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[Olle Westerlund <olle.westerlund@econ.umu.se>]

Testing for endogenity of a regressor

We have the following outcome equation:

(1) lnY=aX+bC+e

were X is assumed to be exogenous variables and C is an indicator variable 
for a multinomial treatment (each individual is exposed to one out of five 
possible treatments).

Treatment selection is governed by the following linear index function:

(2) C=dZ+u

were Z represents another set of set of exogenous variables.

The idea is to control for possible selection bias (i.e. E(e|C,X) # 0) in 
the estimation of the treatment effect using a "selection on observables" 
approach, where Z is added to equation (1) and this equation is estimated 
as a linear control function model.

Before proceeding with this, we would like to test whether C in equation 
(1) is actually endogenous.

Anyone who knows how to perform a endogeneity test in Stata in this case?
Perhaps something analogous to the Durbin- Whu- Hausman test?

Hints appreciated

Olle Westerlund


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