Finding mover-stayer quantile difference due to unobservables using quantile selection corrections

초록

For movers (D=1) from a state and stayers (D=0), it is of interest to know how they differ in their distributions of a response variable Y* given some observed regressors Z (e.g., wage Y* given education Z), which is equivalent to their quantile differences in Y* due to unobservables (e.g., ability) given Z. In many mover/stayer cases, however, Y* is observed only for the movers, enabling the identification of only quantiles of the movers; for example, moving is migration and Y* is the wage in the host country. For this, we propose a practical parametric way to find quantile differences between movers and stayers despite unobserved Y* for the stayers. Our approach has the advantage comparing the movers to the stayers, whereas the existing semiparametric alternatives compare the movers only to the population to dilute the mover-stayer differences. Also, our approach easily allows heteroskedasticity and heterocorrelation in the D and Y* equations. An empirical example demonstrates these points.

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