Hazard Versus Linear Probability Difference-in-Differences Estimators for Demographic Processes

This study examines the properties of the linear probability difference-in-differences estimator when the data are in fact generated by a single-decrement, continuous-time hazard process. We focus on the textbook case of two groups and two periods in which the control and treatment groups are observed before and after treatment. We provide formal derivations and illustrate matters concretely by reexamining economic studies that have relied on the linear probability difference-in-differences estimator when attempting to obtain estimates of the causal effect of unilateral and no-fault divorce. In particular, we show that the increasing then decreasing pattern of effects found by Wolfers (2006) can be generated by a time-invariant effect of treatment in a proportional hazard setting. We conclude that often implicit assumptions about how the data are generated are an important and necessary component of causal identification.