Extending policies to control groups or past periods in nonlinear difference in differences

In difference in differences (DD), a policy (Formula presented.) is applied to a qualified group ((Formula presented.)) at a period. Going beyond simply finding the policy effect, however, the policy maker may desire to find the effect of extending the policy to the (Formula presented.) group or to a pre-policy period. For a continuous outcome (Formula presented.), typically a linear model is adopted where the policy effect is the constant slope of (Formula presented.), in which case the constant effect applies to untreated units or past periods. However, if (Formula presented.) is binary (or noncontinuous, more generally) so that a nonlinear DD occurs and the policy effect is inherently heterogeneous, then extending the policy becomes involved, as the effect depends nonlinearly on covariates. We show how to do policy extensions and inference in nonlinear DD to aid the policy maker in deciding whether to expand the policy or not, and we provide two empirical illustrations.