Endogeneity with binary independent variable

[Dax Tops]

Dear Statalist,
I have an original regression with an endogenous binary independent variable:

regress Y1 = X1 + Xi-Xn etc, where X1 is binary and endogeneous and Xi-Xn are exogenous controls

.
I follow Leone, Rock and Willenborg (2007), by conducting the omitted-variable version of Hausman's test. To do this, I create an IV by regressing X1 on all exogenous controls and an instrument (Z):

probit X1 Xi-Xn Z, where Z is an instrument
predict shat, pr

.
Now I add the fitted values from this regression to my original regression:

regress Y1 X1 shat Xi-Xn

What I understand, if the t-value of shat is significant, an endogeneity problem is present. It is, however, the sign of shat is the opposite of the sign of X1. Is this possible? Can I conclude endogeneity is present here?

[Phil Bromiley]

I would suggest you consider using ivreg or ivreg2 (user written). They are consistent for binary endogenous variables and, at least ivreg2 has built in tests. If you refer to a paper, it is a good idea to give a full citation.