Cross-section SUR and Parks-Kmenta

[carmomi]

Hi,

I have a doubt concerning the equivalence between the panel "Cross-section SUR" class of covariance structures and the Parks-Kmenta model.
The Parks model specifies a model for heteroskedasticity, contemporaneous correlation, and serial correlation AR(1).
I believe that in Eviews7 I need to add an AR(1) term to the list of variables of the regression estimated with "Cross-section SUR" to match the Parks model. Is this correct?

Many thanks in advance.

Miguel

[EViews Glenn]

The Parks-Kmenta specification will handle clustering errors but not the AR(1).

Note that you can add to the Parks-Kmenta SUR by adding in an AR(1) term in EViews but that this tells EViews to assume that there is constant within-cluster correlation of the residuals in the rho-differenced non-linear specification. This may or may not be the specification that you want.

[carmomi]

Many thanks Glenn for the explanation. However, as I´m not an expert I'm still a litle bit confused.

I found some references mentioning that the Parks-Kmenta method specifies a model for heteroskedasticity, a model for contemporaneous correlation, and also the following model for serial correlation AR(1):
Uit=Pi*Uit-1+Vit
where Pi is a coefficient of first-order autoregressiveness (the value of the parameter is allowed to vary from one cross-section unit to another). In other words, the coefficient of the AR(1) process is specific to each cross section unit.

I also found that In the Parks-K estimation the serial correlation of the errors is eliminated first and then the contemporaneous correlation of the errors is eliminated.

I´m just trying to confirm whether:
1) this is correct?
2) this corresponds to the "SUR cross-section" option for panel data estimation in Eviews7 (or do I need to manually enter an AR(1) term?).

Any further hint would be more than welcome.

[EViews Glenn]

Sorry to be so late in responding to this one. I never saw it (it didn't show up in my RSS feed)...

The EViews variant of the specifications is quite similar to PK, but differs in two respects. First, the original PK estimator allows for different autocorrelation coefficients in each cross-section. EViews does not. Second, the PK estimator uses the Prais-Winsten transformation to whiten the data given an estimator of the coefficients and the autocorrelation coefficient for each cross-section. I do not believe that there is a consensus over whether this procedure should be iterated or not--I believe iteration is generally not performed. EViews uses the nonlinear least squares formulation for the estimator in which the model is transformed to nonlinear least squares and the estimates are iterated over both the regular and the common autocorrelation coefficients. As Fair points out in the book cited in our manual, there are some reasons that the nonlinear transformation and iteration are useful, especially in instrumental variables settings.

So the EViews estimator may be viewed as a restricted PK where autocorrelation coefficients are common and where noninear least squares is used to iterate both the mean and the autocorrelation coefficients to convergence.