Group-Heterogeneous Changes-in-Changes and Distributional Synthetic Controls

Abstract: We develop new methods for changes-in-changes and distributional synthetic controls when there exists group level heterogeneity. For changes-in-changes, we allow individuals to belong to a large number of heterogeneous groups. The new method extends the changes-in-changes method in Athey and Imbens (2006) by finding appropriate subgroups within the control groups which share similar group level unobserved characteristics to the treatment groups. For distributional synthetic control, we show that the appropriate synthetic control needs to be constructed using units in potentially different time periods in which they have comparable group level heterogeneity to the treatment group, instead of units that are only in the same time period as in Gunsilius (2023). Implementation and data requirements for these new methods are briefly discussed.