David,
There is some discussion of this issue in the context of bivariate
probit models in Greene (2000, p849-56). To quote from the example in
the text: "Surprisingly, the endogenous nature of one of the variables
on the right-hand side of the first-equation can be ignored in
formulating the log-likelihood". He then goes on to show why this is
the case.
Arne
Ref: Greene WH. 2000. Econometric Analysis. 4th edition.
> I have also improved the explanation in the help file of how -cmp-
> works. But I would be grateful for feedback on how to sharpen the
> explanation further. In particular, -cmp- is essentially just an SUR
> estimator. An interesting and apparently underappreciated fact--and one
> that I have yet to see fully and formally explained--is that SUR
> estimators actually work for a larger class of simultaneous equations
> models, in which dependent variables from some equations *do* appear on
> the rights sides of others. SUR still works for such models if: 1) the
> systems are recursive, i.e., the equations can be arranged so that the
> matrix of coefficients of endogenous variables in each other's equations
> is upper triangular; and 2) the dependent variables enter other
> equations *as observed*--unobserved latent variables don't enter
> directly.
>
> So, for example, -sureg (X=Y) (Y=Z), isure- usually converges to the
> same result as -ivreg X (Y=Z)-. And -biprobit- works for IV models in
> which the first- and second-stage dependent variables are both binary.
> But you wouldn't know from the Stata documentation that these commands
> can do IV. Has anyone seen a thorough discussion of these ideas?
>
> --David
>
> David Roodman
> Research Fellow
> 1776 Massachusetts Avenue NW
> Washington, DC 20036
> Center for Global Development
> Independent Research and Practical Ideas for Global Prosperity
>
>
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