what test should be used to pick the best VAR model?

[chenlili8315]

When I use the sims-Bernanke Decompostion, I used 5 diferent economic model to impose different restrictions on G. In other words, I have 5 G forms, I want to see which one out of the 5 economic model is the best of all. What kind of test should be used ? And can RATS do this kind of test?

Thanks.

Lili

[TomDoan]

Presumably, you have a non-nested set of models. If you have to pick one, using SBC would probably be the best choice, though the difference in parameter count is likely to be small enough that it won't make that much of a difference which information criterion you use. However, if there's a close call, you probably want to report both (or as many as seem to fit well). Remember that this is not like picking an ARMA model or lag length in a VAR where all the competing models are trying to do the same thing (exhaust the serial correlation); different SVAR's have different economic interpretations.

[chenlili8315]

Hi, all:
I tried to used SBC to pick the best VAR model, but I found out that it seems does not work. SBC is the same for two different models with different G-form.Could anyone help me please?
1st Model:

nonlin a b
dec frml[rect] g_form
frml g_form =||27.2689,0,0,0,0,0|-0.00903, 0.05923,0,0,0,0|-0.0031, 0.01151, 0.22978,0,0,0|-0.17761,0.00202,-0.0113,b/(a+b),a/(a+b),a/(a+b)|2.91115,-0.00235,-0.02338,0,1,0|-3.45771,0.01444,0.0613,1/(a+b),-1/(a+b),-1/(a+b)||

com a=0.2,b=0.3
cvmodel(factor=g) %sigma g_form

Covariance Model-Concentrated Likelihood - Estimation by BFGS
Convergence in 29 Iterations. Final criterion was 0.0000034 <= 0.0000100
Observations 115
Log Likelihood -1714.48641620
Log Likelihood Unrestricted -156.81323093
Chi-Squared(13) 3115.34637054
Significance Level 0.00000000

Variable Coeff Std Error T-Stat Signif
*******************************************************************************
1. A -0.000018322 0.000117240 -0.15628 0.87581331
2. B 0.000165403 0.000668353 0.24748 0.80453745


compute aic=%nobs*%logdet+2*(79*6)
compute sbc=%nobs*%logdet+79*6*log(%nobs)
dis 'aic=' aic 'sbc= ' sbc
aic= -6.50871 sbc= 1294.58911

2nd MODEL:

nonlin g12 g32
dec frml[rect] g_form
frml g_form =||27.2689,0,0,0,0,0|-0.00903, 0.05923,0,0,0,0|-0.0031, 0.01151, 0.22978,0,0,0|-0.17761,0.00202,-0.0113,1,g12,0|2.91115,-0.00235,-0.02338,1,1,-1|-3.45771,0.01444,0.0613,0,g32,0||
com g12=-0.2,g32=0.3
cvmodel(factor=g) %sigma g_form

Covariance Model-Concentrated Likelihood - Estimation by BFGS
Convergence in 23 Iterations. Final criterion was 0.0000010 <= 0.0000100
Observations 115
Log Likelihood -1680.06198225
Log Likelihood Unrestricted -156.81323093
Chi-Squared(13) 3046.49750265
Significance Level 0.00000000

Variable Coeff Std Error T-Stat Signif
*******************************************************************************
1. G12 1.83304061 0.90927698 2.01593 0.04380708
2. G32 883.07900451 360.04987003 2.45266 0.01418053

estimate(noprint, residuals=resids13)
compute aic=%nobs*%logdet+2*(79*6)
compute sbc=%nobs*%logdet+79*6*log(%nobs)
dis 'aic=' aic 'sbc= ' sbc
aic= -6.50871 sbc= 1294.58911

Thanks!

[TomDoan]

1. You should be using %LOGL rather than %nobs*%logdet. %LOGDET is computed by the original ESTIMATE of the VAR, and so isn't affected by the CVMODEL.
2. Both of those models fit really badly. I don't know where all you got all those constant values in your G formulas, but they're clearly not what you want.
3. You are misunderstanding the information criteria if you're expecting them to help with this. If the number of estimated parameters is the same, the "penalty function" is the same for each model, so you're just comparing log likelihoods anyway.