AD-AS SVAR

[terrya]

I've tried to figure out how Cover, Enders and Hueng combined short-run and long-run (BQ) restrictions to identify demand-side and supply-side shocks in an AD-AS model. I've attempted to use the shortandlong procedure to do this but have failed in this attempt. I would be grateful if you could give me some advice how to do the coding. It's probably quite simple but I can't solve the problem.

[TomDoan]

@ShortAndLong with the NOESTIMATE option will code up a mapping from a set of underlying parameters to the "B" matrix that will give the required set of restrictions. The problem here is that there are other restrictions imposed on the "B" matrix that aren't just zero restrictions, and they won't have any simple form in the remapped parameter space. Instead, the best approach is to write a standard SVAR using the model's natural parameters and impose the long-run restriction using a PARMSET restriction.

The following is an example. The data set is from Lutkepohl's textbook, which I'm using simply because it's a 3 variable system, not because the particular model makes sense with it.

Code: Select all

open data e1.dat
calendar(q) 1960
data(format=prn,org=columns,skips=6) 1960:01 1982:04 invest income cons
graph(footer="Figure 3.1 West German data",$
  key=upleft,klabels=||"income","consumption","investment"||) 3
# income
# cons
# invest
*
set dinc = log(income/income{1})
set dcons = log(cons/cons{1})
set dinv  = log(invest/invest{1})
*
system(model=varmodel)
variables dinv dinc dcons
lags 1 2
det constant
end(system)
estimate * 1978:4
*
compute masums=inv(%varlagsums)
*
nonlin(parmset=svarparms) gamma alpha f31 f32
dec frml[rect] af bf lrf
frml af = ||1.0,0.0,0.0|$
            0.0,1.0,0.0|$
            f31,f32,1.0||
frml bf = ||1.0,0.0,0.0|$
           gamma/(1+alpha),1/(1+alpha),alpha/(1+alpha)|$
          -gamma/(1+alpha),-1/(1+alpha),1/(1+alpha)||
frml lrf = masums*bf(1)
nonlin(parmset=lrrest) lrf(1)(2,3)==0.0
compute f31=f32=0.0
compute alpha=-.3,gamma=.3
cvmodel(a=af,b=bf,parmset=svarparms+lrrest) %sigma

[abhishek]

Thanks Tom. How did we get this compute alpha=-.3,gamma=.3? Forgive my ignorance if any.

[TomDoan]

Those are just guess values. The actual values are found by the CVMODEL.

[abhishek]

Hi
Even I didn't get af matrix. Can you please write in terms of Var-Covar(Reduced form Residual)=G* Var-covar(Structural Residual)*G'. And then long run restrictions.
Many Thanks

[abhishek]

Thanks Tom.
I want to write Var-Covar(Reduced form Residual)=G* Var-covar(Structural Residual)*G'. From there I want to solve for G. My Var-covar(Structural Residual) is not unit diagonal? How can I do that? What about the Global Identification if I write and try to solve non-linear system?

[TomDoan]

CVMODEL takes care of solving that out. As described above, it's simpler to write the model using natural parameters for the impacts and then impose the long run restriction and let CVMODEL do the work of solving out the system.

[abhishek]

Thanks Tom.
In CVMODEL we can specify A and B. As far as I think there is no option of giving Var-Covar of Structural residual. In the Handbook it's written that it is assumed to be unit diagonal.

[TomDoan]

If you have a model, it would probably help if you would write it out.

[abhishek]

Thanks Tom.

Please find the attached file.

[TomDoan]

That's not going to work. The long-run restriction is enough to distinguish between the last two shocks, but you can't then add in the fact that they're correlated. (If you're looking for a restriction on the "mu" covariance matrix, x17=0 is what you want). Note, by the way, that this has very little to do with what Cover, Enders and Hueng are doing.

[abhishek]

Thanks Tom. If I am not wrong they are also saying that structural shock of demand and supply are correlated. They are using non-zero off diagonal element in "mu" matrix.

[TomDoan]

You're (trying to do) a standard short and long-run restriction model with correlated shocks. They're doing a highly non-standard form of identification which relies on restrictions other than zero loadings.

[abhishek]

Tom Please have a look at this. Thanks for all your help.

[TomDoan]

You can't do it because the system of equations is ill-determined. Your final two equations allow both shocks to have effectively no structure. You then impose upon them that the one of the two has zero long-run restrictions. OK. That nails down one. However, with the non-zero correlation, there's nothing to nail down the other.