We often estimate dose-response functions of outcome Y on temperature by combining binned regression with fixed effects. It can be important to consider the functional form chosen here and what it implies for extrapolation.

- OLS can be strongly influenced by outliers. In fixed effects models with bins, outliers can be less obvious: unusually hot or cold day for a given region in a given season, for example. This means that errors in either the outcome or the RHS become more important, as do infrequently observed days.
- Still, the edges of the response function are determined (in splined or binned models) primarily by regions/seasons that typically experience that kind of weather. Extrapolation a problem for that reason as well.

Here’s what other people say about these questions: - Auffhammer, Hsiang, Schlenker, Sobel 2014 - Hsiang 2016 - Dell, Jones, and Olken 2014