Re: st: GMM with 93+ regressors produces error

["Brian P. Poi" <brian@poiholdings.com>]

On 2/26/2011 4:08 PM, Julian Reif wrote:
> Is it possible to run -gmm- with more than 92 regressors?  I encounter the error "could not evaluate equation 1" when I try to do so.  The following logit example, run on Stata 11.1, reproduces the error:
>
> -------------------
> -------------------
> clear all
> set seed 38
> set obs 93
> gen id =  _n
> expand 10
> gen lhs = uniform()<  0.5
> xi I.id
>
> * These two commands should produce the same coefficient estimates. -gmm- produces an error here though.
> logit lhs _I*
> gmm (lhs - exp({xb: _I*}+{b0})/(1+exp({xb:}+{b0}))), instruments( _I*) onestep derivative(/xb = -1*( exp({xb:}+{b0}) / ((1+exp({xb:}+{b0}))^2) ))	derivative(/b0 = -1*( exp({xb:}+{b0}) / ((1+exp({xb:}+{b0}))^2) ))
>
> * Dropping one regressor makes error message go away
> drop if id==93
> drop _Iid_93
> logit lhs _I*
> gmm (lhs - exp({xb: _I*}+{b0})/(1+exp({xb:}+{b0}))), instruments( _I*) onestep derivative(/xb = -1*( exp({xb:}+{b0}) / ((1+exp({xb:}+{b0}))^2) ))	derivative(/b0 = -1*( exp({xb:}+{b0}) / ((1+exp({xb:}+{b0}))^2) ))
>
>
>
> Julian
> *

There is a limit to how long an expression passed to -generate- or 
-replace- can be, and that is what's causing the error message here. 
When you specify a substitutable expression with -gmm-, it substitutes 
your parameter names with the name of a temporary matrix and the 
appropriate column index.  In your case, -gmm- is replacing your 
substitutable expression with something like

__00002X = lhs - exp( (__000006[1,1] *_Iid_2 + __000006[1,2] *_Iid_3 +
__000006[1,3] *_Iid_4 + __000006[1,4] *_Iid_5 + __000006[1,5] *_Iid_6 + 
__000006[1,6] *_Iid_7 + __000006[1,7] *_Iid_8 ...

where "..." is rather long in your case, __00002X happens to be the 
temporary variable -gmm- is using to hold the residuals and __000006 is 
the temporary matrix of parameters.

When I take the exact expression -gmm- is using here and try and pass it 
to -replace-, I get

.
. replace k = `express2'
expression too long
r(130);

In terms of -gmm-, the only solution is to write a function evaluator 
program instead.


   -- Brian Poi
   -- brian@poiholdings.com

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