Causal Inference for Unequal Baseline Panel Data Under Outcome Convergence
Rachel Lobo (2026)
Abstract
This paper considers causal inference in models where treatment and comparison groups have unequal treatment statuses in the pre-period, or ``unequal baseline’’ treatment. A simple inversion of the Difference-in-Differences (DiD) model fails to identify treatment effects when treatment effects evolve over time, as is the case in many empirical settings. I explore an unequal baseline model with binary treatment and propose a causal inference approach that incorporates dynamic treatment effects. When level outcomes between Switchers and Stayers converge in the post-treatment period, treatment effects are estimable using simple methods and under mild assumptions. I prove that causal inference under this approach is valid for complex potential outcomes models such as interactive fixed effects. I target two parameters: the total treatment effect and the (instantaneous) extensive margin treatment effect. The event study estimation strategy I propose is easy to implement and provides an empirical test of the research design. I apply the methods derived in this paper to examine the role of the Pregnancy Discrimination Act of 1978 on women’s employment.