Simultaneous Equations With A LOT of Heterogenous Groups

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Simultaneous Equations With A LOT of Heterogenous Groups

Let y1ij and y2ij denote the ith observation in group j.  I want to estimate the 2 simultaneous equation system

y1ij = a1j + b*xij + c*zij + error1ij

y2ij = a2j + b*xij + d*wij + error2ij

It is easy for me to do this for a pooled 3SLS regression using PROC SYSLIN, but doing a pooled regression forces a1j to be the same for all j.  I need to account for heterogeneity in some way (not necessarily with a fixed effect model, but that's the example I give above).  The problem is, creating dummy variables for each j is not feasible because there are about 13,000 different j.

Does anyone have a suggestion how to go about this?  I'm open to a random effects model, or GMM, or something else, so long as I can account for both simultaneity and heterogeneity.

Thanks,

Scottt

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