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

 From Carolina Lennon To statalist@hsphsun2.harvard.edu Subject Re: st: re: Solving the moving average in the error structure in a Date Mon, 1 Mar 2010 18:23:44 +0100

```Great Kit, I found the reference.

Hansen, L.P., Hodrick, R.J.. "Forward Exchange-Rates As Optimal Predictors
of Future Spot Rates - An Econometric-Analysis." Journal of Political
Economy 88: 829-853, 1980.

Many thanks
Carol

2010/3/1 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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--
Carolina Lennon

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