Kilian and Lütkepohl (2017) SVAR Analysis

[TomDoan]

We are working on examples from Kilian and Lütkepohl(2017), "Structural Vector Autoregressive Analysis", Cambridge University Press. Note that some of the calculations will require some new features that are being added to RATS, so if you're interested you should get your RATS software up-to-date. (Current is 9.20d).

[TomDoan]

Here's chapter 11. (The first one that's completely done). That's Estimation Subject to Long-Run Restrictions (actually more specifically short- and long-run restrictions).

Note that they have some different approaches to doing some of the calculations, and often provide three or four different ways to estimate an SVAR.

[TomDoan]

This is Chapter 2 ("Vector Autoregressive Models"). These all work with a single three variable system (US GNP growth, Federal Funds rate and inflation).

klchap2.zip

Chapter 2 examples, data

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chap2_laglength.rpf shows several methods of choosing the lag length
chap2_ls.rpf does estimation by LS and restricted LS (the latter being a "near-VAR" estimated by iterated SUR).
chap2_biascorrect.rpf does a small-sample bias correction using closed form formulas
chap2_diagnostics.rpf does several diagnostics on the residuals from the least squares estimates. The text describes these (and other) tests but actually doesn't include any of the results of those.

Note on the diagnostics---we have a rather different attitude towards diagnostics than certain other software packages (which can routinely spit out large numbers of them). This is a good example for taking things more carefully. The diagnostics often have interactions in their assumptions. In particular, the @MVJB (multivariate Jarque-Bera test for normality) assumes the residuals are i.i.d. both under the null and the alternative. If they aren't, the whole test is invalid. In this case, the @MVQSTAT (serial correlation test) comes back OK, which is really, really important in a VAR. However, the @CVSTABTEST(stability test on the covariance matrix) and the @MVARCHTEST (heteroscedasticity test with an alternative of "ARCH"-like behavior) both strongly reject their nulls. If you look at the residuals from the GNP equation,

klresids.png (30.68 KiB) Viewed 150277 times

it's rather obvious that the residuals pre-1980 have a variance quite different from those post-1982, hence the rejection of the stability test and also the rejection of homoscedasticity on the "ARCH" test, which will also reject if large residuals "cluster". Note, however, that the VAR estimates are consistent even if the residuals are heteroscedastic, and they are consistent and have same asymptotic distribution if the residuals are homoscedastic but not Normal, so even if the two tests on the variance were OK (they aren't), the rejection of Normality really would create no serious issue in this case.

[IRJ]

Thank you Tom. Can I be a tad (maybe more than a tad) annoying and ask for nudging up the codes for "Chapter 13: Identification by Sign Restrictions". I am working on sign restrictions and it would be of tremendous help to have these codes.

[IRJ]

Would it be possible to have example code for the counterfactual analyses using historical decompositions provided in Figures 4.4 and 4.7 of Chapter 4 of Kilian and Lütkepohl (2017)?

[TomDoan]

Would it be possible to have example code for the counterfactual analyses using historical decompositions provided in Figures 4.4 and 4.7 of Chapter 4 of Kilian and Lütkepohl (2017)?

This does 4.4 (actually 4.2, 4.3 and 4.4 are all parts of the same analysis). Unfortunately, the structural VAR coefficients are input into it in the Matlab code provided. I assume the underlying SVAR must be discussed in the referenced paper. The details on many of the examples in the text are very limited---most of the textbook is a "greatest hits" collection of Kilian's papers, and provides Matlab code for the papers, not for the more limited analysis included in the text,

figure4_2.rpf

Figures 4.2, 4.3, 4.4

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kilianlee5000000.mat

Data file

(32.15 KiB) Downloaded 682 times

Figure 4.7 has no raw data---all that is provided are the values needed to create the graph.

[TomDoan]

Thank you Tom. Can I be a tad (maybe more than a tad) annoying and ask for nudging up the codes for "Chapter 13: Identification by Sign Restrictions". I am working on sign restrictions and it would be of tremendous help to have these codes.

Unfortunately, much of Chapter 13 is based upon an erroneous result (that you can rank order sign-restricted draws by posterior densities as described in Inoue and Kilian). The posterior densities are, in fact, flat---Inoue and Kilian were missing a term.