Testing for Endogeneity of a Single Explanatory Variable:
(i) Estimate the reduced form for y2 by regressing it on all exogenous variables
(including
those in the structural equation and the additional IVs). Obtain the residuals, v ˆ 2 .
(ii) Add v ˆ 2 to the structural equation (which includes y2) and test for significance of
v ˆ 2 using an OLS regression. If the coefficient on v ˆ 2 is statistically different from zero, we
conclude that y2 is indeed endogenous. We might want to use a heteroskedasticity-robust
t test.
Test for multiple endogeneity
For each suspected
endogenous variable, we obtain the reduced form residuals, as in part (i). Then, we test for
joint significance of these residuals in the structural equation, using an F test. Joint significance
indicates that at least one suspected explanatory variable is endogenous. The number of
exclusion restrictions tested is the number of suspected endogenous explanatory variables.
-----Wooldridge, 5th edition, p.534
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