  Unobserved heterogeneous treatment effects have been emphasized in the recent
policy evaluation literature (see e.g., Heckman and Vytlacil, 2005). This paper
proposes a nonparametric test for unobserved heterogeneous treatment effects in
a treatment effect model with a binary treatment assignment, allowing for
individuals' self-selection to the treatment. Under the standard local average
treatment effects assumptions, i.e., the no defiers condition, we derive
testable model restrictions for the hypothesis of unobserved heterogeneous
treatment effects. Also, we show that if the treatment outcomes satisfy a
monotonicity assumption, these model restrictions are also sufficient. Then, we
propose a modified Kolmogorov-Smirnov-type test which is consistent and simple
to implement. Monte Carlo simulations show that our test performs well in
finite samples. For illustration, we apply our test to study heterogeneous
treatment effects of the Job Training Partnership Act on earnings and the
impacts of fertility on family income, where the null hypothesis of homogeneous
treatment effects gets rejected in the second case but fails to be rejected in
the first application.
