Identification potential output in SVAR à la Blanchard Quah

[wolly77]

Dear guys,
I'm new in this forum. I write you to ask some issues regarding Blanchard Quah procedure in RATS. I'm trying to use this code posted in the official site of Estima to estimate potential output for Italy economy. In the procedure I do not understand some steps. After the VAR estimation, this codes appear:

"compute factor=%bqfactor(%sigma,%varlagsums)
{
if factor(1,2)<0.0
compute factor=factor*%diag(||1.0,-1.0||)
}
history(model=bqmodel,factor=factor,results=histdecomp)
set histdecomp(1,1) = histdecomp(1,1)+means_from_gnp
set histdecomp(1,2) = histdecomp(1,2)+trend_from_ur
do j=1,3
acc histdecomp(j,1)
set histdecomp(j,1) = histdecomp(j,1)*.01
end do j

set histdecomp(1,1) = histdecomp(1,1)+logrgnp(1950:1)
set lessdemand = histdecomp(1,2)+histdecomp(2,2)
graph(footer="Figure 9. Unemployment Fluctuations Absent Demand",min=0.0)
# lessdemand"

I do not understand the mean of condition "if factor(1,2)<0.0.." and I do not understand the means of "histdecomp". Why I have 6 histdecomp in the data Window? What corresponds to?

Thanks in advance to everyone. And I'm sorry for my bad english.

[TomDoan]

Code: Select all

*
* The zero restriction only determines the shape, not the sign, of the
* demand shock. If we want it defined so that the contemporaneous
* response of output is positive (that will be the (1,2) element in the
* factor), we need to flip the sign of the second column if the response
* has the wrong sign.
*
{
if factor(1,2)<0.0
   compute factor=factor*%diag(||1.0,-1.0||)
}

If B is a factor of a symmetric matrix, then you can also obtain a factor by sign flipping any combination of columns. The BQ restriction on the demand shock is that it have a long-run zero response on output. As the comment notes, that determines the shape but not the sign; flip the sign on the demand shock and the lonr-run response will still be zero. By construction, the supply shock will have a positive initial impact, but the second shock produced by %BQFACTOR usually will have a negative initial impact. This flips the sign if necessary to make the demand impact positive.

HISTDECOMP is the historical decomposition of the two series. This is described in section 10.7 of the User's Guide and in the Reference Manual under the HISTORY instruction. This example has quite a bit of added code because of the special processing done to the variables. GNP, for instance, was converted to 100*log difference, then separately de-meaned over two ranges. The removed means have to be added back to the base forecast; similarly the trend removed from the UR has to be added back. Then to get the decomposition of log GNP itself, all three GNP components have to be accumulated, then scaled back by .01 to reverse the 100*. Then the pre-sample value of log GNP has to be added back since it was lost in differencing.

I posted some additional information on the historical decomposition at:

http://www.estima.com/forum/viewtopic.php?f=4&t=655

[wolly77]

Dear Tom, thanks for your reply! I have another question: the code written for bivariate Blanchard Quah model can be used (with the right modifications) to other estimations? For example, I have a bivariate var: industrial production and unemployment (qurterly data for Italy). Unemployment is I(1) and I take the first difference of output and unemployment in my VAR. Can I use the BQ code for making an estimation of potential output? Thanks in advance.

[TomDoan]

That's correct. The same basic idea is also used to estimate "core" inflation in Quah and Vahey(1995), "Measuring Core Inflation?", Economic Journal, vol. 105, pp 1130-44: http://www.estima.com/forum/viewtopic.php?f=8&t=1156

[wolly77]

Thanks Tom, I have another question. If I want to run a VAR with three variables which kind of modifications I need to make in the code?

[TomDoan]

See the final response in:

http://www.estima.com/forum/viewtopic.php?f=4&t=304

The B-Q factorization in practice really only makes sense for 2 variable systems, which is why BQDoDraws was written specifically for 2.