We do not identify any statistically significant effects of temperature on GDP growth

Economic forecasting, Covid-19 forecasting, AGW climate change forecasting, the past couple of decades should have taught us the challenges and dangers of narrow technical experts modeling multi-system, chaotic, complex, non-linear, loosely coupled systems.  The conceptual challenge is enormous and the data sets underpinning the efforts are often relatively sparse, low quality, or poorly defined and of inconsistent measurement quality.

For those watching the efforts it has been an exercise in frustration.  We are shoveling muck into a Rube Goldberg model of obscure design, and then treating the outcomes as if they were informative and and precise when in fact, they are virtually worthless. 

AGW forecasting models have been abysmal and repeatedly wrong to a material degree and yet we treat them as if they were both precise and accurate despite the absence of any evidence supporting that conclusion.  

One aspect of AGW forecasting is the estimation of the relationship between heat and GDP.  The argument is, in general, that the warmer the climate, the lower the GDP.  While generally treated as a given among the chattering class, among economists, historians and climate experts, relationship is far from proven.  

There is a recent paper which encapsulates some of the inside baseball aspects of this consequential debate about modeling.

In a paper by Steven Sexton in 2018, there is a recap of the debate.  From Sexton Response to Burke and Hsiang Critique of“The GDP-Temperature relationship: Implications for climate change damages”

In 2015, Nature published an important paper by Marshall Burke, Solomon Hsiang, and Edward Miguel that identified a global, non-linear relationship between temperature and economic production that implied a 23% reduction in global incomes from projected climate change in 2100. The paper (henceforth BHM) identified this relationship in rich and poor countries and in agricultural and non-agricultural production, upending the conjecture of many economists that poor countries and climate-exposed sectors like agriculture would be at risk, but rich countries and other industries may be spared large losses from climate change. In fact, the earlier work of Melissa Dell, Benjamin Jones, and Benjamin Olken (DJO) that BHM advanced reached precisely that conclusion by identifying a statistically significant linear effect of temperature on GDP growth among only poor countries.

BHM has shaped a lot of media coverage.  However,

The implications of the BHM study cannot be overstated—and have not been lost on scientific and lay audiences. The higher are the expected losses from climate change, the more costs we should incur today to mitigate climate change. If rich countries are relatively spared harms, then traditional development activities to enrich poor countries can mitigate harms from climate change. But if they, too, are at risk, then climate policy should perhaps displace development policy in a world of constrained resources. Both BHM and DJO, further, propose temperature affects GDP growth, not merely the levels of GDP, as has been widely assumed among economists, including those who developed the models estimating the human harms caused by carbon emissions employed by policy makers in the U.S.That is, a temperature shock this year, BHM propose, does not merely affect production or incomes this year before returning to normal next year(if temperatures return to normal). Rather the shock this year also affects production and incomes in subsequent years by slowing economic growth and setting the world on a GDP path that is permanently lower because of the one-time temperature shock. Neither DJO nor BHM points to a developed and peer-reviewed theory for temperature affecting growth rather than levels of GDP. The first paper models a growth effect as a matter of statistical convenience.

Further:

A broader literature dominated by Hsiang relates temperature and other weather shocks to national and sub-national economic outcomes—including GDP levels in some instances, and GDP growth in others. This growing literature makes seemingly ad hoc decisions about how to model the relationship between temperature and economic aggregates, including how to control for determinants of economic outcomes that may correlate with weather but are unobserved by researchers. These “unobservables” can bias estimates of the temperature effects on the economy. Each of these models purports to identify a causal relationship between temperature and economic outcomes. But they specify different causal models in different instances in a fashion seemingly divorced from any theory.  Indeed, theory offers little guidance on the proper set of controls or functional forms to use in this endeavor. 

Thus, observing that there is little theory to guide the statistical modeler’s choices in this setting, we set out to determine whether model performance or predictive ability can discipline researcher discretion and lend greater credibility to the results of these analyses, or at least determine the degree of uncertainty attributable to this modeling ambiguity. We do so by employing the method of cross-validation to assess which among many plausible causal models best explains the data. The idea is simply to estimate models over a subset of the available data and then assess how well the estimated models predict outcomes for a different subset of data. This approach is common across disciplines, and is recently advanced in economics by Susan Athey, among others. It is specifically advocated in the Review of Environmental Economics and Policy(2017) by Elodie Blanc and Wolfram Schlenker specifically for assessing climate impacts:“Another strength of panel models is that they offer a straightforward way to assess prediction performance by comparing model predictions to output observations.”We couple cross-validation with an approach to assess which models are statistically significantly superior in their performance following the Model Confidence Set procedure of Hansen, Lunde, and Nason (Econometrica 2011).

Among the conclusions:

The sets of best-performing models are large, reflecting the limited capacity of the data to discern among these best-performing models. Because these models project dramatically different GDP outcomes in 2100, they yield immense model uncertainty that is ignored in BHM. Accounting for this model uncertainty and the sampling uncertainty that BHM explore, we do not identify any statistically significant effects of temperature on GDP growth. Not in poor countries. Not in rich countries. Not in agriculture. And not in industrial production. Not at the 5% significance level. Not at the 10%significance level. Indeed, not even at the 20% significance level.In estimating the marginal growth effect of temperature across all countries and all GDP, we do not find a statistically significant marginal effect of temperature on GDP growth at even the 50% significance level.

 Burke and Hsiang have a response in The GDP-temperature relationship - some thoughts on Newell, Prest, and Sexton 2018 from October, 2020.

Sexton et al have an update to their paper and response to critiques, also from October 2020.  

It would be presumptuous on part to assess the relative merits given that the esoterica of the criticisms of one another are beyond my direct experience.

As a practical matter, I am inclined towards Sexton, et al based on the old adage that extraordinary claims require extraordinary evidence.  All the institutional world is committed to the belief that there is an AGW effect (still disputed), that there are effective interventions (still disputed) and that only coercive central planning and control can make these interventions work (still disputed.)  

Additionally, there is the broader issue that our experience and capacity to model multi-system, chaotic, complex, non-linear, loosely coupled systems using data sets underpinning those efforts which are often relatively sparse, low quality, or poorly defined and of inconsistent measurement quality is highly constrained and record of success not established.