stoch_simul

stoch_simul
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stoch_simul — computes the solution and simulates the model

Synopsis

stoch_simul [(OPTION [, OPTION...])] [VARIABLE_NAME...] ;

Options

ar = INTEGER: Order of autocorrelation coefficients to compute and to print. Default: 5
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 λ = INTEGER before computing moments. Note that this option is currently not available when computing empirical moments (see periods option). 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
irf = INTEGER: Number of periods on which to compute the IRFs. Setting irf=0, suppresses the plotting of IRF's. Default: 40
relative_irf: Requests the computation of normalized IRFs in percentage of the standard error of each shock
linear: Indicates that the original model is linear (put it rather in the model command)
nocorr: Don't print the correlation matrix (printing them is the default)
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: Doesn't do the graphs. Useful for loops
noprint: Don't print anything. Useful for loops
print: Print results (opposite of the above)
order = INTEGER: Order of Taylor approximation. Acceptable values are 1, 2 and 3. Note that for third order, k_order_solver option is implied, and only empirical moments are available (you must provide a value for periods option). Default: 2
k_order_solver: Use a k-order solver, implemented in C++, instead of the default Dynare solver. When using this option, you must specify the use_dll option, and you need a working compilation environment, i.e. a working mex command (see Section 1, “Software requirements” for more details). 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 matrix oo_.endo_simul. The variables in the oo_.endo_simul matrix, in their order of declaration (as in M_.endo_names) Default: 0
qz_criterium = DOUBLE: Value used to split stable from unstable eigenvalues in reordering the Generalized Schur decomposition used for solving 1^st 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_seed = INTEGER: Specifies 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
simul_algo = INTEGER: Obsolete. Use only the default = 0
solve_algo = INTEGER: See there for the possible values and their meaning
aim_solver: Use the Anderson-Moore Algorithm (AIM) to compute the decision 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: See below
conditional_variance_decomposition = [INTEGER1:INTEGER2]: See below
conditional_variance_decomposition = [INTEGER1 INTEGER2 ...]: Computes a conditional variance decomposition for the specified period(s). Conditional variances are given by var(y_t+k|t). For period 1, the conditional variance decomposition provides the decomposition of the effects of shocks upon impact.

Description

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.

The Taylor approximation is computed around the steady state. If you know how to compute the steady state for your model, you can provide a MATLAB® function doing the computation instead of using the nonlinear solver. The function should be called with the name of the .mod file followed by _steadystate. See fs2000a_steadystate.m in examples/fs2000 directory.

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.

Variance decomposition, correlation, autocorrelation are only displayed for variables with 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 %.

Currently, the IRFs are only plotted 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.

When a list of VARIABLE_NAME is specified, results are displayed only for these variables.

Auxiliary variables for leads and lags

For a stochastic model, Dynare will perform a transformation of the model so that there is only one lead and one lag on endogenous, and no lead/lag on exogenous.

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_LEAG or AUX_EXO_LAG respectively).

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.

Decision rules

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 oberved at the beginning of the period.

First order approximation

y_t = ys + A yh_t-1 + B u_t
where ys is the steady state value of y and yh_t=y_t-ys.

Second order approximation

y_t = ys + 0.5Δ² + A yh_t-1 + B u_t + 0.5C(yh_t-1⊗yh_t-1) + 0.5D(u_t⊗u_t) + E(yh_t-1⊗u_t)
where ys is the steady state value of y, yh_t=y_t-ys, and Δ² is the shift effect of the variance of future shocks.

Output variables

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 global structure oo_.dr. Here is the correspondance with the symbols used in the above description of the decision rules:
Decision rule coefficients
- ys: oo_.dr.ys. The vector rows correspond to variables in the declaration order of the variable names.
- Δ²: oo_.dr.ghs2. The vector rows correspond to re-ordered variables (see below).
- A: oo_.dr.ghx. The matrix rows correspond to re-ordered variables (see below). The matrix columns correspond to state variables (see below).
- B: oo_.dr.ghu. The matrix rows correspond to re-ordered variables (see below). The matrix columns correspond to exogenous variables in declaration order.
- C: oo_.dr.ghxx. The matrix rows correspond to re-ordered variables (see below). The matrix columns correspond to the Kronecker product of the vector of state variables (see below).
- D: oo_.dr.ghuu. The matrix rows correspond to re-ordered variables (see below). The matrix columns correspond to the Kronecker product of exogenous variables in declaration order.
- E: oo_.dr.ghxu. The matrix rows correspond to re-ordered variables (see below). The matrix columns correspond to the Kronecker product of the vector of state variables (see below) by the vector of exogenous variables in declaration order.
When reordered, the variables are stored in the following order: static variables, purely predetermined variables (variables that appear only at the current and lagged periods in the model), variables that are both predetermined and forward-looking (variables that appear at the current, future and lagged periods in the model), purely forward-looking variables (variables that appear only at the current and future periods in the model). In each category, the variables are arranged in declaration order. Variable oo_.dr.order_var maps reordered variables to declaration order, and variable oo_.dr.inv_order_var contains the inverse map. In other words, the first row in transition matrices corresponds to the endogenous declared at position oo_.dr_order_var(1); conversely, first declared variable has row oo_.dr.inv_order_var(1) in transition matrices.
The state variables of the model are purely predetermined variables and variables that are both predetermined and forward-looking. They are ordered in that order. When there are lags on more than one period, the state variables are ordered first according to their lag: first variables from the previous period, then variables from two periods before and so on. Note also that when a variable appears in the model at a lag larger than one period, it is automatically included at all inferior lags.
The mean of the endogenous variables is available in the vector oo_.mean. The variables are arranged in declaration order.
The matrix of variance-covariance of the endogenous variables in the matrix oo_.var. The variables are arranged in declaration 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 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. They are also available in the oo_.endo_simul matrix. The series are arranged by row, in declaration order of the variable names
Impulse responses, when they have been computed, are available in oo_.irfs, with the following naming convention: VARIABLE_NAME_SHOCK_NAME.
(DEPRECATED) They are currently also available in MATLAB® vectors in the global workspace, however they will disappear there in a future version.
Example: oo_.irfs.gnp_ea contains the effect on gnp of a one standard deviation shock on ea.

Examples

Example 1

shocks;
var e;
stderr 0.0348;
end;

stoch_simul;

Performs the simulation of the 2^nd order approximation of a model with a single stochastic shock e, with a standard error of 0.0348.

Example 2

stoch_simul(linear,irf=60) y k;

Performs the simulation of a linear model and displays impulse response functions on 60 periods for variables y and k.

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