior_mode.ESTIMATED_OBJECT.VARIABLE_NAME

MATLAB/Octave variable:
oo_.posterior_std_at_mode
¶ Variable set by the
estimation
command during modefinding. It is based on the inverse Hessian atoo_.posterior_mode
. Fields are of the form:oo_.posterior_std_at_mode.ESTIMATED_OBJECT.VARIABLE_NAME

MATLAB/Octave variable:
oo_.posterior_std
¶ Variable set by the
estimation
command, if it is used withmh_replic > 0
orload_mh_file
option. Fields are of the form:oo_.posterior_std.ESTIMATED_OBJECT.VARIABLE_NAME

MATLAB/Octave variable:
oo_.posterior_var
¶ Variable set by the
estimation
command, if it is used withmh_replic > 0
orload_mh_file
option. Fields are of the form:oo_.posterior_var.ESTIMATED_OBJECT.VARIABLE_NAME

MATLAB/Octave variable:
oo_.posterior_median
¶ Variable set by the
estimation
command, if it is used withmh_replic > 0
orload_mh_file
option. Fields are of the form:oo_.posterior_median.ESTIMATED_OBJECT.VARIABLE_NAME
Example
Here are some examples of generated variables:
oo_.posterior_mode.parameters.alp oo_.posterior_mean.shocks_std.ex oo_.posterior_hpdsup.measurement_errors_corr.gdp_conso

MATLAB/Octave variable:
oo_.dsge_var.posterior_mode
¶ Structure set by the
dsge_var
option of theestimation
command after mode_compute.The following fields are saved:
PHI_tilde
Stacked posterior DSGEBVAR autoregressive matrices at the mode (equation (28) of Del Negro and Schorfheide (2004)).SIGMA_u_tilde
Posterior covariance matrix of the DSGEBVAR at the mode (equation (29) of Del Negro and Schorfheide (2004)).iXX
Posterior population moments in the DSGEBVAR at the mode ( \(inv(\lambda T \Gamma_{XX}^*+ X'X)\)).prior
Structure storing the DSGEBVAR prior.PHI_star
Stacked prior DSGEBVAR autoregressive matrices at the mode (equation (22) of Del Negro and Schorfheide (2004)).SIGMA_star
Prior covariance matrix of the DSGEBVAR at the mode (equation (23) of Del Negro and Schorfheide (2004)).ArtificialSampleSize
Size of the artifical prior sample ( \(inv(\lambda T)\)).DF
Prior degrees of freedom ( \(inv(\lambda Tkn)\)).iGXX_star
Inverse of the theoretical prior “covariance” between X and X (\(\Gamma_{xx}^*\) in Del Negro and Schorfheide (2004)).

MATLAB/Octave variable:
oo_.RecursiveForecast
¶ Variable set by the
forecast
option of theestimation
command when used with the nobs = [INTEGER1:INTEGER2] option (seenobs
).Fields are of the form:
oo_.RecursiveForecast.FORECAST_OBJECT.VARIABLE_NAME
where
FORECAST_OBJECT
is one of the following [6] :Mean
Mean of the posterior forecast distribution.HPDinf/HPDsup
Upper/lower bound of the 90% HPD interval taking into account only parameter uncertainty (corresponding tooo_.MeanForecast
).HPDTotalinf/HPDTotalsup
.Upper/lower bound of the 90% HPD interval taking into account both parameter and future shock uncertainty (corresponding tooo_.PointForecast
)VARIABLE_NAME
contains a matrix of the following size: number of time periods for which forecasts are requested using thenobs = [INTEGER1:INTEGER2]
option times the number of forecast horizons requested by the forecast option. i.e., the row indicates the period at which the forecast is performed and the column the respective kstep ahead forecast. The starting periods are sorted in ascending order, not in declaration order.

MATLAB/Octave variable:
oo_.convergence.geweke
¶ Variable set by the convergence diagnostics of the
estimation
command when used withmh_nblocks=1
option (seemh_nblocks
).Fields are of the form:
oo_.convergence.geweke.VARIABLE_NAME.DIAGNOSTIC_OBJECT
where DIAGNOSTIC_OBJECT is one of the following:
posteriormean
Mean of the posterior parameter distribution.posteriorstd
Standard deviation of the posterior parameter distribution.nse_iid
Numerical standard error (NSE) under the assumption of iid draws.rne_iid
Relative numerical efficiency (RNE) under the assumption of iid draws.nse_x
Numerical standard error (NSE) when using an x% taper.rne_x
Relative numerical efficiency (RNE) when using an x% taper.pooled_mean
Mean of the parameter when pooling the beginning and end parts of the chain specified ingeweke_interval
and weighting them with their relative precision. It is a vector containing the results under the iid assumption followed by the ones using thetaper_steps
option (seetaper_steps
).pooled_nse
NSE of the parameter when pooling the beginning and end parts of the chain and weighting them with their relative precision. Seepooled_mean
.prob_chi2_test
pvalue of a chisquared test for equality of means in the beginning and the end of the MCMC chain. Seepooled_mean
. A value above 0.05 indicates that the null hypothesis of equal means and thus convergence cannot be rejected at the 5 percent level. Differing values along thetaper_steps
signal the presence of significant autocorrelation in draws. In this case, the estimates using a higher tapering are usually more reliable.

Command:
unit_root_vars
VARIABLE_NAME...;
¶
This command is deprecated. Useestimation
optiondiffuse_filter
instead for estimating a model with nonstationary observed variables orsteady
optionnocheck
to preventsteady
to check the steady state returned by your steady state file.
Dynare also has the ability to estimate Bayesian VARs:

Command:
bvar_density
;
¶
Computes the marginal density of an estimated BVAR model, using Minnesota priors.See
bvaralasims.pdf
, which comes with Dynare distribution, for more information on this command.
4.15. Model Comparison¶

Command:
model_comparison
FILENAME[(DOUBLE)]...;
¶ 
Command:
model_comparison
(marginal_density = ESTIMATOR) FILENAME[(DOUBLE)]...;
This command computes odds ratios and estimate a posterior density over a collection of models (see e.g. Koop (2003), Ch. 1). The priors over models can be specified as the DOUBLE values, otherwise a uniform prior over all models is assumed. In contrast to frequentist econometrics, the models to be compared do not need to be nested. However, as the computation of posterior odds ratios is a Bayesian technique, the comparison of models estimated with maximum likelihood is not supported.It is important to keep in mind that model comparison of this type is only valid with proper priors. If the prior does not integrate to one for all compared models, the comparison is not valid. This may be the case if part of the prior mass is implicitly truncated because Blanchard and Kahn conditions (instability or indeterminacy of the model) are not fulfilled, or because for some regions of the parameters space the deterministic steady state is undefined (or Dynare is unable to find it). The compared marginal densities should be renormalized by the effective prior mass, but this not done by Dynare: it is the user’s responsibility to make sure that model comparison is based on proper priors. Note that, for obvious reasons, this is not an issue if the compared marginal densities are based on Laplace approximations.
Options

marginal_density = ESTIMATOR
¶ Specifies the estimator for computing the marginal data density. ESTIMATOR can take one of the following two values:
laplace
for the Laplace estimator ormodifiedharmonicmean
for the Geweke (1999) Modified Harmonic Mean estimator. Default value:laplace
Output
The results are stored in
oo_.Model_Comparison
, which is described below.Example
model_comparison my_model(0.7) alt_model(0.3);
This example attributes a 70% prior over
my_model
and 30% prior overalt_model
.

MATLAB/Octave variable:
oo_.Model_Comparison
¶ Variable set by the
model_comparison
command. Fields are of the form:oo_.Model_Comparison.FILENAME.VARIABLE_NAME
where FILENAME is the file name of the model and VARIABLE_NAME is one of the following:
Prior
(Normalized) prior density over the model.Log_Marginal_Density
Logarithm of the marginal data density.Bayes_Ratio
Ratio of the marginal data density of the model relative to the one of the first declared modelPosterior_Model_Probability
Posterior probability of the respective model.
4.16. Shock Decomposition¶

Command:
shock_decomposition
[VARIABLE_NAME]...;
¶ 
Command:
shock_decomposition
(OPTIONS...) [VARIABLE_NAME]...;
This command computes the historical shock decomposition for a given sample based on the Kalman smoother, i.e. it decomposes the historical deviations of the endogenous variables from their respective steady state values into the contribution coming from the various shocks. Thevariable_names
provided govern for which variables the decomposition is plotted.Note that this command must come after either
estimation
(in case of an estimated model) orstoch_simul
(in case of a calibrated model).Options

parameter_set = OPTION
¶ Specify the parameter set to use for running the smoother. Possible values for OPTION are:
calibration
prior_mode
prior_mean
posterior_mode
posterior_mean
posterior_median
mle_mode
Note that the parameter set used in subsequent commands like
stoch_simul
will be set to the specifiedparameter_set
. Default value:posterior_mean
if Metropolis has been run,mle_mode
if MLE has been run.

datafile = FILENAME
See datafile. Useful when computing the shock decomposition on a calibrated model.

first_obs = INTEGER
See
first_obs
.

nobs = INTEGER
See
nobs
.

use_shock_groups [= STRING]
¶ Uses shock grouping defined by the string instead of individual shocks in the decomposition. The groups of shocks are defined in the
shock_groups
block.

colormap = STRING
¶ Controls the
colormap
used for the shocks decomposition graphs. See colormap in Matlab/Octave manual for valid arguments.

nograph
See
nograph
. Suppresses the display and creation only within theshock_decomposition
command, but does not affect other commands. Seeplot_shock_decomposition
for plotting graphs.

init_state = BOOLEAN
¶ If equal to 0, the shock decomposition is computed conditional on the smoothed state variables in period
0
, i.e. the smoothed shocks starting in period 1 are used. If equal to1
, the shock decomposition is computed conditional on the smoothed state variables in period 1. Default:0
.
Output

MATLAB/Octave variable:
oo_.shock_decomposition
¶ The results are stored in the field
oo_.shock_decomposition
, which is a three dimensional array. The first dimension contains theM_.endo_nbr
endogenous variables. The second dimension stores in the firstM_.exo_nbr
columns the contribution of the respective shocks. ColumnM_.exo_nbr+1
stores the contribution of the initial conditions, while columnM_.exo_nbr+2
stores the smoothed value of the respective endogenous variable in deviations from their steady state, i.e. the mean and trends are subtracted. The third dimension stores the time periods. Both the variables and shocks are stored in the order of declaration, i.e.M_.endo_names
andM_.exo_names
, respectively.


Block:
shock_groups
;
¶ 
Block:
shock_groups
(OPTIONS...);
Shocks can be regrouped for the purpose of shock decomposition. The composition of the shock groups is written in a block delimited byshock_groups
andend
.Each line defines a group of shocks as a list of exogenous variables:
SHOCK_GROUP_NAME = VARIABLE_1 [[,] VARIABLE_2 [,]...]; 'SHOCK GROUP NAME' = VARIABLE_1 [[,] VARIABLE_2 [,]...];
Options

name = NAME
Specifies a name for the following definition of shock groups. It is possible to use several
shock_groups
blocks in a model file, each grouping being identified by a different name. This name must in turn be used in theshock_decomposition
command.
Example
varexo e_a, e_b, e_c, e_d; ... shock_groups(name=group1); supply = e_a, e_b; 'aggregate demand' = e_c, e_d; end; shock_decomposition(use_shock_groups=group1);
This example defines a shock grouping with the name
group1
, containing a set of supply and demand shocks and conducts the shock decomposition for these two groups.

Command:
realtime_shock_decomposition
[VARIABLE_NAME]...;
¶ 
Command:
realtime_shock_decomposition
(OPTIONS...) [VARIABLE_NAME]...;
This command computes the realtime historical shock decomposition for a given sample based on the Kalman smoother. For each period \(T=[\texttt{presample},\ldots,\texttt{nobs}]\), it recursively computes three objects: Realtime historical shock decomposition \(Y(t\vert T)\)
for \(t=[1,\ldots,T]\), i.e. without observing data in
\([T+1,\ldots,\texttt{nobs}]\). This results in a
standard shock decomposition being computed for each
additional datapoint becoming available after
presample
.  Forecast shock decomposition \(Y(T+k\vert T)\) for \(k=[1,\ldots,forecast]\), i.e. the \(k\)step ahead forecast made for every \(T\) is decomposed in its shock contributions.
 Realtime conditional shock decomposition of the difference
between the realtime historical shock decomposition and the
forecast shock decomposition. If
vintage
is equal to0
, it computes the effect of shocks realizing in period \(T\), i.e. decomposes \(Y(T\vert T)Y(T\vert T1)\). Put differently, it conducts a \(1\)period ahead shock decomposition from \(T1\) to \(T\), by decomposing the update step of the Kalman filter. Ifvintage>0
and smaller thannobs
, the decomposition is conducted of the forecast revision \(Y(T+k\vert T+k)Y(T+k\vert T)\).
Like
shock_decomposition
it decomposes the historical deviations of the endogenous variables from their respective steady state values into the contribution coming from the various shocks. Thevariable_names
provided govern for which variables the decomposition is plotted.Note that this command must come after either
estimation
(in case of an estimated model) orstoch_simul
(in case of a calibrated model).Options

parameter_set = OPTION
See
parameter_set
for the possible values.

datafile = FILENAME
See datafile.

first_obs = INTEGER
See
first_obs
.

nobs = INTEGER
See
nobs
.

use_shock_groups [= STRING]
See
use_shock_groups
.

colormap = STRING
See
colormap
.

nograph
See
nograph
. Only shock decompositions are computed and stored inoo_.realtime_shock_decomposition
,oo_.conditional_shock_decomposition
andoo_.realtime_forecast_shock_decomposition
but no plot is made (Seeplot_shock_decomposition
).

presample = INTEGER
First data point from which recursive realtime shock decompositions are computed, i.e. for \(T=[\texttt{presample} \ldots \texttt{nobs}]\).

forecast = INTEGER
Compute shock decompositions up to \(T+k\) periods, i.e. get shock contributions to kstep ahead forecasts.

save_realtime = INTEGER_VECTOR
¶ Choose for which vintages to save the full realtime shock decomposition. Default:
0
..
Output

MATLAB/Octave variable:
oo_.realtime_shock_decomposition
¶ Structure storing the results of realtime historical decompositions. Fields are threedimensional arrays with the first two dimension equal to the ones of
oo_.shock_decomposition
. The third dimension stores the time periods and is therefore of sizeT+forecast
. Fields are of the form:oo_.realtime_shock_decomposition.OBJECT
where OBJECT is one of the following:
pool
Stores the pooled decomposition, i.e. for every realtime shock decomposition terminal period \(T=[\texttt{presample},\ldots,\texttt{nobs}]\) it collects the last period’s decomposition \(Y(T\vert T)\) (see alsoplot_shock_decomposition
). The third dimension of the array will have sizenobs+forecast
.time_*
Stores the vintages of realtime historical shock decompositions ifsave_realtime
is used. For example, ifsave_realtime=[5]
andforecast=8
, the third dimension will be of size13
.

MATLAB/Octave variable:
oo_.realtime_conditional_shock_decomposition
¶ Structure storing the results of realtime conditional decompositions. Fields are of the form:
oo_.realtime_conditional_shock_decomposition.OBJECT
where OBJECT is one of the following:
pool
Stores the pooled realtime conditional shock decomposition, i.e. collects the decompositions of \(Y(T\vert T)Y(T\vert T1)\) for the terminal periods \(T=[\texttt{presample},\ldots,\texttt{nobs}]\). The third dimension is of sizenobs
.time_*
Store the vintages of \(k\)step conditional forecast shock decompositions \(Y(t\vert T+k)\), for \(t=[T \ldots T+k]\). Seevintage
. The third dimension is of size1+forecast
.

MATLAB/Octave variable:
oo_.realtime_forecast_shock_decomposition
¶ Structure storing the results of realtime forecast decompositions. Fields are of the form:
oo_.realtime_forecast_shock_decomposition.OBJECT
where
OBJECT
is one of the following:pool
Stores the pooled realtime forecast decomposition of the \(1\)step ahead effect of shocks on the \(1\)step ahead prediction, i.e. \(Y(T\vert T1)\).time_*
Stores the vintages of \(k\)step outofsample forecast shock decompositions, i.e. \(Y(t\vert T)\), for \(t=[T \ldots T+k]\). Seevintage
.
 Realtime historical shock decomposition \(Y(t\vert T)\)
for \(t=[1,\ldots,T]\), i.e. without observing data in
\([T+1,\ldots,\texttt{nobs}]\). This results in a
standard shock decomposition being computed for each
additional datapoint becoming available after

Command:
plot_shock_decomposition
[VARIABLE_NAME]...;
¶ 
Command:
plot_shock_decomposition
(OPTIONS...) [VARIABLE_NAME]...;
This command plots the historical shock decomposition already computed byshock_decomposition
orrealtime_shock_decomposition
. For that reason, it must come after one of these commands. Thevariable_names
provided govern which variables the decomposition is plotted for.Further note that, unlike the majority of Dynare commands, the options specified below are overwritten with their defaults before every call to
plot_shock_decomposition
. Hence, if you want to reuse an option in a subsequent call toplot_shock_decomposition
, you must pass it to the command again.Options

use_shock_groups [= STRING]
See
use_shock_groups
.

colormap = STRING
See
colormap
.

nodisplay
See
nodisplay
.

graph_format = FORMAT

graph_format = ( FORMAT, FORMAT... )
See
graph_format
.

detail_plot
¶ Plots shock contributions using subplots, one per shock (or group of shocks). Default: not activated

interactive
¶ Under MATLAB, add uimenus for detailed group plots. Default: not activated

screen_shocks
¶ For large models (i.e. for models with more than 16 shocks), plots only the shocks that have the largest historical contribution for chosen selected
variable_names
. Historical contribution is ranked by the mean absolute value of all historical contributions.

steadystate
¶ If passed, the the \(y\)axis value of the zero line in the shock decomposition plot is translated to the steady state level. Default: not activated

type = qoq  yoy  aoa
¶ For quarterly data, valid arguments are:
qoq
for quarteronquarter plots,yoy
for yearonyear plots of growth rates,aoa
for annualized variables, i.e. the value in the last quarter for each year is plotted. Default value: empty, i.e. standard periodonperiod plots (qoq
for quarterly data).

fig_name = STRING
¶ Specifies a userdefined keyword to be appended to the default figure name set by
plot_shock_decomposition
. This can avoid to overwrite plots in case of sequential calls toplot_shock_decomposition
.

write_xls
¶ Saves shock decompositions to Excelfile in the main directory, named
FILENAME_shock_decomposition_TYPE_FIG_NAME.xls
. This option requires your system to be configured to be able to write Excel files. [7]

realtime = INTEGER
¶ Which kind of shock decomposition to plot. INTEGER can take the following values:
0
: standard historical shock decomposition. Seeshock_decomposition
.1
: realtime historical shock decomposition. Seerealtime_shock_decomposition
.2
: conditional realtime shock decomposition. Seerealtime_shock_decomposition
.3
: realtime forecast shock decomposition. Seerealtime_shock_decomposition
.
If no vintage is requested, i.e.
vintage=0
then the pooled objects fromrealtime_shock_decomposition
will be plotted and the respective vintage otherwise. Default:0
.

vintage = INTEGER
¶ Selects a particular data vintage in \([presample,\ldots,nobs]\) for which to plot the results from
realtime_shock_decomposition
selected via therealtime
option. If the standard historical shock decomposition is selected (realtime=0
),vintage
will have no effect. Ifvintage=0
the pooled objects fromrealtime_shock_decomposition
will be plotted. Ifvintage>0
, it plots the shock decompositions for vintage \(T=\texttt{vintage}\) under the following scenarios:realtime=1
: the full vintage shock decomposition \(Y(t\vert T)\) for \(t=[1,\ldots,T]\)realtime=2
: the conditional forecast shock decomposition from \(T\), i.e. plots \(Y(T+j\vert T+j)\) and the shock contributions needed to get to the data \(Y(T+j)\) conditional on \(T=\) vintage, with \(j=[0,\ldots,\texttt{forecast}]\).realtime=3
: plots unconditional forecast shock decomposition from \(T\), i.e. \(Y(T+j\vert T)\), where \(T=\texttt{vintage}\) and \(j=[0,\ldots,\texttt{forecast}]\).
Default:
0
.

4.17. Calibrated Smoother¶
Dynare can also run the smoother on a calibrated model:

Command:
calib_smoother
[VARIABLE_NAME]...;
¶ 
Command:
calib_smoother
(OPTIONS...) [VARIABLE_NAME]...;
This command computes the smoothed variables (and possible the filtered variables) on a calibrated model.A datafile must be provided, and the observable variables declared with
varobs
. The smoother is based on a firstorder approximation of the model.By default, the command computes the smoothed variables and shocks and stores the results in
oo_.SmoothedVariables` and ``oo_.SmoothedShocks
. It also fillsoo_.UpdatedVariables
.Options

datafile = FILENAME
See datafile.

filtered_vars
Triggers the computation of filtered variables. See
filtered_vars
, for more details.

filter_step_ahead = [INTEGER1:INTEGER2]
See
filter_step_ahead
.

prefilter = INTEGER
See
prefilter
.

parameter_set = OPTION
See
parameter_set
for the possible values.

loglinear
See loglinear.

first_obs = INTEGER
See
first_obs
.

filter_decomposition
See
filter_decomposition
.

diffuse_filter = INTEGER
¶ See
diffuse_filter
.

diffuse_kalman_tol = DOUBLE
See
diffuse_kalman_tol
.

4.18. Forecasting¶
On a calibrated model, forecasting is done using the forecast
command. On an estimated model, use the forecast
option of
estimation
command.
It is also possible to compute forecasts on a calibrated or estimated
model for a given constrained path of the future endogenous
variables. This is done, from the reduced form representation of the
DSGE model, by finding the structural shocks that are needed to match
the restricted paths. Use conditional_forecast
,
conditional_forecast_paths
and plot_conditional_forecast
for
that purpose.
Finally, it is possible to do forecasting with a Bayesian VAR using
the bvar_forecast
command.

Command:
forecast
[VARIABLE_NAME...];
¶ 
Command:
forecast
(OPTIONS...) [VARIABLE_NAME...];
This command computes a simulation of a stochastic model from an arbitrary initial point.When the model also contains deterministic exogenous shocks, the simulation is computed conditionally to the agents knowing the future values of the deterministic exogenous variables.
forecast
must be called afterstoch_simul
.forecast
plots the trajectory of endogenous variables. When a list of variable names follows the command, only those variables are plotted. A 90% confidence interval is plotted around the mean trajectory. Use optionconf_sig
to change the level of the confidence interval.Options

periods = INTEGER
Number of periods of the forecast. Default:
5
.

conf_sig = DOUBLE
Level of significance for confidence interval. Default:
0.90
.

nograph
See
nograph
.

nodisplay
See
nodisplay
.

graph_format = FORMAT

graph_format = ( FORMAT, FORMAT... )
Initial Values
forecast
computes the forecast taking as initial values the values specified inhistval
(seehistval
). When nohistval
block is present, the initial values are the one stated ininitval
. Wheninitval
is followed by commandsteady
, the initial values are the steady state (seesteady
).Output
The results are stored in
oo_.forecast
, which is described below.Example
varexo_det tau; varexo e; ... shocks; var e; stderr 0.01; var tau; periods 1:9; values 0.15; end; stoch_simul(irf=0); forecast;

MATLAB/Octave variable:
oo_.forecast
¶ Variable set by the
forecast
command, or by theestimation
command if used with theforecast
option and if no MetropolisHastings has been computed (in that case, the forecast is computed for the posterior mode). Fields are of the form:oo_.forecast.FORECAST_MOMENT.VARIABLE_NAME
where
FORECAST_MOMENT
is one of the following:HPDinf
Lower bound of a 90% HPD interval [8] of forecast due to parameter uncertainty, but ignoring the effect of measurement error on observed variables.HPDsup
Upper bound of a 90% HPD forecast interval due to parameter uncertainty, but ignoring the effect of measurement error on observed variables.HPDinf_ME
Lower bound of a 90% HPD interval [9] of forecast for observed variables due to parameter uncertainty and measurement error.HPDsup_ME
Upper bound of a 90% HPD interval of forecast for observed variables due to parameter uncertainty and measurement error.Mean
Mean of the posterior distribution of forecasts.Median
Median of the posterior distribution of forecasts.Std
Standard deviation of the posterior distribution of forecasts.

MATLAB/Octave variable:
oo_.PointForecast
¶ Set by the
estimation
command, if it is used with theforecast
option and if eithermh_replic > 0
or theload_mh_file
option are used.Contains the distribution of forecasts taking into account the uncertainty about both parameters and shocks.
Fields are of the form:
oo_.PointForecast.MOMENT_NAME.VARIABLE_NAME

MATLAB/Octave variable:
oo_.MeanForecast
¶ Set by the
estimation
command, if it is used with theforecast
option and if eithermh_replic > 0
orload_mh_file
option are used.Contains the distribution of forecasts where the uncertainty about shocks is averaged out. The distribution of forecasts therefore only represents the uncertainty about parameters.
Fields are of the form:
oo_.MeanForecast.MOMENT_NAME.VARIABLE_NAME


Command:
conditional_forecast
(OPTIONS...) [VARIABLE_NAME...];
¶
This command computes forecasts on an estimated or calibrated model for a given constrained path of some future endogenous variables. This is done using the reduced form first order statespace representation of the DSGE model by finding the structural shocks that are needed to match the restricted paths. Consider the an augmented state space representation that stacks both predetermined and nonpredetermined variables into a vector \(y_{t}\):\[y_t=Ty_{t1}+R\varepsilon_t\]Both \(y_t\) and \(\varepsilon_t\) are split up into controlled and uncontrolled ones to get:
\[y_t(contr\_vars)=Ty_{t1}(contr\_vars)+R(contr\_vars,uncontr\_shocks)\varepsilon_t(uncontr\_shocks) + R(contr\_vars,contr\_shocks)\varepsilon_t(contr\_shocks)\]which can be solved algebraically for \(\varepsilon_t(contr\_shocks)\).
Using these controlled shocks, the statespace representation can be used for forecasting. A few things need to be noted. First, it is assumed that controlled exogenous variables are fully under control of the policy maker for all forecast periods and not just for the periods where the endogenous variables are controlled. For all uncontrolled periods, the controlled exogenous variables are assumed to be 0. This implies that there is no forecast uncertainty arising from these exogenous variables in uncontrolled periods. Second, by making use of the first order state space solution, even if a higherorder approximation was performed, the conditional forecasts will be based on a first order approximation. Third, although controlled exogenous variables are taken as instruments perfectly under the control of the policymaker, they are nevertheless random and unforeseen shocks from the perspective of the households. That is, households are in each period surprised by the realization of a shock that keeps the controlled endogenous variables at their respective level. Fourth, keep in mind that if the structural innovations are correlated, because the calibrated or estimated covariance matrix has non zero off diagonal elements, the results of the conditional forecasts will depend on the ordering of the innovations (as declared after
varexo
). As in VAR models, a Cholesky decomposition is used to factorize the covariance matrix and identify orthogonal impulses. It is preferable to declare the correlations in the model block (explicitly imposing the identification restrictions), unless you are satisfied with the implicit identification restrictions implied by the Cholesky decomposition.This command has to be called after
estimation
orstoch_simul
.Use
conditional_forecast_paths
block to give the list of constrained endogenous, and their constrained future path. Optioncontrolled_varexo
is used to specify the structural shocks which will be matched to generate the constrained path.Use
plot_conditional_forecast
to graph the results.Options

parameter_set = OPTION
Specify the parameter set to use for the forecasting. Possible values for OPTION are:
calibration
prior_mode
prior_mean
posterior_mode
posterior_mean
posterior_median
No default value, mandatory option. Note that in case of estimated models,
conditional_forecast
does not support theprefilter
option.

controlled_varexo = (VARIABLE_NAME...)
¶ Specify the exogenous variables to use as control variables. No default value, mandatory option.

periods = INTEGER
Number of periods of the forecast. Default:
40
.periods
cannot be smaller than the number of constrained periods.

replic = INTEGER
Number of simulations. Default:
5000
.

conf_sig = DOUBLE
Level of significance for confidence interval. Default:
0.90
.
Output
The results are not stored in the
oo_
structure but in a separate structureforecasts
, described below, saved to the hard disk into a file calledconditional_forecasts.mat.
Example
var y a; varexo e u; ... estimation(...); conditional_forecast_paths; var y; periods 1:3, 4:5; values 2, 5; var a; periods 1:5; values 3; end; conditional_forecast(parameter_set = calibration, controlled_varexo = (e, u), replic = 3000); plot_conditional_forecast(periods = 10) a y;

MATLAB/Octave variable:
forecasts.cond
¶ Variable set by the
conditional_forecast
command. It stores the conditional forecasts. Fields areperiods+1
by1
vectors storing the steady state (time 0) and the subsequentperiods
forecasts periods. Fields are of the form:forecasts.cond.FORECAST_MOMENT.VARIABLE_NAME
where FORECAST_MOMENT is one of the following:
Mean
Mean of the conditional forecast distribution.ci
Confidence interval of the conditional forecast distribution. The size corresponds toconf_sig
.

MATLAB/Octave variable:
forecasts.uncond
¶ Variable set by the
conditional_forecast
command. It stores the unconditional forecasts. Fields are of the form:forecasts.uncond.FORECAST_MOMENT.VARIABLE_NAME

MATLAB/Octave variable:
forecasts.instruments
¶ Variable set by the
conditional_forecast command
. Stores the names of the exogenous instruments.

MATLAB/Octave variable:
forecasts.controlled_variables
¶ Variable set by the
conditional_forecast
command. Stores the position of the constrained endogenous variables in declaration order.

MATLAB/Octave variable:
forecasts.controlled_exo_variables
¶ Variable set by the
conditional_forecast
command. Stores the values of the controlled exogenous variables underlying the conditional forecasts to achieve the constrained endogenous variables. Fields are[number of constrained periods]
by1
vectors and are of the form:forecasts.controlled_exo_variables.FORECAST_MOMENT.SHOCK_NAME

MATLAB/Octave variable:
forecasts.graphs
¶ Variable set by the
conditional_forecast
command. Stores the information for generating the conditional forecast plots.


Block:
conditional_forecast_paths
;
¶
Describes the path of constrained endogenous, before callingconditional_forecast
. The syntax is similar to deterministic shocks inshocks
, seeconditional_forecast
for an example.The syntax of the block is the same as for the deterministic shocks in the
shocks
blocks (see Shocks on exogenous variables). Note that you need to specify the full path for all constrained endogenous variables between the first and last specified period. If an intermediate period is not specified, a value of 0 is assumed. That is, if you specify only values for periods 1 and 3, the values for period 2 will be 0. Currently, it is not possible to have uncontrolled intermediate periods. In case of the presence ofobservation_trends
, the specified controlled path for these variables needs to include the trend component. When using the loglinear option, it is necessary to specify the logarithm of the controlled variables.

Command:
plot_conditional_forecast
[VARIABLE_NAME...];
¶ 
Command:
plot_conditional_forecast
(periods = INTEGER) [VARIABLE_NAME...];
Plots the conditional (plain lines) and unconditional (dashed lines) forecasts.To be used after
conditional_forecast
.Options

periods = INTEGER
Number of periods to be plotted. Default: equal to periods in
conditional_forecast
. The number of periods declared inplot_conditional_forecast
cannot be greater than the one declared inconditional_forecast
.


Command:
bvar_forecast
;
¶
This command computes (outofsample) forecasts for an estimated BVAR model, using Minnesota priors.See
bvaralasims.pdf
, which comes with Dynare distribution, for more information on this command.
If the model contains strong nonlinearities or if some perfectly
expected shocks are considered, the forecasts and the conditional
forecasts can be computed using an extended path method. The forecast
scenario describing the shocks and/or the constrained paths on some
endogenous variables should be build. The first step is the forecast
scenario initialization using the function init_plan
:

MATLAB/Octave command:
HANDLE = init_plan
(DATES);
¶ Creates a new forecast scenario for a forecast period (indicated as a dates class, see dates class members). This function return a handle on the new forecast scenario.
The forecast scenario can contain some simple shocks on the exogenous
variables. This shocks are described using the function
basic_plan
:

MATLAB/Octave command:
HANDLE = basic_plan
(HANDLE, 'VAR_NAME', 'SHOCK_TYPE', DATES, MATLAB VECTOR OF DOUBLE  [DOUBLE  EXPR [DOUBLE   EXPR] ] );
¶ Adds to the forecast scenario a shock on the exogenous variable indicated between quotes in the second argument. The shock type has to be specified in the third argument between quotes: ’surprise’ in case of an unexpected shock or ’perfect_foresight’ for a perfectly anticipated shock. The fourth argument indicates the period of the shock using a dates class (see dates class members). The last argument is the shock path indicated as a Matlab vector of double. This function return the handle of the updated forecast scenario.
The forecast scenario can also contain a constrained path on an
endogenous variable. The values of the related exogenous variable
compatible with the constrained path are in this case computed. In
other words, a conditional forecast is performed. This kind of shock
is described with the function flip_plan
:

MATLAB/Octave command:
HANDLE = flip_plan
(HANDLE, 'VAR_NAME, 'VAR_NAME', 'SHOCK_TYPE', DATES, MATLAB VECTOR OF DOUBLE  [DOUBLE  EXPR [DOUBLE   EXPR] ] );
¶ Adds to the forecast scenario a constrained path on the endogenous variable specified between quotes in the second argument. The associated exogenous variable provided in the third argument between quotes, is considered as an endogenous variable and its values compatible with the constrained path on the endogenous variable will be computed. The nature of the expectation on the constrained path has to be specified in the fourth argument between quotes: ’surprise’ in case of an unexpected path or ’perfect_foresight’ for a perfectly anticipated path. The fifth argument indicates the period where the path of the endogenous variable is constrained using a dates class (see dates class members). The last argument contains the constrained path as a Matlab vector of double. This function return the handle of the updated forecast scenario.
Once the forecast scenario if fully described, the forecast is
computed with the command det_cond_forecast
:

MATLAB/Octave command:
DSERIES = det_cond_forecast
(HANDLE[, DSERIES [, DATES]]);
¶ Computes the forecast or the conditional forecast using an extended path method for the given forecast scenario (first argument). The past values of the endogenous and exogenous variables provided with a dseries class (see dseries class members) can be indicated in the second argument. By default, the past values of the variables are equal to their steadystate values. The initial date of the forecast can be provided in the third argument. By default, the forecast will start at the first date indicated in the
init_plan command
. This function returns a dset containing the historical and forecast values for the endogenous and exogenous variables.
Example
% conditional forecast using extended path method % with perfect foresight on r path var y r; varexo e u; ... smoothed = dseries('smoothed_variables.csv'); fplan = init_plan(2013Q4:2029Q4); fplan = flip_plan(fplan, 'y', 'u', 'surprise', 2013Q4:2014Q4, [1 1.1 1.2 1.1 ]); fplan = flip_plan(fplan, 'r', 'e', 'perfect_foresight', 2013Q4:2014Q4, [2 1.9 1.9 1.9 ]); dset_forecast = det_cond_forecast(fplan, smoothed); plot(dset_forecast.{'y','u'}); plot(dset_forecast.{'r','e'});

Command:
smoother2histval [
(OPTIONS...)]
¶ The purpose of this command is to construct initial conditions (for a subsequent simulation) that are the smoothed values of a previous estimation.
More precisely, after an estimation run with the
smoother
option,smoother2histval
will extract the smoothed values (fromoo_.SmoothedVariables
, and possibly fromoo_.SmoothedShocks
if there are lagged exogenous), and will use these values to construct initial conditions (as if they had been manually entered throughhistval
).Options

period = INTEGER
¶ Period number to use as the starting point for the subsequent simulation. It should be between 1 and the number of observations that were used to produce the smoothed values. Default: the last observation.

infile = FILENAME
¶ Load the smoothed values from a
_results.mat
file created by a previous Dynare run. Default: use the smoothed values currently in the global workspace.

invars = ( VARIABLE_NAME [VARIABLE_NAME ...] )
¶ A list of variables to read from the smoothed values. It can contain state endogenous variables, and also exogenous variables having a lag. Default: all the state endogenous variables, and all the exogenous variables with a lag.

outfile = FILENAME
¶ Write the initial conditions to a file. Default: write the initial conditions in the current workspace, so that a simulation can be performed.

outvars = ( VARIABLE_NAME [VARIABLE_NAME ...] )
¶ A list of variables which will be given the initial conditions. This list must have the same length than the list given to
invars
, and there will be a onetoone mapping between the two list. Default: same value as optioninvars
.
Use cases
There are three possible ways of using this command:
 Everything in a single file: run an estimation with a
smoother, then run
smoother2histval
(without theinfile
andoutfile
options), then run a stochastic simulation.  In two files: in the first file, run the smoother and then
run
smoother2histval
with theoutfile
option; in the second file, runhistval_file
to load the initial conditions, and run a (deterministic or stochastic) simulation.  In two files: in the first file, run the smoother; in the
second file, run
smoother2histval
with theinfile
option equal to the_results.mat
file created by the first file, and then run a (deterministic or stochastic) simulation.

4.19. Optimal policy¶
Dynare has tools to compute optimal policies for various types of
objectives. ramsey_model
computes automatically the First Order
Conditions (FOC) of a model, given the planner_objective
. You can
then use other standard commands to solve, estimate or simulate this
new, expanded model.
Alternatively, you can either solve for optimal policy under
commitment with ramsey_policy
, for optimal policy under discretion
with discretionary_policy
or for optimal simple rule with osr
(also implying commitment).

Command:
osr
[VARIABLE_NAME...];
¶ 
Command:
osr
(OPTIONS...) [VARIABLE_NAME...];
This command computes optimal simple policy rules for linearquadratic problems of the form:\[\min_\gamma E(y'_tWy_t)\]such that:
\[A_1 E_ty_{t+1}+A_2 y_t+ A_3 y_{t1}+C e_t=0\]where:
 \(E\) denotes the unconditional expectations operator;
 \(\gamma\) are parameters to be optimized. They must be
elements of the matrices \(A_1\), \(A_2\),
\(A_3\), i.e. be specified as parameters in the
params
command and be entered in themodel
block;  \(y\) are the endogenous variables, specified in the
var
command, whose (co)variance enters the loss function;  \(e\) are the exogenous stochastic shocks, specified in
the
varexo
 ommand;  \(W\) is the weighting matrix;
The linear quadratic problem consists of choosing a subset of model parameters to minimize the weighted (co)variance of a specified subset of endogenous variables, subject to a linear law of motion implied by the first order conditions of the model. A few things are worth mentioning. First, \(y\) denotes the selected endogenous variables’ deviations from their steady state, i.e. in case they are not already mean 0 the variables entering the loss function are automatically demeaned so that the centered second moments are minimized. Second,
osr
only solves linear quadratic problems of the type resulting from combining the specified quadratic loss function with a first order approximation to the model’s equilibrium conditions. The reason is that the first order statespace representation is used to compute the unconditional (co)variances. Hence,osr
will automatically selectorder=1
. Third, because the objective involves minimizing a weighted sum of unconditional second moments, those second moments must be finite. In particular, unit roots in \(y\) are not allowed.The subset of the model parameters over which the optimal simple rule is to be optimized, \(\gamma\), must be listed with
osr_params
.The weighting matrix \(W\) used for the quadratic objective function is specified in the
optim_weights
block. By attaching weights to endogenous variables, the subset of endogenous variables entering the objective function, \(y\), is implicitly specified.The linear quadratic problem is solved using the numerical optimizer specified with
opt_algo
.Options
The
osr
command will subsequently runstoch_simul
and accepts the same options, including restricting the endogenous variables by listing them after the command, asstoch_simul
(see Stochastic solution and simulation) plus
opt_algo = INTEGER
¶ Specifies the optimizer for minimizing the objective function. The same solvers as for
mode_compute
(seemode_compute
) are available, except for5
,6
, and10
.

optim = (NAME, VALUE, ...)
A list of NAME`` and VALUE pairs. Can be used to set options for the optimization routines. The set of available options depends on the selected optimization routine (i.e. on the value of option
opt_algo
). Seeoptim
.

maxit = INTEGER
Determines the maximum number of iterations used in
opt_algo=4
. This option is now deprecated and will be removed in a future release of Dynare. Useoptim
instead to set optimizerspecific values. Default:1000
.

tolf = DOUBLE
Convergence criterion for termination based on the function value used in
opt_algo=4
. Iteration will cease when it proves impossible to improve the function value by more than tolf. This option is now deprecated and will be removed in a future release of Dynare. Useoptim
instead to set optimizerspecific values. Default:e7
.

silent_optimizer
See
silent_optimizer
.

huge_number = DOUBLE
Value for replacing the infinite bounds on parameters by finite numbers. Used by some optimizers for numerical reasons (see
huge_number
). Users need to make sure that the optimal parameters are not larger than this value. Default:1e7
.
The value of the objective is stored in the variable
oo_.osr.objective_function
and the value of parameters at the optimum is stored inoo_.osr.optim_params
. See below for more details.After running
osr
the parameters entering the simple rule will be set to their optimal value so that subsequent runs ofstoch_simul
will be conducted at these values.

Command:
osr_params
PARAMETER_NAME...;
¶
This command declares parameters to be optimized byosr
.

Block:
optim_weights
;
¶
This block specifies quadratic objectives for optimal policy problems.More precisely, this block specifies the nonzero elements of the weight matrix \(W\) used in the quadratic form of the objective function in
osr
.An element of the diagonal of the weight matrix is given by a line of the form:
VARIABLE_NAME EXPRESSION;
An offthediagonal element of the weight matrix is given by a line of the form:
VARIABLE_NAME, VARIABLE_NAME EXPRESSION;
Example
var y inflation r; varexo y_ inf_; parameters delta sigma alpha kappa gammarr gammax0 gammac0 gamma_y_ gamma_inf_; delta = 0.44; kappa = 0.18; alpha = 0.48; sigma = 0.06; gammarr = 0; gammax0 = 0.2; gammac0 = 1.5; gamma_y_ = 8; gamma_inf_ = 3; model(linear); y = delta * y(1) + (1delta)*y(+1)+sigma *(r  inflation(+1)) + y_; inflation = alpha * inflation(1) + (1alpha) * inflation(+1) + kappa*y + inf_; r = gammax0*y(1)+gammac0*inflation(1)+gamma_y_*y_+gamma_inf_*inf_; end; shocks; var y_; stderr 0.63; var inf_; stderr 0.4; end; optim_weights; inflation 1; y 1; y, inflation 0.5; end; osr_params gammax0 gammac0 gamma_y_ gamma_inf_; osr y;

Block:
osr_params_bounds
;
¶
This block declares lower and upper bounds for parameters in the optimal simple rule. If not specified the optimization is unconstrained.Each line has the following syntax:
PARAMETER_NAME, LOWER_BOUND, UPPER_BOUND;
Note that the use of this block requires the use of a constrained optimizer, i.e. setting
opt_algo
to1
,2
,5
or9
.Example
osr_params_bounds; gamma_inf_, 0, 2.5; end; osr(solve_algo=9) y;

MATLAB/Octave variable:
oo_.osr.objective_function
¶ After an execution of the
osr
command, this variable contains the value of the objective under optimal policy.

MATLAB/Octave variable:
oo_.osr.optim_params
¶ After an execution of the
osr
command, this variable contains the value of parameters at the optimum, stored in fields of the formoo_.osr.optim_params.PARAMETER_NAME
.

MATLAB/Octave variable:
M_.osr.param_names
¶ After an execution of the
osr
command, this cell contains the names of the parameters.

MATLAB/Octave variable:
M_.osr.param_indices
¶ After an execution of the
osr
command, this vector contains the indices of the OSR parameters inM_.params
.

MATLAB/Octave variable:
M_.osr.param_bounds
¶ After an execution of the
osr
command, this two by number of OSR parameters matrix contains the lower and upper bounds of the parameters in the first and second column, respectively.

MATLAB/Octave variable:
M_.osr.variable_weights
¶ After an execution of the
osr
command, this sparse matrix contains the weighting matrix associated with the variables in the objective function.

MATLAB/Octave variable:
M_.osr.variable_indices
¶ After an execution of the
osr
command, this vector contains the indices of the variables entering the objective function inM_.endo_names
.

Command:
ramsey_model
(OPTIONS...);
¶
This command computes the First Order Conditions for maximizing the policy maker objective function subject to the constraints provided by the equilibrium path of the private economy.The planner objective must be declared with the
planner_objective
command.This command only creates the expanded model, it doesn’t perform any computations. It needs to be followed by other instructions to actually perform desired computations. Note that it is the only way to perform perfect foresight simulation of the Ramsey policy problem.
See Auxiliary variables, for an explanation of how Lagrange multipliers are automatically created.
Options
This command accepts the following options:

planner_discount = EXPRESSION
¶ Declares or reassigns the discount factor of the central planner
optimal_policy_discount_factor
. Default:1.0
.

instruments = (VARIABLE_NAME,...)
¶ Declares instrument variables for the computation of the steady state under optimal policy. Requires a
steady_state_model
block or a_steadystate.m
file. See below.
Steady state
Dynare takes advantage of the fact that the Lagrange multipliers appear linearly in the equations of the steady state of the model under optimal policy. Nevertheless, it is in general very difficult to compute the steady state with simply a numerical guess in
initval
for the endogenous variables.It greatly facilitates the computation, if the user provides an analytical solution for the steady state (in
steady_state_model
block or in a_steadystate.m
file). In this case, it is necessary to provide a steady state solution CONDITIONAL on the value of the instruments in the optimal policy problem and declared with optioninstruments
. Note that choosing the instruments is partly a matter of interpretation and you can choose instruments that are handy from a mathematical point of view but different from the instruments you would refer to in the analysis of the paper. A typical example is choosing inflation or nominal interest rate as an instrument.

Block:
ramsey_constraints
;
¶
This block lets you define constraints on the variables in the Ramsey problem. The constraints take the form of a variable, an inequality operator (> or <) and a constant.Example
ramsey_constraints; i > 0; end;

Command:
ramsey_policy
[VARIABLE_NAME...];
¶ 
Command:
ramsey_policy
(OPTIONS...) [VARIABLE_NAME...];
This command computes the first order approximation of the policy that maximizes the policy maker’s objective function subject to the constraints provided by the equilibrium path of the private economy and under commitment to this optimal policy. The Ramsey policy is computed by approximating the equilibrium system around the perturbation point where the Lagrange multipliers are at their steady state, i.e. where the Ramsey planner acts as if the initial multipliers had been set to 0 in the distant past, giving them time to converge to their steady state value. Consequently, the optimal decision rules are computed around this steady state of the endogenous variables and the Lagrange multipliers.This first order approximation to the optimal policy conducted by Dynare is not to be confused with a naive linear quadratic approach to optimal policy that can lead to spurious welfare rankings (see Kim and Kim (2003)). In the latter, the optimal policy would be computed subject to the first order approximated FOCs of the private economy. In contrast, Dynare first computes the FOCs of the Ramsey planner’s problem subject to the nonlinear constraints that are the FOCs of the private economy and only then approximates these FOCs of planner’s problem to first order. Thereby, the second order terms that are required for a secondorder correct welfare evaluation are preserved.
Note that the variables in the list after the
ramsey_policy
command can also contain multiplier names. In that case, Dynare will for example display the IRFs of the respective multipliers whenirf>0
.The planner objective must be declared with the planner_objective command.
See Auxiliary variables, for an explanation of how this operator is handled internally and how this affects the output.
Options
This command accepts all options of
stoch_simul
, plus:
planner_discount = EXPRESSION
See
planner_discount
.

instruments = (VARIABLE_NAME,...)
Declares instrument variables for the computation of the steady state under optimal policy. Requires a
steady_state_model
block or a_steadystate.m
file. See below.
Note that only a first order approximation of the optimal Ramsey policy is available, leading to a secondorder accurate welfare ranking (i.e.
order=1
must be specified).Output
This command generates all the output variables of
stoch_simul
. For specifying the initial values for the endogenous state variables (except for the Lagrange multipliers), seehistval
.In addition, it stores the value of planner objective function under Ramsey policy in
oo_.planner_objective_value
, given the initial values of the endogenous state variables. If not specified withhistval
, they are taken to be at their steady state values. The result is a 1 by 2 vector, where the first entry stores the value of the planner objective when the initial Lagrange multipliers associated with the planner’s problem are set to their steady state values (seeramsey_policy
).In contrast, the second entry stores the value of the planner objective with initial Lagrange multipliers of the planner’s problem set to 0, i.e. it is assumed that the planner exploits its ability to surprise private agents in the first period of implementing Ramsey policy. This is the value of implementating optimal policy for the first time and committing not to reoptimize in the future.
Because it entails computing at least a second order approximation, this computation is skipped with a message when the model is too large (more than 180 state variables, including lagged Lagrange multipliers).
Steady state
See
Ramsey steady state
.

Command:
discretionary_policy
[VARIABLE_NAME...];
¶ 
Command:
discretionary_policy
(OPTIONS...) [VARIABLE_NAME...];
This command computes an approximation of the optimal policy under discretion. The algorithm implemented is essentially an LQ solver, and is described by Dennis (2007).You should ensure that your model is linear and your objective is quadratic. Also, you should set the
linear
option of themodel
block.Options
This command accepts the same options than
ramsey_policy
, plus:
discretionary_tol = NONNEGATIVE DOUBLE
¶ Sets the tolerance level used to assess convergence of the solution algorithm. Default:
1e7
.

maxit = INTEGER
Maximum number of iterations. Default:
3000
.


Command:
planner_objective
MODEL_EXPRESSION ;
¶
This command declares the policy maker objective, for use withramsey_policy
ordiscretionary_policy
.You need to give the oneperiod objective, not the discounted lifetime objective. The discount factor is given by the
planner_discount
option oframsey_policy
anddiscretionary_policy
. The objective function can only contain current endogenous variables and no exogenous ones. This limitation is easily circumvented by defining an appropriate auxiliary variable in the model.With
ramsey_policy
, you are not limited to quadratic objectives: you can give any arbitrary nonlinear expression.With
discretionary_policy
, the objective function must be quadratic.
4.20. Sensitivity and identification analysis¶
Dynare provides an interface to the global sensitivity analysis (GSA) toolbox (developed by the Joint Research Center (JRC) of the European Commission), which is now part of the official Dynare distribution. The GSA toolbox can be used to answer the following questions:
 What is the domain of structural coefficients assuring the stability and determinacy of a DSGE model?
 Which parameters mostly drive the fit of, e.g., GDP and which the fit of inflation? Is there any conflict between the optimal fit of one observed series versus another?
 How to represent in a direct, albeit approximated, form the relationship between structural parameters and the reduced form of a rational expectations model?
The discussion of the methodologies and their application is described in Ratto (2008).
With respect to the previous version of the toolbox, in order to work properly, the GSA toolbox no longer requires that the Dynare estimation environment is set up.
4.20.1. Performing sensitivity analysis¶

Command:
dynare_sensitivity
;
¶ 
Command:
dynare_sensitivity
(OPTIONS...);
This command triggers sensitivity analysis on a DSGE model.Sampling Options

Nsam = INTEGER
¶ Size of the MonteCarlo sample. Default:
2048
.

ilptau = INTEGER
¶ If equal to
1
, use \(LP_\tau\) quasiMonteCarlo. If equal to0
, use LHS MonteCarlo. Default:1
.

pprior = INTEGER
¶ If equqal to
1
, sample from the prior distributions. If equal to0
, sample from the multivariate normal \(N(\bar{\theta},\Sigma)\), where \(\bar{\theta}\) is the posterior mode and \(\Sigma=H^{1}\), \(H\) is the Hessian at the mode. Default:1
.

prior_range = INTEGER
¶ If equal to
1
, sample uniformly from prior ranges. If equal to0
, sample from prior distributions. Default:1
.

morris = INTEGER
¶ If equal to
0
, ANOVA mapping (Type I error) If equal to1
, Screening analysis (Type II error). If equal to2
, Analytic derivatives (similar to Type II error, only valid when identification=1). Default:1
whenidentification=1
,0
otherwise.

morris_nliv = INTEGER
¶ Number of levels in Morris design. Default:
6
.

morris_ntra = INTEGER
¶ Number trajectories in Morris design. Default:
20
.

ppost = INTEGER
¶ If equal to
1
, use Metropolis posterior sample. If equal to0
, do not use Metropolis posterior sample. Default:0
.NB: This overrides any other sampling option.

neighborhood_width = DOUBLE
¶ When
pprior=0
andppost=0
, allows for the sampling of parameters around the value specified in themode_file
, in the range \(\texttt{xparam1} \pm \left \vert \texttt{xparam1} \times \texttt{neighborhood\_width} \right \vert\). Default:0
.
Stability Mapping Options

stab = INTEGER
¶ If equal to
1
, perform stability mapping. If equal to0
, do not perform stability mapping. Default:1
.

load_stab = INTEGER
¶ If equal to
1
, load a previously created sample. If equal to0
, generate a new sample. Default:0
.

alpha2_stab = DOUBLE
¶ Critical value for correlations \(\rho\) in filtered samples: plot couples of parmaters with \(\left\vert\rho\right\vert>\)
alpha2_stab
. Default:0
.

pvalue_ks = DOUBLE
¶ The threshold \(pvalue\) for significant KolmogorovSmirnov test (i.e. plot parameters with \(pvalue<\)
pvalue_ks
). Default:0.001
.

pvalue_corr = DOUBLE
¶ The threshold \(pvalue\) for significant correlation in filtered samples (i.e. plot bivariate samples when \(pvalue<\)
pvalue_corr
). Default:1e5
.
Reduced Form Mapping Options

redform = INTEGER
¶ If equal to
1
, prepare MonteCarlo sample of reduced form matrices. If equal to0
, do not prepare MonteCarlo sample of reduced form matrices. Default:0
.

load_redform = INTEGER
¶ If equal to
1
, load previously estimated mapping. If equal to0
, estimate the mapping of the reduced form model. Default:0
.

logtrans_redform = INTEGER
¶ If equal to
1
, use logtransformed entries. If equal to0
, use raw entries. Default:0
.

threshold_redform = [DOUBLE DOUBLE]
¶ The range over which the filtered MonteCarlo entries of the reduced form coefficients should be analyzed. The first number is the lower bound and the second is the upper bound. An empty vector indicates that these entries will not be filtered. Default: empty.

ksstat_redform = DOUBLE
¶ Critical value for Smirnov statistics \(d\) when reduced form entries are filtered. Default:
0.001
.

alpha2_redform = DOUBLE
¶ Critical value for correlations \(\rho\) when reduced form entries are filtered. Default:
1e5
.

namendo = (VARIABLE_NAME...)
¶ List of endogenous variables. ‘:’ indicates all endogenous variables. Default: empty.

namlagendo = (VARIABLE_NAME...)
¶ List of lagged endogenous variables. ‘:’ indicates all lagged endogenous variables. Analyze entries [namendo \(\times\) namlagendo] Default: empty.

namexo = (VARIABLE_NAME...)
¶ List of exogenous variables. ‘:’ indicates all exogenous variables. Analyze entries [namendo \(\times\) namexo]. Default: empty.
RMSE Options

rmse = INTEGER
¶ If equal to
1
, perform RMSE analysis. If equal to0
, do not perform RMSE analysis. Default:0
.

load_rmse = INTEGER
¶ If equal to
1
, load previous RMSE analysis. If equal to0
, make a new RMSE analysis. Default:0
.

lik_only = INTEGER
¶ If equal to
1
, compute only likelihood and posterior. If equal to0
, compute RMSE’s for all observed series. Default:0
.

var_rmse = (VARIABLE_NAME...)
¶ List of observed series to be considered. ‘:’ indicates all observed variables. Default:
varobs
.

pfilt_rmse = DOUBLE
¶ Filtering threshold for RMSE’s. Default:
0.1
.

istart_rmse = INTEGER
¶ Value at which to start computing RMSE’s (use
2
to avoid big intitial error). Default:presample+1
.

alpha_rmse = DOUBLE
¶ Critical value for Smirnov statistics \(d\): plot parameters with \(d>\)
alpha_rmse
. Default:0.001
.

alpha2_rmse = DOUBLE
¶ Critical value for correlation \(\rho\): plot couples of parmaters with \(\left\vert\rho\right\vert=\)
alpha2_rmse
. Default:1e5
.

datafile = FILENAME
See datafile.

nobs = INTEGER

nobs = [INTEGER1:INTEGER2]
See
nobs
.

first_obs = INTEGER
See
first_obs
.

prefilter = INTEGER
See
prefilter
.

presample = INTEGER
See
presample
.

nograph
See
nograph
.

nodisplay
See
nodisplay
.

graph_format = FORMAT

graph_format = ( FORMAT, FORMAT... )
See
graph_format
.

conf_sig = DOUBLE
See conf_sig.

loglinear
See loglinear.

mode_file = FILENAME
See
mode_file
.

kalman_algo = INTEGER
See
kalman_algo
.
Identification Analysis Options

identification = INTEGER
¶ If equal to
1
, performs identification analysis (forcingredform=0
andmorris=1
) If equal to0
, no identification analysis. Default:0
.

morris = INTEGER
See
morris
.

morris_nliv = INTEGER
See
morris_nliv
.

morris_ntra = INTEGER
See
morris_ntra
.

load_ident_files = INTEGER
¶ Loads previously performed identification analysis. Default:
0
.

useautocorr = INTEGER
¶ Use autocorrelation matrices in place of autocovariance matrices in moments for identification analysis. Default:
0
.

ar = INTEGER
Maximum number of lags for moments in identification analysis. Default:
1
.

diffuse_filter = INTEGER
See
diffuse_filter
.

4.20.2. IRF/Moment calibration¶
The irf_calibration
and moment_calibration
blocks allow
imposing implicit “endogenous” priors about IRFs and moments on the
model. The way it works internally is that any parameter draw that is
inconsistent with the “calibration” provided in these blocks is
discarded, i.e. assigned a prior density of 0
. In the context of
dynare_sensitivity
, these restrictions allow tracing out which
parameters are driving the model to satisfy or violate the given
restrictions.
IRF and moment calibration can be defined in irf_calibration
and
moment_calibration
blocks:

Block:
irf_calibration
;
¶ 
Block:
irf_calibration
(OPTIONS...);
This block allows defining IRF calibration criteria and is terminated byend;
. To set IRF sign restrictions, the following syntax is used:VARIABLE_NAME(INTEGER),EXOGENOUS_NAME, ; VARIABLE_NAME(INTEGER:INTEGER),EXOGENOUS_NAME, +;
To set IRF restrictions with specific intervals, the following syntax is used:
VARIABLE_NAME(INTEGER),EXOGENOUS_NAME, [DOUBLE DOUBLE]; VARIABLE_NAME(INTEGER:INTEGER),EXOGENOUS_NAME, [DOUBLE DOUBLE];
When
(INTEGER:INTEGER)
is used, the restriction is considered to be fulfilled by a logical OR. A list of restrictions must always be fulfilled with logical AND.Options

relative_irf
See
relative_irf
.
Example
irf_calibration; y(1:4), e_ys, [ 50 50]; //[first year response with logical OR] @#for ilag in 21:40 R_obs(@{ilag}), e_ys, [0 6]; //[response from 5th to 10th years with logical AND] @#endfor end;


Block:
moment_calibration
;
¶ 
Block:
moment_calibration
(OPTIONS...);
This block allows defining moment calibration criteria. This block is terminated byend;
, and contains lines of the form:VARIABLE_NAME1,VARIABLE_NAME2(+/INTEGER), [DOUBLE DOUBLE]; VARIABLE_NAME1,VARIABLE_NAME2(+/INTEGER), +/; VARIABLE_NAME1,VARIABLE_NAME2(+/(INTEGER:INTEGER)), [DOUBLE DOUBLE]; VARIABLE_NAME1,VARIABLE_NAME2((INTEGER:+INTEGER)), [DOUBLE DOUBLE];
When
(INTEGER:INTEGER)
is used, the restriction is considered to be fulfilled by a logical OR. A list of restrictions must always be fulfilled with logical AND.Example
moment_calibration; y_obs,y_obs, [0.5 1.5]; //[unconditional variance] y_obs,y_obs((1:4)), +; //[sign restriction for first year acf with logical OR] @#for ilag in 2:2 y_obs,R_obs(@{ilag}), ; //[2:2 ccf with logical AND] @#endfor @#for ilag in 4:4 y_obs,pie_obs(@{ilag}), ; //[4_4 ccf with logical AND] @#endfor end;
4.20.3. Performing identification analysis¶

Command:
identification
;
¶ 
Command:
identification
(OPTIONS...);
This command triggers identification analysis.Options

ar = INTEGER
Number of lags of computed autocorrelations (theoretical moments). Default:
1
.

useautocorr = INTEGER
If equal to
1
, compute derivatives of autocorrelation. If equal to0
, compute derivatives of autocovariances. Default:0
.

load_ident_files = INTEGER
If equal to
1
, allow Dynare to load previously computed analyzes. Default:0
.

prior_mc = INTEGER
¶ Size of MonteCarlo sample. Default:
1
.

prior_range = INTEGER
Triggers uniform sample within the range implied by the prior specifications (when
prior_mc>1
). Default:0
.

advanced = INTEGER
¶ Shows a more detailed analysis, comprised of an analysis for the linearized rational expectation model as well as the associated reduced form solution. Further performs a brute force search of the groups of parameters best reproducing the behavior of each single parameter. The maximum dimension of the group searched is triggered by
max_dim_cova_group
. Default:0
.

max_dim_cova_group = INTEGER
¶ In the brute force search (performed when
advanced=1
) this option sets the maximum dimension of groups of parameters that best reproduce the behavior of each single model parameter. Default:2
.

periods = INTEGER
When the analytic Hessian is not available (i.e. with missing values or diffuse Kalman filter or univariate Kalman filter), this triggers the length of stochastic simulation to compute Simulated Moments Uncertainty. Default:
300
.

replic = INTEGER
When the analytic Hessian is not available, this triggers the number of replicas to compute Simulated Moments Uncertainty. Default:
100
.

gsa_sample_file = INTEGER
¶ If equal to
0
, do not use sample file. If equal to1
, triggers gsa prior sample. If equal to2
, triggers gsa MonteCarlo sample (i.e. loads a sample corresponding topprior=0
andppost=0
in thedynare_sensitivity
options). Default:0
.

gsa_sample_file = FILENAME
¶ Uses the provided path to a specific user defined sample file. Default:
0
.

parameter_set = OPTION
Specify the parameter set to use. Possible values for OPTION are:
calibration
prior_mode
prior_mean
posterior_mode
posterior_mean
posterior_median
Default:
prior_mean
.

lik_init = INTEGER
See
lik_init
.

kalman_algo = INTEGER
See
kalman_algo
.

nograph
See
nograph
.

nodisplay
See
nodisplay
.

graph_format = FORMAT

graph_format = ( FORMAT, FORMAT... )
See
graph_format
.

4.20.4. Types of analysis and output files¶
The sensitivity analysis toolbox includes several types of
analyses. Sensitivity analysis results are saved locally in
<mod_file>/gsa
, where <mod_file>.mod
is the name of the DYNARE
model file.
4.20.4.1. Sampling¶
The following binary files are produced:
<mod_file>_prior.mat
: this file stores information about the analyses performed sampling from the prior, i.e.pprior=1
andppost=0
;<mod_file>_mc.mat
: this file stores information about the analyses performed sampling from multivariate normal, i.e.pprior=0
andppost=0
;<mod_file>_post.mat
: this file stores information about analyses performed using the Metropolis posterior sample, i.e.ppost=1
.
4.20.4.2. Stability Mapping¶
Figure files produced are of the form <mod_file>_prior_*.fig
and
store results for stability mapping from prior MonteCarlo samples:
<mod_file>_prior_stable.fig
: plots of the Smirnov test and the correlation analyses confronting the cdf of the sample fulfilling BlanchardKahn conditions (blue color) with the cdf of the rest of the sample (red color), i.e. either instability or indeterminacy or the solution could not be found (e.g. the steady state solution could not be found by the solver);<mod_file>_prior_indeterm.fig
: plots of the Smirnov test and the correlation analyses confronting the cdf of the sample producing indeterminacy (red color) with the cdf of the rest of the sample (blue color);<mod_file>_prior_unstable.fig
: plots of the Smirnov test and the correlation analyses confronting the cdf of the sample producing explosive roots (red color) with the cdf of the rest of the sample (blue color);<mod_file>_prior_wrong.fig
: plots of the Smirnov test and the correlation analyses confronting the cdf of the sample where the solution could not be found (e.g. the steady state solution could not be found by the solver  red color) with the cdf of the rest of the sample (blue color);<mod_file>_prior_calib.fig
: plots of the Smirnov test and the correlation analyses splitting the sample fulfilling BlanchardKahn conditions, by confronting the cdf of the sample where IRF/moment restrictions are matched (blue color) with the cdf where IRF/moment restrictions are NOT matched (red color);
Similar conventions apply for <mod_file>_mc_*.fig
files, obtained
when samples from multivariate normal are used.
4.20.4.3. IRF/Moment restrictions¶
The following binary files are produced:
<mod_file>_prior_restrictions.mat
: this file stores information about the IRF/moment restriction analysis performed sampling from the prior ranges, i.e.pprior=1
andppost=0
;<mod_file>_mc_restrictions.mat
: this file stores information about the IRF/moment restriction analysis performed sampling from multivariate normal, i.e.pprior=0
andppost=0
;<mod_file>_post_restrictions.mat
: this file stores information about IRF/moment restriction analysis performed using the Metropolis posterior sample, i.e.ppost=1
.
Figure files produced are of the form
<mod_file>_prior_irf_calib_*.fig
and
<mod_file>_prior_moment_calib_*.fig
and store results for mapping
restrictions from prior MonteCarlo samples:
<mod_file>_prior_irf_calib_<ENDO_NAME>_vs_<EXO_NAME>_<PERIOD>.fig
: plots of the Smirnov test and the correlation analyses splitting the sample fulfilling BlanchardKahn conditions, by confronting the cdf of the sample where the individual IRF restriction<ENDO_NAME>
vs.<EXO_NAME>
at period(s)<PERIOD>
is matched (blue color) with the cdf where the IRF restriction is NOT matched (red color)<mod_file>_prior_irf_calib_<ENDO_NAME>_vs_<EXO_NAME>_ALL.fig
: plots of the Smirnov test and the correlation analyses splitting the sample fulfilling BlanchardKahn conditions, by confronting the cdf of the sample where ALL the individual IRF restrictions for the same couple<ENDO_NAME>
vs.<EXO_NAME>
are matched (blue color) with the cdf where the IRF restriction is NOT matched (red color)<mod_file>_prior_irf_restrictions.fig
: plots visual information on the IRF restrictions compared to the actual Monte Carlo realization from prior sample.<mod_file>_prior_moment_calib_<ENDO_NAME1>_vs_<ENDO_NAME2>_<LAG>.fig
: plots of the Smirnov test and the correlation analyses splitting the sample fulfilling BlanchardKahn conditions, by confronting the cdf of the sample where the individual acf/ccf moment restriction<ENDO_NAME1>
vs.<ENDO_NAME2>
at lag(s)<LAG>
is matched (blue color) with the cdf where the IRF restriction is NOT matched (red color)<mod_file>_prior_moment_calib_<ENDO_NAME>_vs_<EXO_NAME>_ALL.fig
: plots of the Smirnov test and the correlation analyses splitting the sample fulfilling BlanchardKahn conditions, by confronting the cdf of the sample where ALL the individual acf/ccf moment restrictions for the same couple<ENDO_NAME1>
vs.<ENDO_NAME2>
are matched (blue color) with the cdf where the IRF restriction is NOT matched (red color)<mod_file>_prior_moment_restrictions.fig
: plots visual information on the moment restrictions compared to the actual Monte Carlo realization from prior sample.
Similar conventions apply for <mod_file>_mc_*.fig
and
<mod_file>_post_*.fig
files, obtained when samples from
multivariate normal or from posterior are used.
4.20.4.4. Reduced Form Mapping¶
When the option threshold_redform
is not set, or it is empty (the
default), this analysis estimates a multivariate smoothing spline
ANOVA model (the ’mapping’) for the selected entries in the transition
matrix of the shock matrix of the reduce form first order solution of
the model. This mapping is done either with prior samples or with MC
samples with neighborhood_width
. Unless neighborhood_width
is
set with MC samples, the mapping of the reduced form solution forces
the use of samples from prior ranges or prior distributions, i.e.:
pprior=1
and ppost=0
. It uses 250 samples to optimize
smoothing parameters and 1000 samples to compute the fit. The rest of
the sample is used for outofsample validation. One can also load a
previously estimated mapping with a new MonteCarlo sample, to look at
the forecast for the new MonteCarlo sample.
The following synthetic figures are produced:
<mod_file>_redform_<endo name>_vs_lags_*.fig
: shows bar charts of the sensitivity indices for the ten most important parameters driving the reduced form coefficients of the selected endogenous variables (namendo
) versus lagged endogenous variables (namlagendo
); suffixlog
indicates the results for logtransformed entries;<mod_file>_redform_<endo name>_vs_shocks_*.fig
: shows bar charts of the sensitivity indices for the ten most important parameters driving the reduced form coefficients of the selected endogenous variables (namendo
) versus exogenous variables (namexo
); suffixlog
indicates the results for logtransformed entries;<mod_file>_redform_gsa(_log).fig
: shows bar chart of all sensitivity indices for each parameter: this allows one to notice parameters that have a minor effect for any of the reduced form coefficients.
Detailed results of the analyses are shown in the subfolder
<mod_file>/gsa/redform_prior
for prior samples and in
<mod_file>/gsa/redform_mc
for MC samples with option
neighborhood_width
, where the detailed results of the estimation
of the single functional relationships between parameters
\(\theta\) and reduced form coefficient (denoted as \(y\)
hereafter) are stored in separate directories named as:
<namendo>_vs_<namlagendo>
, for the entries of the transition matrix;<namendo>_vs_<namexo>
, for entries of the matrix of the shocks.
The following files are stored in each directory (we stick with prior sample but similar conventions are used for MC samples):
<mod_file>_prior_<namendo>_vs_<namexo>.fig
: histogram and CDF plot of the MC sample of the individual entry of the shock matrix, in sample and out of sample fit of the ANOVA model;<mod_file>_prior_<namendo>_vs_<namexo>_map_SE.fig
: for entries of the shock matrix it shows graphs of the estimated first order ANOVA terms \(y = f(\theta_i)\) for each deep parameter \(\theta_i\);<mod_file>_prior_<namendo>_vs_<namlagendo>.fig
: histogram and CDF plot of the MC sample of the individual entry of the transition matrix, in sample and out of sample fit of the ANOVA model;<mod_file>_prior_<namendo>_vs_<namlagendo>_map_SE.fig
: for entries of the transition matrix it shows graphs of the estimated first order ANOVA terms \(y = f(\theta_i)\) for each deep parameter \(\theta_i\);<mod_file>_prior_<namendo>_vs_<namexo>_map.mat
,<mod_file>_<namendo>_vs_<namlagendo>_map.mat
: these files store info in the estimation;
When option logtrans_redform
is set, the ANOVA estimation is
performed using a logtransformation of each y. The ANOVA mapping is
then transformed back onto the original scale, to allow comparability
with the baseline estimation. Graphs for this logtransformed case,
are stored in the same folder in files denoted with the _log
suffix.
When the option threshold_redform
is set, the analysis is
performed via Monte Carlo filtering, by displaying parameters that
drive the individual entry y
inside the range specified in
threshold_redform
. If no entry is found (or all entries are in the
range), the MCF algorithm ignores the range specified in
threshold_redform
and performs the analysis splitting the MC
sample of y
into deciles. Setting threshold_redform=[inf inf]
triggers this approach for all y
’s.
Results are stored in subdirectories of <mod_file>/gsa/redform_prior
named
<mod_file>_prior_<namendo>_vs_<namlagendo>_threshold
, for the entries of the transition matrix;<mod_file>_prior_<namendo>_vs_<namexo>_threshold
, for entries of the matrix of the shocks.
The files saved are named:
<mod_file>_prior_<namendo>_vs_<namexo>_threshold.fig
,<mod_file>_<namendo>_vs_<namlagendo>_threshold.fig
: graphical outputs;<mod_file>_prior_<namendo>_vs_<namexo>_threshold.mat
,<mod_file>_<namendo>_vs_<namlagendo>_threshold.mat
: info on the analysis;
4.20.4.5. RMSE¶
The RMSE analysis can be performed with different types of sampling options:
 When
pprior=1
andppost=0
, the toolbox analyzes the RMSEs for the MonteCarlo sample obtained by sampling parameters from their prior distributions (or prior ranges): this analysis provides some hints about what parameter drives the fit of which observed series, prior to the full estimation; When
pprior=0
andppost=0
, the toolbox analyzes the RMSEs for a multivariate normal MonteCarlo sample, with covariance matrix based on the inverse Hessian at the optimum: this analysis is useful when maximum likelihood estimation is done (i.e. no Bayesian estimation); When
ppost=1
the toolbox analyzes the RMSEs for the posterior sample obtained by Dynare’s Metropolis procedure.
The use of cases 2 and 3 requires an estimation step beforehand. To
facilitate the sensitivity analysis after estimation, the
dynare_sensitivity
command also allows you to indicate some
options of the estimation command
. These are:
datafile
nobs
first_obs
prefilter
presample
nograph
nodisplay
graph_format
conf_sig
loglinear
mode_file
Binary files produced my RMSE analysis are:
<mod_file>_prior_*.mat
: these files store the filtered and smoothed variables for the prior MonteCarlo sample, generated when doing RMSE analysis (pprior=1
andppost=0
);<mode_file>_mc_*.mat
: these files store the filtered and smoothed variables for the multivariate normal MonteCarlo sample, generated when doing RMSE analysis (pprior=0
andppost=0
).
Figure files <mod_file>_rmse_*.fig store results for the RMSE analysis.
<mod_file>_rmse_prior*.fig
: save results for the analysis using prior MonteCarlo samples;<mod_file>_rmse_mc*.fig
: save results for the analysis using multivariate normal MonteCarlo samples;<mod_file>_rmse_post*.fig
: save results for the analysis using Metropolis posterior samples.
The following types of figures are saved (we show prior sample to fix ideas, but the same conventions are used for multivariate normal and posterior):
<mod_file>_rmse_prior_params_*.fig
: for each parameter, plots the cdfs corresponding to the best 10% RMSEs of each observed series (only those cdfs below the significance thresholdalpha_rmse
);<mod_file>_rmse_prior_<var_obs>_*.fig
: if a parameter significantly affects the fit ofvar_obs
, all possible tradeoff’s with other observables for same parameter are plotted;<mod_file>_rmse_prior_<var_obs>_map.fig
: plots the MCF analysis of parameters significantly driving the fit the observed seriesvar_obs
;<mod_file>_rmse_prior_lnlik*.fig
: for each observed series, plots in BLUE the cdf of the loglikelihood corresponding to the best 10% RMSEs, in RED the cdf of the rest of the sample and in BLACK the cdf of the full sample; this allows one to see the presence of some idiosyncratic behavior;<mod_file>_rmse_prior_lnpost*.fig
: for each observed series, plots in BLUE the cdf of the logposterior corresponding to the best 10% RMSEs, in RED the cdf of the rest of the sample and in BLACK the cdf of the full sample; this allows one to see idiosyncratic behavior;<mod_file>_rmse_prior_lnprior*.fig
: for each observed series, plots in BLUE the cdf of the logprior corresponding to the best 10% RMSEs, in RED the cdf of the rest of the sample and in BLACK the cdf of the full sample; this allows one to see idiosyncratic behavior;<mod_file>_rmse_prior_lik.fig
: whenlik_only=1
, this shows the MCF tests for the filtering of the best 10% loglikelihood values;<mod_file>_rmse_prior_post.fig
: whenlik_only=1
, this shows the MCF tests for the filtering of the best 10% logposterior values.
4.20.4.6. Screening Analysis¶
Screening analysis does not require any additional options with respect to those listed in Sampling Options. The toolbox performs all the analyses required and displays results.
The results of the screening analysis with Morris sampling design are
stored in the subfolder <mod_file>/gsa/screen
. The data file
<mod_file>_prior
stores all the information of the analysis
(Morris sample, reduced form coefficients, etc.).
Screening analysis merely concerns reduced form coefficients. Similar synthetic bar charts as for the reduced form analysis with MonteCarlo samples are saved:
<mod_file>_redform_<endo name>_vs_lags_*.fig
: shows bar charts of the elementary effect tests for the ten most important parameters driving the reduced form coefficients of the selected endogenous variables (namendo
) versus lagged endogenous variables (namlagendo
);<mod_file>_redform_<endo name>_vs_shocks_*.fig
: shows bar charts of the elementary effect tests for the ten most important parameters driving the reduced form coefficients of the selected endogenous variables (namendo
) versus exogenous variables (namexo
);<mod_file>_redform_screen.fig
: shows bar chart of all elementary effect tests for each parameter: this allows one to identify parameters that have a minor effect for any of the reduced form coefficients.
4.20.4.7. Identification Analysis¶
Setting the option identification=1
, an identification analysis
based on theoretical moments is performed. Sensitivity plots are
provided that allow to infer which parameters are most likely to be
less identifiable.
Prerequisite for properly running all the identification routines, is
the keyword identification
; in the Dynare model file. This keyword
triggers the computation of analytic derivatives of the model with
respect to estimated parameters and shocks. This is required for
option morris=2
, which implements Iskrev (2010) identification
analysis.
For example, the placing:
identification;
dynare_sensitivity(identification=1, morris=2);
in the Dynare model file triggers identification analysis using analytic derivatives Iskrev (2010), jointly with the mapping of the acceptable region.
The identification analysis with derivatives can also be triggered by
the commands identification;
This does not do the mapping of
acceptable regions for the model and uses the standard random sampler
of Dynare. It completely offsets any use of the sensitivity analysis
toolbox.
4.21. Markovswitching SBVAR¶
Given a list of variables, observed variables and a data file, Dynare can be used to solve a Markovswitching SBVAR model according to Sims, Waggoner and Zha (2008) [10] . Having done this, you can create forecasts and compute the marginal data density, regime probabilities, IRFs, and variance decomposition of the model.
The commands have been modularized, allowing for multiple calls to the
same command within a <mod_file>.mod
file. The default is to use
<mod_file>
to tag the input (output) files used (produced) by the
program. Thus, to call any command more than once within a
<mod_file>.mod
file, you must use the *_tag
options described
below.

Command:
markov_switching
(OPTIONS...);
¶
Declares the Markov state variable information of a Markovswitching SBVAR model.Options

chain = INTEGER
¶ The Markov chain considered. Default:
none
.

number_of_regimes = INTEGER
¶ Specifies the total number of regimes in the Markov Chain. This is a required option.

duration = DOUBLE  [ROW VECTOR OF DOUBLES]
¶ The duration of the regimes or regimes. This is a required option. When passed a scalar real number, it specifies the average duration for all regimes in this chain. When passed a vector of size equal
number_of_regimes
, it specifies the average duration of the associated regimes (1:number_of_regimes
) in this chain. An absorbing state can be specified through therestrictions
option.

restrictions = [[ROW VECTOR OF 3 DOUBLES],[ROW VECTOR OF 3 DOUBLES],...]
¶ Provides restrictions on this chain’s regime transition matrix. Its vector argument takes three inputs of the form:
[current_period_regime, next_period_regime, transition_probability]
.The first two entries are positive integers, and the third is a nonnegative real in the set [0,1]. If restrictions are specified for every transition for a regime, the sum of the probabilities must be 1. Otherwise, if restrictions are not provided for every transition for a given regime the sum of the provided transition probabilities msut be <1. Regardless of the number of lags, the restrictions are specified for parameters at time
t
since the transition probability for a parameter at t is equal to that of the parameter att1
.
In case of estimating a MSDSGE model, [11] in addition the following options are allowed:

parameters = [LIST OF PARAMETERS]
¶ This option specifies which parameters are controlled by this Markov Chain.

number_of_lags = DOUBLE
¶ Provides the number of lags that each parameter can take within each regime in this chain.
Example
markov_switching(chain=1, duration=2.5, restrictions=[[1,3,0],[3,1,0]]);
Specifies a Markovswitching BVAR with a first chain with 3 regimes that all have a duration of 2.5 periods. The probability of directly going from regime 1 to regime 3 and vice versa is 0.
Example
markov_switching(chain=2, number_of_regimes=3, duration=[0.5, 2.5, 2.5], parameter=[alpha, rho], number_of_lags=2, restrictions=[[1,3,0],[3,3,1]]);
Specifies a Markovswitching DSGE model with a second chain with 3 regimes that have durations of 0.5, 2.5, and 2.5 periods, respectively. The switching parameters are
alpha
andrho
. The probability of directly going from regime 1 to regime 3 is 0, while regime 3 is an absorbing state.

Command:
svar
(OPTIONS...);
¶
Each Markov chain can control the switching of a set of parameters. We allow the parameters to be divided equation by equation and by variance or slope and intercept.Options

coefficients
¶ Specifies that only the slope and intercept in the given equations are controlled by the given chain. One, but not both, of
coefficients
orvariances
must appear. Default:none
.

variances
¶ Specifies that only variances in the given equations are controlled by the given chain. One, but not both, of
coefficients
orvariances
must appear. Default:none
.

equations
¶ Defines the equation controlled by the given chain. If not specified, then all equations are controlled by
chain
. Default:none
.

chain = INTEGER
Specifies a Markov chain defined by
markov_switching
. Default:none
.


Command:
sbvar
(OPTIONS...);
¶
To be documented. For now, see the wiki: https://www.dynare.org/DynareWiki/SbvarOptionsOptions
datafile
,freq
,initial_year
,initial_subperiod
,final_year
,final_subperiod
,data
,vlist
,vlistlog
,vlistper
,restriction_fname
,nlags
,cross_restrictions
,contemp_reduced_form
,real_pseudo_forecast
,no_bayesian_prior
,dummy_obs
,nstates
,indxscalesstates
,alpha
,beta
,gsig2_lmdm
,q_diag
,flat_prior
,ncsk
,nstd
,ninv
,indxparr
,indxovr
,aband
,indxap
,apband
,indximf
,indxfore
,foreband
,indxgforhat
,indxgimfhat
,indxestima
,indxgdls
,eq_ms
,cms
,ncms
,eq_cms
,tlindx
,tlnumber
,cnum
,forecast
,coefficients_prior_hyperparameters

Block:
svar_identification
;
¶
This block is terminated byend;
and contains lines of the form:UPPER_CHOLESKY; LOWER_CHOLESKY; EXCLUSION CONSTANTS; EXCLUSION LAG INTEGER; VARIABLE_NAME [,VARIABLE_NAME...]; EXCLUSION LAG INTEGER; EQUATION INTEGER, VARIABLE_NAME [,VARIABLE_NAME...]; RESTRICTION EQUATION INTEGER, EXPRESSION = EXPRESSION;
To be documented. For now, see the wiki: http://www.dynare.org/DynareWiki/MarkovSwitchingInterface

Command:
ms_estimation
(OPTIONS...);
¶
Triggers the creation of an initialization file for, and the estimation of, a Markovswitching SBVAR model. At the end of the run, the \(A^0\), \(A^+\), \(Q\) and \(\zeta\) matrices are contained in theoo_.ms
structure.General Options

file_tag = FILENAME
¶ The portion of the filename associated with this run. This will create the model initialization file,
init_<file_tag>.dat
. Default:<mod_file>
.

output_file_tag = FILENAME
¶ The portion of the output filename that will be assigned to this run. This will create, among other files,
est_final_<output_file_tag>.out
,est_intermediate_<output_file_tag>.out
. Default:<file_tag>
.

no_create_init
¶ Do not create an initialization file for the model. Passing this option will cause the Initialization Options to be ignored. Further, the model will be generated from the output files associated with the previous estimation run (i.e.
est_final_<file_tag>.out
,est_intermediate_<file_tag>.out
orinit_<file_tag>.dat
, searched for in sequential order). This functionality can be useful for continuing a previous estimation run to ensure convergence was reached or for reusing an initialization file. NB: If this option is not passed, the files from the previous estimation run will be overwritten. Default: off (i.e. create initialization file)
Initialization Options

coefficients_prior_hyperparameters = [DOUBLE1 DOUBLE2 ... DOUBLE6]
¶ Sets the hyper parameters for the model. The six elements of the argument vector have the following interpretations:
1
Overall tightness for \(A^0\) and \(A^+\).2
Relative tightness for \(A^+\).3
Relative tightness for the constant term.4
Tightness on lag decay (range: 1.2  1.5); a faster decay produces better inflation process.5
Weight on nvar sums of coeffs dummy observations (unit roots).6
Weight on single dummy initial observation including constant.Default:
[1.0 1.0 0.1 1.2 1.0 1.0]

freq = INTEGER  monthly  quarterly  yearly
¶ Frequency of the data (e.g.
monthly, 12
). Default:4
.

initial_year = INTEGER
¶ The first year of data. Default:
none
.

initial_subperiod = INTEGER
¶ The first period of data (i.e. for quarterly data, an integer in
[1,4]
). Default:1
.

final_year = INTEGER
¶ The last year of data. Default: Set to encompass entire dataset.

final_subperiod = INTEGER
¶ The final period of data (i.e. for monthly data, an integer in
[1,12]
. Default: When final_year is also missing, set to encompass entire dataset; whenfinal_year
is indicated, set to the maximum number of subperiods given the frequency (i.e. 4 for quarterly data, 12 for monthly,…).

datafile = FILENAME
See datafile.

xls_sheet = NAME
See
xls_sheet
.

xls_range = RANGE
See
xls_range
.

nlags = INTEGER
¶ The number of lags in the model. Default:
1
.

cross_restrictions
¶ Use cross \(A^0\) and \(A^+\) restrictions. Default:
off
.

contemp_reduced_form
¶ Use contemporaneous recursive reduced form. Default:
off
.

no_bayesian_prior
¶ Do not use Bayesian prior. Default:
off
(i.e. use Bayesian prior).

alpha = INTEGER
¶ Alpha value for squared timevarying structural shock lambda. Default:
1
.

beta = INTEGER
¶ Beta value for squared timevarying structural shock lambda. Default:
1
.

gsig2_lmdm = INTEGER
¶ The variance for each independent \(\lambda\) parameter under
SimsZha
restrictions. Default:50^2
.

specification = sims_zha  none
¶ This controls how restrictions are imposed to reduce the number of parameters. Default:
Random Walk
.
Estimation Options

convergence_starting_value = DOUBLE
¶ This is the tolerance criterion for convergence and refers to changes in the objective function value. It should be rather loose since it will gradually be tightened during estimation. Default:
1e3
.

convergence_ending_value = DOUBLE
¶ The convergence criterion ending value. Values much smaller than square root machine epsilon are probably overkill. Default:
1e6
.

convergence_increment_value = DOUBLE
¶ Determines how quickly the convergence criterion moves from the starting value to the ending value. Default:
0.1
.

max_iterations_starting_value = INTEGER
¶ This is the maximum number of iterations allowed in the hillclimbing optimization routine and should be rather small since it will gradually be increased during estimation. Default:
50
.

max_iterations_increment_value = DOUBLE
¶ Determines how quickly the maximum number of iterations is increased. Default:
2
.

max_block_iterations = INTEGER
¶ The parameters are divided into blocks and optimization proceeds over each block. After a set of blockwise optimizations are performed, the convergence criterion is checked and the blockwise optimizations are repeated if the criterion is violated. This controls the maximum number of times the blockwise optimization can be performed. Note that after the blockwise optimizations have converged, a single optimization over all the parameters is performed before updating the convergence value and maximum number of iterations. Default:
100
.

max_repeated_optimization_runs = INTEGER
¶ The entire process described by
max_block_iterations
is repeated until improvement has stopped. This is the maximum number of times the process is allowed to repeat. Set this to0
to not allow repetitions. Default:10
.

function_convergence_criterion = DOUBLE
¶ The convergence criterion for the objective function when
max_repeated_optimizations_runs
is positive. Default:0.1
.

parameter_convergence_criterion = DOUBLE
¶ The convergence criterion for parameter values when
max_repeated_optimizations_runs
is positive. Default:0.1
.

number_of_large_perturbations = INTEGER
¶ The entire process described by
max_block_iterations
is repeated with random starting values drawn from the posterior. This specifies the number of random starting values used. Set this to0
to not use random starting values. A larger number should be specified to ensure that the entire parameter space has been covered. Default:5
.

number_of_small_perturbations = INTEGER
¶ The number of small perturbations to make after the large perturbations have stopped improving. Setting this number much above
10
is probably overkill. Default:5
.

number_of_posterior_draws_after_perturbation = INTEGER
¶ The number of consecutive posterior draws to make when producing a small perturbation. Because the posterior draws are serially correlated, a small number will result in a small perturbation. Default:
1
.

max_number_of_stages = INTEGER
¶ The small and large perturbation are repeated until improvement has stopped. This specifies the maximum number of stages allowed. Default:
20
.

random_function_convergence_criterion = DOUBLE
¶ The convergence criterion for the objective function when
number_of_large_perturbations
is positive. Default:0.1
.

random_parameter_convergence_criterion = DOUBLE
¶ The convergence criterion for parameter values when
number_of_large_perturbations
is positive. Default:0.1
.
Example
ms_estimation(datafile=data, initial_year=1959, final_year=2005, nlags=4, max_repeated_optimization_runs=1, max_number_of_stages=0); ms_estimation(file_tag=second_run, datafile=data, initial_year=1959, final_year=2005, nlags=4, max_repeated_optimization_runs=1, max_number_of_stages=0); ms_estimation(file_tag=second_run, output_file_tag=third_run, no_create_init, max_repeated_optimization_runs=5, number_of_large_perturbations=10);


Command:
ms_simulation
;
¶ 
Command:
ms_simulation
(OPTIONS...);
Simulates a Markovswitching SBVAR model.Options

file_tag = FILENAME
The portion of the filename associated with the
ms_estimation
run. Default:<mod_file>
.

output_file_tag = FILENAME
The portion of the output filename that will be assigned to this run. Default:
<file_tag>
.

mh_replic = INTEGER
The number of draws to save. Default:
10,000
.

drop = INTEGER
The number of burnin draws. Default:
0.1*mh_replic*thinning_factor
.

thinning_factor = INTEGER
¶ The total number of draws is equal to
thinning_factor*mh_replic+drop
. Default:1
.

adaptive_mh_draws = INTEGER
¶ Tuning period for MetropolisHastings draws. Default:
30,000
.

save_draws
¶ Save all elements of \(A^0\), \(A^+\), \(Q\), and \(\zeta\), to a file named
draws_<<file_tag>>.out
with each draw on a separate line. A file that describes how these matrices are laid out is contained indraws_header_<<file_tag>>.out
. A file calledload_flat_file.m
is provided to simplify loading the saved files into the corresponding variablesA0
,Aplus
,Q
, andZeta
in your MATLAB/Octave workspace. Default:off
.
Example
ms_simulation(file_tag=second_run); ms_simulation(file_tag=third_run, mh_replic=5000, thinning_factor=3);


Command:
ms_compute_mdd
;
¶ 
Command:
ms_compute_mdd
(OPTIONS...);
Computes the marginal data density of a Markovswitching SBVAR model from the posterior draws. At the end of the run, the Muller and Bridged log marginal densities are contained in theoo_.ms
structure.Options

file_tag = FILENAME
See
file_tag
.

output_file_tag = FILENAME
See
output_file_tag
.

simulation_file_tag = FILENAME
¶ The portion of the filename associated with the simulation run. Default:
<file_tag>
.

proposal_type = INTEGER
¶ The proposal type:
1
Gaussian.2
Power.3
Truncated Power.4
Step.5
Truncated Gaussian.Default:
3

proposal_lower_bound = DOUBLE
¶ The lower cutoff in terms of probability. Not used for
proposal_type
in[1,2]
. Required for all other proposal types. Default:0.1
.

proposal_upper_bound = DOUBLE
¶ The upper cutoff in terms of probability. Not used for
proposal_type
equal to1
. Required for all other proposal types. Default:0.9
.

mdd_proposal_draws = INTEGER
¶ The number of proposal draws. Default:
100,000
.

mdd_use_mean_center
¶ Use the posterior mean as center. Default:
off
.


Command:
ms_compute_probabilities
;
¶ 
Command:
ms_compute_probabilities
(OPTIONS...);
Computes smoothed regime probabilities of a Markovswitching SBVAR model. Output.eps
files are contained in<output_file_tag/Output/Probabilities>
.Options

file_tag = FILENAME
See
file_tag
.

output_file_tag = FILENAME
See
output_file_tag
.

filtered_probabilities
¶ Filtered probabilities are computed instead of smoothed. Default:
off
.

real_time_smoothed
¶ Smoothed probabilities are computed based on time
t
information for \(0\le t\le nobs\). Default:off


Command:
ms_irf
;
¶ 
Command:
ms_irf
(OPTIONS...);
Computes impulse response functions for a Markovswitching SBVAR model. Output.eps
files are contained in<output_file_tag/Output/IRF>
, while data files are contained in<output_file_tag/IRF>
.Options

file_tag = FILENAME
See
file_tag
.

output_file_tag = FILENAME
See
output_file_tag
.

simulation_file_tag = FILENAME
See
simulation_file_tag
.

horizon = INTEGER
¶ The forecast horizon. Default:
12
.

filtered_probabilities
Uses filtered probabilities at the end of the sample as initial conditions for regime probabilities. Only one of
filtered_probabilities
,regime
andregimes
may be passed. Default:off
.

error_band_percentiles = [DOUBLE1 ...]
¶ The percentiles to compute. Default:
[0.16 0.50 0.84]
. Ifmedian
is passed, the default is[0.5]
.

shock_draws = INTEGER
¶ The number of regime paths to draw. Default:
10,000
.

shocks_per_parameter = INTEGER
¶ The number of regime paths to draw under parameter uncertainty. Default:
10
.

thinning_factor = INTEGER
Only \(1/ \texttt{thinning\_factor}\) of the draws in posterior draws file are used. Default:
1
.

free_parameters = NUMERICAL_VECTOR
¶ A vector of free parameters to initialize theta of the model. Default: use estimated parameters

parameter_uncertainty
¶ Calculate IRFs under parameter uncertainty. Requires that
ms_simulation
has been run. Default:off
.

regime = INTEGER
¶ Given the data and model parameters, what is the ergodic probability of being in the specified regime. Only one of
filtered_probabilities
,regime
andregimes
may be passed. Default:off
.

regimes
¶ Describes the evolution of regimes. Only one of
filtered_probabilities
,regime
andregimes
may be passed. Default:off
.

median
¶ A shortcut to setting
error_band_percentiles=[0.5]
. Default:off
.


Command:
ms_forecast
;
¶ 
Command:
ms_forecast
(OPTIONS...);
Generates forecasts for a Markovswitching SBVAR model. Output.eps
files are contained in<output_file_tag/Output/Forecast>
, while data files are contained in<output_file_tag/Forecast>
.Options

file_tag = FILENAME
See
file_tag
.

output_file_tag = FILENAME
See
output_file_tag
.

simulation_file_tag = FILENAME
See
simulation_file_tag
.

data_obs_nbr = INTEGER
¶ The number of data points included in the output. Default:
0
.

error_band_percentiles = [DOUBLE1 ...]
See
error_band_percentiles
.

shock_draws = INTEGER
See
shock_draws
.

shocks_per_parameter = INTEGER
See
shocks_per_parameter
.

thinning_factor = INTEGER
See
thinning_factor
.

free_parameters = NUMERICAL_VECTOR
See
free_parameters
.

parameter_uncertainty

regime = INTEGER
See
regime
.

regimes
See
regimes
.

median
See
median
.

horizon = INTEGER
See
horizon
.


Command:
ms_variance_decomposition
;
¶ 
Command:
ms_variance_decomposition
(OPTIONS...);
Computes the variance decomposition for a Markovswitching SBVAR model. Output.eps
files are contained in<output_file_tag/Output/Variance_Decomposition>
, while data files are contained in<output_file_tag/Variance_Decomposition>
.Options

file_tag = FILENAME
See
file_tag
.

output_file_tag = FILENAME
See
output_file_tag
.

simulation_file_tag = FILENAME
See
simulation_file_tag
.

horizon = INTEGER
See
horizon
.

filtered_probabilities

no_error_bands
¶ Do not output percentile error bands (i.e. compute mean). Default:
off
(i.e. output error bands)

error_band_percentiles = [DOUBLE1 ...]
See
error_band_percentiles
.

shock_draws = INTEGER
See
shock_draws
.

shocks_per_parameter = INTEGER
See
shocks_per_parameter
.

thinning_factor = INTEGER
See
thinning_factor
.

free_parameters = NUMERICAL_VECTOR
See
free_parameters
.

parameter_uncertainty

regime = INTEGER
See
regime
.

regimes
See
regimes
.

4.22. Displaying and saving results¶
Dynare has comments to plot the results of a simulation and to save the results.

Command:
rplot
VARIABLE_NAME...;
¶
Plots the simulated path of one or several variables, as stored inoo_.endo_simul
by eitherperfect_foresight_solver
,simul
(see Deterministic simulation) orstoch_simul
with optionperiods
(see Stochastic solution and simulation). The variables are plotted in levels.

Command:
dynatype
(FILENAME) [VARIABLE_NAME...];
¶
This command prints the listed variables in a text file named FILENAME. If no VARIABLE_NAME is listed, all endogenous variables are printed.

Command:
dynasave
(FILENAME) [VARIABLE_NAME...];
¶
This command saves the listed variables in a binary file named FILENAME. If no VARIABLE_NAME are listed, all endogenous variables are saved.In MATLAB or Octave, variables saved with the
dynasave command
can be retrieved by the command:load mat FILENAME
4.23. Macroprocessing language¶
It is possible to use “macro” commands in the .mod
file for doing
the following tasks: including modular source files, replicating
blocks of equations through loops, conditionally executing some code,
writing indexed sums or products inside equations…
The Dynare macrolanguage provides a new set of macrocommands which
can be inserted inside .mod
files. It features:
 File inclusion
 Loops (for structure)
 Conditional inclusion (
if/then/else
structures) Expression substitution
Technically, this macro language is totally independent of the basic
Dynare language, and is processed by a separate component of the
Dynare preprocessor. The macro processor transforms a .mod
file
with macros into a .mod
file without macros (doing
expansions/inclusions), and then feeds it to the Dynare parser. The
key point to understand is that the macroprocessor only does text
substitution (like the C preprocessor or the PHP language). Note that
it is possible to see the output of the macroprocessor by using the
savemacro
option of the dynare
command (see Dynare invocation).
The macroprocessor is invoked by placing macro directives in the
.mod
file. Directives begin with an atsign followed by a pound
sign (@#
). They produce no output, but give instructions to the
macroprocessor. In most cases, directives occupy exactly one line of
text. In case of need, two backslashes (\\
) at the end of the line
indicate that the directive is continued on the next line. The main
directives are:
@#includepath
, paths to search for files that are to be included,@#include
, for file inclusion,@#define
, for defining a macroprocessor variable,@#if, @#ifdef, @#ifndef, @#else, @#endif
for conditional statements,@#for, @#endfor
for constructing loops.
The macroprocessor maintains its own list of variables (distinct of
model variables and of MATLAB/Octave variables). These macrovariables
are assigned using the @#define
directive, and can be of four
types: integer, character string, array of integers, array of strings.
4.23.1. Macro expressions¶
It is possible to construct macroexpressions which can be assigned to macrovariables or used within a macrodirective. The expressions are constructed using literals of the four basic types (integers, strings, arrays of strings, arrays of integers), macrovariables names and standard operators.
String literals have to be enclosed between double quotes (like
"name"
). Arrays are enclosed within brackets, and their elements
are separated by commas (like [1,2,3]
or ["US", "EA"]
).
Note that there is no boolean type: false is represented by integer zero and true is any nonnull integer. Further note that, as the macroprocessor cannot handle noninteger real numbers, integer division results in the quotient with the fractional part truncated (hence, \(5/3=3/3=1\)).
The following operators can be used on integers:
 Arithmetic operators:
+, , *, /
 Comparison operators:
<, >, <=, >=, ==, !=
 Logical operators:
&&, , !
 Integer ranges, using the following syntax:
INTEGER1:INTEGER2
(for example,1:4
is equivalent to integer array[1,2,3,4]
)
The following operators can be used on strings:
 Comparison operators:
==, !=
 Concatenation of two strings:
+
 Extraction of substrings: if
s
is a string, thens[3]
is a string containing only the third character ofs
, ands[4:6]
contains the characters from 4th to 6th
The following operators can be used on arrays:
 Dereferencing: if
v
is an array, thenv[2]
is its 2nd element. Concatenation of two arrays:
+
. Difference

: returns the first operand from which the elements of the second operand have been removed. Extraction of subarrays: e.g.
v[4:6]
. Testing membership of an array:
in
operator (for example:"b"
in["a", "b", "c"]
returns1
) Getting the length of an array:
length
operator (for example:length(["a", "b", "c"])
returns3
and, hence,1:length(["a", "b", "c"])
is equivalent to integer array[1,2,3]
)
Macroexpressions can be used at two places:
 Inside macro directives, directly;
 In the body of the
.mod
file, between an atsign and curly braces (like@{expr}
): the macro processor will substitute the expression with its value.
In the following, MACRO_EXPRESSION designates an expression constructed as explained above.
4.23.2. Macro directives¶

Macro directive:
@#includepath
"PATH"
¶ 
Macro directive:
@#includepath
MACRO_VARIABLE
This directive adds the colonseparated paths contained in PATH to the list of those to search when looking for a.mod
file specified by@#include
. Note that these paths are added after any paths passed usingI
.Example
@#includepath "/path/to/folder/containing/modfiles:/path/to/another/folder" @#includepath folders_containing_mod_files

Macro directive:
@#include
"FILENAME"
¶ 
Macro directive:
@#include
MACRO_VARIABLE
This directive simply includes the content of another file at the place where it is inserted. It is exactly equivalent to a copy/paste of the content of the included file. Note that it is possible to nest includes (i.e. to include a file from an included file). The file will be searched for in the current directory. If it is not found, the file will be searched for in the folders provided byI
and@#includepath
.Example
@#include "modelcomponent.mod" @#include location_of_modfile

Macro directive:
@#define
MACRO_VARIABLE = MACRO_EXPRESSION
¶
Defines a macrovariable.Example
@#define x = 5 // Integer @#define y = "US" // String @#define v = [ 1, 2, 4 ] // Integer array @#define w = [ "US", "EA" ] // String array @#define z = 3 + v[2] // Equals 5 @#define t = ("US" in w) // Equals 1 (true)
Example
@#define x = [ "B", "C" ] @#define i = 2 model; A = @{x[i]}; end;
The latter is strictly equivalent to:
model; A = C; end;

Macro directive:
@#if
MACRO_EXPRESSION
¶

Macro directive:
@#ifdef
MACRO_VARIABLE
¶

Macro directive:
@#ifndef
MACRO_VARIABLE
¶

Macro directive:
@#else
()¶

Macro directive:
@#endif
()¶
Conditional inclusion of some part of the.mod
file. The lines between@#if
,@#ifdef
or@#ifndef
and the next@#else
or@#endif
is executed only if the condition evaluates to a nonnull integer. The@#else
branch is optional and, if present, is only evaluated if the condition evaluates to0
.Example
Choose between two alternative monetary policy rules using a macrovariable:
@#define linear_mon_pol = 0 // or 1 ... model; @#if linear_mon_pol i = w*i(1) + (1w)*i_ss + w2*(piepiestar); @#else i = i(1)^w * i_ss^(1w) * (pie/piestar)^w2; @#endif ... end;
Example
Choose between two alternative monetary policy rules using a macrovariable. As
linear_mon_pol
was not previously defined in this example, the second equation will be chosen:model; @#ifdef linear_mon_pol i = w*i(1) + (1w)*i_ss + w2*(piepiestar); @#else i = i(1)^w * i_ss^(1w) * (pie/piestar)^w2; @#endif ... end;

Macro directive:
@#for
MACRO_VARIABLE in MACRO_EXPRESSION
¶

Macro directive:
@#endfor
()¶
Loop construction for replicating portions of the.mod
file. Note that this construct can enclose variable/parameters declaration, computational tasks, but not a model declaration.Example
model; @#for country in [ "home", "foreign" ] GDP_@{country} = A * K_@{country}^a * L_@{country}^(1a); @#endfor end;
The latter is equivalent to:
model; GDP_home = A * K_home^a * L_home^(1a); GDP_foreign = A * K_foreign^a * L_foreign^(1a); end;

Macro directive:
@#echo
MACRO_EXPRESSION
¶
Asks the preprocessor to display some message on standard output. The argument must evaluate to a string.

Macro directive:
@#error
MACRO_EXPRESSION
¶
Asks the preprocessor to display some error message on standard output and to abort. The argument must evaluate to a string.
4.23.3. Typical usages¶
4.23.3.1. Modularization¶
The @#include
directive can be used to split .mod
files into
several modular components.
Example setup:
modeldesc.mod
Contains variable declarations, model equations and shocks declarations.
simul.mod
Includesmodeldesc.mod
, calibrates parameters and runs stochastic simulations.
estim.mod
Includesmodeldesc.mod
, declares priors on parameters and runs Bayesian estimation.
Dynare can be called on simul.mod
and estim.mod
, but it makes
no sense to run it on modeldesc.mod
.
The main advantage is that it is no longer needed to manually copy/paste the whole model (at the beginning) or changes to the model (during development).
4.23.3.2. Indexed sums of products¶
The following example shows how to construct a moving average:
@#define window = 2
var x MA_x;
...
model;
...
MA_x = 1/@{2*window+1}*(
@#for i in window:window
+x(@{i})
@#endfor
);
...
end;
After macroprocessing, this is equivalent to:
var x MA_x;
...
model;
...
MA_x = 1/5*(
+x(2)
+x(1)
+x(0)
+x(1)
+x(2)
);
...
end;
4.23.3.3. Multicountry models¶
Here is a skeleton example for a multicountry model:
@#define countries = [ "US", "EA", "AS", "JP", "RC" ]
@#define nth_co = "US"
@#for co in countries
var Y_@{co} K_@{co} L_@{co} i_@{co} E_@{co} ...;
parameters a_@{co} ...;
varexo ...;
@#endfor
model;
@#for co in countries
Y_@{co} = K_@{co}^a_@{co} * L_@{co}^(1a_@{co});
...
@#if co != nth_co
(1+i_@{co}) = (1+i_@{nth_co}) * E_@{co}(+1) / E_@{co}; // UIP relation
@#else
E_@{co} = 1;
@#endif
@#endfor
end;
4.23.3.4. Endogeneizing parameters¶
When doing the steady state calibration of the model, it may be useful to consider a parameter as an endogenous (and viceversa).
For example, suppose production is defined by a CES function:
\[y = \left(\alpha^{1/\xi} \ell^{11/\xi}+(1\alpha)^{1/\xi}k^{11/\xi}\right)^{\xi/(\xi1)}\]
The labor share in GDP is defined as:
\[\textrm{lab\_rat} = (w \ell)/(p y)\]
In the model, \(\alpha\) is a (share) parameter, and lab_rat
is an endogenous variable.
It is clear that calibrating \(\alpha\) is not straightforward;
but on the contrary, we have real world data for lab_rat
, and it
is clear that these two variables are economically linked.
The solution is to use a method called variable flipping, which
consists in changing the way of computing the steady state. During
this computation, \(\alpha\) will be made an endogenous variable
and lab_rat
will be made a parameter. An economically relevant
value will be calibrated for lab_rat
, and the solution algorithm
will deduce the implied value for \(\alpha\).
An implementation could consist of the following files:
modeqs.mod
This file contains variable declarations and model equations. The code for the declaration of \(\alpha\) and
lab_rat
would look like:@#if steady var alpha; parameter lab_rat; @#else parameter alpha; var lab_rat; @#endif
steady.mod
This file computes the steady state. It begins with:
@#define steady = 1 @#include "modeqs.mod"Then it initializes parameters (including
lab_rat
, excluding \(\alpha\)), computes the steady state (using guess values for endogenous, including \(\alpha\)), then saves values of parameters and endogenous at steady state in a file, using thesave_params_and_steady_state
command.
simul.mod
This file computes the simulation. It begins with:
@#define steady = 0 @#include "modeqs.mod"Then it loads values of parameters and endogenous at steady state from file, using the
load_params_and_steady_state
command, and computes the simulations.
4.23.4. MATLAB/Octave loops versus macroprocessor loops¶
Suppose you have a model with a parameter \(\rho\), and you want to make simulations for three values: \(\rho = 0.8, 0.9, 1\). There are several ways of doing this:
With a MATLAB/Octave loop
rhos = [ 0.8, 0.9, 1]; for i = 1:length(rhos) rho = rhos(i); stoch_simul(order=1); endHere the loop is not unrolled, MATLAB/Octave manages the iterations. This is interesting when there are a lot of iterations.
With a macroprocessor loop (case 1)
rhos = [ 0.8, 0.9, 1]; @#for i in 1:3 rho = rhos(@{i}); stoch_simul(order=1); @#endforThis is very similar to the previous example, except that the loop is unrolled. The macroprocessor manages the loop index but not the data array (
rhos
).
With a macroprocessor loop (case 2)
@#for rho_val in [ "0.8", "0.9", "1"] rho = @{rho_val}; stoch_simul(order=1); @#endforThe advantage of this method is that it uses a shorter syntax, since list of values directly given in the loop construct. Note that values are given as character strings (the macroprocessor does not know floating point values). The inconvenience is that you can not reuse an array stored in a MATLAB/Octave variable.
4.24. Verbatim inclusion¶
Pass everything contained within the verbatim block to the
<mod_file>.m
file.

Block:
verbatim
;
¶
By default, whenever Dynare encounters code that is not understood by the parser, it is directly passed to the preprocessor output.In order to force this behavior you can use the
verbatim
block. This is useful when the code you want passed to the<mod_file>.m
file contains tokens recognized by the Dynare preprocessor.Example
verbatim; % Anything contained in this block will be passed % directly to the <modfile>.m file, including comments var = 1; end;
4.25. Misc commands¶

Command:
set_dynare_seed
(INTEGER)
¶ 
Command:
set_dynare_seed
(`default')

Command:
set_dynare_seed
(`clock')

Command:
set_dynare_seed
(`reset')

Command:
set_dynare_seed
(`ALGORITHM', INTEGER)
Sets the seed used for random number generation. It is possible to set a given integer value, to use a default value, or to use the clock (by using the latter, one will therefore get different results across different Dynare runs). Thereset
option serves to reset the seed to the value set by the lastset_dynare_seed
command. On MATLAB 7.8 or above, it is also possible to choose a specific algorithm for random number generation; accepted values aremcg16807
,mlfg6331_64
,mrg32k3a
,mt19937ar
(the default),shr3cong
andswb2712
.

Command:
save_params_and_steady_state
(FILENAME);
¶
For all parameters, endogenous and exogenous variables, stores their value in a text file, using a simple name/value associative table. for parameters, the value is taken from the last parameter initialization.
 for exogenous, the value is taken from the last
initval
block.  for endogenous, the value is taken from the last steady
state computation (or, if no steady state has been computed,
from the last
initval
block).
Note that no variable type is stored in the file, so that the values can be reloaded with
load_params_and_steady_state
in a setup where the variable types are different.The typical usage of this function is to compute the steadystate of a model by calibrating the steadystate value of some endogenous variables (which implies that some parameters must be endogeneized during the steadystate computation).
You would then write a first
.mod
file which computes the steady state and saves the result of the computation at the end of the file, usingsave_params_and_steady_state
.In a second file designed to perform the actual simulations, you would use
load_params_and_steady_state
just after your variable declarations, in order to load the steady state previously computed (including the parameters which had been endogeneized during the steady state computation).The need for two separate
.mod
files arises from the fact that the variable declarations differ between the files for steady state calibration and for simulation (the set of endogenous and parameters differ between the two); this leads to differentvar
andparameters
statements.Also note that you can take advantage of the
@#include
directive to share the model equations between the two files (see Macroprocessing language).

Command:
load_params_and_steady_state
(FILENAME);
¶
For all parameters, endogenous and exogenous variables, loads their value from a file created withsave_params_and_steady_state
. for parameters, their value will be initialized as if they
had been calibrated in the
.mod
file.  for endogenous and exogenous variables, their value will be
initialized as they would have been from an
initval
block .
This function is used in conjunction with
save_params_and_steady_state
; see the documentation of that function for more information. for parameters, their value will be initialized as if they
had been calibrated in the

MATLAB/Octave command:
dynare_version
;
¶
Output the version of Dynare that is currently being used (i.e. the one that is highest on the MATLAB/Octave path).

MATLAB/Octave command:
write_latex_definitions
;
¶
Writes the names, LaTeX names and long names of model variables to tables in a file named<<M_.fname>>_latex_definitions.tex
. Requires the following LaTeX packages:longtable
.

MATLAB/Octave command:
write_latex_parameter_table
;
¶
Writes the LaTeX names, parameter names, and long names of model parameters to a table in a file named<<M_.fname>>_latex_parameters.tex.
The command writes the values of the parameters currently stored. Thus, if parameters are set or changed in the steady state computation, the command should be called after a steadycommand to make sure the parameters were correctly updated. The long names can be used to add parameter descriptions. Requires the following LaTeX packages:longtable, booktabs
.

MATLAB/Octave command:
write_latex_prior_table
;
¶
Writes descriptive statistics about the prior distribution to a LaTeX table in a file named<<M_.fname>>_latex_priors_table.tex
. The command writes the prior definitions currently stored. Thus, this command must be invoked after theestimated_params
block. If priors are defined over the measurement errors, the command must also be preceeded by the declaration of the observed variables (withvarobs
). The command displays a warning if no prior densities are defined (ML estimation) or if the declaration of the observed variables is missing. Requires the following LaTeX packages:longtable, booktabs
.

MATLAB/Octave command:
collect_latex_files
;
¶
Writes a LaTeX file named<<M_.fname>>_TeX_binder.tex
that collects all TeX output generated by Dynare into a file. This file can be compiled usingpdflatex
and automatically tries to load all required packages. Requires the following LaTeX packages:breqn
,psfrag
,graphicx
,epstopdf
,longtable
,booktabs
,caption
,float,
amsmath
,amsfonts
, andmorefloats
.
Footnotes
[1]  Note that arbitrary MATLAB or Octave expressions can be put
in a .mod file, but those expressions have to be on
separate lines, generally at the end of the file for
postprocessing purposes. They are not interpreted by Dynare,
and are simply passed on unmodified to MATLAB or
Octave. Those constructions are not addresses in this
section. 
[2]  In particular, for big models, the compilation step can be very timeconsuming, and use of this option may be counterproductive in those cases. 
[3]  See option conf_sig to change the size of the HPD interval. 
[4]  See option conf_sig to change the size of the HPD interval. 
[5]  When the shocks are correlated, it is the decomposition of orthogonalized shocks via Cholesky decomposition according to the order of declaration of shocks (see Variable declarations) 
[6]  See forecast for more information. 
[7]  In case of Excel not being installed, https://mathworks.com/matlabcentral/fileexchange/38591xlwrite–generatexlsx–fileswithoutexcelonmaclinuxwin may be helpful. 
[8]  See option conf_sig to change the size of the HPD interval. 
[9]  See option conf_sig to change the size of the HPD interval. 
[10]  If you want to align the paper with the description herein, please note that \(A\) is \(A^0\) and \(F\) is \(A^+\). 
[11]  An example can be found at https://github.com/DynareTeam/dynare/blob/master/tests/msdsge/test_ms_dsge.mod. 