I want to estimate the effect of adoption of a policy (POL1) by firms on their Value (Y). The adoption of POL1 is driven by self-selection. A new law forces a subgroup of firms to adopt a policy called POL2. Adopting POL2 does not guarantee adoption of POL1, and adopting POL1 does not guarantee adoption of POL2. While the connection between POL1 and POL2 has not been explored deeply in literature, I have a few reasons to believe that adopting POL1 will make it easier to comply with POL2. Given these reasons, I am planning a DiD with Treatment firms being firms that were forced to adopt POL2 and also adopted POL1 after the law was passed. The control firms are firms that were not forced to adopt POL2 and also never adopted POL1. The matching is based on nearest neighbour, Mahalanobis distance on industry, Y and some firm characteristics in the PRE period. The model is
deltaY= Y_POST - Y_PRE = b0 + b1.POL1 + Xb2 + e
The sample has 60 treatment firms and hence, the model above has 120 observations.
Please let me know (a) what do I need to do to justify the model above, and (b) is there some cleaner way to arrive at the needed inference?
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