We present a novel data set of subnational economic output, Gross Regional Product (GRP), for more than 1500 regions in 77 countries that allows us to empirically estimate historic climate impacts at different time scales. Employing annual panel models, long-difference regressions and cross-sectional regressions, we identify effects on productivity levels and productivity growth. We do not find evidence for permanent growth rate impacts but we find robust evidence that temperature affects productivity levels considerably. An increase in global mean surface temperature by about 3.5°C until the end of the century would reduce global output by 7–14% in 2100, with even higher damages in tropical and poor regions. Updating the DICE damage function with our estimates suggests that the social cost of carbon from temperature-induced productivity losses is on the order of 73–142$/tCO2 in 2020, rising to 92–181$/tCO2 in 2030. These numbers exclude non-market damages and damages from extreme weather events or sea-level rise. © 2020 The Authors