Primary Submission Category: Weighting
Poisson regression under heterogeneous treatment effects
Authors: Georgy Kalashnov, Lihua Lei,
Presenting Author: Georgy Kalashnov*
We study the properties of Poisson regression under heterogeneous treatment effects as a better choice compared to log-linear regression in policy evaluation setting. Log-linear regression aggregates multiplicative individual effects from both large and small subjects with equal weights. However, a policy evaluation study is interested in a ratio of the means rather than mean of the ratios, which is to give weights proportional to the subject sizes. We show that Poisson regression estimates exactly the ratio of means in different specifications. We show that a Poisson regression on treatment and controls estimates a convex average of the individual effects in the spirit of Angrist (1998) in the case when the effects are small and average treatment on control, when the effects are large and positive, and average treatment on the treated, when the effects are small. We also show a double robust way to estimate an average treatment effect in Poisson regression.