Re: st: ivprobit and wald test of exogeneity

["Brian P. Poi" <bpoi@stata.com>]

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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