Staying home and avoiding unnecessary contact is an important part of the effort to contain COVID-19 and limit deaths. Every state in the United States enacted policies to encourage distancing, and some mandated staying home. Understanding how these policies interact with individuals voluntary responses to the COVID-19 epidemic is critical for estimating the transmission dynamics of the pathogen and assessing the impact of policies. We use the variation in policy responses along with smart device data, which measures the amount of time Americans stayed home, to show that there was substantial voluntary avoidance behavior. We disentangle the extent to which observed shifts in behavior are induced by policy and find evidence of a non-trivial voluntary response to local reported COVID-19 cases and deaths, such that around 45 cases in a home county is associated with the same amount of time at home as a stay-at-home order. People responded to the risk of contracting COVID-19 and to policy orders, though the response to policy orders crowds out or displaces a large share of the voluntary response, suggesting that, during early stages of the U.S. outbreak, better compliance with social distancing recommendations could have been achieved with policy crafted to complement voluntary behavior. Significance StatementAmericans are spending substantially more time at home to reduce the spread of COVID-19. This behavioral shift is a mix of voluntary disease avoidance and policy-induced behavioral changes. Both need to be accounted for. Disentangling voluntary from policy-induced behavioral changes is critical for governments relaxing or renewing restrictions. A substantial share of the behavioral response appears to be voluntary, but this behavior was offset by strong stay-at-home orders. Local testing and rapid reporting is a first step to making better use of voluntary behavioral changes.