Identification and Estimation with Incomplete Data

Abstract

This paper is concerned with identification and estimation of econometric models when the sampling process produces missing observations. Missing observations occur frequently in applications due, for example, to non-response to questions on a survey or attrition from a panel. Missing observations usually cause population parameters of interest in applications to be unidentified except under untestable and often controversial assumptions. However, it is often possible to find identified, informative, bounds on these parameters that do not rely on untestable assumptions about the process through which data become missing. The bounds contain all logically possible values of the population parameters. Moreover, every parameter value within the bounds is consistent with some model of the process that generates missing observations. The bounds can be estimated consistently from data and often enable substantively important conclusions to be drawn without making untestable assumptions about missing observations. There are also situations in which the bounds are very wide. This is an indication that the data contain little information about the population parameters of interest and that substantive conclusions rely mainly on identifying assumptions that cannot be tested.