A Continuous Difference-in-Differences Model for Heterogeneous Policy Impacts

The conventional Difference-in-Differences (DID) framework regards exogenous policy shocks as a quasi-natural experiment, whereby the policy grouping variable pertains to the regional dimension and the policy time variable pertains to the temporal dimension, both of which are expressed as binary variables. The policy impact is inferred by assessing whether the region was influenced by the policy or not. However, in instances where different regions are impacted by policies to varying degrees during distinct points in time, the policy grouping variable in the regional dimension is no longer binary, but continuous. In light of this, a continuous DID model is formulated.