Specification Tests for the Propensity Score

47 Pages Posted: 21 Nov 2016 Last revised: 13 Mar 2019

See all articles by Pedro H. C. Sant'Anna

Pedro H. C. Sant'Anna

Vanderbilt University - College of Arts and Science - Department of Economics

Xiaojun Song

Peking University - Guanghua School of Management

Date Written: February 7, 2019

Abstract

This paper proposes new nonparametric diagnostic tools to assess the asymptotic validity of different treatment effects estimators that rely on the correct specification of the propensity score. We derive a particular restriction relating the propensity score distribution of treated and control groups, and develop specification tests based upon it. The resulting tests do not suffer from the "curse of dimensionality" when the vector of covariates is high-dimensional, are fully data-driven, do not require tuning parameters such as bandwidths, and are able to detect a broad class of local alternatives converging to the null at the parametric rate $n^{-1/2}$, with $n$ the sample size. We show that the use of an orthogonal projection on the tangent space of nuisance parameters facilitates the simulation of critical values by means of a multiplier bootstrap procedure, and can lead to power gains. The finite sample performance of the tests is examined by means of a Monte Carlo experiment and an empirical application. Open-source software is available for implementing the proposed tests.

Keywords: Goodness-of-fit, Integrated Moments, Empirical Processes, Multiplier Bootstrap, Treatment Effects

JEL Classification: C12, C31, C35, C52

Suggested Citation

Sant'Anna, Pedro H. C. and Song, Xiaojun, Specification Tests for the Propensity Score (February 7, 2019). Available at SSRN: https://ssrn.com/abstract=2872084 or http://dx.doi.org/10.2139/ssrn.2872084

Pedro H. C. Sant'Anna

Vanderbilt University - College of Arts and Science - Department of Economics ( email )

Box 1819 Station B
Nashville, TN 37235
United States

HOME PAGE: http://https://sites.google.com/site/pedrohcsantanna/

Xiaojun Song (Contact Author)

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

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