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Re: st: Endogenous Regressors Predicted by the Same IV


From   Austin Nichols <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Endogenous Regressors Predicted by the Same IV
Date   Mon, 1 Mar 2010 13:11:09 -0500

Lloyd Dumont <lloyddumont@yahoo.com> :
Kit points out that your equation is underidentified, but if you are
willing to assume that the products of Z_1 with X_4,.. X_10 are
uncorrelated with the error, you have 7 additional excluded
instruments to use.  Run IV first using e.g. -ivreg2- (on SSC)
ignoring the binary outcome, as the diagnostics for linear IV are
better developed and will give you a sense of dp/dX in any case. The
key diagnostics here are weak IV stats and the overid test, since you
have a pretty weak argument for your exclusion restrictions and no
guarantee of strong correlations. Then you can go to -ivprobit- or
-cmp- (SSC) or the like, if linear IV looks good.

On Mon, Mar 1, 2010 at 11:01 AM, Kit Baum <baum@bc.edu> wrote:
> No can do. This is a textbook case of under(un)identification. You need at least three Z variables to identify the equation, whether or not the estimation technique is OLS, probit, etc.

On Mon, Mar 1, 2010 at 10:48 AM, Lloyd Dumont <lloyddumont@yahoo.com> wrote:
> I’m pretty sure that what we’re trying to do is mathematically estimable under certain assumptions.  So, we are trying to figure out the syntax for the estimating procedure.  And, then we’d like to clarify the assumptions that have to hold for us to accept the estimates.
>
> We are ultimately trying to estimate a dep var we will call Y_dep.  Y_dep is being predicted by X_1, X_2, …X_10.  But, X_1, X_2, and X_3 are all endogenous.  We believe they can all be predicted by the same instrumental variable, Z_1.  And, furthermore, we are willing to accept that Z_1 has no direct effect on Y_dep beyond its effects through X_1, X_2, and X_3.

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