Understanding the historical response of economic output to temperature
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To understand how economic output around the world has historically responded to changes in temperature, we assembled data on economic output and on climate variables (temperature and precipitation) for every country in the world where data were available.

We then analyzed these data using statistical techniques that help us isolate the effects of temperature and precipitation from other country-level or global factors that might also affect economic output. Our approach is described in detail in the supplemental information of our paper, but the thought experiment is fairly simple: take any country in the world, and compare its economic output in a year that is hotter than normal for that country to its economic output in an average temperature year for that country. Then take countries with similar average temperatures, and calculate the economic effect of increasing temperatures as the average effect across those countries.

What we find when we do this is shown in the figure below. Countries with cool average temperatures, such as countries in northern europe, tend to see higher than average growth in economic output when temperatures are warmer than average. Countries with relatively hot average temperatures, such as countries in the tropics, tend to see slower than average economic growth when temperatures warm.

This gives us the “nonlinear” response in the title of the paper. Looking across all countries in the world, we find that the effect of warming temperatures depends on what your average temperature was to start. The warmer your average temperature to start, the more negative the impacts of additional warming.