Copyright © 1996, 2004 Michel Juillard
Permission is granted to make and distribute verbatim copies of this manual provided the copyright notice and this permission notice are preserved on all copies.
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Table of Contents
Dynare is a pre-processor and a collection of GAUSS, MATLAB or SCILAB routines which solve non-linear models with forward looking variables. It is the result of research carried at CEPREMAP by several people (see Laffargue, 1990, Boucekkine, 1995, and Juillard, 1996, Collard and Juillard 2001a and 2001b). Although it can be put to other use, Dynare has been built in order to study the transitory dynamics of non-linear models with consistent expectations.
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, Dynare uses a Newton-type algorithm, first proposed by Laffargue (1990), instead of a first order technique like the one proposed by Fair and Taylor (1983), and used in earlier generation simulation programs. We believe this approach to be in general both faster and more robust. The details of the algorithm used in Dynare can be found in Juillard (1996).
In a stochastic context, Dynare computes one or several simulations corresponding to a random draw of the shocks. Starting with version 2.3 (not available for GAUSS), Dynare uses a second order Taylor approximation of the expectation functions (see Judd, 1996, Collard and Juillard, 2001a, 2001b, and Schmitt-Grohe and Uribe, 2002).
Table of Contents
In practice, the simulation process is done in two steps: in the first one, the model and the processing instructions written by the user in a @emph{model file} are interpreted and the proper GAUSS, MATLAB or SCILAB instructions are generated; in the second step, the program actually computes the simulation. Both steps are triggered by a single keyword: @command{dynare}.
This version of Dynare works only under Windows 95/98/NT/2000. For a Unix version, please, write me.
The Gauss version of Dynare has been written with Gauss version 3.2. It most likely doesn't work with previous versions.
The Matlab version has been written with Matlab 6.5.1.
The Scilab version has been tested with Scilab 2.7.
In case of update from a previous version, it is a good idea to copy the old version in a backup directory so as to be able to revert to it in case of problems. None of the previous files are usefull anymore, so you are strongly encouraged to remove them from directory c:\dynare.
Unpack the zip file in the directory c:\ (If you want to use another directory, see below). The Gauss version in automatically installed in c:\dynare\gauss, the Matlab version in c:\dynare\matlab and the Scilab version in c:\dynare\scilab.
If you had any previous version of Dynare, use the Gauss editor or any text editor to remove all references to it from the library file user.lcg.
After unpacking the archive, start the Gauss program and type the following:
library pgraph lib user c:\dynare\gauss\dynare.src lib user c:\dynare\gauss\dynare1.src lib user c:\dynare\gauss\dynare2.src lib user c:\dynare\gauss\dynare3.src
If you installed Dynare for Gauss in a directory different from c:\dynare\gauss, change the above instructions accordingly and edit the following line in dynare.src
declare string PARSER = "c:\\dynare\\gauss\\dynare_g ";
After unpacking the archive, start the Matlab program and use the menu File/Set path to add c:\dynare\matlab to the list of your paths.
If you installed Dynare for Matlab in a directory different from c:\dynare\matlab, change the above instructions accordingly and edit the following line in dynare.m
command = ['c:\dynare\matlab\dynare_m ' x];
In the top directory of your Scilab distribution (identified by the presence of the scilab.star file), create a file scilab.ini containing
load('c:/dynare/scilab/lib');
or add this lines to your scilab.ini file if it already exists. Alternatively, the line can be added to the file scilab.star, after similar statements. This second solution has the advantage of keeping access to Dynare even after the command clear.
If you installed Dynare for Scilab in a directory different from c:\dynare\scilab, change the above instructions accordingly and edit the following line in dynare.sci
command = 'c:\dynare\scilab\dynare_s '+fname;
Then, restart Scilab and run the command uplib().
Table of Contents
dynare — executes Dynare
dynare [ filename[.mod] ]
dynare executes instruction included in filename.mod. filename.mod is the name of the model file containing the model and the processing instructions.
In Gauss, dynare creates an intermediary file filename.gau with the instructions for the simulations. The Gauss version still accepts the former .mdl extension, but it is now deprecated.
In Matlab, dynare creates three intermediary files:
filename.m with the instructions for the simulations
filename_ff.m with the dynamic model equations
filename_fff.m with the long run static model equations
In Scilab, dynare creates three intermediary files:
filename.sci with the instructions for the simulations
filename_ff.sci with the dynamic model equations
filename_fff.sci with the long run static model equations
These files may be looked at to understand errors reported at the simulation stage.
periods —
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 option PERIODS in SIMUL and STOCH_SIMUL.
Set 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.
var —
var [ VARIABLE_NAME [,] VARIABLE_NAME [,] ... ]
This required command declares the endogenous variables in the model. The variable names must start with a letter and can't contain the following characters : ()+-*/^=!;:@@#. or accentuated characters.
In GAUSS, setting _longname = 1 allows the use of more than 8 characters in the variable names and makes a distinction between lower and upper case letters.
varexo —
varexo [ VARIABLE_NAME [,] VARIABLE_NAME [,] ... ]
parameters —
parameters [ PARAMETER_NAME [,] PARAMETER_NAME [,] ... ]
model —
model [ ; [(LINEAR)] EQUATION_LIST @b{end}; ]
The equations of the model are written in a block delimited by model; and end;.
There must be as many equations as there are endogenous variables in the model. The lead and lag of the variables are written in parenthesis immediately after the variable name. Leads or lags of more than one period are allowed. All the functions available in GAUSS, MATLAB or SCILAB, respectively, are recognized. Each equation must be terminated by a semicolon (;).
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.
The option LINEAR declares the model as being linear. It avoids to have to declare initial values for computing the steady state and it sets automatically ORDER=1 in STOCH_SIMUL.
model; c = - k + aa*x*k(-1)^alph + (1-delt)*k(-1); c^(-gam) = (aa*alph*x(+1)*k^(alph-1) + 1 - delt)*c(+1)^(-gam)/(1+bet); end;
Used in perfect foresight mode, the types of forward-loking 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, trigger a shock in first period, and study the trajectory of return at the initial equilbrium. To do that, one needs initval and shock(see next section).
Another one is to study, how an economy, starting from arbitrary initial conditions converges toward equilibrium. To do that, one needs initval and endval;
For models with lags on more than one period, the command histval permits to specify different historical initial values in different periods.
initval —
initval;
[INITIALIZATION_STATEMENT
[INITIALIZATION_STATEMENT]
...
]
end;
INITIALIZATION_STATEMENT : VARIABLE_NAME = EXPRESSION;
EXPRESSION is any valid expression returning a numerical value and can contain already initialized variable names.
The initval; ... end; block serves two purposes. It set the initial and, possibly, terminal conditions for the simulation and provides numerical initialization for various computation tasks (steady, simul, stoch_simul).
Theoreticaly, initial conditions are only necessary for lagged variables. However, as initval provides also numerical initialization, it is necessary to provide values for all variables in the model, except if the model is declared as linear.
For stochastic models, it isn't necessary to delcare 0 as initial values for exogneous stochastic variables as it is the only possible value.
When the initval block is followed by the command steady, it is not necessary to provide exact initialization values for the endogenous variables. steady will use the values provided in the initval block as initial guess in the non-linear equation solver and computes exact values for the endogenous variables at the steady state. The steady state is defined by keeping constant the value of the exogenous variables.
endval —
endval [INITIALIZATION_STATEMENT
[INITIALIZATION_STATEMENT]
...
]
end;
INITIALIZATION_STATEMENT : VARIABLE_NAME = EXPRESSION;
EXPRESSION is any valid expression returning a numerical value and can contain already initialized variable names.
The optional endval; ... end; block serves two purposes. It set the terminal conditions for the simulation with the LBJ alogrithm, when those differ from the initial conditions. When it is the case, the endval block also provides the numerical initialization for various computation tasks (steady, simul), starting in period 1.
Theoreticaly, terminal conditions are required in the LBJ algorithm only for forward variables. However, as endval provides also numerical initialization, it is necessary to provide values for all variables in the model.
When the endval block is followed by the command steady, it is not necessary to provide exact values for the endogenous variables. steady will use the values provided in the endval block as initial guess in the non-linear equation solver and computes exact values for the endogenous variables at the steady state. The steady state is defined by keeping constant the value of the exogenous variables.
histval —
histval [INITIALIZATION_STATEMENT
[INITIALIZATION_STATEMENT]
...
]
end;
INITIALIZATION_STATEMENT : VARIABLE_NAME (integer) = EXPRESSION;
EXPRESSION is any valid expression returning a numerical value and can contain already initialized variable names.
In models with lags on more than one period, the optional histval; ... end; block permits to specify different historical initial values for different periods.
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.
If your lagged variables are linked by identities, be careful to satisfy these identities when you set historical initial values.
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 non-zero elements of the matrix of variance-covariance of the shocks can be entered with the shocks command. Or, the entire matrix can be direclty entered with Sigma_e. Note that, starting with version 2.5.2, the direct specification of the @b{internal} matrix Sigma_e_, prone to errors, is discouraged.
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.
shocks —
shocks [SHOCK STATEMENT
[SHOCK STATEMENT]
...
]
end;
SHOCK STATEMENT: var VARIABLE NAME; periods PERIOD STATEMENT; values} VALUE STATEMENT;
PERIOD STATEMENT: NUMBER[:NUMBER] or LIST OF NUMBERS VALUE STATEMENT: EXPRESSION
The VALUE STATEMENT must be a valid expression returning a scalar value or a vector when the shock applies to a range of periods and takes a different values in each of these periods.
For deterministic simulations, the shocks block specifies temporary changes in the value of an exogenous variables. For permanent shocks, use an endval block.
SHOCK STATEMENT:
@b{var} VARIABLE NAME[,VARIABLE NAME] = expression ;
For stochastic simulations (available only in the MATLAB or SCILAB versions), the shocks block specifies the non zero elements of the covariance matrix of the shocks.
Sigma_e —
Sigma_e [ [ MATRIX ELEMENT [,] MATRIX ELEMENT [,] ... ; MATRIX ELEMENT ... ]; ]
MATRIX ELEMENT = (expression) or NUMBER
The matrix of variance-covariance of the shocks can be directly specified as a upper (or lower) triangular matrix. Dynare builds the corresponding symmetrix matrix. Each row of the triangular matrix, except the last one, must be terminated by a semi-colon ';'. For a given element, an expression using predefined parameters is allowed but must be placed between parentheses. THE ORDER OF THE COVARIANCES IN THE MATRIX IS THE SAME AS THE ONE USED IN THE VAREXO DECLARATION.
In previous versions, it was possible to directly set Dynare's internal covariance matrix Sigma_e_. This is still possible for compatibility with older .mod files, but STRONGLY DISCOURAGED as too prone to error. When setting Sigma_e_ directly, the order of the exogenous shocks is the ALPHABETICAL order of their names.
DYNARE has special commands for the computation of the static equilibrium of the model (steady, of the eigenvalues of the linearized model (check) for dynamics local analysis, of a deterministic simulation (simul) and for stochastic simulations (stoch_simul).
steady —
steady [ (OPTIONS) ] ;
SOLVE_ALGO = Integer
0: uses MATLAB Optimization Toolbox FSOLVE (default if Optimization Toolbox version >= 6.5 is available)
1: uses DYNARE's own nonlinear equation solver (default otherwise)
2: splits the model into recursive blocks and solves each block in turn. Maybe useful for large models with bad guess values for the steady state (Thanks to Manfred Gilli for showing me Matlab's function DMPERM).
Computes the equilibrium value of the endogenous variables for the value of the exogenous variables specified in the previous initval or endval block.
steady uses an iterative procedure and takes as initial guess the value of the endogenous variables set in the previous initval or endval 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.
check —
check ;
Computes the eigenvalues of the model linearized around the values specified by the last initval, endval or steady statement. Generally, the eigenvalues are only meaningfull 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.
simul —
simul [ (OPTIONS) ] ;
stoch_simul —
stoch_simul [(OPTIONS)] [LIST OF VARIABLES] ;
AR = Integer Order of autocorrelation coefficients to compute and to print (default = 5)
DR_ALGO = [0,1] Specify the algorithm used for computing the quadratic approximation of the decision rules: @table @asis
0: uses a ``pure'' perturbation approach as in Schmitt-Grohe and Uribe (2002) (default)
1: moves the point around which the Taylor expansion is computed toward the means of the distribution as in Collard and Juillard (2001) @end table
DROP = Integer Number of points dropped at the beginning of simulation before computing the summary statistics (default = 100)
HP_FILTER = Integer Uses HP filter with lambda = Integer before computing moments (default: no filter)
HP_NGRID = Integer Number of points in the grid for the discreet Inverse Fast Fourier Transform used in the HP filter computation. It may be necessary to increase it for highly autocorrelated processes (default = 512)
IRF = Integer Number of periods on which to compute the IRFs (default = 40)
LINEAR Indicates that the original model is linear (put it rather in the MODEL command).
NOCORR Doesn't print the correlation matrix (default = PRINT)
NOFUNCTIONS Doesn't print the coefficients of the approximated solution
NOMOMENTS Doesn't print moments of the endogenous variables
PERIODS = Integer Specify the number of periods to use in simulations. At order=1, no simulation is necessary to compute theoretical moments and IRFs. A number of PERIODS larger than one triggers automatically SIMUL=1 (default = 0).
ORDER = [1,2] Order of Taylor approximation (default = 2)
QZ_CRITERIUM = Double or Integer Value used to split stable from unstable eigenvalues in reordering the Generalized Schur decomposition used for solving 1st order problems (default 1.000001)
REPLIC = Integer Number of simulated series used to compute the IRFs (default = 1, if order = 1, and 50 otherwise)
SIMUL Computes a stochastic simulation of the model for the number of periods specified in the PERIODS statement. Uses INITVAL values, possibly recomputed by STEADY, as initial values for the simulation. The simulated endogenous variables are made available to the user in a vector for each variable and in the global matrix y_. The variables are ordered alphabeticaly in the y_ matrix (default: no simulation)
SIMUL_SEED = Integer Specify a seed for the random generator so as to obtain the same random sample at each run of the program. Otherwise a different sample is used for each run (default: seed not specified).
all STEADY options (see STEADY)
When a LIST OF VARIABLES is specified, results are displayed only for these variables.
stoch_simul computes a Taylor approximation of the decision and transition functions for the model, 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 the varexo command.
Variance decomposition, correlation, autocorrelation are only displayed for variables with positive variance. Impulse response functions are only ploted for variables with response larger than 1e-10.
Currently, the IRF's are only ploted for 12 variables. Select the ones you want to see, if your model contains more than 12 endogenous variables.
Currently, the HP filter is only available when computing theoretical moments, not for for moments of simulated variables.
The covariance matrix of the shocks is specified either with the shocks command or with the Sigma_e command.
stoch_simul sets several fields in global variable oo_. The descriptive statistics are theoretical moments when no simulation is requested and otherwise represent the moments of the simulated variables.
the coefficients of the decision rules are stored in oo_.dr. The variables are stored row by row in the following order: static variables, purely predetermined variables, variables that are both predetermined and forward-looking, purely forward-looking variables. In each category the variables are arraanged alphabetically. The coefficients on the state variables are arranged in columns by increasing order of lags and alphabetically inside each lag.
The mean of the endogenous variables is available in the vector oo_.mean. The variables are arranged in alphabetical order.
The matrix of variance-covariance of the endogenous variables in the matrix oo_.var. The variables are arranged in alphabetical order.
The matrix of autocorrelation of the endogenous variables are made available in cell array oo_.autocorr. The element number of the matrix in the cell array corresponds to the order of autocorrelation. The option AR (default ar=5) specifies the number of autocorrelation matrices available.
Simulated variables, when they have been computed, are available in Matlab vectors with the same name as the endogenous variables.
Impulse responses, when they have been computed, are available in Matlab vectors witht the following naming convention variable name_shock name.
gnp_ea contains the effect on gnp of a one standard deviation shock on ea.
Provided that you have observations on some endogenous variables, it is possible to use Dynare to estimate some or all parameters. Both maximum likelihood and Bayesian techniques are available.
varobs — lists the observed variables
varobs variable name ...
varobs lists the name of observed endogenous variables for the estimation procedure. These variables must be available in the data file.
The estimated parameters are available in global variables with the same name.
The smooth estimates for the state variables are available in oo_.variable name_smooth.
The smooth estimates for the shocks are available in oo_.variable name_smooth.
The smooth estimates for the measurement errors, if applicable, are available in oo_.variable name_obs_err_smooth.
observation_trends — specifies linear trends for observed variables
observation_trends;
variable name
(trend expression)
{
end;
}
estimated_params — specifies the estimated parameters and their prior
Syntax I (maximum likelihood estimation)
estimated_params;
[
stderr
] {
parameter name
} [
, init_val
] [
, lower bound
] [
, upper_bound
] ;
...
end;
Syntax II (Bayesian estimation)
estimated_params;
[
stderr
] {
parameter name
} [
, prior shape
] [
, prior mean
] [
, prior standard deviation
] [
, prior 3rd parameter
] [
, prior 4th parameter
] [
, scale parameter
] ;
...
end;
The estimated_params;....end; block lists all parameter to be estimated and specifies bounds and priors when required.
Each line corresponds to an estimated parameter and follows this syntax:
STDERR is a keyword indicating that the standard error of the shock name or of the observation error associated with observed variable name is to be estimated
parameter name is a string containing the name of a parameter, exogenous shock or endogenous variable
prior shape is prior density among BETA_PDF, GAMMA_PDF, NORMAL_PDF, INV_GAMMA_PDF, INV_GAMMA1_PDF, INV_GAMMA2_PDF, UNIFORM_PDF
prior mean is the mean of the prior
prior standard deviation is the second parameter of the prior (the standard deviation, expect for the inverse gamma)
prior 3rd parameter is a third parameter of the prior used for generalized BETA (default 0)
prior 4th parameter is a fourth parameter of the prior used for generalized BETA (default 1)
scale parameter is the scale parameter to be used for the jump distribution of the Metropolis-Hasting algorithm
at minimum, one must specify the name of the parameter and an initial guess. That will trigger unconstrained maximum likelihood estimation
as one uses options more towards the end of the list, all previous options must be filled: if you want to do Bayesian estimation, you must set a lower and upper bound for optimization; if you want to specify jscale, you must specify prior_p3 and prior_p4. Use default values, if these parameters don't apply. (This will be improved in a next version).
estimated_params_init — specifies the estimated parameters and their prior
estimated_params_init;
{
parameter name
} {
, init val
}
...
end;
The estimated_params_init;....end; block declares numerical initial values for the optimizer when these ones are different from the prior mean
Each line corresponds to an estimated parameter and follows this syntax:
STDERR is a keyword indicating that the standard error of the shock name or of the observation error associated with observed variable name is to be estimated
parameter name is a string containing the name of a parameter, exogenous shock or endogenous variable
initial value is a number specifying a guess value for the estimated parameter
estimated_params_bounds — specifies lower and upper bounds for the estimated parameters
estimated_params_bounds;
[
stderr
] {
parameter name
} [
, lower bound
] [
, upper bound
] ;
....
end;
The estimated_params;....end; block lists all parameter to be estimated and specifies bounds and priors when required.
Each line corresponds to an estimated parameter and follows this syntax:
STDERR is a keyword indicating that the standard error of the shock name or of the observation error associated with observed variable name is to be estimated
parameter name is a string containing the name of a parameter, exogenous shock or endogenous variable
lower bound is a number used as lower bound to help the optimization procedure
upper bound is a number used as upper bound to help the optimization procedure (all estimation results reported at the bound should be looked at with suspicion as we don't intend to do constrained optimization)
estimation — computes estimation.
estimation
[(OPTIONS)]
;
datafile = string: the datafile (a .m file or a .mat file)
nobs = integer: the number of observations to be used (default: all observations in the file)
first_obs = integer: the number of the first observation to be used (default = 1)
prefilter = 1: the estimation procedure demeans the data (alternatives not yet implemented)
presample = integer: the number of observations to be skipped before evaluating the likelihood (default = 1)
loglinear: computes a log--linear approximation of the model instead of a linear (default) approximation. The data must correspond to the definition of the variables used in the modelx.
nograph: no graphs should be plotted
lik_init: integer: type of initialization of Kalman filter.
1 (default): 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.
conf_sig = number: the level for the confidence intervals reported in the results (default = 0.90)
mh_replic = integer: number of replication for Metropolis Hasting algorithm. For the time being, mh_replic should be larger than 1200 (default = 20000.)
mh_nblocks = integer: number of paralletl chains for Metropolis Hasting algorithm (default = 2).
mh_drop = floating point: the fraction of initially generated parameter vectors to be dropped before using posterior simulations (default = 0.5)
mh_jscale = floating point: the scale to be used for the jumping distribution in MH algorithm. The default value is rarely satisfactory. This option must be tune to obtain, ideally, an accpetation rate of 25% in the Metropolis-Hastings algorithm (default = 0.2).
mh_init_scale=number: the scale to be used for drawing the initial value of the Metropolis-Hastings chain (default=2*mh_scale).
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) in a file called <model name>_mode.
mode_compute=integer: specifies the optimizer for the mode computation.
0: the mode isn't computed. mode_file must be specified
1: uses Matlab fmincon.
2: uses Matlab Lester Ingber's Adaptive Simulated Annealing.
3: uses Matlab fminunc.
4 (default): uses Chris Sim's csminwel.
mode_check: when mode_check is set, Dynare plots the posterior density for values around the computed mode for each estimated parameter in turn. This is helpful to diagnose problems with the optimizer.
prior_trunc=number: probability of extreme values of the prior density that is ignored when computing bounds for the parameters (default=1e-32).
load_mh_file: when load_mh is declared, Dynare adds to previous Metropolis-Hastings simulations instead of starting from scratch.
optim=(fmincon options): can be used to set options for fmincon, the optimizing function of Matlab Optimizaiton toolbox. Use Matlab syntax for these options
(default: ('display','iter','LargeScale','off','MaxFunEvals',100000,'TolFun',1e-8,'TolX',1e-6))
nodiagnostic: doesn't compute the convergence diagnostics for Metropolis (default: diagnostics are computed and displayed).
If no jscale parameter is used in estimated_params, the procedure uses "mh_jscale" for all parameters. If "mh_jscale" option isn't set, the procedure uses 0.2 for all parameters.
results from posterior optimization (also for maximum likelihood)
marginal log density
mean and shortest confidence interval from posterior simulation
Metropolis-Hastings convergence graphs that still need to be documented
graphs with prior, posterior and mode
graphs of smoothed shocks, smoothed observation errors, smoothed and historical variables
Fabrice Collard (GREMAQ, University of Toulouse) has written a guide to stochastic simulations with DYNARE entitled "Dynare in Practice" which is in guide.pdf.
1995. “An alternative methodology for solving nonlinear forward-looking models”. 711-734. Journal of Economic Dynamics and Control.
2001. “Accuracy of stochastic perturbation methods: The case of asset pricing models”. 979-999. Journal of Economic Dynamics and Control.
2004. “Comparing Dynamic Equilibrium Economies to Data: A Bayesian Approach”. 153-187. Journal of Econometrics.
2001. “A Higher-Order Taylor Expansion Approach to Simulation of Stochastic Forward-Looking Models with an Application to a Non-Linear Phillips Curve”. 125-139. Computational Economics.
1983. “Solution and Maximum Likelihood Estimation of Dynamic Nonlinear Rational Expectation Models”. 1169-1185. Econometrica.
1996. “Approximation, Perturbation, and Projection Methods in Economic Analysis”. 511-585. Handbook of Computational Economics. 1996. North Holland Press.
“A Method for Taking Models to the Data”. 2004. 1205-26. Journal of Economic Dynamics and Control.
1996. DYNARE: A program for the resolution and simulation of dynamic models with forward variables through the use of a relaxation algorithm. CEPREMAP. Couverture Orange.
“Résolution d'un modèle macroéconomique avec anticipations rationnelles”. 1990. 97-119. Annales d'Economie et Statistique.
2003. Do Central Banks Target Exchange Rates? A Structural Investigation. University of Pennsylvania.
2002. Comparing New Keynesian Models of the Business Cycle: A Bayesian Approach.
2000. 645-70. “Loss Function-based evaluation of DSGE models”. Journal of Applied Econometrics.
2002. Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function. Rutgers Univsersity.
2002. An Estimated Stochastic Dynamic General Equilibrium Model of the Euro Area. European Central Bank. ECB Working Paper.