We study a natural policy experiment - the Massachusetts healthcare reform law - to examine the impact of universal healthcare on overall patient volume and the subsequent allocation of patients across the different emergency departments (EDs). We find that the policy has differential effects on the hospitals in the state. Specifically, compared to EDs with high pre-policy workloads, we observe a disproportionate increase in volume at EDs with lower levels of pre-policy workload. We propose a structural model to explain this demand smoothing phenomenon. We first show that service time increases with utilization. We then develop a model of patient choice to determine whether patients are influenced by service times and travel distances. We find that utility maximizing patients choose to avoid long waits at busy hospitals and expand their choice set of hospitals instead. Patient heterogeneity also significantly underlies the wait-travel trade-off decision. The implications of these findings – an overall volume increase, an increase in service times following an increase in utilization, and the propensity of patients to avoid overcrowded EDs - help to explain the self-correcting demand smoothing phenomenon in Massachusetts. These findings offer new insights into the ongoing debate on healthcare reform in the US and provide guidance into the implementation of the recently enacted healthcare bill, which shares significant features with the Massachusetts policy experiment.