COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1740 Nonparametric Tests of Conditional Treatment Effects Sokbae Lee (University College London) November 2009 We develop a general class of nonparametric tests for treatment effects conditional on
covariates. We consider a wide spectrum of null and alternative hypotheses regarding
conditional treatment effects, including (i) the null hypothesis of the conditional
stochastic dominance between treatment and control groups; (ii) the null hypothesis that
the conditional average treatment effect is positive for each value of covariates; and
(iii) the null hypothesis of no distributional (or average) treatment effect conditional
on covariates against a one-sided (or two-sided) alternative hypothesis. The test
statistics are based on L1-type functionals of uniformly consistent
nonparametric kernel estimators of conditional expectations that characterize the null
hypotheses. Using the Poissionization technique of Giné, et al. (2003), we show that
suitably studentized versions of our test statistics are asymptotically standard normal
under the null hypotheses and also show that the proposed nonparametric tests are
consistent against general fixed alternatives. Furthermore, it turns out that our tests
have non-negligible powers against some local alternatives that are n–1/2
different from the null hypotheses, where n is the sample size. We provide a more
powerful test for the case when the null hypothesis may be binding only on a strict subset
of the support and also consider an extension to testing for quantile treatment effects.
We illustrate the usefulness of our tests by applying them to data from a randomized, job
training program (LaLonde (1986)) and by carrying out Monte Carlo experiments based on
this dataset. |
