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

[Christopher F Baum <baum@bc.edu>]

<>
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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