## SVAR estimation with zero long-run restrictions

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Nikolor
Posts: 3
Joined: Tue May 02, 2017 9:01 am

### SVAR estimation with zero long-run restrictions

Hello,

I am trying to estimate a bivariate SVAR with zero long-run restrictions a la Blanchard and Quah (1989), with GDP growth and inflation as endogenous variables. My goal is to extract the structural shocks from the estimated SVARs based on data from different countries and calculate the correlations of the structural shocks across countries. I distinguish between two types of shocks, aggregate demand shocks and aggregate supply shocks. The former are assumed to have zero long-run effect on GDP, and this is the restriciton I impose to identify the SVAR. I need 4 restrictions for identification since the SVAR is bivariate, meaning 4 unknowns in the short-run matrix S. The other 3 restrictions are standard, meaning that the variance of the structural shocks is equal to 1 and their covariance is equal to 0.

When I try to estimate the SVAR in Eviews I impose the following pattern on the long-run matrix F: F(1,1)=0 and the rest of the elements are free parameters. After that, I extract the structural shocks, the first one being the aggregate demand shock and the second the aggregate supply shock and then I compute the correlations with the shocks of other countries. Based on a paper, which results I am trying to replicate, these correlations are positive. However, in my estimations I find correlations of the same absolute value, but with a negative sign. I re-estimated the SVAR, but this time I imposed the following pattern on the long-run matrix F: F(1,2)=0 while the rest of the parameters are free. Then I extract the structural shocks in the opposite order this time, the first one being the supply shock and the second one being the demand shock. After this step the correlations have the correct sign.

Could you please explain to me why I get these differences in the results? To my view, moving the zero restriction on matrix F one place to the right, should not change the results, having in mind that the structural shocks will be in inverse order. The paper I am following imposes the zero restriction on the F(1,1) element.

Thank you in advance!

EViews Matt
EViews Developer
Posts: 312
Joined: Thu Apr 25, 2013 7:48 pm

### Re: SVAR estimation with zero long-run restrictions

Hello,

This sounds like a sign indeterminacy issue. The signs of the elements of the various result matrices (A, B, S, F) are not always uniquely defined by the supplied data and matrix restrictions. Consequently, the results provided by EViews can be just one possibility out of an entire family of solutions. In your particular case, with just a single zero restriction on an element of F, the columns of S/F are free to change sign. For your bivariate SVAR, this means that for whatever S results EViews reports, there are three additional solutions:

Code: Select all

`[ -S(1,1)  S(1,2) ]     [ S(1,1)  -S(1,2) ]     [ -S(1,1)  -S(1,2) ][ -S(2,1)  S(2,2) ]     [ S(2,1)  -S(2,2) ]     [ -S(2,1)  -S(2,2) ]`

The above is simply every possible combination of negating the columns of S. Changing the columns of S causes the shocks/impulse responses to change, but since it sounds like you observed a change of both signs, I suspect that it's the last solution above (all columns negated) that will correspond to the paper you're attempting to match.

Nikolor
Posts: 3
Joined: Tue May 02, 2017 9:01 am

### Re: SVAR estimation with zero long-run restrictions

Hello,

Thank you very much for your explanation. That helped me a lot! So, could it be that if I impose extra restrictions e.g. on matrices A or B, then the signs of the elements of the S matrix will be uniquely determined? But since my bivariate SVAR is exactly identified, if I impose extra restrictions then I will get overidentification I guess.

EViews Matt
EViews Developer
Posts: 312
Joined: Thu Apr 25, 2013 7:48 pm

### Re: SVAR estimation with zero long-run restrictions

In general, this sign issue is orthogonal to the SVAR identification issue. It's simply a mathematical consequence of the SVAR technique that it produces multiple solutions differing only in sign, none of which is mathematically "more correct" than any other. Sign-restricted SVARs are their own topic of research for this very reason. A perfectly identified model doesn't necessary lead to a sign-unique solution, and we can go into some of the mathematics if you'd like, but the short answer is that the signs are ultimately an assumption chosen by the user/researcher. Whether those assumptions are expressed pre-estimation in the form of restrictions or post-estimation by sign-adjusting the results matters little.

Nikolor
Posts: 3
Joined: Tue May 02, 2017 9:01 am

### Re: SVAR estimation with zero long-run restrictions

Thank you very much for your help. With your explanation I managed to make sense of my SVAR results and get reassurance that the diverging results were not a consequence of a wrong identification scheme. I am new to the SVAR literature, so I guess I will have some questions related to their estimation in the future, for which I will probably seek help again in this forum.

EViews Matt
EViews Developer
Posts: 312
Joined: Thu Apr 25, 2013 7:48 pm

Very good.