Thursday, January 05, 2006

Re: st: ivprobit and wald test of exogeneity

On Thu, 5 Jan 2006, Tinna wrote:

> Dear Statalisters, > > -ivprobit- reports results from a "wald test of exogeneity" > > I am unfamiliar with this test and am having a tough time finding > information regarding it. There is no reference of it in -help > ivprobit- and my Internet search is failing miserably. > > Currently I am using Durbin-Wu-Hausman for exogeneity checking, but > cant but wonder about this mysterious test being reported by stata. > > Can anyone guide me toward the answer? > > Tinna >

Tinna,

This test is mentioned along with the theory behind -ivprobit- in Wooldridge's "Econometric Analysis of Cross Section and Panel Data" (2002, pp. 472-477).

For the maximum likelihood variant with a single endogenous variable, the test is simply a Wald test that the correlation parameter rho is equal to zero. That is, the test simply asks whether the error terms in the structural equation and the reduced-form equation for the endogenous variable are correlated. If there are multiple endogenous variables, then it is a joint test of the covariances between the k reduced form equations' errors and the structural equation's error.

In the two-step estimator, in the second stage we include the residuals from the first-stage OLS regression(s) as regressors. The Wald test is a test of significance on those residuals' coefficients.

-- Brian Poi -- bpoi at stata.com

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