VAR Model Estimation and Granger Causality Tests

ASU VAR Model Estimation and Granger Causality Tests Questions

Macro-Econometrics

 Homework Assignment #8 (150 points)

The data set VAR Model Data.XLS contains quarterly data for real U.S. from 1967:Q1 to 2010:Q3. The data are:

1) Real GDP (RGDP)

2) GDP Deflator (PGDP)

3) Price of raw materials (PRAW)

4) Federal funds rate (FFR)

Construct the following three variables:

lrgdpt = ln(RGDPt)

lpgdpt = ln(PGDPt)

lprawt = ln(PRAWt)

where ln is the natural log.

(a). Estimate a four-variable VAR model using lrgdp, lpdp, lpraw, and ffr. Estimate the model from 1969:Q1 through 2010:Q2. Specify this version of the model with 8 lags of each variable. Include a constant, but do not include any seasonal dummy variables. You do not need to report the coefficients. Report the multivariate AIC and SBC for this model.

b). Estimate a second four-variable VAR model using 4 lags of each variable. Be sure to estimate the VAR model so that it has the same sample period as the model in part a. Report the multivariate AIC and SBC for this model. Which model is selected by the two criteria? Do they pick the same model?

(c). Conduct Granger causality tests for the 4-lag VAR model. Using your results and a 5% significance level, fill in the following table: Null Hypothesis P-value for Test Reject or Not Reject Null? LPGDP does not cause LRGPD LPRAW does not cause LPGDP FFR does not cause LPRAW LRGDP does not cause FFR Generally speaking what do the Granger causality tests mean from a forecasting point of view?

(d). Use the 4-variable VAR to identify 4 sets of structural shocks (#1, #2, #3, and #4). Set up the VAR with the following factorization:

(a) lrgdp does not respond contemporaneously to shock #2 and #3 and #4.

(b) lpgdp does not respond contemporaneously to shock #3 and #4.

(c) lpraw does not respond contemporaneously to shock #4.

Another way to describe the factorization is:

(a) lrgdp responds contemporaneously only to shock #1.

 (b) lpgdp responds contemporaneously only to shock #1 and #2.

(c) lpraw responds contemporaneously only to shock #1 and #2 and #3.

(d) ffr responds contemporaneously to all shocks.

Briefly describe how shock #1 affects each of the four model variables in the short-run and in the long-run. Similarly, how does shock #4 affect all model variables?

(e). What economic meaning can you assign to each of the shocks?

 (Based on economic theory, it seems reasonable to think in terms of: aggregate supply shocks, aggregate demand shocks, monetary policy shocks, and raw materials shocks.) Are there any anomalies that lead you to question the structural specification?