Testing missing at random using instrumental variables - Christoph Breunig (Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk, 2015)
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. A nonparametric testing procedure based on integrated squared distance is proposed. The statistic's asymptotic distribu- tion 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 miss- ing completely at random conditional on covariates X (MCAR(X)). 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.
Keywords: C12; C14; 330; incomplete data; missing-data mechanism; selection model; nonparametric hypothesis testing; consistent testing; instrumental variable; series estimation