Re: st: Recovering Jacobian from gmm estimate

["Brian P. Poi" <bpoi@stata.com>]

On 10/04/2013 10:52 AM, Tony Stata wrote:
> Hello everyone,
>
> To calculate the asymptotic variance of the gmm estimate, Stata
> numerically calculates the Jacobian matrix (unless the analytic
> derivatives are supplied manually). What is the best way to recover
> this matrix and store it locally?
>
> A few comments:
>
> (i) For reference, I'm referring to the G_bar(Beta_hat) matrix in
> equation 5 in the gmm section of the Stata Reference Manual (Release
> 12)
>
> (ii) It would be possible to numerically calculate the Jacobian after
> estimation, but that could be computationally costly, and Stata has
> already done that computation, so it would be nice to avoid that
> redundancy
>
> (iii) From what I can tell, all the other matrices in the asymptotic
> variance calculation are being saved in e() by gmm: e(W) is the weight
> matrix, e(S) is the moment var-cov matrix, and e(V) is the parameter
> var-cov matrix, but I can't find the Jacobian
>
> Thanks!

Tony,

Although not documented, you can get the final G matrix in the saved results.  It is stored as e(G).  Note that this matrix does not have the row and column names set.  We'll get this added to the documentation in a future update.

Here's a silly example:

   . sysuse auto
   . gmm (mpg - {b0} - {b1}*gear), inst(gear turn head) onestep vce(unadj)
   . mat G = e(G)
   . mat W = e(W)
   . mat V = invsym(G'*W*G) / 74     /* N = 74 observations */
   . di sqrt(V[1,1])
   3.5392953
   . di sqrt(V[2,2])
   1.1609056


   -- Brian Poi
   -- bpoi@stata.com


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