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In combating the spread of COVID-19, some governments have been reluctant to adopt lockdown policies due to their perceived economic costs. Such costs can, however, arise even in the absence of restrictive policies, if individuals' independent reaction to the virus slows down the economy. This paper finds that imposing lockdowns leads to lower overall costs to the economy than staying open. We combine detailed location trace data from 40 million mobile devices with difference-in-differences estimations and a modification of the epidemiological SIR model that allows for societal and political response to the virus. In that way, we show that voluntary reaction incurs substantial economic costs, while the additional economic costs arising from lockdown policies are small compared to their large benefits in terms of reduced medical costs. Our results hold for practically all realistic estimates of lockdown efficiency and voluntary response strength. We quantify the counterfactual costs of voluntary social distancing for various US states that implemented lockdowns. For the US as a whole, we estimate that lockdowns reduce the costs of the pandemic by 1.7% of annual GDP per capita, compared to purely voluntary responses.