The distributional impact of climate change

Poorer, hotter countries are more vulnerable to climate change and will experience more negative impacts. The pattern of vulnerability between countries is used to impute impacts for income deciles within countries, for administrative regions, and for grid cells. Almost three‐quarters of people will face worse impacts than their country average. Between‐country variation is larger than within‐country variation for income deciles and regions, and about as large for grid cells. I here revisit earlier estimates of the economic impact of climate change and extend the analysis to impute the distribution of impacts within countries.


Introduction
Poorer countries are more vulnerable to climate change. This qualitative insight has long been around, 1 but quantification has lagged as estimating the impacts of climate change is difficult. I here revisit earlier estimates of the economic impact of climate change 2 and extend the analysis to impute the distribution of impacts within countries.
Estimates of the economic impact of climate change are important because they form the basis for estimates of the benefits of climate policy and, in the form of the social costs of carbon, directly compare to the costs of greenhouse gas emission reduction. The distribution of those impacts between and within countries matters because the global total impact and the social cost of carbon are sensitive to its distribution 3-6 -unless one assumes that utility is linear in consumption 7 or that impacts of climate change will be compensated. 8 Furthermore, high and low impacts are not random, but rather depend on fundamental factors at least some of which are partially malleable by policy. 9 The distribution of impacts between countries informs inter-national climate negotiations, especially on the discussion around loss and damage and the implied historical responsibility and liability. It should also guide the allocation of the monies in the Adaptation Fund and other international development assistance. The distribution of impacts within countries informs the targeting of national adaptation projects and other policy interventions to reduce vulnerability to climate change.
While a greater resolution of the estimates of the economic impacts of climate change is welcome for the reasons given above, more detail does not equate to higher accuracy. Some things average out on a national or continental scale, and therefore do not matter at that resolution. When models calibrated at a coarse resolution are used to impute numbers at a fine resolution (as is done below), things that are irrelevant at the coarse resolution are also assumed to be irrelevant at the fine resolution. One example is the particular vulnerability of the coast to sea-level rise and tropical storms. 10 Food producers and consumers are differently affected by impacts on crops. Another example is the special position of cities and the synergy between global warming and the urban heat island effect. 11 The downscaled estimates discussed below should therefore not be taken at face value. Rather, these estimates are used to demonstrate that resolution matters and to encourage further economic research at a finer scale. The paper proceeds as follows. The section "The total impact of climate change" revisits estimates of the economic impact of climate change. This material is not original but needed to understand what follows. Section "Distribution of impacts" presents new estimates of the economic impact of climate change per country 2,12 and per income decile, 13 and, for the first time, estimates of the impact per subnational region and for grid cells. Section "Measures of inequality" shows measures of inequality. the welfare equivalent income change, or Hicksian equivalent variation. These numbers should be read as follows: a global warming of 2.5 • C would make the average person feel as if she had lost 1.3% of her income, and 1.3% is the average of the 11 dots at 2075.

Methods
The estimates in Figure 1 use a range of methods. In the enumerative method, researchers take estimates of the many impacts of climate change for all parts of the world in their natural units from the relevant literature, estimate the values of these impacts (using either market prices or monetary valuation methods), multiply the quantities and prices, and add everything up. [14][15][16][17][18][19][20][21][22][23][24][25][26] The result is an estimate of the direct cost-price times quantity-of climate change. The direct cost is a poor approximation of the change in welfare, for instance, because it ignores price changes, but it is an approximation nonetheless. The enumerative approach omits interactions between sectors, such as changes in water resources affecting agriculture.
Other studies use the same physical impact estimates as the enumerative studies above, but as shocks to a computable general equilibrium model. 27,28 These estimates include both price changes and interactions between economics sectors, be it through output, intermediate or input markets, and between economies through international trade and investment. The typical welfare measure used in these studies is the Hicksian Equivalent Variation, an exact welfare measure. Computable general equilibrium models are based on the national accounts, and thus misrepresent subsistence agriculture and omit direct impacts on welfare, such as on health or nature.
Yet, other studies regress an economic indicator on climate. 29,30 Agricultural land prices, for instance, reflect the productivity of the land and hence the value of the climate that allows plants to grow. 31 Price differences due to climate variation are used to estimate the direct cost of climate change. Household expenditure 32 and self-reported happiness 33,34 have also been used. The main advantage of the Ricardian method is that it is based on actual, rather than modeled behavior. The main disadvantage is that climate variations over space are used to derive the impact of climate change over time. Space and time are different things.
One estimate elicits expert views. 35 The study was done before anyone could reasonably claim expertise on the economic impacts of climate change. Views were expressed about the impact of climate change on global output, which can be interpreted as a measure of economic activity (but not welfare) as well as a measure of income (and thus welfare).

Weather and climate
Climate, the 30-year average of weather, varies only slowly over time. In Ricardian studies, the impact of climate is identified from cross-sectional variation. However, many other things vary over space too. Panel data help unless confounders do not change much over time. To overcome this problem, a number of papers estimate the impacts of weather on a range of economic indicators. [36][37][38][39][40] From an economic perspective, weather is random and its impact therefore properly identified. Unfortunately, the impact of a weather shock is not the same as the impact of climate change. 41 See Refs. 42 and 43 for the rather restrictive conditions under which weather variability is informative about climate change. Particularly, weather studies estimate the short-run response of the economy, whereas the interest is in the long-run response, with adjustments in capital, behavior, and technology. Extrapolating the impact of weather shocks will not lead to credible estimates of the impact of climate change.

Combining estimates
Besides the primary estimates, Figure 1 also shows a curve. Seven alternative impact functions, proposed in the literature, were fitted to the data. The curve shown is the Bayesian model average, that is, the seven impact functions are weighted according to their fit to the primary estimates. The 90% confidence interval shown is based on the uncertainty reported in 7 of the 27 primary estimates. Using the combined forecast error would imply a confidence and symmetry that is not there. See Ref. 12 for details. For years 1850 to 2018, the temperature shown in Figure 1 is the 30-year running mean. For 2019-2200, the temperature roughly follows the RCP8.5 scenario so that the two estimates for high warming can be shown. The return to coal assumed in RCP8.5 is now considered unlikely. 46,47 Figure 1 shows that initial warming may be positive on net, while further warming would lead to net damages. The initial benefits, due to reduced costs of heating in winter, reduced cold-related mortality and morbidity, and carbon dioxide fertilization, are mostly in the past. For future warming, the negative impacts dominate, such as summer cooling costs, infectious diseases, and sea-level rise.

Results
There are 11 estimates for 2.5 • C. Researchers disagree on the sign of the net impact, but agree on the order of magnitude: the welfare loss (or gain) caused by climate change is equivalent to the welfare loss caused by an income drop of a few percent-a century of climate change is about as bad as losing a year of economic growth.
The uncertainty is rather large, however. The error bars are probably an underestimate of the true uncertainty, as experts tend to be overconfident and estimates are incomplete. Climate economists also know each other well. The uncertainty is rightskewed. Negative surprises are more likely than positive surprises of similar magnitude. Adding risk aversion, we may argue that a century of climate change is no worse than losing a decade of economic growth. Figure 1 shows the global average impact of climate change, a metric useless for most purposes. Below, I discuss impact estimates with more granularity.

Countries
Thirteen of the 27 studies include estimates of the continental impacts of climate change or, in the studies involving David Maddison, national impact estimates. Regressing the estimated continental impact for 2.5 • C warming on per capita income and average annual temperature, with dummies α s for the studies, yields where I c is the impact in country c (in %GDP), y c is its average income (in 2010 market exchange dollars per person per year), and T c is the average annual temperature (in degrees Celsius). Hotter countries have more negative impacts. Richer countries have more positive impacts. Equation (1) does not capture the special vulnerability of delta and island nations, and it assumes that vulnerability can be proxied by income and temperature. For each of the studies, this equation is used to impute national impacts, making sure that the continental or global totals match those in the original estimates. The function shown in Figure 1 is then used to shift all impacts to 2.5 • C warming. b For each country, the average and standard deviation across studies is taken. Figure 2 shows results for individual countries for 2.5 • C warming. Hotter, poorer countries see more negative impacts. In fact, the majority of countries show a negative impact even though the global average impact is roughly zero. This is because the world economy is concentrated in a few, rich countries. The world average counts dollars, rather than countries, let alone people.
b Note that I use the global function to shift the imputed national impacts. Ref. 12 shows that this is more robust than estimating national impact functions.
Poorer countries are more vulnerable to climate change for three reasons. First, poorer countries have a higher share of their economic activity in sectors, such as agriculture, which are directly exposed to the vagaries of weather. Second, poorer countries tend to be in hotter places. This makes adaptation more difficult as there are no analogs for human behavior and technology. Cities in temperate climates need to look at subtropical cities to discover how to cope in a warmer climate, and subtropical cities at tropical ones. The hottest cities will need to invent, from scratch, how to deal with greater heat. Third, poorer countries tend to have a limited adaptive capacity. 48,49 Adaptive capacity depends on a range of factors, such as the availability of technology, the ability to pay for those technologies, the political will to mobilize resources for the public good, and the government's competence in raising funds and delivering projects. All these factors are worse in developing countries.
Some impacts of climate change may be felt more keenly in richer countries, impacts on nature being the prime example. The impact studies surveyed above suggest that such impacts are relatively small, so that the overall income elasticity of vulnerability to climate change is indeed negative. Figure 2 shows that poorer countries are more vulnerable to climate change. Aggregating results by country hides information. If poorer countries are more vulnerable, then poorer people should also be more vulnerable than richer people in the same country. Poorer people are more likely to work outdoors, their health is worse, and they are less likely to have heating and air conditioning. The provision of public goods, including coastal protection and irrigation, also tends to be slanted toward the better off. The pattern of vulnerability between countries is therefore likely to be repeated within countries. As there is no evidence on the pattern of vulnerability to climate change within countries, I assume that the pattern within countries is identical to the pattern between countries. Figure 3 again shows the impact of 2.5 • C warming. The impacts are further downscaled, to income deciles, based on data from the University of Texas Inequality Project, using the same semielasticity used to downscale continental to national impact estimates; see Eq. (1). Specifically, assume that the impact I c,p on income class p in country c equals

Income classes
Note that Eq. (2) is not estimated; it is used for imputation. Figure 3 plots the impact by decile against the impact per country. By comparison, it also plots country impact against country impact; this is the same data as shown in Figure 2. Most income deciles show an impact that is worse than the country average. This is because the average counts dollars rather than people, and the income distribution is skewed. For the world as a whole, 72.6% of people are projected to incur worse impacts then their country average. This number is higher in countries with a more skewed income distribution.

Regions
The data on income distribution do not have geographic coordinates. Therefore, the estimate of the impact of climate change by income decile assumes that rich and poor people in the same country share the same climate. This is not likely. Most countries show distinct regional patterns of development, and larger countries span different climate zones. The reasons why poorer countries are more vulnerable to climate change than richer countries, and poorer people more vulnerable than richer people also apply to poorer regions within countries. If such regions tend to be hotter already, as suggested by Refs. 30, 50, and 40, then they are even more vulnerable to climate change.
The Global Data Lab has data on per capita income for subnational administrative units, 51 that is, provinces, states, or the local equivalent. I refer to these units as regions. I used their shape files to compute the average temperature for the period 1981-2010 from the gridded Climate Research Unit data. 52,c Figure 4 repeats Figure 2, plotting the impact of 2.5 • C warming against current income and temperature. The pattern is the same as before, because the assumptions are the same as above. Poorer regions are more vulnerable to climate change, as are hotter regions. As some regions are poorer, richer, hotter, or colder than their country average, the pattern in Figure 4 is more pronounced: the lows are lower and the highs are higher.

Grid cells
The regional impact estimates above use regional average temperatures, computed from gridded temperatures. That is, the above estimates assume that everyone in a province or state shares the same cli-mate. This is a reasonable approximation for small regions, but not for big ones. I therefore downscale the estimates further, to the 0.5 × 0.5 • grid at which temperature and population numbers are reported. Specifically, I assume that everyone in a grid cell  within a region has the same income. d The impact per capita follows from Eq. (1). I use the 0.5 × 0.5 • Gridded Population of the World data to compute the total impact per country, and shift the gridded impact to match the national impact above. Figure 5 shows the results for the impact of 2.5 • C global warming on the current economy. The pattern is as above, with positive impacts in richer, colder places and negative impacts in poorer, hotter ones. Compared with the results above, there is also variation within regions. This is not immediately visible in Figure 5, but becomes apparent below.

Measures of inequality
The Lorenz curve is a standard way to depict income inequality. The Lorenz curve orders people (or countries) by their (average) income and plots cumulative income against cumulative number of people. For comparison, the Lorenz curve is typically shown together with the curve for equal income. The area between the two curve is the numerator of the Gini coefficient, and the area under the equal income curve is its denominator. This works well for absolute quantities, but not for changes, particularly if those changes can be posid The MATLAB code is on GitHub. tive or negative. Figure 6 therefore shows an variant of the Lorenz curve, here dubbed the Lorenz' curve. In the top left panel, I order people by their relative impact, with the highest positive impact first. For comparison, I show the curve with equal relative impact. e,f The two curves are far apart, highlighting the skewed distribution of the impacts of climate change.
The top right panel of Figure 6 shows the Lorenz' curve for the impact per income decile, the bottom left panel per region, and the bottom right panel for grid cells. For comparison, the Lorenz' curve is also shown for the cases in which the relative impact is the same for all deciles, regions, or cells within their countries. For deciles and regions, impact inequalities between countries are larger than inequalities within countries. Impact inequalities within countries do matter for grid cells.
Besides the graphical representation of inequalities, I show four indicators. The first one is the Gini coefficient G =ȳ c R c P c − c R c y c P c y c R c P c (5) e I also show the curve for equal absolute impact, which is the straight line that people expect. f If utility is the natural logarithm of per capita income, equal relative impact on consumption implies equal absolute impact on utility. where y c is the average income in country c,ȳ is the global average income, R c is the rank order of per capita income of country c with R c = 1 for the richest country, and P c is the size of the population and the Atkinson index (for an inequity aversion of one)  in text for explanation) of impact inequality and the Gini, Theil-T, Theil-L, and Atkinson indicators of income inequality without (none) and with (actual) the impact of climate change. For income deciles and regional impacts, results are shown for the estimated impact ("actual") and the national average impact ("average").
These indicators are calculated for current income, and for current income minus the estimated impact of climate change. For income deciles and regions, I use the estimated impact as well as the average impact for the country so as to assess the relative contributions of between-and within-country variations. I also compute something like the Gini coefficient for the impacts. The Gini coefficient is defined as the area between equal income curve and the Lorenz curve, divided by the area under the equal income curve. The Gini coefficient therefore uses a zero income as the worst case. As shown in Figure 6, I use impact instead of income and thus order from best to worst. The best case, however, is not zero but positive. I therefore use the highest positive impact as the base, computing the area between the equal relative impact and the highest positive impact. Specifically, G =Ī c r c y c P c − c r c I c y c P c I c r c y c P c + I C y C c P c (9) where I c is the relative impact of climate change in country c and r c is its rank with r c = 1 denoting the worst-off country and r c = C the best-off one. I call this the Gini coefficient. Table 1 shows the results. At the national level, the impacts are not distributed equally and, as the poorer are hit harder, worsen the income distribution.
Changes in inequality indices are hard to interpret. I therefore consider a hypothetical scenario: everyone pays the same absolute tax, a poll tax. The revenues are used to give everyone the same relative income subsidy. This necessarily skews the income distribution: the rich pay relatively little and gain absolutely a lot, while the poor pay relatively a lot and gain absolutely little. The tax and subsidy makes everyone who earns less (more) than the average $7611 per person per year worse (better) off. I then find the tax and subsidy that change the inequality indices by the same amount as climate change. For the national impact estimates, the change in the Gini coefficient caused by climate change is equivalent to levying a poll tax of $105 per person per year, and using the proceeds to give everyone a subsidy of 1.4% of their income. The poorest country in the sample is Burundi, with an average income $151/person/year; the average Burundian would lose $103 per year. Monaco is the richest country; the average Monegasque earns $160,228/year and would gain another $2138/year. For the Theil-T index, tax and subsidy are about a fifth higher, and for Theil-L and Atkinson about a fifth lower.
The Gini coefficient for the impacts shows that the distribution gets more uneven when we move beyond country averages to consider the withincountry distribution. This is more pronounced for the regions than for the income deciles, because the regions vary in both climate and income. As above, it is even starker for grid cells.
The indicators for income inequality by region or decile show that the distribution of impacts between 73 Ann. N.Y. Acad. Sci. 1504 (2021) 63-75 © 2020 The Authors. Annals of the New York Academy of Sciences published by Wiley Periodicals LLC on behalf of New York Academy of Sciences countries is more important than the distribution of impacts within countries, as the indicators change more when country-average impacts are used then when decile-or region-specific impacts are used. However, for the analysis on the grid cell level, within-county variation is about as important as between-country variation.

Discussion and conclusion
A meta-analysis of previously published estimates of the economic impact of climate change shows that poorer people in hotter places are more vulnerable to climate change. I use these insights to downscale national impact estimates to income deciles within countries, to subnational administrative units, and to the grid. For the majority of people, the impact of climate change will be worse than their country average. Between-country variation is more important than within-country variation, except for the grid cell analysis in which they are about as important.
There are several caveats to these results. First and foremost, I rely heavily on imputation, extrapolating results for a course resolution to a fine resolution. Primary estimates on fine social and spatial scales are hard needed, be it for sectors (e.g., Refs. 53 and 54) or countries (e.g., Ref. 55). The resolution needs to be fine. The urban heat island effect, for instance, has a synergetic impact with climate change 11 but is less pronounced in wealthier neighborhoods. 56 I assume that differences between countries can be interpolated to differences within countries, even though differences within countries are often smaller as because of a common legal system, fiscal redistribution, and the shared provision of public goods. New regional estimates of the economic impact of climate change would also refine our estimates of the income elasticity and the sensitivity of impacts to the current climate.
This paper confirms that the differences in vulnerability to climate change are profound. The distribution of the impact of climate matters. Differences in vulnerability between countries are important because they affect the international negotiations, through discussions on historical responsibility and liability for impacts. Estimates of impact differentials should also guide the allocation of development aid for adaptation to climate change. The distribution of impacts also affects optimal targets. The distribution of impacts within countries should inform government decisions about targeting adaptation and social programs toward those who need them most.