Background: Countries have adopted different approaches, at different times, to reduce the transmission TRANS of coronavirus disease MESHD 2019 (COVID-19). Cross-country comparison could indicate the relative efficacy of these approaches. We assess various non-pharmaceutical interventions (NPIs) over time, comparing the effects of self-imposed (i.e. voluntary) behavior change and of changes enforced via official regulations, by statistically examining their impacts on subsequent death MESHD rates in 13 European countries. Methods and findings: We examine two types of NPI: the introduction of government-enforced closure policies over time; and self-imposed alteration of individual behaviors in response to awareness of the epidemic, in the period prior to regulations. Our proxy for the latter is Google mobility data, which captures voluntary behavior change when disease MESHD salience is sufficiently high. The primary outcome variable is the rate of change in COVID-19 fatalities per day, 16-20 days after interventions take place. Linear multivariate regression analysis is used to evaluate impacts. Voluntarily reduced mobility, occurring prior to government policies, decreases the percent change in deaths MESHD per day by 9.2 percentage points (95% CI 4.5-14.0 pp). Government closure policies decrease the percent change in deaths MESHD per day by 14.0 percentage points (95% CI 10.8-17.2 pp). Disaggregating government policies, the most beneficial are intercity travel TRANS restrictions, cancelling public events, and closing non-essential workplaces. Other sub-components, such as closing schools and imposing stay-at-home rules, show smaller and statistically insignificant impacts. Conclusions: This study shows that NPIs have substantially reduced fatalities arising from COVID-19. Importantly, the effect of voluntary behavior change is of the same order of magnitude as government-mandated regulations. These findings, including the substantial variation across dimensions of closure, have implications for the phased withdrawal of government policies as the epidemic recedes, and for the possible reimposition of regulations if a second wave occurs, especially given the substantial economic and human welfare consequences of maintaining lockdowns.