Dynare Reference Manual: 4.17 Sensitivity and identification analysis

4.17 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.

Sensitivity analysis results are saved locally in <mod_file>/GSA, where <mod_file>.mod is the name of the DYNARE model file.

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4.17.1 Sampling

The following binary files are produced:

<mod_file>_prior.mat: this file stores information about the analyses performed sampling from the prior ranges, i.e. pprior=1 and ppost=0;
<mod_file>_mc.mat: this file stores information about the analyses performed sampling from multivariate normal, i.e. pprior=0 and ppost=0;
<mod_file>_post.mat: this file stores information about analyses performed using the Metropolis posterior sample, i.e. ppost=1.

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4.17.2 Stability Mapping

Figure files produced are of the form <mod_file>_prior_*.fig and store results for stability mapping from prior Monte-Carlo samples:

<mod_file>_prior_stab_SA_*.fig: plots of the Smirnov test analyses confronting the cdf of the sample fulfilling Blanchard-Kahn conditions with the cdf of the rest of the sample;
<mod_file>_prior_stab_indet_SA_*.fig: plots of the Smirnov test analyses confronting the cdf of the sample producing indeterminacy with the cdf of the original prior sample;
<mod_file>_prior_stab_unst_SA_*.fig: plots of the Smirnov test analyses confronting the cdf of the sample producing unstable (explosive roots) behavior with the cdf of the original prior sample;
<mod_file>_prior_stable_corr_*.fig: plots of bivariate projections of the sample fulfilling Blanchard-Kahn conditions;
<mod_file>_prior_indeterm_corr_*.fig: plots of bivariate projections of the sample producing indeterminacy;
<mod_file>_prior_unstable_corr_*.fig: plots of bivariate projections of the sample producing instability;
<mod_file>_prior_unacceptable_corr_*.fig: plots of bivariate projections of the sample producing unacceptable solutions, 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).

Similar conventions apply for <mod_file>_mc_*.fig files, obtained when samples from multivariate normal are used.

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4.17.3 Reduced Form Mapping

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 out-of-sample validation. One can also load a previously estimated mapping with a new Monte-Carlo sample, to look at the forecast for the new Monte-Carlo 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); suffix log indicates the results for log-transformed 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); suffix log indicates the results for log-transformed 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_stab, where the detailed results of the estimation of the single functional relationships between parameters $\theta$ and reduced form coefficient 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.

Moreover, analyses for log-transformed entries are denoted with the following suffixes ( denotes the generic reduced form coefficient):

log: $y^* = \log(y)$ ;
minuslog: $y^* = \log(-y)$ ;
logsquared: $y^* = \log(y^2)$ for symmetric fat tails;
logskew: $y^* = \log(\vert y + \lambda\vert)$ for asymmetric fat tails.

The optimal type of transformation is automatically selected without the need of user intervention.

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4.17.4 RMSE

The RMSE analysis can be performed with different types of sampling options:

When pprior=1 and ppost=0, the toolbox analyzes the RMSEs for the Monte-Carlo 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 and ppost=0, the toolbox analyzes the RMSEs for a multivariate normal Monte-Carlo 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 Monte-Carlo sample, generated when doing RMSE analysis (pprior=1 and ppost=0);
<mode_file>_mc_*.mat: these files store the filtered and smoothed variables for the multivariate normal Monte-Carlo sample, generated when doing RMSE analysis (pprior=0 and ppost=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 Monte-Carlo samples;
<mod_file>_rmse_mc*.fig: save results for the analysis using multivariate normal Monte-Carlo 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_*.fig: for each parameter, plots the cdfs corresponding to the best 10% RMSEs of each observed series;
<mod_file>_rmse_prior_dens_*.fig: for each parameter, plots the pdfs corresponding to the best 10% RMESs of each observed series;
<mod_file>_rmse_prior_<name of observedseries>_corr_*.fig: for each observed series plots the bi-dimensional projections of samples with the best 10% RMSEs, when the correlation is significant;
<mod_file>_rmse_prior_lnlik*.fig: for each observed series, plots in red the cdf of the log-likelihood corresponding to the best 10% RMSEs, in green the cdf of the rest of the sample and in blue 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 red the cdf of the log-posterior corresponding to the best 10% RMSEs, in green the cdf of the rest of the sample and in blue 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 red the cdf of the log-prior corresponding to the best 10% RMSEs, in green the cdf of the rest of the sample and in blue the cdf of the full sample; this allows one to see idiosyncratic behavior;
<mod_file>_rmse_prior_lik_SA_*.fig: when lik_only=1, this shows the Smirnov tests for the filtering of the best 10% log-likelihood values;
<mod_file>_rmse_prior_post_SA_*.fig: when lik_only=1, this shows the Smirnov test for the filtering of the best 10% log-posterior values.

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4.17.5 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 Monte-Carlo 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.

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4.17.6 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 trigger 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.

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4.17.7 Performing Sensitivity and Identification Analysis

Command: dynare_sensitivity ;

Command: dynare_sensitivity (OPTIONS…);

Description

This command triggers sensitivity analysis on a DSGE model.

Options Sampling Options

nsam = INTEGER: Size of the Monte-Carlo sample. Default: 2048
ilptau = INTEGER: If equal to 1, use $LP_\tau$ quasi-Monte-Carlo. If equal to 0, use LHS Monte-Carlo. Default: 1
pprior = INTEGER: If equal to 1, sample from the prior distributions. If equal to 0, sample from the multivariate normal $N(\bar{\theta},\Sigma)$ , where $\bar{\theta}$ is the posterior mode and $\Sigma=H^{-1}$ , is the Hessian at the mode. Default: 1
prior_range = INTEGER: If equal to 1, sample uniformly from prior ranges. If equal to 0, sample from prior distributions. Default: 1
morris = INTEGER: If equal to 0, ANOVA mapping (Type I error) If equal to 1, Screening analysis (Type II error) If equal to 2, Analytic derivatives (similar to Type II error, only valid when identification=1).Default: 1 when identification=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 to 0, do not use Metropolis posterior sample. NB: This overrides any other sampling option. Default: 0
neighborhood_width = DOUBLE: When pprior=0 and ppost=0, allows for the sampling of parameters around the value specified in the mode_file, in the range xparam1 $\pm\left\vert@code{xparam1}\times@code{neighborhood_width}\right\vert$ . Default: 0

Stability Mapping Options

stab = INTEGER: If equal to 1, perform stability mapping. If equal to 0, do not perform stability mapping. Default: 1
load_stab = INTEGER: If equal to 1, load a previously created sample. If equal to 0, 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: 0.3
ksstat = DOUBLE: Critical value for Smirnov statistics : plot parameters with ksstat. Default: 0.1
pvalue_ks = DOUBLE: The threshold for significant Kolmogorov-Smirnov test (i.e. plot parameters with pvalue_ks). Default: 0.001
pvalue_corr = DOUBLE: The threshold for significant correlation in filtered samples (i.e. plot bivariate samples when pvalue_corr). Default: 0.001

Reduced Form Mapping Options

redform = INTEGER: If equal to 1, prepare Monte-Carlo sample of reduced form matrices. If equal to 0, do not prepare Monte-Carlo sample of reduced form matrices. Default: 0
load_redform = INTEGER: If equal to 1, load previously estimated mapping. If equal to 0, estimate the mapping of the reduced form model. Default: 0
logtrans_redform = INTEGER: If equal to 1, use log-transformed entries. If equal to 0, use raw entries. Default: 0
threshold_redform = [DOUBLE DOUBLE]: The range over which the filtered Monte-Carlo 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 when reduced form entries are filtered. Default: 0.1
alpha2_redform = DOUBLE: Critical value for correlations $\rho$ when reduced form entries are filtered. Default: 0.3
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 to 0, do not perform RMSE analysis. Default: 0
load_rmse = INTEGER: If equal to 1, load previous RMSE analysis. If equal to 0, make a new RMSE analysis. Default: 0
lik_only = INTEGER: If equal to 1, compute only likelihood and posterior. If equal to 0, 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 : plot parameters with alpha_rmse. Default: 0.002
alpha2_rmse = DOUBLE: Critical value for correlation $\rho$ : plot couples of parmaters with $\left\vert\rho\right\vert=$ alpha2_rmse. Default: 1.0
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 anlysis (forcing redform=0 and morris=1) If equal to 0, 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
lik_init = INTEGER: See lik_init.

Command: identification ;

Command: identification (OPTIONS…);

Description

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 to 0, 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 Monte-Carlo 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 to 1, triggers gsa prior sample. If equal to 2, triggers gsa Monte-Carlo sample (i.e. loads a sample corresponding to pprior=0 and ppost=0 in the dynare_sensitivity options). Default: 0
gsa_sample_file = FILENAME: Uses the provided path to a specific user defined sample file. Default: 0
parameter_set = calibration | prior_mode | prior_mean | posterior_mode | posterior_mean | posterior_median: Specify the parameter set to use. 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.

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