I have worried about related issues for some while, and now that someone has done the hard work I find the results disturbing and possibly significant:
Econometric models of temperature impacts on GDP are increasingly used to inform global warming damage assessments. But theory does not prescribe estimable forms of this relationship. By estimating 800 plausible specifications of the temperature-GDP relationship, we demonstrate that a wide variety of models are statistically indistinguishable in their out-of-sample performance, including models that exclude any temperature effect. This full set of models, however, implies a wide range of climate change impacts by 2100, yielding considerable model uncertainty. The uncertainty is greatest for models that specify effects of temperature on GDP growth that accumulate over time; the 95% confidence interval that accounts for both sampling and model uncertainty across the best-performing models ranges from 84% GDP losses to 359% gains. Models of GDP levels effects yield a much narrower distribution of GDP impacts centered around 1–3% losses, consistent with damage functions of major integrated assessment models. Further, models that incorporate lagged temperature effects are indicative of impacts on GDP levels rather than GDP growth. We identify statistically significant marginal effects of temperature on poor country GDP and agricultural production, but not rich country GDP, non-agricultural production, or GDP growth.
That is from Richard G Newell, Brian C. Prest, and Steven E. Sexton. Via the excellent Kevin Lewis.