The GDP-Temperature relationship: Implications for climate change damages

Abstract

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.

Introduction

It has long been understood that economic outcomes are related to climate. This climate-economy relationship determines the scope and magnitude of market impacts from climate change over the next 100 years and beyond. Consequently, an understanding of the climate-economy relationship is central to projections of damages from anticipated climate change, and to policymaking that weighs the benefits and costs of climate change mitigation. Yet estimation of the scope and magnitude of climate impacts on the economy is hindered by the temporal invariance of climate over relevant time frames and by the correlation of cross-sectional climate variation with other regional heterogeneity that may effect economic performance, including historical effects of settlement and colonization (e.g., Acemoglu et al. 2002; Easterly and Levine 2003; Rodrik et al. 2004; Dell et al. 2014).

A recent literature, therefore, employs panel econometric methods to estimate the response of economic outcomes to weather, which is commonly defined as realizations from distributions of climatic variables, like temperature, wind, and precipitation (Dell et al. 2014; Hsiang 2016; Auffhammer 2018). This literature has estimated economically and statistically significant effects of weather on a variety of economic outcomes, including crop yields, industrial output, and labor productivity.¹ A subset of this literature also relates weather and weather shocks to economic aggregates like gross domestic product (GDP) (Hsiang 2010; Barrios et al. 2010; Anttila-Hughes and Hsiang 2011; Deryugina 2011; Dell et al. 2012; Hsiang and Narita 2012; Burke et al. 2015, 2018).

Much of this empirical research is intended to inform estimation of climate change damages and determinations of efficient climate change mitigation programs (Dell et al. 2014; Deryugina and Hsiang 2014; Hsiang 2016; National Academies of Sciences 2017; Burke et al. 2018). Integrated assessment models (IAMs), commonly used in analysis of climate change mitigation costs and benefits, rely upon the enumeration and aggregation of relevant, sector-specific impacts (National Academies of Sciences 2017). Given the sparseness of empirical estimates of sectoral impacts around the world, such models often must extrapolate impacts out of sample. Therefore, growing interest centers on the econometric estimation of climate impacts on economic aggregates that subsume sectoral effects, obviating the need to fully enumerate and estimate them. The aggregate econometric approach also complements the enumerative approach by potentially validating estimated magnitudes of damages. However, economic aggregates such as GDP are not direct welfare measures, and do not reflect non-market values affected by climate change. These should also be incorporated into welfare analysis.

Moreover, the econometric approach confronts two challenges in estimating aggregate economic impacts of climate change. First, identification of climate effects from weather variation requires strong assumptions about dynamic processes like adaptation and the persistence of idiosyncratic temperature responses amid secular climate change (Dell et al. 2014; Hsiang 2016). Second, theory does not prescribe specific, estimable, structural relationships between climate and economic outcomes (Dell et al. 2014; Hsiang 2016; Schlenker and Auffhammer 2018). Researchers, therefore, have made varying assumptions about the functional forms of these relationships.

For instance, by relating country-level, aggregate per capita economic growth to a log-linear function of temperature and precipitation, and controlling for country-specific effects and secular trends, Dell et al. (2012), henceforth DJO, estimated that only poor country growth is harmed by positive temperature shocks. In contrast to DJO, Burke et al. (2015), henceforth BHM, specified a quadratic relationship between temperature and per capita GDP growth that suggests rich and poor countries alike suffer from global warming and that both agricultural and industrial output growth are impeded. Employing parametric country-specific quadratic trends, the preferred model of BHM estimates a globally optimal temperature for GDP growth of 13 °C and predicts global income losses of 23% by 2100 due to unmitigated climate change. The same econometric approach is employed by Burke et al. (2018) to estimate a cumulative $20 trillion in global damages avoided by 2100 if global warming is limited to 1.5 °Celsius (C) rather than 2 °C.

Whereas DJO and BHM each estimate a relationship between temperature and GDP growth, Hsiang (2010), Deryugina and Hsiang (2014) and Deryugina and Hsiang (2017) postulated a non-linear relationship between temperature and GDP levels. Hsiang (2010) relied principally upon a linear model to identify statistically and economically significant effects of annual average temperature on aggregate output and sectoral production in the Caribbean and Central America. His estimation of a piece-wise linear function relating daily average temperature to annual production indicated production losses occur only on extremely hot days with average temperatures of 27–29 °C. Specifying a similar piece-wise linear relationship between daily temperatures and GDP levels, Deryugina and Hsiang (2014) and Deryugina and Hsiang (2017) estimated U.S. production losses at daily average temperatures as low as 15 °C.²

Economists have long observed that theory often does not precisely define estimable forms of economic relationships, reserving to empiricists significant discretion in defining functional forms and selecting conditioning variables.³ The consequences of that selection for inference have also long been enumerated.⁴ As Hendry (1980) and Leamer (1983) observed, given that parameter sensitivity is indicative of specification error, empiricists often endeavor to demonstrate the robustness of parameter estimates to alternative assumptions. Yet, as Leamer (2010) contends, such sensitivity analyses or robustness checks are, themselves, often performed in ad hoc ways. Rigorous model selection tools can be applied in these settings to empirically ground model selection via processes less dependent upon researcher discretion.

Thus, this paper systematically assesses the sensitivity of temperature parameter estimates to modeling assumptions and considers the implications of model uncertainty for estimates of climate change impacts on GDP. It evaluates competing models in the literature and a range of variants using a rigorous cross validation approach that is commonly employed in causal inference.⁵ Models are evaluated according to out-of-sample model fit criteria as is particularly appropriate for models that are intended to predict future economic outcomes given expectations about future climatic conditions. Moreover, we invoke the substantial literature on data-driven, predictive model comparison (e.g., White 1996; Diebold and Mariano 1995; Hansen 2005; Hansen et al. 2011) to identify the set of models that are statistically superior to alternatives conditional on prediction procedures. This approach is standard (e.g., Diebold and Mariano 1995; West 1996), and was employed by Auffhammer and Steinhauser (2012) in the related context of modeling carbon emissions in the United States.

We use a country-level panel of economic growth, temperature, and rainfall to estimate the global relationship between GDP and temperature. Eight hundred models are estimated. They vary along four key dimensions: the assumed functional form for temperature and precipitation, methods of controlling for potentially confounding time trends, the persistence of temperature effects on GDP as indicated by the choice of GDP growth or levels as the relevant dependent variable, and the inclusion of temperature (and precipitation) lags as covariates. These models are evaluated by several cross-validation techniques to determine their relative performance, as well as their implications for damages from future warming.

Cross validation and statistical tests of model superiority reveal considerable model uncertainty that implies GDP impacts by 2100 ranging from substantial losses to substantial gains. Estimates of GDP impacts vary considerably more across those models assuming temperature effects on GDP growth, rather than GDP levels, reflecting the compounding of growth effects over time. For each cross validation approach, the set of superior models is dominated by levels models, but includes growth models. For superior growth models, the 95% confidence interval of GDP impacts in 2100 is −84% to +359%, reflecting considerable model and sampling uncertainty. In contrast, the 95% confidence region for superior levels models is −8.5% to +1.8%, and is centered around GDP losses of 1–2%. The model preferred by BHM that predicts GDP losses of 23% is excluded from all model sets of superior predictive ability.

Growth models yield immense uncertainty about global warming impacts. Across just those growth models that specify a non-linear temperature function, the combined model and sampling uncertainty yield a standard deviation of predicted impacts equal to 132% of GDP, with model uncertainty comparable in magnitude to sampling uncertainty.⁶ Models specifying impacts on GDP levels, not growth, yield far less uncertainty in climate impacts; the standard deviation is equal to less than 3% of GDP for model, sampling, and combined uncertainty. Considerable growth model uncertainty affords little policy guidance and suggests caution is warranted when such estimates are incorporated into IAMs (e.g., Moore and Diaz 2015) or used to estimate the social cost of carbon (Ricke et al. 2018). Levels models, in contrast, are associated with less model uncertainty and project a range of impacts consistent with damage estimates embodied in leading IAMs.

Non-linear temperature specifications dominate the model sets of superior predictive ability in our prediction procedure. These include quadratic and cubic temperature functions, as well as temperature splines. These non-linear temperature models, however, do not perform statistically better in out-of-sample validation than models that exclude temperature entirely. In fact, the root mean-squared prediction errors of many of these models are not distinguishable to four decimal places, which reflects the relatively small share of variation explained by temperature. By forecast and backcast cross-validation approaches, models with any country-specific trends are statistically inferior to those that exclude trends, indicative of overfitting by models that include them.

Accounting for uncertainty among models of superior performance in our estimation procedure, we find that the marginal effect of temperature on GDP growth is not distinguishable from zero at annual average temperatures observed in our data. The marginal effect of temperature on GDP levels is more precisely estimated than the effect on GDP growth, yet there is still a wide range of temperatures for which the confidence intervals include zero.

We also explore temperature impacts on GDP by country-level income group and by agricultural versus industrial production. Among poor countries, we find consistently negative mean effects of temperature on GDP levels, which are statistically significant at the 10% significance level above 18 °C. Likewise, we find evidence of substantial temperature impacts on agricultural GDP levels, with a mean impact that is negative above 10 °C but statistically indistinguishable from zero effect at conventional levels of scientific certainty.

We find no statistically significant growth effects among poor countries or within the agriculture sector. Neither do we find statistically significant evidence of GDP level or growth effects among rich countries or non-agricultural production. These results are consistent with theories that industrialized countries with greater capacities to adapt to temperature and climate and economic sectors less exposed to weather and climate are less affected by climate change (Poterba 1993; Mendelsohn et al. 1994; Kahn 2005; Stern 2006; Nordhaus 2008; Tol 2009; Deryugina and Hsiang 2014).

The paper is organized as follows. The next section reviews the literature on the relationship between temperature and economic aggregates, highlighting the variety of modeling assumptions employed in the literature. Section 3 describes our method of assessing the impact of these alternative assumptions, and section 4 presents results of the model cross validation and implications for causal inference and climate damage projections. Section 5 concludes.