Testing missing at random using instrumental variables

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 distribution under the MAR hypothesis is derived. In particular, our results can be applied to testing missing completely at random (MCAR). A Monte Carlo study examines finite sample performance of our test statistic. An empirical illustration analyzes the nonresponse mechanism in labor income questions.