Variance decomposition with BVAR model

[AhmedSahlool]

Dear Tom,

I hope that finds you well,

I’m implementing a full SVAR model of 8 variables identified with short and long run restrictions. I use Bayesian estimation with Litterman Independent Normal Wishart Prior. I use the @SURGibbsSetup procedure to estimate such a model:

I use the procedure @FEVDTABLE to get the FEVD's. However the resulting decomposition doesn't sum to 100. Is there a reason for that.

Thanks in advance for taking the time to answer.

Best,

Ahmed Sahloul

[TomDoan]

Dear Tom,

I hope that finds you well,

I’m implementing a full SVAR model of 8 variables identified with short and long run restrictions. I use Bayesian estimation with Litterman Independent Normal Wishart Prior. I use the @SURGibbsSetup procedure to estimate such a model:

I use the procedure @FEVDTABLE to get the FEVD's. However the resulting decomposition doesn't sum to 100. Is there a reason for that.

Thanks in advance for taking the time to answer.

Best,

Ahmed Sahloul

See http://www.estima.com/forum/viewtopic.php?f=4&t=1832

[AhmedSahlool]

Thank you for your quick reply,

I already saw this post, but I didn't understand the point of the median and your comment concerning the error bands, because my concern is about the FEVD's and not their error bands.

Would you kindly give me more clarifications.

Thank you again.

[TomDoan]

If A, B and C are random variables and A+B+C=100, then their means must add up to 100. However, their medians (which is what @MCFEVDTABLE computes) don't have to. @MCFEVDTABLE doesn't compute means and standard errors because those are misleading due to the highly asymmetrical nature of the components; in particular, the mean can be outside the 5-95% band of values. The fact that you don't want to compute the error bands doesn't change the fact that the mean is highly misleading.

[AhmedSahlool]

Thank you for the explanation,

and in this case, I take the results, make the sum, and compute the percentage of each variable? and the case of impulse response function, should I use the option: Center=Median?

On the other hand, would you kindly tell me how the error bands could determine the statistical significance of the impulse response function and the FEVD's?

Thank you for your help.

[TomDoan]

Thank you for the explanation,

and in this case, I take the results, make the sum, and compute the percentage of each variable? and the case of impulse response function, should I use the option: Center=Median?

You can use @MCGRAPHIRF for the impulse responses. Either median with error bands determined by percentiles, or mean with standard error bands are "standard". I prefer the former, but neither is wrong.

On the other hand, would you kindly tell me how the error bands could determine the statistical significance of the impulse response function and the FEVD's?

For the IRF's, it's whether the far band covers zero. You can't do statistical significance for FEVD's since 0 is the absolute lower bound and has zero probability of occurring.

[AhmedSahlool]

Dear Tom

sorry for bothering,

would you kindly help me of the following issue:

If in my BVAR (8 variables), I have two stationary variables; one around a trend and the second is the result of first difference "Inflation", should I search for cointegration among the rest of variables?

Thank you in advance.

[TomDoan]

Only to the extent that they affect your long-run restrictions. If two variables are cointegrated, you can't independently constrain them to have zero LR restrictions---if one is zero, so is the other.

[AhmedSahlool]

In my BVAR I include:

(US GDP, Oil Price, Terms of Trade, US short run interest rate, Foreign direct investment to GDP) identified with short run restrictions

(Domestic GDP, trade balance to GDP, and Inflation rate) identified with Long run restrictions,

The domestic GDP was found to be stationary around deterministic trend, and the inflation to be stationary.

So co-integration relationships will exist most probably among the variables identified with short run restrictions; the first block containing mostly foreign variables.

So should i also search for co-integration in this block? does their ignorance affect the Bayesian estimation?

Another question "sorry for asking many questions":

Do you have any comments on such a model, estimated in first difference, identified with short and long run restrictions, and with informative Minnesota independent normal wishart prior, using surgibbs procedure? and the small open economy "block exogeniety" is used for identification and is included only in the prior, so I have a full VAR.

Thank you very much in advance.

[TomDoan]

Why do you care about the long-run and short-run restrictions when you're trying to forecast? The forecasts depend only upon the lag coefficients, and those aren't affected by the "structural" part of the SVAR. It would be a very bad idea to estimate in first differences with a Minnesota prior.

[AhmedSahlool]

Yes, I agree with you, and I don't forecast with the structural model. The identification restrictions are used only when I need to get the IRF and FEVD.

My concern was about neglecting the cointegartion relationships in the foreign block identified with short-run restrictions. is this correct?

Why estimating in 1st difference will be a bad idea with a Minnesota prior?

I found that many papers estimate BVAR in level, with the argument that bayesian inference is not affected by the presence of unit roots. What do you think?

Other papers estimate the VAR in level, but introduce some variables in 1st difference, depending on the economic context, e.g. the gdp in 1st difference to get the business cycle, would this cause estimation problems?

Thank you very much

[TomDoan]

Why do you want to use a BVAR, rather than a VAR, for analyzing the shocks? Part of the problem is that you're confusing two completely different branches of the VAR literature. BVAR's are generally done in levels because there is no advantage to doing them in differences or mixed levels and differences---if any variables are cointegrated, a model in differences is misspecified, while the model is levels isn't, and if none of the variables are cointegrated, while the model in differences is OK, so is the model in levels. So there is no downside to using levels. On the other hand, for identifying shocks with long-run restrictions, you have to know which variables are cointegrated (generally, it's assumed that they aren't) because the long-run response matrix isn't full rank if any of the series are cointegrated, so you have to allow for that.

[AhmedSahlool]

Thank you for the explanation,

Thus, the application that I found mixing the variables in level and in first difference, was mainly due to the economic application studied and not due to technical econometric issues; studying the most important factors determining the economic growth.

http://www.imf.org/external/pubs/ft/wp/2008/wp0846.pdf

Thank again for your time.

[TomDoan]

I'm confused about how that paper relates to your questions. They've assumed away cointegration, and basically assumed away unit roots largely by choice of variables (the only two that are iffy are the interest rates). And they're only doing Cholesky factors rather than anything more complicated. In effect, they're taking a forecasting model and examining its IRF's.

[AhmedSahlool]

Thank you for reading the paper,

Just to explain the different questions that I ask, causing your confusion, let me explain to you what I want to do.

My application is a mix of different applications. I would like to determine the different sources of shocks for the Egyptian economic growth, so I'm estimating a BVAR that includes:

Foreign block (US GDP, Oil Price, Terms of Trade, US short run interest rate, Foreign direct investment to GDP) and domestic one (Domestic GDP, trade balance to GDP, and Inflation rate).

I use informative Minnesota independent normal wishart prior, using surgibbs procedure. The "block exogeniety" assumption is imposed via the prior, giving their coefficients a tight variance. So the model is a full VAR.

My first question was: should I estimate this model in level or in first difference. and your answer is that the BVAR's are generally done in levels because there is no advantage to doing them in differences or mixed levels and differences. And in this case the problem of cointegration is not relevant.

The paper that I give you the reference, carries out the same economic analysis as mine, even if it's more simple. They use a mix of variables in level and in 1st difference. That's why I wanted to know if this could cause any estimation problems. And I didn't find your answer to this "may be there is something that I didn't get".

I use the Gibbs sampler for estimation, and I asked you in another post, if I can use the resulting new model for forecasting and comparing its performance to a classic VAR and I try to do this now.

Then, in order to identify this model I use short and long restrictions. Short for the foreign bloc and long for the domestic one. I get the IRF and FEVD.

I see that in some applications, you use simulate, but I don't know what is the real difference between simulate and forecast. Would you kindly explain me the difference.

I hope that it's not confusing any more, and kindly tell me if you find any thing that is not logic, confusing or that would cause estimation errors.

Thank you very much.