Bounds on Treatment Effects under Stochastic Monotonicity Assumption in Sample Selection Models

Author:

Yuta Okamoto

Keyword:

Economics, Econometrics, Econometrics (econ.EM)

journal:

date:

2023-10-31 16:00:00

Abstract

This paper discusses the partial identification of treatment effects in sample selection models when the exclusion restriction fails and the monotonicity assumption in the selection effect does not hold exactly, both of which are key challenges in applying the existing methodologies. Our approach builds on Lee's (2009) procedure, who considers partial identification under the monotonicity assumption, but we assume only a stochastic (and weaker) version of monotonicity, which depends on a prespecified parameter $\vartheta$ that represents researchers' belief in the plausibility of the monotonicity. Under this assumption, we show that we can still obtain useful bounds even when the monotonic behavioral model does not strictly hold. Our procedure is useful when empirical researchers anticipate that a small fraction of the population will not behave monotonically in selection; it can also be an effective tool for performing sensitivity analysis or examining the identification power of the monotonicity assumption. Our procedure is easily extendable to other related settings; we also provide the identification result of the marginal treatment effects setting as an important application. Moreover, we show that the bounds can still be obtained even in the absence of the knowledge of $\vartheta$ under the semiparametric models that nest the classical probit and logit selection models.

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