Zero-inflated regression for unobserved effects panel data models and difference-in-differences estimation

We introduce a statistical model combining a continuous response regression model, which can take either positive or negative values, and a mass at zero. The proposed zero-inflated regression model may be appropriate in many empirical circumstances such as unobserved effects panel data models, difference-in-differences treatment effect estimation and, more generally, when the dependent variable is expressed in terms of variation over time. We provide a mathematical formalization by means of conditional mixtures, and we first show that in this context the classical ordinary least squares estimator is generally biased. We then propose a subset estimator based on the subsample of units for which the dependent variable has non-null values and derive its asymptotic properties under a conditional independence assumption. Such an estimator can be used, along with a binary response model for the conditional probability of facing a mass at zero, to compute the partial effects arising from zero-inflated regression models. We prove the asymptotic normality of the estimator as well as consistency of the empirical bootstrap. Then, we focus on unobserved effects panel data models and on difference-in-differences estimation under zero inflation and propose an estimator of the average treatment effect that is proven to be consistent. We finally provide a Monte Carlo simulation study as well as empirical illustrations showing the usefulness of the proposed approach and bringing new insights on the size of the bias in commonly used regression models, which are based on the assumption that the response variable is continuous.