Impulse Response Functions From VECMs

In the comments and discussion associated with an earlier post on "Testing for Granger Causality" an interesting question arose. If we're using a VAR model for constructing Impulse Response Functions, then typically we'll want to compute and display confidence bands to go with the IRFs, because the latter are  simply "point predictions". The theory for this is really easy, and in the case of EViews it's just a trivial selection to get asymptotically valid confidence bands.

But what about IRFs from a VECM - how do we get confidence bands in this case? This is not nearly so simple, because of the presence of the error-correction term(s) in the model. EViews doesn't supply confidence bands with the IRFs in the case of VECMs. What alternatives do we have?

In responding to a question from "Nick from the Netherlands" I drew attention to the paper by Benwitz et al. (2001), and I also mentioned Helmut Lütkepohl's free software, JMulTi. I'd not played with the latter previously, and when I read the "manual" I erroneously came to the conclusion that it provides confidence bands for IRFs only in the VAR case.

Not so! [Hat-Tip to "Paul" for drawing my attention to this.]

In fact, you can easily compute and plot bootstrapped confidence bands for IRFs generated by a VECM using JMulTi. Here's how.

• Downloading and installing the free JMulTi software takes just a couple of minutes.
• Fire up JMulTi :

(You won't see any data series names listed in the right panel)

• Select "File" / "Import Data", and choose a data-set:

• Select "Initial Analysis" and choose the series you want to analyze - the tabs are self-explanatory.

• Moving from the "Workbench" you can go through your tests for unit roots and your cointegration testing:

• I'm going to skip the rest of the basic testing and assume that we have found cointegration and we're ready to estimate a VECM. This is how we specify the model:

• Here's what we see when we select the "Estimate" tab:

• Now we select the "Structural Analysis" tab, then the "Specify IRA" tab, and choose our bootstrapped confidence intervals for the IRFs:

• After selecting the "Bootstrap Confidence Intervals" button (bottom right), we select the "Display Impulse Responses" tab, and select and highlight which IRFs we want. I've chosen to look at the response of P to a shock in GNP:

• The "Configure Plot" button enable us to "pretty up" the graphs that follow, and then we choose the "Display IR" button. We get the following numerical results (including the desired confidence intervals):

• And here's the corresponding plot (after I selected "View" / "Options" and got rid of the black background):

So, there we have it! The Blanchard-Quah data-set used in this illustration is provided with the JMulTi software, but I've also put it on the Data page that goes with this blog, in a .DAT file. Keep in  mind that getting the confidence interval for an IRF from a VAR model is no problem - here we were dealing with the case of a VECM.

Thanks again "Paul"!

Note: The link to the following reference will be helpful only if your computer's IP address gives you access to the electronic version of the publication in question. That's why a written References section is provided.

Reference

Benkwitz, A., H. Lütkepohl and J. Wolters (2001). Comparison of bootstrap confidence intervals for impulse responses of German monetary systems.  Macroeconomic Dynamics, 5, 81-100.

© 2011, David E. Giles