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Re: st: ivprobit and wald test of exogeneity

From   "Brian P. Poi" <>
Subject   Re: st: ivprobit and wald test of exogeneity
Date   Thu, 5 Jan 2006 17:22:19 -0600 (CST)

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?



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

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