economics multi-part question and need support to help me learn.
short answer the all questions and post the screenshot&code.
Requirements: short answer
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:
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?
Eviews Handout B
This handout provides a brief introduction to estimating and identifying VAR models in Eviews. This handout is not meant to be a complete description of this topic. For a more detailed discussion see the appropriate sections in the Eviews manual, available under the Help tab within Eviews.
Estimating a Reduced-form VAR Model
Suppose that you have set up a Eviews workfile with the following variables: dlgdp and dlp (real GDP growth and inflation, respectively). Click on Quick => Estimate VAR, and a window will appear where you can enter the specifications of your VAR. First, enter the endogenous variables, as you wish to estimate them. In this case, you should type “dlgdp dlp”. Note that there is a space between the variable names. Next enter the range of lagged dependent variables to be estimated. For example, typing in “ 1 2” will estimate an 2-variable VAR. Finally, enter any exogenous variables that you want in your VAR. For example, you might want a constant and a time trend. Your screen should look something like this:
Once you hit OK, the VAR output will be produced. Here is what I obtained in this example:
1st half of output:
2nd half of output:
Note that the output gives you both the standard errors and the t-statistics for all estimated coefficients. However, given the large number of coefficients in the VAR model, we don’t usually pay attention to individual coefficients.
In addition, there are several summary statistics both for individual equations and for the system as a whole. Again, we are typically interested in how the system as a whole rather than focusing on individual equations. There are two summary elements that you will often find useful. First, the determinant of the variance-covariance matrix is useful is you want to construct a LR test, as discussed in the text. Second, the AIC and SBC can also be used to judge the model against other specifications.
The homework assignment asks you to look at the Granger causality tests. To see these results, click on View => Lag Structure => Granger Causality/Block Exogeneity Tests.
Now suppose we wish to place short-run or long-run restrictions on the VAR. This done by clicking on Proc => Estimate Structural Factorization. You will need to type your restrictions in the box at the bottom of the window that opens up. There are some cryptic instructions at the top of the window. Eviews uses @e1, @e2, etc to hold the VAR residuals. It uses @u1, @u2, etc. to hold the structural shocks. So, just enter the following, for example, if you wish to have a specification where shock #2 does not affect variable 1 contemporaneously:
@e1 = C(1)*@u1
@e2 = C(2)*@u1 + C(3)*@u2
You can also place long-run restrictions, as discussed in the text and in the lecture, by telling Eviews which shock should have no long-run effect on which variable. The following states that shock #1 will be restricted to have no long-run effect on variable 2:
@LR2(@u1) = 0
Once you have identified your structural model, you are ready to analyze its dynamics. You can produce impulse response functions by clicking on View => Impluse Response. Be sure to tell Eviews that you want impulse responses based on your structural identification under the “Impluse Definition” tab.
Clicking on View => Variance Decomposition produces tables or graphs of the variance decomposition. Again, make sure you tell Eviews that you want these based on your structural identification. The default, as above, is a Cholesky decomposition, based on the ordering of your variables.