Protocol for estimating the impact of climate change on economic growth and inequality under climate policies

Summary The impact of climate change on economic inequality has attracted increasing attention from both government and academia. Here, we present a protocol for estimating both the impact of climate change on economic growth and economic growth inequality under multiple climate policies. We describe steps for constructing an uncertainty analysis framework, collecting and pre-processing data, and estimating the climate-economic response. We then detail procedures of predicting climate policy impact and calculating inter-country economic growth inequality. For complete details on the use and execution of this protocol, please refer to Tang et al. (2023).1


SUMMARY
The impact of climate change on economic inequality has attracted increasing attention from both government and academia.Here, we present a protocol for estimating both the impact of climate change on economic growth and economic growth inequality under multiple climate policies.We describe steps for constructing an uncertainty analysis framework, collecting and pre-processing data, and estimating the climate-economic response.We then detail procedures of predicting climate policy impact and calculating inter-country economic growth inequality.For complete details on the use and execution of this protocol, please refer to Tang et al. (2023). 1

BEFORE YOU BEGIN
As climate change becomes more severe, it is important to assess whether climate policies can synergistically mitigate climate change, promote economic growth, and improve economic inequality.The protocol given below describes the general design of the study, with specific steps on how to construct an uncertainty analysis framework for assessing climate policy.Based on this, the protocol calculates the impact of climate policies under multiple scenarios on future economic growth at the near-, medium-, and long-term scales.Furthermore, it measures the dynamic evolution of the growth of global economic inequality during the 21st century.

Study design
This study first estimates the loss-response relationship between climate change and economic growth; Second, select four representative climate policy scenarios ranging from strict to lax, in order of 1.5 C scenario (SSP1-19), 2 C scenario (SSP1-26), gap-filling mitigated overshoot scenario (SSP5-34), and unmitigated scenario (SSP5-85); Third, simulate and predict the economic costs of climate policies and the economic benefits from damage avoidance; Finally, assess whether strict climate policies can synergistically mitigate climate change, promote economic growth, and improve economic inequality.Figure 1 summarizes the logical framework proposed in this paper.
Specifically, this study considers 1961-2017 as the baseline period and three alternative baseline periods (1971-2017, 1978-2017, 1991-2017) to estimate the loss-response relationship between climate change and economic growth.Then, two medium-and long-term projection periods, i.e., mid-century (2045-2055), and end-century (2090-2100) are defined to assess the potential impacts of 4 representative climate policies ranging from strict to lenient on future economic growth in 171 countries.Further, we select 18 representative countries to assess the economic impacts of climate policies at different time scales in the near (2030-2040), medium (2050-2060), and long term (2070-2080, 2090-2100).Finally, we measure the dynamic evolution of global economic growth inequality under 68 scenarios over the 21st century (2015-2100).
In this work, our computer configuration is Intel i9-13900K, RTX1660 Ti independent display card, 2 TB hard drive, 64 GB of memory.
For the processing of meteorological data, we used the NCAR Command Language (NCL, Version 6.6.2).The NCL is a free interpreted language designed specifically for scientific data processing and visualization, which is a product of the Computational & Information Systems Laboratory at the National Center for Atmospheric Research (NCAR) and sponsored by the National Science Foundation.

Timing: 2 weeks
Aiming at assessing the long-term potential economic impacts of near-term climate policies under multiple scenarios, we construct an uncertainty analysis framework with four uncertainty dimensions: climate policy, climate damages, policy costs, and mitigation burdens.Figure 2 shows the uncertainty analysis framework proposed in this paper.
The first dimension is the climate scenario, which refers to four representative climate policy scenarios from strict to loose (SSP1-19, SSP1-26, SSP5-34, SSP5-85).It reflects the varying degrees of global average warming from low to high by the end of the 21st century (2100).The second dimension is climate damage, which is estimated from the loss-response relationship between climate change and economic growth.It captures the unequal impact of varying degrees of climate damage on economic growth.Third, the mitigation cost dimension involves calculating the mitigation costs of different regions using multiple integrated assessment models (IAMs) that include endogenous economic growth modules (AIM/GCE, REMIND-MAGPIE and MESSAGE-GLOBIUM), as they represent the effect of mitigation on growth. 2 Last, the mitigation burden dimension is used to portray the a.The observed climate data are obtained from the database of the Climate Research Center at the University of Delaware.This database provides 0.5 degree grid monthly average temperature and total precipitation data for the global land area from 1900 to 2017 (Version 5.0), 3 as interpolated from meteorological station data.Further, average monthly temperature and precipitation data over the period 1961 to 2017 to obtain annual averages.i. Calculates temperature and precipitation on a country-year scale weighted by administrative area within global land areas.
Note: Administrative area is a geographical area within a country or region that is managed and controlled by the government.It is defined as land area at the national level and is used to weight climate variables to measure annual average temperature and total annual precipitation for each country.
ii.Combined with the raster data of world population density provided by the National Aeronautics and Space Administration (NASA), 4 we calculate the average temperature and precipitation on a country-year scale weighted by population density in the global land area.four scenarios.Considering the availability of four representative SSP-RCP scenarios, as well as securing the same realization number and initial conditions (variant level ''r1i1''), only ten GCMs are available.Therefore, we have selected these 10 models for the study of this paper.We also look forward to more institutions running these four experiments in the future to provide more models data.Besides, in this study, we use the results of multi-GCMs ensemble mean to reduce the effect of simulation bias for a single model.
iii.To simplify the analysis, this study averages the 10 GCM outputs for future temperature predictions.iv.In order to obtain the multi-model ensemble mean-based results, this study uses bi-linear interpolation method to reduce the 10 GCM outputs to a consistent 0.5 degree resolution.
As shown in Figures 4A, 4C, 4E, and 4G.v. Consistent with the climate data pre-processing methods observed during historical periods, we perform population weighting on the multi-GCMs ensemble mean (as shown in Figures 4B, 4D, 4F, and 4H).

KEY RESOURCES TABLE STEP-BY-STEP METHOD DETAILS
In this section, we first estimate the response relationship between climate change and economic growth.On this basis, the impact of future warming on economic growth under climate policy is projected.Finally, we measure the evolutionary trend of cross-country economic growth inequality between the 21st century under different climate policies and scenarios.

Timing: 5 days
This step distinguishes between short-term weather shocks and long-term climate change impacts on economic growth.The differentiated impacts of short-term weather fluctuations versus long-term climate change on economic growth are effectively identified by defining short-term weather variables as annual temperature and precipitation and their differentials, and long-term climate variables as the differentials of annual temperature and precipitation deviations from their historical norms (the past decades).
1. Short-term weather-economic relationship.a. Define climate variables.i. Annual averages: arithmetic mean of population-weighted temperature (precipitation) for 12 months per year ii.Differential forms: the magnitude of temperature (precipitation) change in year t compared to year t-1.b.Set forms of specifications, compare and select the best performing equation as the baseline model.i. Linear. 5,6i.Nonlinear.Note: In the specifications, this study includes the rate of temperature change (DTr i;t ), which reflects the speed of temperature change.The results indicate that for the same amount of warming (DT i;t ), the faster the temperature rises, the slightly lower the economic growth.For example, rapid 2 C warming over 10 years has greater negative impact on economic growth than slow 2 C warming over 100 years.
a. Define climate variables.
Note: Climate change usually refers to changes in the average state of the climate that occur over a longer period of time. 10,11The larger the deviation, the greater the magnitude of climate change.
b. Identify changes in long-term climate conditions.
Note: Referring to Kahn et al. ( 2021), 12 this study defines climate variables as the difference between annual temperature/precipitation and their moving averages over the past few decades.
c. Define history norms.
Note: Typically, climate norms are measured by the moving average of the past 30 years. 13Robustness check.
Note: Define climate variables as the difference between the annual temperature and precipitation variables deviating from their 20-, 40-, and 50-year's moving averages.When using different numbers of decades as historical norms, we choose the most appropriate data set among the four balanced panels mentioned above to reduce sample loss.For example, when using the 20-year moving average as the historical norm, we choose the balanced panel dataset of 111 sample countries between 1978 and 2017; when defining the historical norm as 30, 40, and 50 years, we use the balanced panel dataset of 147 countries between 1991 and 2017.
Predicting the potential impact of climate policies on economic growth

Timing: 5 weeks
This step selects four climate policy scenarios ranging from stringent to lax, reflecting different scenarios of low to high global average warming by the end of the century.On this basis, the uncertainty impacts of climate damages, policy costs and mitigation burdens on future economic growth are considered by constructing an uncertainty analysis framework.

Note:
We select the SSP pathways that can meet the warming limit targets (e.g., 1.5 C, 2 C, carbon peak and carbon neutrality) in the scenarios provided by CMIP6.For example, the Sustainable Development Pathway (SSP1) and the Fossil-fueled Development Pathway (SSP5). 14,15rotocol b.Representative Concentration Pathways (RCPs).
Note: Representative Concentration Pathways (RCPs) refer to an integrated set of concentration and emission scenarios, including a series of radiative forcing different pathways.The RCPs are designed to provide insight into the possible consequences of anthropogenic changes in emission concentrations and associated climate change.They are used as input parameters for climate change prediction models under the influence of human activities in the 21st century. 16SSP-RCP scenarios.
Note: Download the latest socio-economic forecast data.The SSP database provides countrylevel baseline economic growth rates for the period 2010 to 2100 under different SSP pathways.The SSP Database provides growth projections generated by three different research groups (OECD, IIASA and PIK); we focus on the projections from the OECD group, as this group predicts more countries than others.

Note:
The CMIP6 produces a series of updated global climate model (GCM) outputs.For our study, we use monthly surface temperature for the future period (2015-2100), and the future temperature projections are provided by dozens of global climate models (GCMs) running under four forcing pathways.Considering the availability of four representative SSP-RCP scenarios, as well as securing the same realization number and initial conditions (variant level ''r1i1''), only ten GCMs are available.They are CanESM5, CNRM-ESM2-1, FGOALS-g3, GISS-E2-1-G, GISS-E2-1-H, MIROC-ES2L, IPSL-CM6A-LR, MIROC-ES2L, MRI-ESM2-0 and UKESM1-0-LL.We average these available GCM outputs as future temperature projections.Notably, the horizontal resolutions of the available climate models are different.To get multimodel ensemble mean-based results, we downscale the GCM outputs to a 0.5-degree resolution by using the bi-linear interpolation method.

Construction of uncertainty analysis framework.
Note: As we mentioned above, this paper constructs an uncertainty analysis framework with four uncertainty dimensions: Note: Based on this framework, this study assesses not only the cumulative impact of climate policies on economic growth across countries (from 2015 to 2100), but also the uncertainty impact of climate policies on future economic growth over different ranges in the near, medium, and long term.
b. Improve the prediction algorithm.
Note: Based on the uncertainty analysis framework, our study further improves the prediction algorithm to more accurately identify the differential policy effects between different RCP scenarios under the same SSP pathway.Specifically, we construct two indices: the ''mitigation burden index'' and the ''moderating damage index'' to identify the heterogeneous burden effects of mitigation policies and heterogeneous damages of climate change.

Calculate inter-country economic growth inequality under climate policies
Timing: 1 week This step measures the degree of inequality in global economic growth for 68 scenarios under the uncertainty analysis framework.Further, the analysis focused on trends in the evolution of inequality dynamics in the median estimates.
Note: These two ratios use population-weighted country-level empirical cumulative distribution functions (CDFs) of GDP per capita to calculate the degree of difference in GDP per capita between the world's poorest and richest countries.These two metrics are the eight most popular indices of income inequality identified by Sala-i-Martin. 18Calculate the 90:10 ratio.
Note: First, the annual GDP per capita of each country is ranked in ascending order for each year from 2015 to 2100; Second, the population of each country is accumulated for each year starting with the country with the lowest GDP per capita.Third, when the accumulated population is 10% (90%) of the total global population, the GDP per capita value of the corresponding country is the 10th (90th) percentile value.Last, the 90th percentile GDP value is divided by the 10th percentile GDP value to obtain the 90:10 ratio. 8,18Calculate the 80:20 ratio.

Note:
The calculation of the 80:20 ratio is similar to that of the 90:10 ratio, except that the 80th percentile GDP value is divided by the 20th percentile GDP value to obtain the 80:20 ratio.The higher the value of the 80:20 (90:10) ratio, the greater the per capita income gap between the highest quintile (decile) and lowest quintile (decile) countries, indicating a greater degree of inequality in global economic growth.
d. Calculate the dynamic evolution of global economic growth inequality.
Note: Calculate the 90:10 and 80:20 ratios for each of the 68 scenarios in the uncertainty analysis framework between 2015 and 2100 to measure the dynamic evolution of inequality in economic growth.

EXPECTED OUTCOMES Statistical characteristics of the observed climate
Table 1 presents the descriptive statistical results of population-weighted annual average temperature (in C) and annual total precipitation (in mm) for each country from 1961 to 2017.The global average temperature is generally showing an upward trend.The difference between annual average temperature and historical normal gradually increases, from 0.345 C (twenty years) to 0.573 C (fifty years).During this period, the annual average temperature of each country was 19.985 C, but the climate conditions varied greatly among different countries.In 2010, the average annual temperature in Mauritania was as high as 29.925 C, while in 1979, the average annual temperature in Iceland was only À0.352 C.
During the same period, Table 1 shows that the difference between the annual total precipitation and the historical climate average gradually increased, from 130 mm (twenty years) to 143.4 mm (fifty years).This means that on a global scale, the overall precipitation has shown an increasing trend over the past 57 years.However, the distribution of precipitation is very uneven and shows significant differences from different sample countries.In 1999, the total annual precipitation of the the Arab Republic of Egypt was only 8.9 mm, reflecting that a serious drought event occurred in the country that year; However, in 1970, the total annual precipitation in Costa Rica was as high as 4299.8mm, and rainstorm caused huge economic losses.

Impacts of climate policies on economic growth in different future periods
This study analyzes the economic impact of climate policy from two different temporal perspectives: (1) A cumulative perspective across different periods of this century (2015-2100).( 2) Different time scales for the near term, medium term, and long term.
Firstly, we measure the impact of strict climate policies on economic growth in various countries, that is, the relative impact of global warming on economic growth in low RCP scenarios (compared to high RCP scenarios) under the same SSP path.
Then, we analyze the impact of climate policies on the economic growth of 171 countries worldwide from a long-term cumulative perspective of the 21st century (2015-2100).Compared to the 2 C target (SSP1-26), achieving the 1.5 C target (SSP1-19) will increase the per capita GDP of Madagascar, an island country in the African region, by 0.51%.And compared to the high emission scenario (SSP1-26), the probability of Madagascar benefiting under the low emission scenario (SSP1-19) is as high as 71%.Similarly, implementing the 1.5 C climate policy will increase the per capita According to Table 2, during the Middle century (2024-2055), the median per capita cumulative GDP of the five regions under the SSP1-19 scenario is lower than the median per capita cumulative GDP of each region under the SSP1-26 scenario.Similar results appear in the SSP5 path (SSP5-34 vs. SSP5-85).This means that in the short to medium term, the cost of implementing strict climate policies will outweigh the economic benefits of avoiding climate damage, reflecting that the net benefits of strict climate policies in the short to medium term will be negative.
However, this result will change in the late 21st century.According to Table 2, the end of the century (2090-2100), the median estimates of cumulative GDP per capita for the five regions under the low RCP scenario (SSP1-19, SSP5-34) exceed the corresponding median estimates for each region under the high RCP scenario (SSP1-26, SSP5-85) in the same SSP.
In terms of the 18 representative countries, as we expected, the stricter the climate policy, the higher the policy cost required at the beginning of its implementation.According to Table 3, implementing the 1.5 C policy will slow down countries' economic growth in the first half of this century compared to the 2 C policy.
Besides, we also expect that an immediate implementation of the strict 1.5 C policy would allow vulnerable poor countries prone to natural disasters to reap significant potential gains from the first half of this century.The results of the study are also consistent with our expectations.For example, Laos is one of the least developed countries in the world with poor infrastructure, such as the dam collapse that occurred in 2018, making it difficult to withstand severe extreme weather events. 19If global warming continues and exceeds 1.5 C, increasingly severe meteorological hazards such as heavy rainfall and flooding will cause huge economic losses for poor and vulnerable countries like Laos. 20

Calculate inter-country economic growth inequality under climate policies
We use 80:20 and 90:10 ratios to measure the trend of inequality in global economic growth under climate policies.In this section, we use the equivalent burden case as an example for our analysis.Figure 5B illustrates the trend in economic inequality for the 90:10 ratio.In general, economic inequality between the world's poorest and richest countries shows a decreasing trend.However, in the second half of the 21st century (2050-2100), inequality is slightly higher in the carbon peaking and carbon neutrality scenario (SSP5-34) than in the scenario without any climate action (SSP5-85).For example, the 90:10 ratio in 2100 is 3.93 (SSP5-34)/3.89(SSP5-85).Again, this result reflects the fact that achieving the double carbon goal will impose an economic burden on the world's poor countries and requires attention to equitable international burden-sharing mechanisms.

LIMITATIONS
It should be noted that the estimated climate-economic response is calculated from macroeconomic data.Therefore, the differential impact of subdivided economic sectors by climate change is not considered.Besides, economic inequalities caused by cost-sharing policies and income distribution policies are not considered.Therefore, further in-depth studies are needed.

TROUBLESHOOTING Problem 1
How to estimate the response between subdivided economic sectors and climate change?
Given the limited availability of sector-level economic output data, this protocol does not assess the impact of climate warming and precipitation anomalies at the subsector level.However, the use of macroeconomic data tends to lose a great deal of useful information, such as the inability to reasonably quantify the extent of climate damage to various economic sectors (related to Steps 1 and 2), For example, technological progress may play a positive role in reducing the climate vulnerability of economies, and the estimates in this study may overestimate the extent to which climate damage will affect future economic growth (related to Steps 7).

Potential solution
Future research could delve into the positive role that technological advances may play in enhancing the adaptability of economies.

Problem 5
There is a lack of discussion of the impact of climate change on domestic economic inequality.
This study focuses on the impact of climate change on economic growth inequality at the global scale, but does not explore this impact on economic inequality within developing countries.The issue is important because the impact of climate change is more severe in developing countries (related to Steps 8).

Potential solution
Future research could delve into the impact of climate change on economic inequality within developing countries.For example, explore the impact of climate change on domestic economic inequality in the Chinese context, and further explore the differential impact of climate warming on China and the world.

Lead contact
Further information and requests should be directed to the lead author, Hongbo Duan (hbduan@ ucas.ac.cn).

Materials availability
This study did not generate new unique materials.
(a) climate damages, (b) climate policy, (c) policy costs, and (d) mitigation burdens (see Tang et al. (2023) 1 for details).7.Predict future economic growth under climate policies.a. Compute the results for each of the 68 scenarios under the uncertainty analysis framework.
Lagged effects: gradually incorporate 0th to 5th order lagged terms for temperature and precipitation variables into the baseline model.e. Robustness: changing periods, sample countries, and econometric methods.
iii.Hot country vs. Cold country.Note:(1) Poor/Rich country is defined as having below-median/above-median PPP-adjusted per capita GDP in the first year the country enters the datasets.(2) Colonized/Non-colonial country refers to a country that has/hasn't experienced colonialism.(3) Hot/Cold country is defined as having above-median/below-median annual average temperature in the first year the country enters the datasets.

Table 1 .
Descriptive statistics of temperature and precipitation from 1961 to 2017 Note: T (DT) and P (DP) denote the annual average temperature (change) and total annual precipitation (change) at the national level, respectively.Dlny and DTr refer to national economic growth rate and temperature change rate, respectively.GDP of Somalia, a coastal country in the African region, by 0.2% with a 54% probability.When looking at poor countries in the Asian region, the per capita GDP of Laos and Cambodia under the 1.5 C scenario will increase by 0.82% and 0.21% with a probability of 100% and 83%, respectively (compared to the 2 C scenario).These results indicate that compared to the 2 C target, the economic benefits of avoiding climate damage under the stricter 1.5 C target may exceed the policy costs.Most of these benefiting countries are the poorest in the world and are concentrated in the climate fragile regions of Africa and Asia.Furthermore, we explore the economic impacts of climate policies on five major regions (OECD, REF, ASIA, MAF, and LAM) and 18 representative countries from different perspectives in the near, medium, and long term.These 18 countries include nearly half of the world's population, including the world's major Economic power, major developing countries, countries prone to natural disasters, and the world's poorest coastal countries (see Tang et al. (2023) 1 for details).

Table 2 .
Five major global regions: Median predictions of relative changes in cumulative GDP per capita

Table 3 .
Eighteen representative countries: Median predictions of relative changes in cumulative GDP per capita Socioeconomic development in the long term may increase the resilience of economic growth to climate change.