  In this paper we develop statistical methods for causal inference in
epidemics. Our focus is in estimating the effect of social mobility on deaths
in the Covid-19 pandemic. We propose a marginal structural model motivated by a
modified version of a basic epidemic model. We estimate the counterfactual time
series of deaths under interventions on mobility. We conduct several types of
sensitivity analyses. We find that the data support the idea that reduced
mobility causes reduced deaths, but the conclusion comes with caveats. There is
evidence of sensitivity to model misspecification and unmeasured confounding
which implies that the size of the causal effect needs to be interpreted with
caution. While there is little doubt the the effect is real, our work
highlights the challenges in drawing causal inferences from pandemic data.
