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re: st: re: Solving the moving average in the error structure in a


From   Christopher F Baum <baum@bc.edu>
To   statalist@hsphsun2.harvard.edu
Subject   re: st: re: Solving the moving average in the error structure in a
Date   Mon, 1 Mar 2010 12:13:15 -0500

<>
Carolina said

I know that the following question is a little out of scope (since it does not relate to the stata commands), but just in case it is easy for you to reply...Do you know where I can find a reference justifying "that there is no reason for a MA error structure to induce bias in the OLS coefficients"? It would of great help. Indeed, some referees did not like my overlapping regressions because of the bias cused by the MA errors in the point estimates. (My regressions were of the type: xtreg, fe cluster) Therefore, if I can justify it would be just perfect.

Any decent econometrics textbook discusses the consequences of violating the IID error assumption (usually when discussing generalized least squares, or robust standard errors, etc.) Generally speaking we know that AR(1) errors do not cause bias in point estimates. Nor do AR(2) errors, or AR(3) errors, etc. Now a finite MA process, if invertible, can always be expressed as an infinite-order AR process, so what you have is a OLS model with dummy variables with errors orthogonal to the regressors (by assumption of exogeneity). The fact that they can be expressed as a finite-order MA or an infinite- order AR should not matter. See Hansen and Hodrick's article on why overlapping data induce MA(j) where j is one less than the degree of overlap, and the solution being to use Newey-West with j lags. I don't have the H-H cite handy but have mentioned it not too long ago on this list. I don't think -xtgls- will help, as I believe it only allows for AR(1) errors.
Kit
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