# st: Orthogonal deviations GMM DPD estimator?

 From "Salvati, Jean" <[email protected]> To <[email protected]> Subject st: Orthogonal deviations GMM DPD estimator? Date Tue, 14 Dec 2004 18:16:42 -0500

```Hello,

By any chance, has anyone tried to implement the orthogonal deviations
(OD) GMM DPD estimator in Stata? This estimator is discussed for example
in Arellano and Bover (1995) and Alvarez and Arellano (2003).

I've started writing a Stata program that implements this estimator, but
I'm having some issues.

This estimator is implemented in Ox and in Eviews 5. However the Ox and
Eviews implementation don't seem to yield the same results (but it's
possible that I didn't correctly specify the model in Ox), and I can't
match either the Ox results or the Eviews results with my Stata program.

Using first-differences instead of OD in my program, I was able to match
the xtabond and xtabond2 results. Therefore I am *quite* confident in my
code.

However, it seems that there are more judgment calls to be made in the
OD implementation than in the FD implementation. In particular, there
may be more than one way of computing the orthogonal deviations
themselves. Here is how I do it:

- For each variable and for each period, compute the average of all
- To compute this average, use the actual number of available leads in
the sample (let's call this number n_leads).
- Compute the difference between the current value of the variable and
the average of all its available leads:

gen od_x_temp = x - avg_leads_of_x

ratio in equation (24) in the paper by Arellano and Bover).

Then I generate untransformed instruments and compute the GMM 1-step
estimator the same way as with first-differences, except that I use the
identity matrix as the "H" matrix.

Comments and suggestions are welcome. If someone wants to look at the
code, I can send it. Thanks.

Jean Salvati

References
----------

Manuel Arellano and Olympia Bover, 1995, "Another look at the
instrumental variable estimation of error-components models", Journal of
Econometrics

Javier Alvarez and Manuel Arellano, 2003, "The time-series and
cross-section asymptotics of dynamic panel data estimators",
Econometrica.

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