Abstract
We use theory and empirics to distinguish between the impact of temperature on transition (temporary) and steady-state (permanent) growth in output per capita. Standard economic theory suggests that the long-run growth rate of output per capita is determined entirely by the growth rate of total factor productivity (TFP). We find evidence suggesting that the level of temperature affects the level of TFP, but not the growth rate of TFP. This implies that a change in temperature will have a temporary impact on growth in output per capita. To highlight the quantitative importance of distinguishing between permanent and temporary changes in economic growth, we use our empirical estimates and theoretical framework to project the impacts of future increases in temperature caused by climate change. We find losses that are substantial, but smaller than those in the existing empirical literature that assumes a change in temperature permanently affects economic growth.
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Notes
The 2% decrease in output does not account for the endogenous response of capital accumulation to the change in productivity caused by the climate damage.
This comparison understates the quantitative difference between the two approaches, because climate-economy models use global average temperature as a sufficient statistic for a wide range of climate impacts, while the econometric literature focuses only on changes in local ambient temperature and abstracts from other impacts like natural disasters and sea level rise.
We do find evidence of growth effects in some specifications that use region-by-year fixed effects or allow country fixed effects to differ before and after 1990. However, even when the growth effects coefficients are statistically significant, the signs of the growth effects differ across these specifications and almost all of the estimated country-period interactions or region-by-year fixed effects are statistically insignificant.
If we instead include both growth and level effects, our projections imply that future temperature changes increase global GDP per capita by 14.9% with a large confidence interval of (− 56.4, 300.9).
This aggregate number masks considerable heterogeneity. Given the nonlinear impact of temperature on TFP, hotter countries are more negatively impacted by climate change. For example, GDP per capita falls by 8.5% in India, a relatively hot country, but only by 2.3% in the US, a comparatively colder country.
See Auffhammer (2018) for a review of the empirical literature on the broader impacts of climate change.
Our simple model abstracts from the distinction between weather and climate. Weather refers to specific outcomes (e.g., temperature and precipitation) in a unit of space (e.g., country) over a specific time (year). Climate refers the distribution of potential weather outcomes. Our simple model has a fixed savings rate and no forward looking behavior. Consequently, climate has no impact on the economic dynamics conditional on weather.
Since we are focused on long-run increases in temperature from climate change, we define growth and level effects in terms of permanent changes in temperature. However, we can also consider how a temporary change in temperature would affect the level and growth rate of GDP per capita in both cases. A temporary change in temperature will have a temporary impact on the growth rate of output per capita, regardless of whether there are level or growth effects. A temporary change in temperature will have a permanent effect on the level of GDP per capita if there are growth effects and no impact on the long-run level of GDP per capita if there are level effects.
The defining feature of the Solow model is a constant savings rate. The theoretical distinctions between level and growth effects are the same in a more general neoclassical growth model with an endogenous savings rate. Regardless of whether the savings rate is endogenous, the long-run growth rate of income per capita is determined entirely by the growth rate of TFP. A change in the level of TFP only affects the growth rate of GDP per capita along the transition path.
In the empirical analysis, we allow for the possibility that both effects exist simultaneously. In the case where both exist, the long-run impact of temperature on the growth rate of GDP per capita still depends only on the growth effect.
There is also some evidence that the approach used in macroeconomic models is consistent with the implicit theoretical framework underlying the empirical analyses that focus on growth effects. For example, the dynamics of GDP in a world with only level effects (Fig. 1) are quite similar to those labeled as a “permanent growth effect” in Burke et al. (2015) (see panel a of figure ED2).
We use variables rgdpna, rrna, and pop to measure output, capital, and population, respectively.
Across all specifications, Arellano-Bond tests reject the null of no autocorrelation of order one, but fail to reject the null of no autocorrelation of order two. To be conservative and consistent with Bond et al. (2010), we correct for autocorrelation of order two.
Appendix Table B1 reports results with standard errors clustered by country. In this case, we continue to reject the null of no level effects. We still cannot reject the null hypothesis of no growth effects, but the p-value is lower than in our main results (\(p=0.12\)). As shown in Appendix Figure C1 and Fig. 8, these growth effects would imply a substantial economic benefit from future temperature change for most countries.
The optimal temperature for column 1 equals \(-\gamma _1/(2\gamma _2)\). Based on our structural equations for TFP growth, (9) and (10), this is the value of temperature that maximizes the growth rate of TFP in the absence of level effects (\(\beta _1=\beta _2=0\)). Similarly, the optimal temperature in column 2 equals \(-\beta _1/(2\beta _2)\). This is the level of temperature that maximizes the level of TFP, in the absence of growth effects (\(\gamma _1=\gamma _2=0\)). We do not report an optimal temperature for column 3, because this object is not well defined when there are both growth and level effects. Due to rounding, our results differ from those calculated directly from the estimates reported in the table.
Appendix Table B5 presents the first-stage results.
The violation of the exclusion restriction could imply that we should include more lags of the dependent variable in our baseline specification. Appendix Table B6 presents the OLS results with four lags of the dependent variable. Only the first lag is significant and the results are similar to our baseline results in Table 1.
Following the existing literature, our main results assume that the temperature coefficients are homogeneous across countries. In Appendix Table B7, we follow Bond et al. (2010) and implement a version of the Pesaran and Smith (1995) mean group estimator. To do so, we estimate separate time series regressions for each country and report the median of the country-level coefficients and a robust estimate of the mean. To account for time fixed effects, all variables in the country-level regressions are measured relative to the average across countries within a given year. The coefficients in these regressions are similar to our baseline results, but the confidence intervals are much larger and all of the temperature variables are insignificant.
Allowing for country-specific trends implies that the impacts of temperature on TFP are no longer identified from country-specific trends in the growth rate of temperature (e.g., as a result of climate change).
We performed this test separately for the linear and quadratic terms. We also performed a test with ten lags and arrived at the same result. We excluded this specification from the table due to space constraints.
Our main results account for heterogeneous marginal impacts of temperature with a quadratic term. In Appendix Table B16, we allow for additional heterogeneity by interacting annual temperature with average temperature over the sample period, along the lines of Carleton et al. (2022). We find no evidence for heterogeneity beyond the quadratic term. In Appendix Table B17, we interact temperature with lagged temperature to determine whether the impact of temperature in a given year depends on recent temperature shocks. We do not find evidence for this interaction.
Burke et al. (2015) also include country-specific quadratic time trends. Appendix Table B18 recreates Table 2 and includes quadratic time trends to be directly comparable to Burke et al. (2015). For completeness, columns 2 and 4 add lagged dependent variables to the specifications in columns 1 and 3.
Column 3 assumes a different data generating process and finds a nonlinear relationship between the level of temperature and the level of GDP per capita. If this was the true data generating process, it would imply that there are no transition dynamics following a temperature shock. Note that this case is different than the case of a level effect. In the level effect case, a shock to temperature induces transition dynamics in capital and slows economic growth in the short run.
In the appendix to their paper, Dell et al. (2012) find growth effects in specifications similar to column 6 of Table 2. They model heterogeneous marginal effects of temperature by considering linear specifications with temperature coefficients that differ by level of development. Following Burke et al (2015), our nonlinear specification captures these heterogeneous marginal effects. Since poorer countries tend to have temperatures above the optimum, the marginal impact of an increase in temperature will be larger, on average, in poorer countries. Our results in Appendix Tables B14 and B15, as well as Appendix Section C.3 in Burke et al. (2015), suggest that modeling heterogeneous impacts through nonlinearities in temperature is a better match for data. Even after accounting for the nonlinear impacts of temperature, our results in columns 5 and 6 of Table 2 demonstrate that accounting for capital dynamics is important for distinguishing between growth and level effects.
To be consistent with the existing literature and columns 1 and 5 of Table 2, we do not include the lagged dependent variable in the specification with capital as the dependent variable. If we do include the lagged dependent variable in this specification, then both the level and growth effect coefficients are insignificant. Also, it is important to note that these regressions do not control for how close capital is to its balanced growth level and should therefore be interpreted with caution.
Newell et al. (2021) undertake a large-scale sensitivity analysis focusing on GDP per capita regressions without lagged dependent variables.
The projections are from the World Meteorological Organization and can be downloaded from https://climexp.knmi.nl/start.cgi. To calculate the projected temperature for each country-year, we add the projected change in temperature from 2010 to the observed value of the 2010 temperature. Note that for a small set of countries, we only have the projected change in temperature from 2010 to 2100 rather than yearly projections. For these countries, we linearly interpolate the temperature change in each year based on the projected temperature change from 2010 to 2100.
A key contribution of our approach is to project the future impacts of climate change in a Solow-style model that maintains the distinction between transition (temporary) and steady-state (permanent) growth in income per capita. One drawback of using a Solow model is that our projections abstract from the impact of changes in productivity on the savings rate.
Mongolia is the coldest country in our data with an annual average temperature in 2010 of -1.7\(^\circ\)C. It is far north, has average elevation of over 5000 feet and is completely landlocked. Starting from such a low temperature implies that Mongolia experiences considerable gains.
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We are grateful to Laura Bakkensen, Felix Kubler, Peter Pedroni, Sanjay Singh, David Weil, Dan Wilson, and Nick Wilson, as well as seminar participants at the Federal Reserve Board of Governors, Williams College, and the IMF/BAM/IMFER conference on Transformational Recovery. We also thank the Editors and three anonymous referees for helpful comments. The views expressed in this paper are our own and do not reflect the views of the Federal Reserve System or its staff.
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Casey, G., Fried, S. & Goode, E. Projecting the Impact of Rising Temperatures: The Role of Macroeconomic Dynamics. IMF Econ Rev 71, 688–718 (2023). https://doi.org/10.1057/s41308-023-00203-0
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DOI: https://doi.org/10.1057/s41308-023-00203-0