Continuous Difference-in-Differences (DID) Model: Addressing Heterogeneous Policy Impacts

The conventional Difference-in-Differences (DID) methodology considers exogenous policy shocks as a quasi-natural experiment, whereby the policy grouping variable is encoded as a dummy variable in the regional dimension and the policy time variable is encoded as a dummy variable in the time dimension. The policy effect is evaluated based on whether or not a region is impacted by the policy. However, in cases where different regions are impacted to varying degrees under these two policy time points, the policy grouping variable in the regional dimension becomes a continuous variable rather than a binary one. To address this issue, a continuous DID model is formulated as follows.