Blanchard and Perotti (2002)

[MC128]

Hi Tom and everyone,

I am trying to replicate the study of Blanchard and Perotti (2002) for both the cases of deterministic and stochastic trends. The latter setting involves differencing the variables and then substracting a changing mean in the regression (see p.1340 of the paper), in order to deal with the problem of unit roots. One question that I have is that that I am not sure of the exact specification of the regression. Will it be something like:

d(y_t) = A(L)d(y_t-1) + changing mean + error term?

Another question is that will the structure of the A and B matrix (i.e. A*u_t = B*e_t) be altered by differencing the endogenous variables? (u_t is the residuals and e_t is the structural shock)

One final question is that, if we wanna study SVAR using classical estimation, then will unit roots be a serious concern? I am asking this because many papers on SVAR didn't put analyze the problem of unit roots (or cointegration).

Thank you so much. I will be grateful for any advice!

MC

[TomDoan]

Hi Tom and everyone,

I am trying to replicate the study of Blanchard and Perotti (2002) for both the cases of deterministic and stochastic trends. The latter setting involves differencing the variables and then substracting a changing mean in the regression (see p.1340 of the paper), in order to deal with the problem of unit roots. One question that I have is that that I am not sure of the exact specification of the regression. Will it be something like:

d(y_t) = A(L)d(y_t-1) + changing mean + error term?

Another question is that will the structure of the A and B matrix (i.e. A*u_t = B*e_t) be altered by differencing the endogenous variables? (u_t is the residuals and e_t is the structural shock)

One final question is that, if we wanna study SVAR using classical estimation, then will unit roots be a serious concern? I am asking this because many papers on SVAR didn't put analyze the problem of unit roots (or cointegration).

Thank you so much. I will be grateful for any advice!

MC

The changing mean is handled by pre-processing the series. The simplest way to do that calculation is with the ESMOOTH instruction:

Code: Select all

esmooth(trend=linear,alpha=.025,gamma=0.00,initial=full,smoothed=gdptrend) loggdp

That will give you the moving trend. The detrended series is computed with

Code: Select all

set gdpdetrend = loggdp-gdptrend

You do that to all three series and use the detrended series in the VAR.

Obviously, you get different results, but the contemporaneous model is the same whether you detrend the data prior to running the regression, or include deterministic terms in the regression. The unit root situation generally matters only if you're imposing some form of long-run restrictions.

[MC128]

Dear Tom,

Thank you so much for your quick reply! May I also ask for some clarifications?

In your example given, does "loggdp" corresponds to the differenced real gdp? So we subtract the differenced variables from the moving trend?

Second, so the identification scheme is unaltered in the case of stochastic trend compared to the deterministic trend?
For example, in the deteministic trend case:

y_t = deterministic trend + A(L)*y_t-1 + u_t

In the stochastic trend case:

d(y_t) = B(L)*d(y_t-1) + u_t

where d corresponds to differenced and detrended variables (as discussed). In both of these two cases, the same identification scheme A*u_t=B*e_t apply?

Finally, if we are not concerned with long run restrictions, then it is not really necessary to test for unit roots?

Many thanks for your help!!

MC