With or Without U? Binning Bias and the Causal Effects of Temperature Extremes

Estimates of climate impacts show that extreme temperatures have large and wide-spread effects. To estimate these effects, a common approach counts days in different temperature ranges and considers how exposure to these distinct 'bins' affects outcomes. This often produces non-linear, U-shaped results, in which high and low temperatures have the largest effects. We show that non-linear approaches like these can generate spurious findings. Specifically, global warming induces trends in extreme temperature exposure that correlate mechanically with a location's baseline temperature. Substantial bias emerges if trends in the outcome variable also correlate with baseline temperature for any reason. We demonstrate this problem theoretically, in simulations, and with real outcomes. We then develop solutions. In applications using US data, some results in the literature are unaffected by these corrections, while other results change substantially.