Testing Missing at Random using Instrumental Variables

Christoph Breunig
Monday, November 17, 2014 - 2:00pm
Spandauer Straße 1, Room 23

This paper proposes a test for missing at random (MAR). The MAR assumption is shown to be testable given instrumental variables which are independent of response given potential outcomes. Given such instruments, MAR is shown to be equivalent to an identified conditional moment restriction. A nonparametric testing procedure is proposed which replaces the conditional moment by series estimators and is based on integrated squared distance. For this test statistic, the asymptotic distribution under the MAR hypothesis is derived. We demonstrate that our results can be easily extended to a test of missing completely at random (MCAR) and to situations where also realizations of the instruments might be missing. A Monte Carlo study examines finite sample performance of our test statistic. An empirical illustration concerns pocket prescription drug spending with missing values; we reject MCAR but fail to reject MAR where covariates are birth years of participants.