Evaluating the Maximum MSE of Mean Estimators with Missing Data

Abstract

In this article, we present the wald_mse command, which computes the maximum mean squared error of a user-specified point estimator of the mean for a population of interest in the presence of missing data. As pointed out by Manski (1989, Journal of Human Resources 24: 343–360; 2007, Journal of Econometrics 139: 105–115), the presence of missing data results in the loss of point identification of the mean unless one is willing to make strong assumptions about the nature of the missing data. Despite this, decision makers may be interested in reporting a single number as their estimate of the mean as opposed to an estimate of the identified set. It is not obvious which estimator of the mean is best suited to this task, and there may not exist a universally best choice in all settings. To evaluate the performance of a given point estimator of the mean, wald_mse allows the decision maker to compute the maximum mean squared error of an arbitrary estimator under a flexible specification of the missing-data process.