Difference in Differences for Stayers and Movers with a Time-Varying QualiÂ…cation

When a treatment in difference in differences (DD) is applied to a group of individuals with a time-constant qualifi…cation/eligibility such as gender or race, there is no issue of choosing to be (un-)treated. But if the quali…fication is time-varying, then the individuals may alter their qualifi…cations to get (un-)treated. In this case, the conventional DD ignoring quali…fication changes is invalid in general, and it is interesting to know whether the newly qualifi…ed (the “in-movers”) will experience the same treatment effect as those already qualifi…ed (the “in-stayers”). In this paper, we explore identifying treatment effects with DD when the quali…fication is time-varying, and propose ‘the effect on the in-stayers’ as the main effect of interest. The identi…fication is implemented with a simple nonparametric estimator or with least squares estimator for panel linear models. An empirical analysis is provided using Korean data for the effects of the Basic Elder Pension on health-care expenditure, which shows that the conventional DD ignoring quali…fication changes is misleading by mixing the effect on the in-stayers with the effect on the in-movers.