On reduced form estimation of the effect of policy interventions on the COVID-19 pandemic

Several studies have estimated the effects of various nonpharmaceutical interventions on the COVID-19 pandemic using a 'reduced form' approach. In this paper, I show that many different SIR models can generate virtually identical dynamics of the number of reported cases during the early stages of the epidemic and lead to the same reduced form estimates. In some of these models, policy interventions effectively reduce the transmission rate; in others, the growth of the reported number of cases slows down even though policy has little or no effect on the transmission rate. Thus, the effect of policy cannot be uniquely determined based on the reduced form estimates. This result holds regardless of whether time series or panel data is used in reduced form estimation. I also demonstrate that the reduced form estimates of the policy effect based on panel data specifications with two-way fixed effects can have the wrong sign.