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<front>
<journal-meta>
<journal-id journal-id-type="nlm-ta">PLOS Clim</journal-id>
<journal-id journal-id-type="publisher-id">plos</journal-id>
<journal-id journal-id-type="pmc">plosclimate</journal-id>
<journal-title-group>
<journal-title>PLOS Climate</journal-title>
</journal-title-group>
<issn pub-type="epub">2767-3200</issn>
<publisher>
<publisher-name>Public Library of Science</publisher-name>
<publisher-loc>San Francisco, CA USA</publisher-loc>
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<article-meta>
<article-id pub-id-type="doi">10.1371/journal.pclm.0000621</article-id>
<article-id pub-id-type="publisher-id">PCLM-D-24-00256</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Research Article</subject>
</subj-group>
<subj-group subj-group-type="Discipline-v3">
<subject>Earth sciences</subject><subj-group><subject>Atmospheric science</subject><subj-group><subject>Climatology</subject><subj-group><subject>Climate change</subject></subj-group></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3">
<subject>Earth sciences</subject><subj-group><subject>Atmospheric science</subject><subj-group><subject>Climatology</subject><subj-group><subject>Climate change</subject><subj-group><subject>Anthropogenic climate change</subject></subj-group></subj-group></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3">
<subject>Earth sciences</subject><subj-group><subject>Atmospheric science</subject><subj-group><subject>Climatology</subject><subj-group><subject>Climate change</subject><subj-group><subject>Global warming</subject></subj-group></subj-group></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3">
<subject>Earth sciences</subject><subj-group><subject>Atmospheric science</subject><subj-group><subject>Climatology</subject><subj-group><subject>Climate change</subject><subj-group><subject>Radiative forcing</subject></subj-group></subj-group></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3">
<subject>Social sciences</subject><subj-group><subject>Economics</subject><subj-group><subject>Macroeconomics</subject></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3">
<subject>Earth sciences</subject><subj-group><subject>Atmospheric science</subject><subj-group><subject>Atmospheric chemistry</subject><subj-group><subject>Greenhouse gases</subject></subj-group></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3">
<subject>Physical sciences</subject><subj-group><subject>Chemistry</subject><subj-group><subject>Environmental chemistry</subject><subj-group><subject>Atmospheric chemistry</subject><subj-group><subject>Greenhouse gases</subject></subj-group></subj-group></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3">
<subject>Ecology and environmental sciences</subject><subj-group><subject>Environmental chemistry</subject><subj-group><subject>Atmospheric chemistry</subject><subj-group><subject>Greenhouse gases</subject></subj-group></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3">
<subject>Earth sciences</subject><subj-group><subject>Atmospheric science</subject><subj-group><subject>Climatology</subject><subj-group><subject>El Niño-Southern Oscillation</subject></subj-group></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3">
<subject>Earth sciences</subject><subj-group><subject>Marine and aquatic sciences</subject><subj-group><subject>Oceanography</subject><subj-group><subject>El Niño-Southern Oscillation</subject></subj-group></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3">
<subject>Social sciences</subject><subj-group><subject>Economics</subject><subj-group><subject>Development economics</subject><subj-group><subject>Economic growth</subject></subj-group></subj-group></subj-group></subj-group></article-categories>
<title-group>
<article-title>Rising temperatures, melting incomes: Country-specific macroeconomic effects of climate scenarios</article-title>
<alt-title alt-title-type="running-head">Rising temperatures, melting incomes: Country-specific macro effects of climate scenarios</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes" equal-contrib="yes" xlink:type="simple">
<contrib-id authenticated="true" contrib-id-type="orcid">https://orcid.org/0000-0002-2501-2062</contrib-id>
<name name-style="western">
<surname>Mohaddes</surname>
<given-names>Kamiar</given-names>
</name>
<role content-type="http://credit.niso.org/contributor-roles/conceptualization/">Conceptualization</role>
<role content-type="http://credit.niso.org/contributor-roles/data-curation/">Data curation</role>
<role content-type="http://credit.niso.org/contributor-roles/formal-analysis/">Formal analysis</role>
<role content-type="http://credit.niso.org/contributor-roles/investigation/">Investigation</role>
<role content-type="http://credit.niso.org/contributor-roles/methodology/">Methodology</role>
<role content-type="http://credit.niso.org/contributor-roles/validation/">Validation</role>
<role content-type="http://credit.niso.org/contributor-roles/visualization/">Visualization</role>
<role content-type="http://credit.niso.org/contributor-roles/writing-original-draft/">Writing – original draft</role>
<role content-type="http://credit.niso.org/contributor-roles/writing-review-editing/">Writing – review &amp; editing</role>
<xref ref-type="aff" rid="aff001"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff002"><sup>2</sup></xref>
<xref ref-type="corresp" rid="cor001">*</xref>
</contrib>
<contrib contrib-type="author" equal-contrib="yes" xlink:type="simple">
<contrib-id authenticated="true" contrib-id-type="orcid">https://orcid.org/0000-0001-8297-798X</contrib-id>
<name name-style="western">
<surname>Raissi</surname>
<given-names>Mehdi</given-names>
</name>
<role content-type="http://credit.niso.org/contributor-roles/conceptualization/">Conceptualization</role>
<role content-type="http://credit.niso.org/contributor-roles/data-curation/">Data curation</role>
<role content-type="http://credit.niso.org/contributor-roles/formal-analysis/">Formal analysis</role>
<role content-type="http://credit.niso.org/contributor-roles/investigation/">Investigation</role>
<role content-type="http://credit.niso.org/contributor-roles/methodology/">Methodology</role>
<role content-type="http://credit.niso.org/contributor-roles/validation/">Validation</role>
<role content-type="http://credit.niso.org/contributor-roles/visualization/">Visualization</role>
<role content-type="http://credit.niso.org/contributor-roles/writing-original-draft/">Writing – original draft</role>
<role content-type="http://credit.niso.org/contributor-roles/writing-review-editing/">Writing – review &amp; editing</role>
<xref ref-type="aff" rid="aff002"><sup>2</sup></xref>
<xref ref-type="aff" rid="aff003"><sup>3</sup></xref>
</contrib>
</contrib-group>
<aff id="aff001"><label>1</label> <addr-line>Judge Business School and King’s College, University of Cambridge, Cambridge, United Kingdom</addr-line></aff>
<aff id="aff002"><label>2</label> <addr-line>climaTRACES Lab, University of Cambridge, Cambridge, United Kingdom</addr-line></aff>
<aff id="aff003"><label>3</label> <addr-line>International Monetary Fund, Washington, District of Columbia, United States of America</addr-line></aff>
<contrib-group>
<contrib contrib-type="editor" xlink:type="simple">
<name name-style="western">
<surname>Hsueh</surname>
<given-names>Lily</given-names>
</name>
<role>Editor</role>
<xref ref-type="aff" rid="edit1"/></contrib>
</contrib-group>
<aff id="edit1"><addr-line>Arizona State University, UNITED STATES OF AMERICA</addr-line></aff>
<author-notes>
<corresp id="cor001">* E-mail: <email xlink:type="simple">km418@cam.ac.uk</email></corresp>
<fn fn-type="conflict" id="coi001">
<p>The authors have declared that no competing interests exist.</p>
</fn>
</author-notes>
<pub-date pub-type="epub"><day>24</day><month>9</month><year>2025</year></pub-date>
<pub-date pub-type="collection"><year>2025</year></pub-date>
<volume>4</volume>
<issue>9</issue>
<elocation-id>e0000621</elocation-id>
<history>
<date date-type="received"><day>4</day><month>11</month><year>2024</year></date>
<date date-type="accepted"><day>14</day><month>7</month><year>2025</year></date>
</history>
<permissions>
<copyright-year>2025</copyright-year>
<copyright-holder>Mohaddes and Raissi</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/" xlink:type="simple">
<license-p>This is an open access article distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/4.0/" xlink:type="simple">Creative Commons Attribution License</ext-link>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.</license-p></license>
</permissions>
<self-uri content-type="pdf" xlink:href="info:doi/10.1371/journal.pclm.0000621"/>
<abstract>
<p>Quantifying the macroeconomic impact of climate change has been a focal point in academic and policy discussions since the early 1990s. The estimates of (global) GDP losses at future warming levels vary widely due to differing methodologies, complicating the formulation of effective climate policies. This study aims to bridge the gap between these varying estimates by quantifying <italic>country-specific</italic> annual per-capita GDP losses from global warming using the most recent climate scenarios of the Intergovernmental Panel on Climate Change (IPCC) under different mitigation, adaptation, and climate variability assumptions. Motivated by the need to inform policy decisions, we hypothesize that without substantial mitigation and adaptation efforts, global GDP per capita could decline by up to 24 percent under high-emissions climate scenarios by 2100. To test this hypothesis, we conduct a series of counterfactual exercises, investigating the cumulative income effects of annual temperature increases by the end of the century. Our findings reveal significant disparities in income losses across the <ext-link ext-link-type="uri" xlink:href="http://files.econ.cam.ac.uk/people-files/faculty/km418/Annual_Country_Specific_Income_Loss_Estimates_of_SSP_Scenarios.xlsx" xlink:type="simple">174 countries</ext-link> in our sample, highlighting that the impacts of climate change are not uniform but depend on the projected paths of temperatures and their variability.</p>
</abstract>
<funding-group>
<funding-statement>The author(s) received no specific funding for this work.</funding-statement>
</funding-group>
<counts>
<fig-count count="7"/>
<table-count count="1"/>
<page-count count="15"/>
</counts>
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<custom-meta id="data-availability">
<meta-name>Data Availability</meta-name>
<meta-value>Yes, the data has been uploaded as part of this submission as <xref ref-type="sec" rid="sec006">Supporting information</xref> files.</meta-value>
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</front>
<body>
<sec id="sec001" sec-type="intro">
<title>1. Introduction</title>
<p>Climate change—marked by rising average temperatures and sea levels, shifting precipitation patterns, and more frequent and intense extreme weather events—poses a critical challenge to the global economy. While the physical manifestations of climate change are visibly alarming, its macroeconomic implications are equally significant but difficult to quantify—Most models are unable to account for tipping points, non-market damages (e.g., mortality, conflicts, food insecurity), and spillovers. Inference about damages up to 2100 based on past data is inherently difficult. Current literature has established that climate change can lead to significant GDP per capita losses; however, estimates of these impacts vary widely—from negligible to catastrophic—due to differing methodologies and assumptions [<xref ref-type="bibr" rid="pclm.0000621.ref001">1</xref>]. This paper aims to bridge the gap between these varying estimates by providing plausible <italic>country-specific</italic> annual per-capita GDP losses from global warming based on the methodology in [<xref ref-type="bibr" rid="pclm.0000621.ref002">2</xref>], but using a wider and more up-to-date set of climate scenarios under different mitigation (i.e., reducing greenhouse gas emissions), adaptation (i.e., adjusting to climate change impacts), and climate variability (i.e., fluctuations in weather patterns) assumptions. A key objective of the paper is to consider the uncertainty of warming predictions of climate models by providing a range of GDP per capita impacts within an empirical approach that deals with many of the econometric pitfalls of earlier studies. We also compare our income loss estimates with those from select papers in the literature, utilizing a common baseline scenario to rule out implausibly small and excessively large estimates. We, therefore, contribute to a more nuanced understanding of the macroeconomic impacts of climate change.</p>
<p>While understanding the economic impact of rising temperatures is crucial for climate policy design, the most used estimates in the literature differ by orders of magnitude. For a worst-case global warming scenario, [<xref ref-type="bibr" rid="pclm.0000621.ref003">3</xref>] estimate a 60% loss in global GDP per capita by 2100, while [<xref ref-type="bibr" rid="pclm.0000621.ref004">4</xref>] conducts a meta-study of existing literature and reports a negligible income loss. This wide range of estimates arises from disagreements about whether a temperature increase will affect GDP levels or GDP growth rates (see, for instance, [<xref ref-type="bibr" rid="pclm.0000621.ref005">5</xref>–<xref ref-type="bibr" rid="pclm.0000621.ref009">9</xref>] and <xref ref-type="fig" rid="pclm.0000621.g001">Fig 1A</xref>) and from different model specifications (including how extreme weather events, climate variability and adaptation are considered). Most papers that relate temperature to GDP levels yield income loss estimates that are relatively small. More recent studies, that relate temperature to GDP growth (possibly nonlinearly), show that a shift to a higher (non-decreasing) temperature reduces per capita output growth significantly (with compounding level effects) compared to a “ no further warming” baseline. For example, the Network for Greening the Financial Sector (NGFS) measures the global GDP impact of climate change relative to a baseline scenario “in which climate change does not occur”. [<xref ref-type="bibr" rid="pclm.0000621.ref006">6</xref>] argue that “if future adaptation mimics past adaptation, unmitigated warming is expected to reshape the global economy by reducing average global incomes roughly 23% by 2100 and widening global income inequality, relative to scenarios without climate change”. However, according to [<xref ref-type="bibr" rid="pclm.0000621.ref004">4</xref>,<xref ref-type="bibr" rid="pclm.0000621.ref010">10</xref>,<xref ref-type="bibr" rid="pclm.0000621.ref011">11</xref>], the hypothesis that a one-off rise in temperature affects the growth rate of the economy permanently is inconsistent with growth theory. To arrive at a more nuanced quantification of the GDP impacts of climate change, we follow [<xref ref-type="bibr" rid="pclm.0000621.ref002">2</xref>] in distinguishing between a one-off shift to permanently higher temperatures and persistent above-norms temperature increases (i.e., climate vs. climate change); modelling adaptation implicitly (by varying adaptation speeds from one decade to a century) and climate variability explicitly (i.e., by accounting for the natural fluctuations of temperature around its rising trend)—Understanding interannual and interdecadal natural climate variability is crucial for GDP impact assessments, not least because climate change significantly alters the frequency, intensity, and patterns of climate variability. Interannual climate variability is observed as changes in climate patterns from one year to the next. A well-known example is the El Niño Southern Oscillation (ENSO), which includes both El Niño and La Niña events (see, for instance, [<xref ref-type="bibr" rid="pclm.0000621.ref012">12</xref>] and [<xref ref-type="bibr" rid="pclm.0000621.ref013">13</xref>] for details). Interdecadal climate variability refers to fluctuations in climate that occur over periods of several decades. Examples include the Pacific Decadal Oscillation (PDO) and the Atlantic Multidecadal Oscillation (AMO)—and conducting a range of counterfactual exercises relative to a baseline under which temperature in each country increases according to its historical trend of 1960–2014.</p>
<fig id="pclm.0000621.g001" position="float"><object-id pub-id-type="doi">10.1371/journal.pclm.0000621.g001</object-id><label>Fig 1</label><caption><title>GDP impact of increases in temperature: Level vs. growth effects.</title><p>Notes: <xref ref-type="fig" rid="pclm.0000621.g001">Fig 1B</xref> shows the results in [<xref ref-type="bibr" rid="pclm.0000621.ref002">2</xref>] under RCP8.5 with and without climate variability.</p></caption>
<graphic mimetype="image" position="float" xlink:href="info:doi/10.1371/journal.pclm.0000621.g001" xlink:type="simple"/></fig>
<p>Specifically, [<xref ref-type="bibr" rid="pclm.0000621.ref002">2</xref>] establish a relationship between deviations in temperature (weather) from 30-year moving averages (climate) and GDP per capita across countries. Note that regressing GDP per capita growth on temperature levels leads to biased impact estimates because GDP growth is stationary while temperature is positively trended due to global warming. Relatedly, [<xref ref-type="bibr" rid="pclm.0000621.ref002">2</xref>] demonstrate that a sustained increase in above-norm temperature—indicative of climate change—correlates with decreased long-term economic growth. This suggests that while temporary temperature fluctuations may result in short-term economic impacts, climate change can alter the long-term averages and variability of weather, thereby affecting an economy’s growth potential over time. The impact on GDP per capita accumulates as temperatures continue to rise and adaptation measures are implemented gradually; however, these effects may stabilize if temperatures eventually level off [<xref ref-type="bibr" rid="pclm.0000621.ref002">2</xref>] calculate annual income losses resulting from climate change by analyzing weather anomalies over time for 174 countries under different climate scenarios. They project that if temperatures increase persistently by 0.04<sup>∘</sup> C per year under a high-emissions scenario (RCP 8.5), real GDP per capita worldwide could decline by 7–13% by 2100, compared to a baseline where temperatures follow their trends from 1960-2014 (<xref ref-type="fig" rid="pclm.0000621.g001">Fig 1B</xref>). In contrast, adhering to the Paris Agreement’s goal of capping the temperature increase to 0.01<sup>∘</sup> C annually would reduce this loss to about 1%. While adapting to climate change may reduce these negative long-term growth effects, it is highly unlikely to completely eliminate them. See also [<xref ref-type="bibr" rid="pclm.0000621.ref014">14</xref>] who provided evidence for the damage that climate change causes in the United States using within-country data on Gross State Product (GSP) GSP per capita, labour productivity and employment as well as output growth in ten economic sectors (such as agriculture, construction, manufacturing, services, retail and wholesale trade). They show that while certain sectors in the U.S. economy might have adapted to higher temperatures, economic activity in the U.S. overall and at the sectoral level continues to be sensitive to deviations of temperature and precipitation from their historical norms.</p>
<p>Given that the planet has already warmed by 1.2<sup>∘</sup>C compared to pre-industrial averages, its impact on GDP per capita (alongside past adaptation) is already reflected in historical growth observations. To highlight the size of this observed damage, we estimate a weighted-average global income loss of 2 percent (USD 1.6 trillion) from above-norm temperature increases over 1960-2014. However, global warming is projected to accelerate under various IPCC climate scenarios, and hence its impact on the economy will be more detrimental than in the past, unless countries close the mitigation ambition and policy implementation gaps that are needed to abide by the Paris agreement temperature goals. We use the latest IPCC climate scenarios in our counterfactual exercises to better reflect uncertainties of climate change, technological pathways, and policies. We investigate the cumulative income effects of continuous above-norm temperature increases (by assuming that GDP per capita in each country is affected by temperature only when it deviates from its historical norm, serving as country-specific but time-varying thresholds or climates) over 2015–2100 relative to a baseline under which temperature in each country increases according to its trend of 1960–2014. We also report the associated income losses relative to a scenario without climate change and with extremely-slow adaptation.</p>
<p>Prior research projects the GDP impact of temperature increases for some future year, typically 2100, assuming a “ no further warming” counterfactual (e.g., [<xref ref-type="bibr" rid="pclm.0000621.ref003">3</xref>,<xref ref-type="bibr" rid="pclm.0000621.ref006">6</xref>,<xref ref-type="bibr" rid="pclm.0000621.ref007">7</xref>]). Since there are no pathways to a scenario in which baseline temperatures remain constant, we compare the per capita GDP impact of temperature increases under different climate scenarios to a baseline under which temperature in each country rises according to its historical trend of 1960–2014. We find that the global income effects of persistent increases in average temperatures by 0.04<sup>∘</sup>C per year, assuming very limited mitigation and adaptation action, ranges from -10% to -11% by the end of this century. Furthermore, climate variability amplifies the projected income losses, with estimates surging to 12–14% globally with significant variations across countries. The upper bound of these losses allow for temperature increases to affect the variability of temperature shocks commensurately. Accounting for transition risks (in addition to physical risks) would lead to larger losses (especially for advanced economies, see, for instance, [<xref ref-type="bibr" rid="pclm.0000621.ref015">15</xref>] and [<xref ref-type="bibr" rid="pclm.0000621.ref016">16</xref>]). While adaptation presents a viable pathway to reducing the detrimental long-term growth effects of climate change, it falls short of completely eliminating these impacts. We, therefore, underscore the pressing need for climate change mitigation policies to slowing global warming. Abiding by the Paris Agreement goals, thereby limiting the temperature increase to 0.01 degrees Celsius per year, generates a positive income gain of about 0.25 percent globally.</p>
<p>To have better comparability to the literature, we also conduct an exercise in which adaptation is assumed to be extremely slow (i.e., we use 100-year historical norms) and income losses from temperature increases based on the 1960–2014 trends are compared to a “ no further warming” scenario. Overall, our analysis results in per capita income losses of 20 to 24 percent under the high-emissions climate scenarios by 2100, with significant variations across countries. Our income loss estimates encompass findings from several studies in the literature; however, they are considerably smaller than damages reported by [<xref ref-type="bibr" rid="pclm.0000621.ref003">3</xref>] and [<xref ref-type="bibr" rid="pclm.0000621.ref008">8</xref>]. Establishing a reliable range for GDP impact assessments is essential for incorporating climate-related risks into macro-fiscal frameworks and for effectively informing and guiding climate action initiatives.</p>
<p>The rest of the paper is organized as follows. <xref ref-type="sec" rid="sec002">Sect 2</xref> briefly describes the IPCC climate scenarios. <xref ref-type="sec" rid="sec003">Sect 3</xref> discusses the methodology used for the counterfactual analysis. <xref ref-type="sec" rid="sec004">Sect 4</xref> estimates the cumulative income effects of annual increases in temperatures under different climate scenarios. Finally, <xref ref-type="sec" rid="sec005">Sect 5</xref> offers some concluding remarks.</p>
</sec>
<sec id="sec002">
<title>2. Climate scenarios</title>
<p>Climate scenarios describe how the future might unfold under different levels of radiative forcing (the warming effect caused by greenhouse gases) and socio-economic pathways. Representative Concentration Pathways (RCPs) are scenarios of future greenhouse gas concentrations that describe the level of radiative forcing by 2100. Four independent radiative forcing pathways or RCPs were created by modelling groups to produce distinct and discernible climate change outcomes – RCP2.6, RCP4.5, RCP6.0 and RCP8.5 – each named after the approximate radiative forcing in 2100.</p>
<p>Shared Socio-economic Pathways (SSPs) describe potential future pathways of societal development, focusing on factors like population and education, urbanization, and economic development. The SSPs provide a framework for understanding how different socioeconomic conditions could influence greenhouse gas emissions and climate change. Five SSPs have been developed by the scientific community to span a range of outcomes that describe the challenges of climate change mitigation and adaptation.</p>
<p>SSPs are meant to be used in combination with RCPs in a scenario matrix to explore the impact of climate change mitigation on future global warming. SSPs without RCPs lack a specific quantitative translation to temperature, making comparisons across SSP scenarios difficult. RCPs without explicit SSPs assume an unspecified socio-economic context (energy, land-use, and emission pathways), limiting their ability to fully portray the nuances of future societal dynamics impacting emissions.</p>
<p>Within the RCP-SSP scenario matrix (<xref ref-type="fig" rid="pclm.0000621.g002">Fig 2</xref>), this paper focuses on SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5. The choice of climate scenarios is informed by the baseline global temperature pathways under current policies as well as (un)mitigated pathways. The first Global Stocktake (IPCC 2023) estimates that global temperature increase will be in the range of 2.1-2.8<sup>∘</sup>C by 2100 with implementation of the latest nationally determined contributions. However, current policies are not consistent with these commitments, which means that the world is set to experience a temperature increase at the upper bound of the above range. This is largely consistent with SSP2-4.5 and close to the 1960-2014 trend temperature increase baseline. An aspirational global warming scenario consistent with Paris Agreement is also considered (SSP1-2.6). Moreover, two pessimistic scenarios reflecting policy reversals (SSP3-7.0), or continued expansion of fossil fuels (SSP5-8.5) are used to highlight the risks of faster temperature increases. The 90th percentile of the ensemble of climate models for SSP3-7.0— that is, SSP3-7.0 (90th percentile)— is used to highlight a “ hotter” world as SSP5-8.5 is deemed unrealistic.</p>
<fig id="pclm.0000621.g002" position="float"><object-id pub-id-type="doi">10.1371/journal.pclm.0000621.g002</object-id><label>Fig 2</label><caption><title>How are RCPs, SSPs, and NFGS scenarios related?</title><p>Sources: The authors, [<xref ref-type="bibr" rid="pclm.0000621.ref017">17</xref>], and [<xref ref-type="bibr" rid="pclm.0000621.ref018">18</xref>].</p></caption>
<graphic mimetype="image" position="float" xlink:href="info:doi/10.1371/journal.pclm.0000621.g002" xlink:type="simple"/></fig>
</sec>
<sec id="sec003">
<title>3. Counterfactual analysis</title>
<p>We perform a number of counterfactual exercises to measure the cumulative output per capita effects of persistent increases in annual temperatures above their norms over the period 2015–2100 using the Half-Panel Jackknife Fixed Effects (HPJ-FE) estimates of the following Autoregressive Distributed Lag (ARDL) model:</p>
<disp-formula id="pclm.0000621.e006"><alternatives><graphic id="pclm.0000621.e006g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e006" xlink:type="simple"/><mml:math display="block" id="M6"><mml:mrow><mml:mrow><mml:mi>φ</mml:mi><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:mi>L</mml:mi><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mo>Δ</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>β</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>L</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>Δ</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mi>ε</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></disp-formula>
<p>where <italic>y</italic><sub><italic>it</italic></sub> is the log of real GDP per capita of country <italic>i</italic> in year <italic>t</italic>, <italic>a</italic><sub><italic>i</italic></sub> is the country-specific fixed effect, <inline-formula id="pclm.0000621.e007"><alternatives><graphic id="pclm.0000621.e007g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e007" xlink:type="simple"/><mml:math display="inline" id="M7"><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">|</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msubsup><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo fence="true" form="postfix" stretchy="true">|</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula> measures the absolute value of temperature relative to its historical norms, <italic>T</italic><sub><italic>it</italic></sub> is the population-weighted average temperature of country <italic>i</italic> in year <italic>t</italic>, and <inline-formula id="pclm.0000621.e008"><alternatives><graphic id="pclm.0000621.e008g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e008" xlink:type="simple"/><mml:math display="inline" id="M8"><mml:mrow><mml:msubsup><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:mfrac><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>ℓ</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>−</mml:mo><mml:mi>ℓ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula> is the time-varying historical norm of temperature over the preceding <italic>m</italic> years in each <italic>t</italic>. Climate norms are typically computed using 30-year moving averages (see, for instance, [<xref ref-type="bibr" rid="pclm.0000621.ref019">19</xref>] and [<xref ref-type="bibr" rid="pclm.0000621.ref020">20</xref>]), but to check the robustness of our results and model adaptation, we also consider historical norms computed using moving averages with <italic>m</italic> = 10, 20, 40, 50, and 100. <italic>m</italic> = 30 also corresponds to the official World Meteorological Organization definition of climate. <inline-formula id="pclm.0000621.e009"><alternatives><graphic id="pclm.0000621.e009g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e009" xlink:type="simple"/><mml:math display="inline" id="M9"><mml:mrow><mml:mi>φ</mml:mi><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:mi>L</mml:mi><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>ℓ</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msubsup><mml:msub><mml:mi>φ</mml:mi><mml:mrow><mml:mi>ℓ</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mi>L</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>, <inline-formula id="pclm.0000621.e010"><alternatives><graphic id="pclm.0000621.e010g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e010" xlink:type="simple"/><mml:math display="inline" id="M10"><mml:mrow><mml:mi>β</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>L</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>ℓ</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msubsup><mml:msub><mml:mi>β</mml:mi><mml:mrow><mml:mi>ℓ</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mi>L</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>, and <italic>L</italic> is the lag operator.</p>
<p>Pre-multiplying both sides of the above equation by the inverse of <inline-formula id="pclm.0000621.e011"><alternatives><graphic id="pclm.0000621.e011g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e011" xlink:type="simple"/><mml:math display="inline" id="M11"><mml:mrow><mml:mi>φ</mml:mi><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:mi>L</mml:mi><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula> yields</p>
<disp-formula id="pclm.0000621.e012"><alternatives><graphic id="pclm.0000621.e012g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e012" xlink:type="simple"/><mml:math display="block" id="M12"><mml:mrow><mml:mrow><mml:mo>Δ</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mover><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mo stretchy="false">~</mml:mo></mml:mover><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>ψ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>L</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>Δ</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>ϑ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>L</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:msub><mml:mi>ε</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives> <label>(1)</label></disp-formula>
<p>where <inline-formula id="pclm.0000621.e013"><alternatives><graphic id="pclm.0000621.e013g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e013" xlink:type="simple"/><mml:math display="inline" id="M13"><mml:mrow><mml:msub><mml:mover><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mo stretchy="false">~</mml:mo></mml:mover><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>φ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:msup><mml:mi> </mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>, <inline-formula id="pclm.0000621.e014"><alternatives><graphic id="pclm.0000621.e014g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e014" xlink:type="simple"/><mml:math display="inline" id="M14"><mml:mrow><mml:mi>ϑ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>L</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>ϑ</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ϑ</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mi>L</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>ϑ</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msup><mml:mi>L</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mi>…</mml:mi></mml:mrow></mml:math></alternatives></inline-formula> and <inline-formula id="pclm.0000621.e015"><alternatives><graphic id="pclm.0000621.e015g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e015" xlink:type="simple"/><mml:math display="inline" id="M15"><mml:mrow><mml:mi>ψ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>L</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mi>φ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>L</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:msup><mml:mi> </mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mi>β</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>L</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>ψ</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ψ</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mi>L</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>ψ</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msup><mml:mi>L</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mi>…</mml:mi></mml:mrow></mml:math></alternatives></inline-formula> We are suppressing the dependence of <italic>x</italic><sub><italic>it</italic></sub> on <italic>m</italic> to simplify the exposition.</p>
<p>The counterfactual effects of climate change can be derived by comparing the output trajectory of country <italic>i</italic> over the period <inline-formula id="pclm.0000621.e016"><alternatives><graphic id="pclm.0000621.e016g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e016" xlink:type="simple"/><mml:math display="inline" id="M16"><mml:mrow><mml:mi>T</mml:mi><mml:mspace width="0.167em"/><mml:mrow><mml:mo>+</mml:mo></mml:mrow><mml:mspace width="0.167em"/><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula> to <inline-formula id="pclm.0000621.e017"><alternatives><graphic id="pclm.0000621.e017g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e017" xlink:type="simple"/><mml:math display="inline" id="M17"><mml:mrow><mml:mi>T</mml:mi><mml:mspace width="0.167em"/><mml:mrow><mml:mo>+</mml:mo></mml:mrow><mml:mspace width="0.167em"/><mml:mi>h</mml:mi></mml:mrow></mml:math></alternatives></inline-formula> under the baseline scenario denoted by <inline-formula id="pclm.0000621.e018"><alternatives><graphic id="pclm.0000621.e018g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e018" xlink:type="simple"/><mml:math display="inline" id="M18"><mml:mrow><mml:msubsup><mml:mi>b</mml:mi><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula> and <inline-formula id="pclm.0000621.e019"><alternatives><graphic id="pclm.0000621.e019g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e019" xlink:type="simple"/><mml:math display="inline" id="M19"><mml:mrow><mml:msubsup><mml:mi>σ</mml:mi><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>, with an alternative expected trajectory having the counterfactual values of <inline-formula id="pclm.0000621.e020"><alternatives><graphic id="pclm.0000621.e020g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e020" xlink:type="simple"/><mml:math display="inline" id="M20"><mml:mrow><mml:msubsup><mml:mi>b</mml:mi><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula> and <inline-formula id="pclm.0000621.e021"><alternatives><graphic id="pclm.0000621.e021g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e021" xlink:type="simple"/><mml:math display="inline" id="M21"><mml:mrow><mml:msubsup><mml:mi>σ</mml:mi><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>. Denoting the values of <italic>x</italic><sub><italic>it</italic></sub> for <inline-formula id="pclm.0000621.e022"><alternatives><graphic id="pclm.0000621.e022g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e022" xlink:type="simple"/><mml:math display="inline" id="M22"><mml:mrow><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mi>T</mml:mi><mml:mspace width="0.167em"/><mml:mrow><mml:mo>+</mml:mo></mml:mrow><mml:mspace width="0.167em"/><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mspace width="0.167em"/><mml:mrow><mml:mo>+</mml:mo></mml:mrow><mml:mspace width="0.167em"/><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mspace width="0.167em"/><mml:mrow><mml:mo>+</mml:mo></mml:mrow><mml:mspace width="0.167em"/><mml:mi>h</mml:mi></mml:mrow></mml:math></alternatives></inline-formula> under these two scenarios by <inline-formula id="pclm.0000621.e023"><alternatives><graphic id="pclm.0000621.e023g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e023" xlink:type="simple"/><mml:math display="inline" id="M23"><mml:mrow><mml:msubsup><mml:mi>𝐱</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>,</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo fence="true" form="postfix" stretchy="true">}</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>, and <inline-formula id="pclm.0000621.e024"><alternatives><graphic id="pclm.0000621.e024g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e024" xlink:type="simple"/><mml:math display="inline" id="M24"><mml:mrow><mml:msubsup><mml:mi>𝐱</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>,</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo fence="true" form="postfix" stretchy="true">}</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>, the counterfactual output change can be written as</p>
<disp-formula id="pclm.0000621.e025"><alternatives><graphic id="pclm.0000621.e025g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e025" xlink:type="simple"/><mml:math display="block" id="M25"><mml:mrow><mml:mrow><mml:msub><mml:mi>ξ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>h</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>𝔼</mml:mi><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>h</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">|</mml:mo><mml:msub><mml:mi>ϝ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msubsup><mml:mi>𝐱</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo fence="true" form="postfix" stretchy="true"/></mml:mrow><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:mi>𝔼</mml:mi><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>h</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">|</mml:mo><mml:msub><mml:mi>ϝ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msubsup><mml:mi>𝐱</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo fence="true" form="postfix" stretchy="true"/></mml:mrow><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></disp-formula>
<p>where <inline-formula id="pclm.0000621.e026"><alternatives><graphic id="pclm.0000621.e026g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e026" xlink:type="simple"/><mml:math display="inline" id="M26"><mml:mrow><mml:msub><mml:mi>ϝ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mi>;</mml:mi><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>. Cumulating both sides of (<xref ref-type="disp-formula" rid="pclm.0000621.e012">1</xref>) from <inline-formula id="pclm.0000621.e027"><alternatives><graphic id="pclm.0000621.e027g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e027" xlink:type="simple"/><mml:math display="inline" id="M27"><mml:mrow><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mi>T</mml:mi><mml:mrow><mml:mo>+</mml:mo></mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula> to <italic>T</italic> + <italic>h</italic> and taking conditional expectations under the two scenarios we have</p>
<disp-formula id="pclm.0000621.e028"><alternatives><graphic id="pclm.0000621.e028g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e028" xlink:type="simple"/><mml:math display="block" id="M28"><mml:mrow><mml:mrow><mml:msub><mml:mi>ξ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>h</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>h</mml:mi></mml:mrow></mml:munderover><mml:msub><mml:mi>ψ</mml:mi><mml:mrow><mml:mi>h</mml:mi><mml:mo>−</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>−</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives> <label>(2)</label></disp-formula>
<p>The impact of climate change clearly depends on the magnitude of <inline-formula id="pclm.0000621.e029"><alternatives><graphic id="pclm.0000621.e029g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e029" xlink:type="simple"/><mml:math display="inline" id="M29"><mml:mrow><mml:msubsup><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>−</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>.</p>
<p>We consider the output effects of country-specific average annual increases in temperatures over the period 2015–2100 under various SSP scenarios, and compare them with a baseline scenario under which temperature in each country increases according to its historical trend of 1960–2014. However, owing to the non-linear nature of our output-growth specification, changes in trend temperature do not translate on a one-to-one basis to absolute changes in temperature. Future temperature changes over the counterfactual horizon, <inline-formula id="pclm.0000621.e030"><alternatives><graphic id="pclm.0000621.e030g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e030" xlink:type="simple"/><mml:math display="inline" id="M30"><mml:mrow><mml:mi>T</mml:mi><mml:mrow><mml:mo>+</mml:mo></mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>, <inline-formula id="pclm.0000621.e031"><alternatives><graphic id="pclm.0000621.e031g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e031" xlink:type="simple"/><mml:math display="inline" id="M31"><mml:mrow><mml:mtext> </mml:mtext><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo></mml:mrow></mml:math></alternatives></inline-formula> can be represented by</p>
<disp-formula id="pclm.0000621.e032"><alternatives><graphic id="pclm.0000621.e032g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e032" xlink:type="simple"/><mml:math display="block" id="M32"><mml:mrow><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mtext> for </mml:mtext><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives> <label>(3)</label></disp-formula>
<p>where we allow for the trend change in the temperature to vary over time. Suppose also that, as before, the historical norm variable associated with <italic>T</italic><sub><italic>i</italic>,<italic>T</italic> + <italic>j</italic></sub>, namely <inline-formula id="pclm.0000621.e033"><alternatives><graphic id="pclm.0000621.e033g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e033" xlink:type="simple"/><mml:math display="inline" id="M33"><mml:mrow><mml:msubsup><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>, is constructed using the past <italic>m</italic> years. Then it is easy to show that</p>
<disp-formula id="pclm.0000621.e034"><alternatives><graphic id="pclm.0000621.e034g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e034" xlink:type="simple"/><mml:math display="block" id="M34"><mml:mrow><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msubsup><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:mfrac><mml:mrow><mml:mi>m</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mover><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mo stretchy="true">¯</mml:mo></mml:mover><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mtext> </mml:mtext><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>,</mml:mo><mml:mi>h</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives> <label>(4)</label></disp-formula>
<p>where <inline-formula id="pclm.0000621.e035"><alternatives><graphic id="pclm.0000621.e035g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e035" xlink:type="simple"/><mml:math display="inline" id="M35"><mml:mrow><mml:msub><mml:mover><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mo stretchy="true">¯</mml:mo></mml:mover><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mi>m</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi><mml:mo>−</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>. The realised values of <inline-formula id="pclm.0000621.e036"><alternatives><graphic id="pclm.0000621.e036g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e036" xlink:type="simple"/><mml:math display="inline" id="M36"><mml:mrow><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">|</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msubsup><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo fence="true" form="postfix" stretchy="true">|</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula> depend on the probability distribution of weather shocks, <inline-formula id="pclm.0000621.e037"><alternatives><graphic id="pclm.0000621.e037g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e037" xlink:type="simple"/><mml:math display="inline" id="M37"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>, as well as the trend change in temperature, given by <italic>b</italic><sub><italic>Ti</italic>,<italic>j</italic></sub>. As a first order approximation, and in order to obtain analytic expressions, we assume that temperature shocks, <inline-formula id="pclm.0000621.e038"><alternatives><graphic id="pclm.0000621.e038g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e038" xlink:type="simple"/><mml:math display="inline" id="M38"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>, over <inline-formula id="pclm.0000621.e039"><alternatives><graphic id="pclm.0000621.e039g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e039" xlink:type="simple"/><mml:math display="inline" id="M39"><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula> are serially uncorrelated, Gaussian random variables with zero means and variances, <inline-formula id="pclm.0000621.e040"><alternatives><graphic id="pclm.0000621.e040g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e040" xlink:type="simple"/><mml:math display="inline" id="M40"><mml:mrow><mml:msubsup><mml:mi>σ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>. Under these assumptions and using the results in Lemma 3.1 of [<xref ref-type="bibr" rid="pclm.0000621.ref021">21</xref>], we have</p>
<disp-formula id="pclm.0000621.e041"><alternatives><graphic id="pclm.0000621.e041g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e041" xlink:type="simple"/><mml:math display="block" id="M41"><mml:mrow><mml:mrow><mml:mi>𝔼</mml:mi><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">|</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msubsup><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo fence="true" form="postfix" stretchy="true">|</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>μ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">[</mml:mo><mml:mo>Φ</mml:mo><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>μ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>ω</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:mo>Φ</mml:mo><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:mfrac><mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mi>μ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>ω</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mo fence="true" form="postfix" stretchy="true">]</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mi>ω</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mi>ϕ</mml:mi><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>μ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>ω</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives> <label>(5)</label></disp-formula>
<p>where <inline-formula id="pclm.0000621.e042"><alternatives><graphic id="pclm.0000621.e042g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e042" xlink:type="simple"/><mml:math display="inline" id="M42"><mml:mrow><mml:mo>Φ</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mo>.</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula> and <inline-formula id="pclm.0000621.e043"><alternatives><graphic id="pclm.0000621.e043g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e043" xlink:type="simple"/><mml:math display="inline" id="M43"><mml:mrow><mml:mi>ϕ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mo>.</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula> are the cumulative and density distribution functions of a standard Normal variate, respectively, and</p>
<disp-formula id="pclm.0000621.e044"><alternatives><graphic id="pclm.0000621.e044g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e044" xlink:type="simple"/><mml:math display="block" id="M44"><mml:mrow><mml:mrow><mml:msub><mml:mi>μ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:mfrac><mml:mrow><mml:mi>m</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mtext>, and </mml:mtext><mml:msubsup><mml:mi>ω</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mi>σ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:mfrac><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></disp-formula>
<p>It is clear from the above expressions that the responses of our climate variables to a postulated rise in temperature most crucially depend on the volatility of temperature around its trend, <inline-formula id="pclm.0000621.e045"><alternatives><graphic id="pclm.0000621.e045g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e045" xlink:type="simple"/><mml:math display="inline" id="M45"><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>, which differs markedly across countries.</p>
<p>For the baseline scenario, we set <italic>m</italic> = 30 and consider the following counterfactual <italic>country-specific</italic> changes in the trend temperature over the period <inline-formula id="pclm.0000621.e046"><alternatives><graphic id="pclm.0000621.e046g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e046" xlink:type="simple"/><mml:math display="inline" id="M46"><mml:mrow><mml:mi>T</mml:mi><mml:mrow><mml:mo>+</mml:mo></mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>, for <inline-formula id="pclm.0000621.e047"><alternatives><graphic id="pclm.0000621.e047g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e047" xlink:type="simple"/><mml:math display="inline" id="M47"><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>,</mml:mo><mml:mi>H</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula> as compared to the historical trend rise in temperature (namely <inline-formula id="pclm.0000621.e048"><alternatives><graphic id="pclm.0000621.e048g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e048" xlink:type="simple"/><mml:math display="inline" id="M48"><mml:mrow><mml:msubsup><mml:mi>b</mml:mi><mml:mrow><mml:mi>𝒯</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>):</p>
<disp-formula id="pclm.0000621.e049"><alternatives><graphic id="pclm.0000621.e049g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e049" xlink:type="simple"/><mml:math display="block" id="M49"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>b</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msubsup><mml:mi>b</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:mi>j</mml:mi><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mtext>, for all </mml:mtext><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>,</mml:mo><mml:mi>H</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives> <label>(6)</label></disp-formula>
<p>where <italic>d</italic><sub><italic>i</italic></sub> is the average incremental change in the trend rise in temperature for country <italic>i</italic>. We set <italic>d</italic><sub><italic>i</italic></sub> to ensure that the average rise in temperature over the counterfactual period in country <italic>i</italic> is equal to the hypothesised value of <inline-formula id="pclm.0000621.e050"><alternatives><graphic id="pclm.0000621.e050g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e050" xlink:type="simple"/><mml:math display="inline" id="M50"><mml:mrow><mml:msubsup><mml:mi>b</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>, and note that</p>
<disp-formula id="pclm.0000621.e051"><alternatives><graphic id="pclm.0000621.e051g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e051" xlink:type="simple"/><mml:math display="block" id="M51"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>b</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msup><mml:mi>H</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>H</mml:mi></mml:mrow></mml:munderover><mml:msubsup><mml:mi>b</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msup><mml:mi>H</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>H</mml:mi></mml:mrow></mml:munderover><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>H</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>H</mml:mi></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives> <label>(7)</label></disp-formula>
<p>where <italic>T</italic><sub><italic>i</italic>,<italic>T</italic> + <italic>H</italic></sub> denotes the level of temperature at the end of the counterfactual period. Averaging (<xref ref-type="disp-formula" rid="pclm.0000621.e049">6</xref>) over <italic>j</italic> we have</p>
<disp-formula id="pclm.0000621.e052"><alternatives><graphic id="pclm.0000621.e052g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e052" xlink:type="simple"/><mml:math display="block" id="M52"><mml:mrow><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>2</mml:mn><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:msubsup><mml:mi>b</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>−</mml:mo><mml:msubsup><mml:mi>b</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>H</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives> <label>(8)</label></disp-formula>
<p>In our empirical application we set <inline-formula id="pclm.0000621.e053"><alternatives><graphic id="pclm.0000621.e053g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e053" xlink:type="simple"/><mml:math display="inline" id="M53"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>H</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mn>2099</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula> and <inline-formula id="pclm.0000621.e054"><alternatives><graphic id="pclm.0000621.e054g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e054" xlink:type="simple"/><mml:math display="inline" id="M54"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mn>2015</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>, with implied <italic>H</italic> = 85. For <italic>T</italic><sub><italic>i</italic>,2099</sub>, where <inline-formula id="pclm.0000621.e055"><alternatives><graphic id="pclm.0000621.e055g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e055" xlink:type="simple"/><mml:math display="inline" id="M55"><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>,</mml:mo><mml:mi>N</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>, we consider five sets of values based on IPCC’s projections under SSP scenarios (see <xref ref-type="fig" rid="pclm.0000621.g002">Fig 2</xref>). In effect, this specification assumes that over the counterfactual period temperature in country <italic>i</italic> increases by <italic>jd</italic><sub><italic>i</italic></sub> per annum over the period <inline-formula id="pclm.0000621.e056"><alternatives><graphic id="pclm.0000621.e056g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e056" xlink:type="simple"/><mml:math display="inline" id="M56"><mml:mrow><mml:mi>T</mml:mi><mml:mrow><mml:mo>+</mml:mo></mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula> to <inline-formula id="pclm.0000621.e057"><alternatives><graphic id="pclm.0000621.e057g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e057" xlink:type="simple"/><mml:math display="inline" id="M57"><mml:mrow><mml:mi>T</mml:mi><mml:mrow><mml:mo>+</mml:mo></mml:mrow><mml:mi>j</mml:mi><mml:mspace width="0.167em"/></mml:mrow></mml:math></alternatives></inline-formula>, relative to its historical trend value of <inline-formula id="pclm.0000621.e058"><alternatives><graphic id="pclm.0000621.e058g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e058" xlink:type="simple"/><mml:math display="inline" id="M58"><mml:mrow><mml:msubsup><mml:mi>b</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>.</p>
<p>We also assume that the postulated trend rise in temperature, specified in (<xref ref-type="disp-formula" rid="pclm.0000621.e049">6</xref>), does not affect the volatility of temperature shocks, and set <inline-formula id="pclm.0000621.e059"><alternatives><graphic id="pclm.0000621.e059g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e059" xlink:type="simple"/><mml:math display="inline" id="M59"><mml:mrow><mml:msubsup><mml:mi>σ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula> to its pre-counterfactual value of <inline-formula id="pclm.0000621.e060"><alternatives><graphic id="pclm.0000621.e060g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e060" xlink:type="simple"/><mml:math display="inline" id="M60"><mml:mrow><mml:msubsup><mml:mi>σ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mspace width="0.167em"/></mml:mrow></mml:math></alternatives></inline-formula>. This is a conservative assumption and most likely will result in an under-estimation of the adverse effects of temperature increases, since one would expect rising temperature to be associated with an increase in volatility. Moreover, accounting for international spillover effects of climate change, individual countries’ long-term growth effects could be larger. With these considerations in mind, and using (<xref ref-type="disp-formula" rid="pclm.0000621.e028">2</xref>), the mean counterfactual impact of the temperature change on output is given by</p>
<disp-formula id="pclm.0000621.e061"><alternatives><graphic id="pclm.0000621.e061g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e061" xlink:type="simple"/><mml:math display="block" id="M61"><mml:mrow><mml:mrow><mml:mrow><mml:msub><mml:mo>Δ</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>𝔼</mml:mi><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:msubsup><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">|</mml:mo><mml:msub><mml:mi>ϝ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi></mml:mrow></mml:msub><mml:mo fence="true" form="postfix" stretchy="true"/></mml:mrow><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:mi>𝔼</mml:mi><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:msubsup><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">|</mml:mo><mml:msub><mml:mi>ϝ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi></mml:mrow></mml:msub><mml:mo fence="true" form="postfix" stretchy="true"/></mml:mrow><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mspace linebreak="newline"/><mml:mo>=</mml:mo><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>h</mml:mi></mml:mrow></mml:munderover><mml:msub><mml:mi>ψ</mml:mi><mml:mrow><mml:mi>h</mml:mi><mml:mo>−</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">[</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:msubsup><mml:mi>b</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:mi>j</mml:mi><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msubsup><mml:mi>σ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo stretchy="false">)</mml:mo><mml:mo>−</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:msubsup><mml:mi>b</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msubsup><mml:mi>σ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo stretchy="false">)</mml:mo><mml:mo fence="true" form="postfix" stretchy="true">]</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></alternatives> <label>(9)</label></disp-formula>
<p>where we base the estimates of <inline-formula id="pclm.0000621.e062"><alternatives><graphic id="pclm.0000621.e062g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e062" xlink:type="simple"/><mml:math display="inline" id="M62"><mml:mrow><mml:msubsup><mml:mi>b</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula> and <inline-formula id="pclm.0000621.e063"><alternatives><graphic id="pclm.0000621.e063g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e063" xlink:type="simple"/><mml:math display="inline" id="M63"><mml:mrow><mml:msubsup><mml:mi>σ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula> on the pre-counterfactual period 1960-2014, and use</p>
<disp-formula id="pclm.0000621.e064"><alternatives><graphic id="pclm.0000621.e064g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e064" xlink:type="simple"/><mml:math display="block" id="M64"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>g</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:msubsup><mml:mi>b</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msubsup><mml:mi>σ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msubsup><mml:mi>μ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">[</mml:mo><mml:mo>Φ</mml:mo><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>μ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mrow><mml:msubsup><mml:mi>ω</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:mfrac><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:mo>Φ</mml:mo><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:mfrac><mml:mrow><mml:mo>−</mml:mo><mml:msubsup><mml:mi>μ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mrow><mml:msubsup><mml:mi>ω</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:mfrac><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mo fence="true" form="postfix" stretchy="true">]</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:msubsup><mml:mi>ω</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mi>ϕ</mml:mi><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>μ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mrow><mml:msubsup><mml:mi>ω</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:mfrac><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives> <label>(10)</label></disp-formula>
<disp-formula id="pclm.0000621.e065"><alternatives><graphic id="pclm.0000621.e065g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e065" xlink:type="simple"/><mml:math display="block" id="M65"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>g</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:msubsup><mml:mi>b</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msubsup><mml:mi>σ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msubsup><mml:mi>μ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">[</mml:mo><mml:mo>Φ</mml:mo><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>μ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mrow><mml:msubsup><mml:mi>ω</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:mfrac><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:mo>Φ</mml:mo><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:mfrac><mml:mrow><mml:mo>−</mml:mo><mml:msubsup><mml:mi>μ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mrow><mml:msubsup><mml:mi>ω</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:mfrac><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mo fence="true" form="postfix" stretchy="true">]</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:msubsup><mml:mi>ω</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mi>ϕ</mml:mi><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>μ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mrow><mml:msubsup><mml:mi>ω</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:mfrac><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives> <label>(11)</label></disp-formula>
<disp-formula id="pclm.0000621.e066"><alternatives><graphic id="pclm.0000621.e066g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e066" xlink:type="simple"/><mml:math display="block" id="M66"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>μ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:mfrac><mml:mrow><mml:mi>m</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:msubsup><mml:mi>b</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mtext> , </mml:mtext><mml:msubsup><mml:mi>μ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:mfrac><mml:mrow><mml:mi>m</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:msubsup><mml:mi>b</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:mtext> </mml:mtext></mml:mrow></mml:mrow></mml:math></alternatives> <label>(12)</label></disp-formula>
<p>and <inline-formula id="pclm.0000621.e067"><alternatives><graphic id="pclm.0000621.e067g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e067" xlink:type="simple"/><mml:math display="inline" id="M67"><mml:mrow><mml:msubsup><mml:mi>ω</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mi>σ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:msup><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:mfrac><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>. To obtain <inline-formula id="pclm.0000621.e068"><alternatives><graphic id="pclm.0000621.e068g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e068" xlink:type="simple"/><mml:math display="inline" id="M68"><mml:mrow><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">{</mml:mo><mml:msub><mml:mover><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mo stretchy="false">^</mml:mo></mml:mover><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo fence="true" form="postfix" stretchy="true">}</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula> we use the HPJ-FE estimates of <inline-formula id="pclm.0000621.e069"><alternatives><graphic id="pclm.0000621.e069g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e069" xlink:type="simple"/><mml:math display="inline" id="M69"><mml:mrow><mml:msubsup><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">{</mml:mo><mml:msub><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mrow><mml:mi>ℓ</mml:mi></mml:mrow></mml:msub><mml:mo fence="true" form="postfix" stretchy="true">}</mml:mo></mml:mrow><mml:mrow><mml:mi>l</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula> and <inline-formula id="pclm.0000621.e070"><alternatives><graphic id="pclm.0000621.e070g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e070" xlink:type="simple"/><mml:math display="inline" id="M70"><mml:mrow><mml:msubsup><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">{</mml:mo><mml:msub><mml:mi>φ</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub><mml:mo fence="true" form="postfix" stretchy="true">}</mml:mo></mml:mrow><mml:mrow><mml:mi>l</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula> from the ARDL equation with <inline-formula id="pclm.0000621.e071"><alternatives><graphic id="pclm.0000621.e071g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e071" xlink:type="simple"/><mml:math display="inline" id="M71"><mml:mrow><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">|</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msubsup><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo fence="true" form="postfix" stretchy="true">|</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula> as the climate variable. These estimates and their standard errors are reported in <xref ref-type="table" rid="pclm.0000621.t001">Table 1</xref>. <xref ref-type="fig" rid="pclm.0000621.g003">Fig 3</xref> plots the estimates of <inline-formula id="pclm.0000621.e072"><alternatives><graphic id="pclm.0000621.e072g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e072" xlink:type="simple"/><mml:math display="inline" id="M72"><mml:mrow><mml:msub><mml:mi>ψ</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula> for <inline-formula id="pclm.0000621.e073"><alternatives><graphic id="pclm.0000621.e073g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e073" xlink:type="simple"/><mml:math display="inline" id="M73"><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mi>…</mml:mi><mml:mo>,</mml:mo><mml:mn>20</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>, for which the estimated mean lag is <inline-formula id="pclm.0000621.e074"><alternatives><graphic id="pclm.0000621.e074g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e074" xlink:type="simple"/><mml:math display="inline" id="M74"><mml:mrow><mml:mfrac><mml:mrow><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mo>∞</mml:mo></mml:mrow></mml:msubsup><mml:mi>j</mml:mi><mml:msub><mml:mover><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mo stretchy="false">^</mml:mo></mml:mover><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mo>∞</mml:mo></mml:mrow></mml:msubsup><mml:msub><mml:mover><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mo stretchy="false">^</mml:mo></mml:mover><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mn>3.1943</mml:mn></mml:mrow></mml:math></alternatives></inline-formula> years.</p>
<fig id="pclm.0000621.g003" position="float"><object-id pub-id-type="doi">10.1371/journal.pclm.0000621.g003</object-id><label>Fig 3</label><caption><title><inline-formula id="pclm.0000621.e100"><alternatives><graphic id="pclm.0000621.e100g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e100" xlink:type="simple"/><mml:math display="inline" id="M100"><mml:mrow><mml:mo stretchy="false">{</mml:mo><mml:msub><mml:mi>ψ</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo stretchy="false">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula> for <inline-formula id="pclm.0000621.e101"><alternatives><graphic id="pclm.0000621.e101g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e101" xlink:type="simple"/><mml:math display="inline" id="M101"><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mi>…</mml:mi><mml:mo>,</mml:mo><mml:mn>20</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>.</title><p>Source: [<xref ref-type="bibr" rid="pclm.0000621.ref002">2</xref>].</p></caption>
<graphic mimetype="image" position="float" xlink:href="info:doi/10.1371/journal.pclm.0000621.g003" xlink:type="simple"/></fig>
<table-wrap id="pclm.0000621.t001" position="float"><object-id pub-id-type="doi">10.1371/journal.pclm.0000621.t001</object-id><label>Table 1</label><caption><title>Effects of climate change on per capita real GDP growth, 1960–2014</title></caption>
<alternatives><graphic id="pclm.0000621.t001g" mimetype="image" position="float" xlink:href="info:doi/10.1371/journal.pclm.0000621.t001" xlink:type="simple"/><table><colgroup>
<col align="left" valign="middle"/>
<col align="left" valign="middle"/>
<col align="left" valign="middle"/>
<col align="left" valign="middle"/>
<col align="left" valign="middle"/>
<col align="left" valign="middle"/>
</colgroup>
<thead>
<tr>
<th align="left"><inline-formula id="pclm.0000621.e075"><alternatives><graphic id="pclm.0000621.e075g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e075" xlink:type="simple"/><mml:math display="inline" id="M75"><mml:mrow><mml:msub><mml:mover><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mo>^</mml:mo></mml:mover><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula></th>
<th align="left">-0.0038 </th>
<th align="left"><inline-formula id="pclm.0000621.e076"><alternatives><graphic id="pclm.0000621.e076g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e076" xlink:type="simple"/><mml:math display="inline" id="M76"><mml:mrow><mml:msub><mml:mover><mml:mrow><mml:mi>φ</mml:mi></mml:mrow><mml:mo>^</mml:mo></mml:mover><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula></th>
<th align="left">0.2643<sup>***</sup></th>
<th align="left">No. of Countries <inline-formula id="pclm.0000621.e078"><alternatives><graphic id="pclm.0000621.e078g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e078" xlink:type="simple"/><mml:math display="inline" id="M78"><mml:mrow><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:mi>N</mml:mi><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula></th>
<th align="left">174</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left"/>
<td align="left">(0.0021)</td>
<td align="left"/>
<td align="left">(0.0500)</td>
<td align="left"><inline-formula id="pclm.0000621.e079"><alternatives><graphic id="pclm.0000621.e079g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e079" xlink:type="simple"/><mml:math display="inline" id="M79"><mml:mrow><mml:mo>max</mml:mo><mml:mi>T</mml:mi></mml:mrow></mml:math></alternatives></inline-formula></td>
<td align="left">50</td>
</tr>
<tr>
<td align="left"><inline-formula id="pclm.0000621.e080"><alternatives><graphic id="pclm.0000621.e080g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e080" xlink:type="simple"/><mml:math display="inline" id="M80"><mml:mrow><mml:msub><mml:mover><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mo>^</mml:mo></mml:mover><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula></td>
<td align="left">-0.0056 </td>
<td align="left"><inline-formula id="pclm.0000621.e081"><alternatives><graphic id="pclm.0000621.e081g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e081" xlink:type="simple"/><mml:math display="inline" id="M81"><mml:mrow><mml:msub><mml:mover><mml:mrow><mml:mi>φ</mml:mi></mml:mrow><mml:mo>^</mml:mo></mml:mover><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula></td>
<td align="left">0.0785<sup>***</sup></td>
<td align="left"><inline-formula id="pclm.0000621.e083"><alternatives><graphic id="pclm.0000621.e083g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e083" xlink:type="simple"/><mml:math display="inline" id="M83"><mml:mrow><mml:mrow><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:math></alternatives></inline-formula></td>
<td align="left">38.36</td>
</tr>
<tr>
<td align="left"/>
<td align="left">(0.0029)</td>
<td align="left"/>
<td align="left">(0.0266)</td>
<td align="left"><inline-formula id="pclm.0000621.e084"><alternatives><graphic id="pclm.0000621.e084g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e084" xlink:type="simple"/><mml:math display="inline" id="M84"><mml:mrow><mml:mo>min</mml:mo><mml:mi>T</mml:mi></mml:mrow></mml:math></alternatives></inline-formula></td>
<td align="left">2</td>
</tr>
<tr>
<td align="left"><inline-formula id="pclm.0000621.e085"><alternatives><graphic id="pclm.0000621.e085g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e085" xlink:type="simple"/><mml:math display="inline" id="M85"><mml:mrow><mml:msub><mml:mover><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mo>^</mml:mo></mml:mover><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula></td>
<td align="left">-0.0084<sup>***</sup></td>
<td align="left"><inline-formula id="pclm.0000621.e087"><alternatives><graphic id="pclm.0000621.e087g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e087" xlink:type="simple"/><mml:math display="inline" id="M87"><mml:mrow><mml:msub><mml:mover><mml:mrow><mml:mi>φ</mml:mi></mml:mrow><mml:mo>^</mml:mo></mml:mover><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula></td>
<td align="left">0.0547<sup>**</sup></td>
<td align="left">No. of Obs. <inline-formula id="pclm.0000621.e089"><alternatives><graphic id="pclm.0000621.e089g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e089" xlink:type="simple"/><mml:math display="inline" id="M89"><mml:mrow><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:mi>N</mml:mi><mml:mo>×</mml:mo><mml:mi>T</mml:mi><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula></td>
<td align="left">6,674</td>
</tr>
<tr>
<td align="left"/>
<td align="left">(0.0031)</td>
<td align="left"/>
<td align="left">(0.0216)</td>
<td align="left"/>
<td align="left"/>
</tr>
<tr>
<td align="left"><inline-formula id="pclm.0000621.e090"><alternatives><graphic id="pclm.0000621.e090g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e090" xlink:type="simple"/><mml:math display="inline" id="M90"><mml:mrow><mml:msub><mml:mover><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mo>^</mml:mo></mml:mover><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula></td>
<td align="left">-0.0090<sup>***</sup></td>
<td align="left"><inline-formula id="pclm.0000621.e092"><alternatives><graphic id="pclm.0000621.e092g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e092" xlink:type="simple"/><mml:math display="inline" id="M92"><mml:mrow><mml:msub><mml:mover><mml:mrow><mml:mi>φ</mml:mi></mml:mrow><mml:mo>^</mml:mo></mml:mover><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula></td>
<td align="left">-0.0016</td>
<td align="left"/>
<td align="left"/>
</tr>
<tr>
<td align="left"/>
<td align="left">(0.0026)</td>
<td align="left"/>
<td align="left">(0.0327)</td>
<td align="left"/>
<td align="left"/>
</tr>
<tr>
<td align="left"><inline-formula id="pclm.0000621.e093"><alternatives><graphic id="pclm.0000621.e093g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e093" xlink:type="simple"/><mml:math display="inline" id="M93"><mml:mrow><mml:msub><mml:mover><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mo>^</mml:mo></mml:mover><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula></td>
<td align="left">-0.0060<sup>***</sup></td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
</tr>
<tr>
<td align="left"/>
<td align="left">(0.0021)</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
</tr>
</tbody>
</table>
</alternatives><table-wrap-foot>
<fn id="t001fn001"><p>Notes: Estimates are based on <inline-formula id="pclm.0000621.e095"><alternatives><graphic id="pclm.0000621.e095g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e095" xlink:type="simple"/><mml:math display="inline" id="M95"><mml:mrow><mml:mo>Δ</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mspace width="0.167em"/><mml:mrow><mml:mo>+</mml:mo></mml:mrow><mml:mspace width="0.167em"/><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>ℓ</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msubsup><mml:msub><mml:mi>φ</mml:mi><mml:mrow><mml:mi>ℓ</mml:mi></mml:mrow></mml:msub><mml:mo>Δ</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>−</mml:mo><mml:mi>ℓ</mml:mi></mml:mrow></mml:msub><mml:mspace width="0.167em"/><mml:mrow><mml:mo>+</mml:mo></mml:mrow><mml:mspace width="0.167em"/><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>ℓ</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msubsup><mml:msubsup><mml:mi>β</mml:mi><mml:mrow><mml:mi>ℓ</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi> </mml:mi><mml:mrow><mml:mi>′</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:msubsup><mml:mo>Δ</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>−</mml:mo><mml:mi>ℓ</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mspace width="0.167em"/><mml:mrow><mml:mo>+</mml:mo></mml:mrow><mml:mspace width="0.167em"/><mml:msub><mml:mi>ε</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula> where <italic>y</italic><sub><italic>it</italic></sub> is the log of real GDP per capita of country <italic>i</italic> in year <italic>t</italic>, <inline-formula id="pclm.0000621.e096"><alternatives><graphic id="pclm.0000621.e096g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e096" xlink:type="simple"/><mml:math display="inline" id="M96"><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">|</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msubsup><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo fence="true" form="postfix" stretchy="true">|</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>, <italic>T</italic><sub><italic>it</italic></sub> is the population-weighted average temperature of country <italic>i</italic> in year <italic>t</italic>, and <inline-formula id="pclm.0000621.e097"><alternatives><graphic id="pclm.0000621.e097g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e097" xlink:type="simple"/><mml:math display="inline" id="M97"><mml:mrow><mml:msubsup><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula> is the historical temperature norm of country <italic>i</italic> (based on moving averages of the past 30 years). The coefficients are estimated by the HPJ-FE procedure and the standard errors are based on the estimator proposed in Proposition 4 of [<xref ref-type="bibr" rid="pclm.0000621.ref022">22</xref>]. Asterisks indicate statistical significance at 1% (<sup>***</sup>), 5% (<sup>**</sup>), and 10% ( ) levels.</p></fn>
</table-wrap-foot>
</table-wrap>
<p>To study the role of climate volatility in determining GDP per capita losses, instead of setting <inline-formula id="pclm.0000621.e102"><alternatives><graphic id="pclm.0000621.e102g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e102" xlink:type="simple"/><mml:math display="inline" id="M102"><mml:mrow><mml:msubsup><mml:mi>σ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mi>σ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>, we allow temperature increases to affect the variability of temperature shocks commensurately. That is, we keep the coefficient of variation unchanged, and therefore set <inline-formula id="pclm.0000621.e103"><alternatives><graphic id="pclm.0000621.e103g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e103" xlink:type="simple"/><mml:math display="inline" id="M103"><mml:mrow><mml:msubsup><mml:mi>σ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:msubsup><mml:mi>μ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>/</mml:mo><mml:msubsup><mml:mi>μ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:msubsup><mml:mi>σ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>.</p>
<p>We compare the per capita GDP impact of temperature increases under various SSP scenarios to a baseline scenario under which temperature in each country rises according to its historical trend of 1960–2014. However, to have a better comparability to previous studies, we also perform a counterfactual exercise where temperature increases under the historical trend of 1960–2014 are compared to a baseline scenario no further warming and assuming that adaptation is extremely slow (i.e., historical norms are computed using moving averages with <italic>m</italic> = 100 in counterfactuals from 2015 onwards).</p>
</sec>
<sec id="sec004">
<title>4. GDP losses from global warming</title>
<p>We report the real GDP per capita losses (gains) from trend temperature changes under various SSP-RCP scenarios for the year 2100 compared to: (i) a baseline under which temperature in each country increases according to its historical trend of 1960–2014 (<xref ref-type="fig" rid="pclm.0000621.g004">Fig 4</xref>, yellow bar); and (ii) a commonly adopted baseline in the literature without climate change and with extremely-slow adaptation. Since the benchmark for measuring temperature anomalies is a moving average temperature (e.g., calculated over the thirty years preceding each observation), the critical factor in determining income losses is not the absolute level of temperature but rather changes in its trend. If the temperature trend stays constant, economic growth remains unaffected despite increases in temperature. Conversely, if the trend accelerates, growth declines further (the red bars in <xref ref-type="fig" rid="pclm.0000621.g004">Fig 4</xref>). A deceleration in the trend leads to faster economic growth (the green bar in <xref ref-type="fig" rid="pclm.0000621.g004">Fig 4</xref>), and if temperatures stabilize, growth returns to its baseline rate. We make all of the 174 <italic>country-specific</italic> estimates of annual income losses available to download from <ext-link ext-link-type="uri" xlink:href="http://files.econ.cam.ac.uk/people-files/faculty/km418/Annual_Country_Specific_Income_Loss_Estimates_of_SSP_Scenarios.xlsx" xlink:type="simple">here</ext-link>. <xref ref-type="fig" rid="pclm.0000621.g005">Fig 5</xref> shows that income losses under various SSP-RCP scenarios vary significantly across countries depending on the <italic>country-specific</italic> projected paths of temperatures, climate variability, and adaptation efforts; however, losses (gains) follow the logic above.</p>
<fig id="pclm.0000621.g004" position="float"><object-id pub-id-type="doi">10.1371/journal.pclm.0000621.g004</object-id><label>Fig 4</label><caption><title>Additional global temperature increase under different scenarios (2014 to 2100).</title><p>Source: Authors calculations based on IPCC AR6 Physical Science Report. Notes: Reports temperature increases relative to the 2014 average global surface temperature. At the time of the Paris Agreement’s adoption in 2015, global temperatures were estimated to be 0.98<sup>∘</sup>C above pre-industrial levels, with the agreement aiming to limit warming to well below 2<sup>∘</sup>C, and pursue efforts to limit it to 1.5<sup>∘</sup>C.</p></caption>
<graphic mimetype="image" position="float" xlink:href="info:doi/10.1371/journal.pclm.0000621.g004" xlink:type="simple"/></fig>
<fig id="pclm.0000621.g005" position="float"><object-id pub-id-type="doi">10.1371/journal.pclm.0000621.g005</object-id><label>Fig 5</label><caption><title>Frequency distribution of income losses across 174 countries by 2100.</title><p>Notes: We consider income losses from increases in temperatures under various IPCC climate scenarios relative to a baseline in which temperatures increase according to their 1960-2014 trends. Numbers are PPP GDP weighted averages of <inline-formula id="pclm.0000621.e107"><alternatives><graphic id="pclm.0000621.e107g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e107" xlink:type="simple"/><mml:math display="inline" id="M107"><mml:mrow><mml:msub><mml:mo>Δ</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>, see <xref ref-type="disp-formula" rid="pclm.0000621.e061">Eq (9)</xref>, with <italic>h</italic> = 86 (corresponding to the year 2100). Under the “No Adaptation” assumption, historical norms are formed over 100 years (i.e., <italic>m</italic> = 100). We keep <inline-formula id="pclm.0000621.e108"><alternatives><graphic id="pclm.0000621.e108g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e108" xlink:type="simple"/><mml:math display="inline" id="M108"><mml:mrow><mml:msubsup><mml:mi>σ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:msubsup><mml:mi>μ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>/</mml:mo><mml:msubsup><mml:mi>μ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:msubsup><mml:mi>σ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula> under the “Volatile Climate” assumption.</p></caption>
<graphic mimetype="image" position="float" xlink:href="info:doi/10.1371/journal.pclm.0000621.g005" xlink:type="simple"/></fig>
<p>Averaging the losses across countries, using PPP-GDP weights, we report that the global income effects of trend temperature increases relative to baseline (i) ranges from 5.4% under SSP3-7.0 (90th) to 11% under SSP5-8.5 with slower adaptation (<xref ref-type="fig" rid="pclm.0000621.g006">Fig 6</xref>)—SSP3-7.0 is a high-emissions scenario under which global warming accelerates and temperature increases by 3.6<sup>∘</sup>C in 2100, with respect to its pre-industrial average level. To provide a faster-warming scenario, we also utilize the 90th percentile of the SSP3-7.0 climate ensemble. Global temperature with this high-emission, fast-warming scenario increases by approximately 4.4<sup>∘</sup>C. This warming level is similar to the ensemble median warming level under SSP5-8.5. Climate variability amplifies the projected economic losses, with estimates under SSP3-7.0 (90th) (Volatile Climate) and SSP5-8.5 (Volatile Climate) surging to 12–14% globally with a considerable variation in income losses across countries (<xref ref-type="fig" rid="pclm.0000621.g005">Fig 5</xref>). However, while adaptation—encompassed within the “Faster Adaptation” scenarios in <xref ref-type="fig" rid="pclm.0000621.g005">Figs 5</xref> and <xref ref-type="fig" rid="pclm.0000621.g006">6</xref>—present a viable pathway to reducing the detrimental long-term growth effects of trend temperature increases, they fall short of completely eliminating these adverse impacts. This limitation suggests that adaptation, although beneficial, cannot serve as a standalone solution but rather as a critical component of a broader, more comprehensive approach to addressing the impacts of climate change. We, therefore, underscore the pressing need for climate change mitigation policies to slow global warming. Abiding by the Paris Agreement goals, thereby limiting the temperature increase to 0.01 degrees Celsius per year, generates an income benefit of 0.25 percent globally. This is because under SSP1-2.6, emissions decline at a rapid pace; the warming trend slows down; and global mean temperature stabilizes around 2<sup>∘</sup>C (a level that is 0.6<sup>∘</sup>C lower than what would result if temperatures were continuing to increase according to their historical trend of 1960–2014). Under SSP2-4.5, emissions would grow in line with their observed historical trends and current policies, and the global mean temperature would increase by 2.7<sup>∘</sup>C with respect to its pre-industrial average level (this is very close to baseline (i) in <xref ref-type="fig" rid="pclm.0000621.g006">Fig 6</xref>). Considering the additional income losses from temperature warming under the 1960–2014 trends relative to a baseline without climate change and assuming extremely-slow adaptation efforts brings the total losses under SSP5-8.5 scenario to 24 percent. This is the worst-case scenario in our counterfactuals.</p>
<fig id="pclm.0000621.g006" position="float"><object-id pub-id-type="doi">10.1371/journal.pclm.0000621.g006</object-id><label>Fig 6</label><caption><title>Global income losses from rising temperatures by 2100.</title><p>Notes: We consider persistent increases in temperatures based on various climate scenarios in <xref ref-type="fig" rid="pclm.0000621.g004">Fig 4</xref>. Solid-color bars are PPP GDP weighted averages of <inline-formula id="pclm.0000621.e109"><alternatives><graphic id="pclm.0000621.e109g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e109" xlink:type="simple"/><mml:math display="inline" id="M109"><mml:mrow><mml:msub><mml:mo>Δ</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>, see Eq (<xref ref-type="disp-formula" rid="pclm.0000621.e061">9</xref> ), with <italic>h</italic> = 86 (corresponding to the year 2100). Pattern-fill bars show global income losses from a continuation of 1960-2014 trend temperature increases compared to a baseline scenario without climate change. For “Faster Adaptation”, <italic>m</italic> = 10. For “Slower Adaptation”, <italic>m</italic> = 50. For “No Adaptation”, <italic>m</italic> = 100. For “Volatile Climate”, <inline-formula id="pclm.0000621.e110"><alternatives><graphic id="pclm.0000621.e110g" mimetype="image" position="anchor" xlink:href="info:doi/10.1371/journal.pclm.0000621.e110" xlink:type="simple"/><mml:math display="inline" id="M110"><mml:mrow><mml:msubsup><mml:mi>σ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mrow><mml:mo fence="true" form="prefix" stretchy="true">(</mml:mo><mml:msubsup><mml:mi>μ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>/</mml:mo><mml:msubsup><mml:mi>μ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo fence="true" form="postfix" stretchy="true">)</mml:mo></mml:mrow><mml:msubsup><mml:mi>σ</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>.</p></caption>
<graphic mimetype="image" position="float" xlink:href="info:doi/10.1371/journal.pclm.0000621.g006" xlink:type="simple"/></fig>
<p>To put our results into perspective, <xref ref-type="fig" rid="pclm.0000621.g007">Fig 7</xref> compares our income loss estimates (shaded area) with those from select papers in the literature. While our counterfactual estimates are conservative (given the caveats mentioned in the introduction), they are non-negligible especially when the reference point of comparison is harmonized across studies. However, our loss estimates are significantly lower than [<xref ref-type="bibr" rid="pclm.0000621.ref003">3</xref>] and [<xref ref-type="bibr" rid="pclm.0000621.ref008">8</xref>]. The underlying reasons are explained in [<xref ref-type="bibr" rid="pclm.0000621.ref023">23</xref>]. While almost all countries are likely to experience a fall in GDP per capita in the absence of climate change policies, the size of income effects varies considerably across countries and regions.</p>
<fig id="pclm.0000621.g007" position="float"><object-id pub-id-type="doi">10.1371/journal.pclm.0000621.g007</object-id><label>Fig 7</label><caption><title>GDP impact of increases in temperature.</title><p>Sources: [<xref ref-type="bibr" rid="pclm.0000621.ref002">2</xref>,<xref ref-type="bibr" rid="pclm.0000621.ref004">4</xref>], and authors’ estimates (shown as the shaded area in the chart). Notes: Projected GDP impact is for some future year, typically 2100. The shaded area represents the GDP per capita losses from our counterfactual exercise in <xref ref-type="sec" rid="sec003">Sect 3</xref> with the upper bound based on <italic>m</italic> = 30 and the lower bound based on <italic>m</italic> = 100.</p></caption>
<graphic mimetype="image" position="float" xlink:href="info:doi/10.1371/journal.pclm.0000621.g007" xlink:type="simple"/></fig>
<p>The differential impact of average temperature increases across countries further emphasize the complexity of loss estimates. Countries situated in hotter climates and those classified as low-income likely face disproportionately higher losses, ranging from 30-60% above the global average. This disparity not only highlights the exacerbated vulnerability of these countries but also stresses the need for tailored climate strategies that address their specific challenges. Conversely, countries in colder climates are not spared from the adverse effects of climate change. The faster rate of temperature increases in these areas introduces unique challenges, despite [<xref ref-type="bibr" rid="pclm.0000621.ref002">2</xref>]’s finding that the marginal effect of average temperature increases in cold countries is 40 percent lower than that of the global average.</p>
</sec>
<sec id="sec005">
<title>5. Concluding remarks</title>
<p>We estimated <italic>country-specific</italic> annual per-capita GDP losses from global warming using the most-recent climate scenarios of the IPCC under different mitigation, adaptation, and climate variability assumptions. We also showed that without significant mitigation and adaptation efforts, global GDP per capita could decline by up to 24 percent under the high-emissions climate scenarios by 2100, with these income losses varying greatly across the 174 countries in our sample, depending on the projected paths of temperature increases and their variability. Our findings emphasize the importance of mitigating climate change and implementing adaptation measures to minimize these negative effects. However, even with adaptation policies, the long-term growth effects of climate change are likely to persist, particularly in countries with hotter climates and lower incomes. Future research could focus on incorporating these estimated physical climate risks into macro-fiscal frameworks and for effectively informing and guiding country-specific climate action.</p>
</sec>
<sec id="sec006" sec-type="supplementary-material">
<title>Supporting information</title>
<p><italic>Country-specific</italic> annual per-capita GDP losses from global warming under different climate scenarios are reported in <xref ref-type="supplementary-material" rid="pclm.0000621.s003">S1 Table</xref> using databases <xref ref-type="supplementary-material" rid="pclm.0000621.s001">S1 Data</xref> and <xref ref-type="supplementary-material" rid="pclm.0000621.s002">S2 Data</xref>. All STATA do and ado files needed to replicate the empirical findings in our paper are publicly available and can be accessed at: <ext-link ext-link-type="uri" xlink:href="https://data.mendeley.com/datasets/hytzz8wftw/1" xlink:type="simple">https://data.mendeley.com/datasets/hytzz8wftw/1</ext-link>.</p>
<supplementary-material id="pclm.0000621.s001" mimetype="application/x-stata-dta" position="float" xlink:href="info:doi/10.1371/journal.pclm.0000621.s001" xlink:type="simple">
<label>S1 Data</label>
<caption>
<title>Database.</title>
<p>This file serves as the main database for the analysis.</p>
<p>(DTA)</p>
</caption>
</supplementary-material>
<supplementary-material id="pclm.0000621.s002" mimetype="application/x-stata-dta" position="float" xlink:href="info:doi/10.1371/journal.pclm.0000621.s002" xlink:type="simple">
<label>S2 Data</label>
<caption>
<title>Trend temperature change.</title>
<p>This file contains the ‘di’ values for different climate scenarios, used to estimate the GDP per capita impacts.</p>
<p>(DTA)</p>
</caption>
</supplementary-material>
<supplementary-material id="pclm.0000621.s003" mimetype="application/vnd.openxmlformats-officedocument.spreadsheetml.sheet" position="float" xlink:href="info:doi/10.1371/journal.pclm.0000621.s003" xlink:type="simple">
<label>S1 Table</label>
<caption>
<title>Country-specific income loss estimates.</title>
<p>(XLSX)</p>
</caption>
</supplementary-material>
</sec>
</body>
<back>
<ack>
<p>We are grateful to Indermit Gill, Zeina Hasna, Florence Jaumotte, Somik V. Lall, Steven Pennings, M. Hashem Pesaran, Jui-Chung Yang as well as conference and seminar participants at the International Monetary Fund (IMF), BNP Paribas, the World Bank, University of Southern California, the British Academy, and the Eighth Conference on the Econometric Models of Climate Change (EMCC-VIII) for helpful comments and suggestions. We gratefully acknowledge support from the Keynes Fund and the Cambridge Endowment for Research in Finance (CERF). We would also like to thank the editor in charge of our paper and three anonymous referees for helpful suggestions.The views expressed in this paper are those of the authors and do not necessarily represent those of the IMF or its policy.</p>
</ack>
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