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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

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

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