Testing for Monotonicity in Unobservables Under Unconfoundedness

50 Pages Posted: 13 Jun 2014

See all articles by Stefan Hoderlein

Stefan Hoderlein

Boston College

Liangjun Su

Tsinghua University

Halbert L. White, Jr.

University of California, San Diego (UCSD) - Department of Economics

Thomas Yang

Boston College

Date Written: June 5, 2014

Abstract

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

Hoderlein, Stefan and Su, Liangjun and White, Halbert L. and Yang, Thomas, Testing for Monotonicity in Unobservables Under Unconfoundedness (June 5, 2014). Available at SSRN: https://ssrn.com/abstract=2448681 or http://dx.doi.org/10.2139/ssrn.2448681

Stefan Hoderlein

Boston College ( email )

140 Commonwealth Avenue
Chestnut Hill, MA 02467
United States

Liangjun Su (Contact Author)

Tsinghua University ( email )

B606 Lihua Building
School of Economics and Management
Beijing, Beijing 100084
China

Halbert L. White

University of California, San Diego (UCSD) - Department of Economics ( email )

9500 Gilman Drive
La Jolla, CA 92093-0508
United States
858-534-3502 (Phone)
858-534-7040 (Fax)

HOME PAGE: http://www.econ.ucsd.edu/~mbacci/white/

Thomas Yang

Boston College ( email )

140 Commonwealth Avenue
Chestnut Hill, MA 02467
United States

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