Policy Evaluation with Nonlinear Trended Outcomes: Covid-19 Vaccination Rates in the United States

This paper discusses pitfalls in two way fixed effects (TWFE) regressions when the outcome variables contain nonlinear and possibly stochastic trend components. If a policy change shifts trend paths of outcome variables, TWFE estimation can distort results and invalidate inference, especially in a context of evolving policy decisions. A robust solution is proposed by allowing for dynamic club membership empirically using a relative convergence test procedure. The determinants of respective club memberships are assessed by panel ordered logit regressions. The approach allows for policy evolution and shifts in outcomes according to a convergence cluster framework with transitions over time and the possibility of eventual convergence to a single cluster as policy impacts mature. The long run impact of a policy can thus be examined via its impact on convergence club membership. An application to new weekly US Covid-19 vaccination policy data reveals that federal level vaccine mandates produced a merger of state vaccination rates into a single convergence cluster by mid-September 2021.