Correlated random coefficient (CRC) models provide a useful framework for estimating average treatment effects (ATE) with panel data by accommodating heterogeneous treatment effects and flexible patterns of selection. In their simplest form, they lead to the well-known difference-in-differences estimator. CRC models yield estimates of ATE for movers (i.e., cross-sectional units whose treatment status changed over time) while ATE for stayers (i.e., cross-sectional units who retained the same treatment status over time) are not identified. We study additional restrictions on selection into treatment that lead to the identification of ATE for stayers by an extrapolation from quantities identified by the CRC model. We discuss estimation and testing of the extrapolation's validity, then use our results to estimate the returns to agricultural technology adoption among maize farmers in Kenya.
