The Econometrics of Data Combination

Economists who use survey or administrative data for inferences regarding a population may want to combine information obtained from two or more samples drawn from the population. This is the case if there is no single sample that contains all relevant variables. A special case occurs if longitudinal or panel data are needed but only repeated cross-sections are available. In this chapter we survey sample combination. If two (or more) samples from the same population are combined, there are variables that are unique to one of the samples and variables that are observed in each sample. What can be learned by combining such samples, depends on the nature of the samples, the assumptions that one is prepared to make, and the goal of the analysis. The most ambitious objective is the identification and estimation of the joint distribution, but often we settle for the estimation of economic models that involve these variables or a subset thereof. Sometimes the goal is to reduce biases due to mismeasured variables. We consider sample merger by matching on identifiers that may be imperfect in the case that the two samples have a substantial number of common units. For the case that the two samples are independent, we consider (conditional) bounds on the joint distribution. Exclusion restrictions will narrow these bounds. We also consider inference under the strong assumption of conditional independence.