  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.
