Panel GMM, system estimation and White's diagonal matrix

[tvonbrasch]

Hi,

I have a question regarding system estimation using panel data with GMM and the w-option (White’s diagonal weighting matrix). In what dimensions (if any) does this estimator impose independence of the residuals ? (in addition to assuming that disturbances are uncorrelated with the set of instruments). In particular, does it impose that the sum of residuals is uncorrelated across equations?

Thomas

[EViews Glenn]

Hi T,

The White diagonal in GMM panel is generally employed when we assume no correlation between residuals across equations, and no correlation between residuals across observations (even within cross-sections). It is a very strong assumption, but doesn't require independence. So under these assumptions, we do not have independence of the sums-of-squares across equations.

Having said that, there is one other (I think important and often overlooked) related point: one can always estimate a GMM or other linear regression model with a weighting matrix which is not optimal given the error structure, so long as the conditional mean is specified correctly. Thus, we can use a White diagonal even if there are various forms of cross-observation and cross-equation correlation. We will get consistency of the coefficient estimates, but not efficiency, and the estimates of the coefficient covariance will not be estimated properly unless we employ a valid robust covariance estimator.

In my view (some might disagree), this result implies that the choice of a weighting matrix doesn't necessarily imply that you are comitting to a particular error structure. Whatever weighting matrix we use, the assumed error structure of the residuals will be an externally imposed assumption unrelated to the choice of weighting matrix. I firmly believe that one really should choose an assumption regarding the error structure, then pick a weighting matrix and covariance estimator for efficiency and robustness properties.

So the bottom line is that I would argue that you'll get independence of the SSRs if you are willing to impose it :)

Hope this answers the question.

-g

[tvonbrasch]

Excellent, thanks for your extensive reply, Glenn. This was clarifying. Highly appreciated.
t