Testing for Monotonicity in Unobservables Under Unconfoundedness
50 Pages Posted: 13 Jun 2014
Date Written: June 5, 2014
Monotonicity in a scalar unobservable is a now common assumption when modeling heterogeneity in structural models. Among other things, it allows one to recover the underlying structural function from certain conditional quantiles of observables. Nevertheless, monotonicity is a strong assumption and in some economic applications unlikely to hold, e.g., random coefficient models. Its failure can have substantive adverse consequences; having a test for this hypothesis is hence desirable. This paper provides such a test for cross-section data. We show how to exploit an exclusion restriction together with a conditional independence assumption, which in the binary treatment literature is commonly called unconfoundedness, to construct a test. Our statistic is asymptotically normal under local alternatives and consistent against nonparametric alternatives. Monte Carlo experiments show that a suitable bootstrap procedure yields tests with reasonable level behavior and useful power. We apply our test to study the role of unobserved ability in determining Black-White wage differences and to study whether Engel curves are monotonically driven by a scalar unobservable.
Keywords: Control variables, Covariates, Endogenous variables, Exogeneity, Monotonicity, Nonparametric, Nonseparable, Specification test, Unobserved heterogeneity
JEL Classification: C12, C14, C21, C26
Suggested Citation: Suggested Citation