MSBVAR (version 0.9-2)

mc.irf: Monte Carlo Integration / Simulation of Impulse Response Functions

Description

Simulates a posterior of impulse response functions (IRF) by Monte Carlo integration. This can handle Bayesian and frequentist VARs and Bayesian (structural) VARs estimated with the szbvar, szbsvar or reduced.form.var functions. The decomposition of the contemporaneous innovations is handled by a Cholesky decomposition of the error covariance matrix in reduced form (B)VAR object, or for the contemporaneous structure in S-VAR models. Simulations of IRFs from the Bayesian model utilize the posterior estimates for that model.

Usage

mc.irf(varobj, nsteps, draws=1000, A0.posterior=NULL, sign.list=rep(1, ncol(varobj$Y)))

Arguments

varobj

VAR objects for a fitted VAR model from either reduced.form.var, szbvar or szbsvar.

nsteps

Number of periods over which to compute the impulse responses

draws

Number of draws for the simulation of the posterior distribution of the IRFs (if not a szbsvar object. For the MSBVAR model, this is the value of $N2$ from the MCMC sampling (default). You probably should use more than the default given here.

A0.posterior

Posterior sample objects generated by gibbs.A0() for B-SVAR models, based on the structural identification in varobj$ident.

sign.list

A list of signs (length = number of variables) for normalization given as either 1 or -1.

Value

VAR/BVAR:An mc.irf.VAR or mc.irf.BVAR class object object that is the array of impulse response samples for the Monte Carlo samples

impulse

$ draws X nsteps X (m*m)$ array of the impulse responses

B-SVAR: mc.irf.BSVAR object which is an $(N2, nsteps, m^2)$ array of the impulse responses for the associated B-SVAR model in varobj and the posterior $A(0)$.MS-BVAR mc.irf.MSBVAR object which is a list of two arrays. The first array are $(N2, nsteps, m^2, h)$ array of the short-run, regime specific impulse shock-response combinations. The second array are the regime averaged, long run responses based on the ergodic regime probabilities. This second list item is an array of dimensions $(N2, nsteps, m^2)$.

Details

VAR/BVAR:

Draws a set of posterior samples from the VAR coefficients and computes impulse responses for each sample. These samples can then be summarized to compute MCMC-based estimates of the responses using the error band methods described in Sims and Zha (1999).

B-SVAR: Generates a set of N2 draws from the impulse responses for the Bayesian SVAR model in varobj. The function takes as its arguments the posterior moments of the B-SVAR model in varobj, the draws of the contemporaneous structural coefficients $A(0)$ from gibbs.A0, and a list of signs for normalization. This function then computes a posterior sample of the impulse responses based on the Schur product of the sign list and the draws of $A(0)$ and draws from the normal posterior pdf for the other coefficients in the model.

The computations are done using compiled C++ code as of version 0.3.0. See the package source code for details about the implementation.

MSBVAR:

Computes a set of regime specific impulse responses. There will be $h$ of the $m x m$ responses, per the discussion above (shocks in columns, equations / responses in rows. The default is for these to be presented serially. Finally, a regime averaged set of responses, based on the ergodic probability of being in each regime is presented as the "long run" responses. At present this is experimental and open to changes.

References

Brandt, Patrick T. and John R. Freeman. 2006. "Advances in Bayesian Time Series Modeling and the Study of Politics: Theory Testing, Forecasting, and Policy Analysis" Political Analysis 14(1):1-36.

Sims, C.A. and Tao Zha. 1999. "Error Bands for Impulse Responses." Econometrica 67(5): 1113-1156.

Hamilton, James. 1994. Time Series Analysis. Chapter 11.

Waggoner, Daniel F. and Tao A. Zha. 2003. "A Gibbs sampler for structural vector autoregressions" Journal of Economic Dynamics \& Control. 28:349--366.

See Also

See also as plot.mc.irf for plotting methods and error band construction for the posterior of these impulse response functions, szbsvar for estimation of the posterior moments of the B-SVAR model, gibbs.A0 for drawing posterior samples of $A(0)$ for the B-SVAR model before the IRF computations, and msbvar and gibbs.msbvar for the specification and computation of the posterior for the MSBVAR models.

Examples

# Example 1
data(IsraelPalestineConflict)
varnames <- colnames(IsraelPalestineConflict)

fit.BVAR <- szbvar(Y=IsraelPalestineConflict, p=6, z=NULL,
                   lambda0=0.6, lambda1=0.1,
                   lambda3=2, lambda4=0.25, lambda5=0, mu5=0,
                   mu6=0, nu=3, qm=4,
                   prior=0, posterior.fit=FALSE)

# Draw from the posterior pdf of the impulse responses.
posterior.impulses <- mc.irf(fit.BVAR, nsteps=10, draws=5000)

# Plot the responses
plot(posterior.impulses, method=c("Sims-Zha2"), component=1,
                 probs=c(0.16,0.84), varnames=varnames)

# Example 2
ident <- diag(2)
varobj <- szbsvar(Y=IsraelPalestineConflict, p=6, z = NULL,
                  lambda=0.6, lambda1=0.1, lambda3=2, lambda4=0.25,
                  lambda5=0, mu5=0, mu6=0, ident, qm = 4)

A0.posterior <- gibbs.A0(varobj, N1=1000, N2=1000)

# Note you need to explcitly reference the sampled A0.posterior object
# in the following call for R to find it in the namespace!

impulse.sample <- mc.irf(varobj, nsteps=12, A0.posterior=A0.posterior)

plot(impulse.sample, varnames=colnames(IsraelPalestineConflict),
     probs=c(0.16,0.84))