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Assessing the contribution of mobility declines to the control of Covid-19 diffusion is an urgent challenge of global import. We analyze the temporal correlation between transmission rates and societal mobility levels using daily mobility data from Google and Apple in an international panel of 99 countries during the period of March-December 2020. Reduced form regression estimates that flexibly control for time trends suggest that globally, a 10 percentage point reduction in mobility is associated with a 0.05–0.07 reduction in the value of the effective reproduction number, R(t). However, the strength of the association varies substantially across world regions and over time, being initially positive and strong in most world regions during the 2020 spring period, but becoming weaker over the summer, especially in Europe and Asia. We further find evidence that the strength of the association between mobility and transmission rates is reduced where facial coverings rules were implemented.