Since the first Intergovernmental Panel on Climate Change () report, anthropogenic climate change has been the subject of large research efforts. Increased knowledge has raised growing concerns about its potential catastrophic impacts on both ecosystems and human societies if greenhouse gas (GHG) emissions continue unmitigated. In addition to the worsening of mean climate conditions in many places, numerous studies emphasize the risks associated with increased frequency and/or magnitude of extreme events (e.g., droughts, heat waves, storms, floods), rising sea level, and glacier melting . These risks have drawn attention to potential catastrophic consequences for the world economy . Yet, several other studies on damage induced on the world economy by unmitigated global warming have proposed a much less worrying picture of the future, with economic damage limited to only a few points of the world gross domestic product (GDP)

World GDP is probably a misnomer, as we should rather refer to global world product instead. We will nonetheless retain the common usage of “world GDP”.

The literature on the broad topic of damage functions (see , for a review) can be organized into two main approaches linking climate change to economic damage: an enumerative approach, which estimates physical impacts at a sectorial level from natural sciences, gives them a price, and then adds them up e.g.,, versus a statistical (or econometric) approach based on observed variations of income across space or time to isolate the effect of climate on economies e.g.,.

Each method has its pros and cons, some of which have already been acknowledged in the literature.

The main advantage of the enumerative approach is that it is based on natural sciences experiments, models, and data . It distinguishes between the different economic sectors and explicitly accounts for climate impacts on each of them. Yet, results established for a small number of locations and for the recent past are usually extrapolated to the world and to a distant future in order to obtain global estimates of climate change impacts. The validity of such extrapolation remains dubious, and it can lead to large errors. Moreover, accounting for potential future adaptations is a real challenge and therefore a major source of uncertainty in the projections. This method also implies being able to correctly identify all the different channels through which climate affects the economy, which is by no means an easy task. And finally, it does not take into account interactions between sectors or price changes induced by changes in demand or supply .

Despite different underlying methodological choices, several studies investigating future climatic damage conclude that global warming would cost only a few points of the world's income . A 3 ∘C increase in the global average temperature in 2100 would allegedly lead to a decrease in the world's GDP by only 1 %–4 %. Even a global temperature increase above 5 ∘C is claimed by certain authors to cost less than 7 % of the world future GDP .

Some statistical studies looking at GDP growth e.g., emphasize the long-run consequences and lead to higher damage projections than those previously mentioned. In particular, (hereafter BHM) evaluate the impact of global warming on growth at the country scale using temperature, precipitation, and GDP data for 165 countries over 1960–2010. According to their benchmark model, the temperature increase induced by strong GHG emissions (scenario RCP8.5) would reduce average global income by roughly 23 % in 2100. This relatively high figure, however, is a decrease in potential GDP, itself identified with the projected growth trajectory according to Shared Socioeconomic Pathway 5 SSP5, high growth rate;. As a result, under a global temperature increase of about 4 ∘C, only 5 % of countries would be poorer in 2100 with respect to today, and world GDP would still be higher than today. It must be noted that these results strongly depend on the underlying baseline scenario: if a lower reference growth rate is assumed (SSP3), the percentage of countries absolutely poorer in 2100 rises to 43 %.

Capturing the impact of warming on growth rather than on GDP level may appear more realistic. Indeed, it allows global warming to have permanent effects and also accounts for resource consumption to counter the impacts of warming, reducing investments in R & D and capital and hence economic growth . There is, however, no consensus on the matter. In a recent work, (hereafter NPS) evaluate the out-of-sample predictive accuracy of different econometric GDP–temperature relationships at the country level through cross-validation and conclude that their results favor models with nonlinear effects on GDP level rather than growth, implying, for their statistically best fitted model, world GDP losses due to unmitigated warming of only 1 %–2 % in 2100.

Studies on future climate change damage to the global economy usually do not pretend to account for all possible future impacts. This is obvious for the enumerative methods applied at the global scale: being exhaustive is not realistically feasible. But this is also true for statistical approaches. , for instance, gives three major caveats to his statistically based projections of climate change damage: (1) the model is incomplete; (2) estimates do not incorporate any nonmarket impacts or abrupt climate change, especially on ecosystems; and (3) the climate–economy equilibrium hypothesis used is highly simplified. also acknowledge that their econometric model only captures effects for which historical temperature has been a proxy. Yet, despite these major caveats, results from both approaches are widely cited as “climate change” damage estimates , as if they were really accounting for the whole range of future impacts, and some are used to estimate the so-called social cost of carbon . The authors themselves do not always clearly distinguish “climate change” impacts, which in the strict sense of the term should be applied to exhaustive estimates, from the non-exhaustive impacts accounted for by the specifically chosen proxy variable.

In our view, in addition to this common semantic confusion, at least two of the aforementioned caveats are highly problematic: (1) extrapolating relationships outside their calibration range (which concerns both enumerative and statistical methods) and (2) known and unknown missing impacts for which the chosen predicting climatic variables are not good explanatory variables. The fact that the channels of damage are not explicit in the statistical approach is convenient but also rather concerning: we simply cannot know which impacts are missed, except for a few of them (e.g., sea level rise).

A global warming of 4 ∘C at the end of the century would drive the global climatic system to a state that has never been experienced in the whole of human history, with growing concerns about the potential nonlinearities in the way the Earth system as a whole may evolve: ecosystems have tipping points (e.g., ); the ice loss from the Greenland and Antarctic ice sheets has already clearly accelerated since the middle of the 2000s ; the projected wet-bulb temperature rise in the tropics could reach levels that do not presently occur on Earth and that would simply be above the threshold for human survival . Thus, the question is the following: to what extent are we missing the point when using aggregated statistical approaches to estimate future damage?

One could argue that we are not so sure about what a 4 ∘C warmer planet would look like, since we lack any analog from the recent past. Yet, we actually have an example of a climate change of similar magnitude, albeit of a different sign: the last glacial period. In this paper, we focus on two representative examples of the statistical approach, the BHM and NPS functions, and use the LGM climate to test their relevance to assess the damage expected from a large and rapid climate change.

The choice of these two functions was based on the following considerations.

While there might be controversies regarding the paper of related to the model specifications, interpretation, and statistical significance of the results or even the validity of the approach, the approach is well-published in leading peer-reviewed journals. Their work has been widely cited in the literature and has been used to compute the social cost of carbon e.g.,. The authors also published several other papers based on similar methodologies e.g.,.

We decided to perform an ad absurdum demonstration of the strong limitations of such approaches because we believe that it is a useful complementary contribution to a more mathematical and statistical critique, which is not our purpose here. As documented by for older functional forms, the literature on damage functions has had tremendous political implication and even found its way into IPCC reports. Therefore, we believe it is important to add new elements to the existing critiques.

We chose to focus on the statistical approach because it inherently includes the effect of both cooling and warming. This is not the case for enumerative approaches, which are primarily designed for a warming and could not be applied to a cooling. They may nonetheless lead to implausible results as well, especially at the global scale (see the aforementioned caveats), but illustrating the disconnect between their damage projections and climate sciences would have required a different approach than the one we use here (e.g., questioning their assumptions sector by sector or providing damage estimates for impacts not taken into account).

In order to assess the economic damage of a hypothetical return to an ice age, we compute the evolution of average GDP per capita by country with or without the corresponding global cooling, following the methodology described in BHM using the replication data provided with their publication. Details are available therein. We differ from BHM in two ways.

For the simplicity of the demonstration, we chose to consider only one functional form linking temperature to GDP from BHM and NPS: we use either the BHM formula with their main specification (temperature impacts GDP growth, pooled response, short-run effect), whose results are the most commented on in their paper, or the preferred specification of NPS temperature impacts GDP level, best model by K-fold validation; full details in.

Criticism of potential mathematical development, variable choices, or data issues in the BHM or NPS work is beyond the scope of this paper. Our aim is limited to using their respective base equations as they are to test their realism for a large climate change scenario. Following BHM, we also use the socioeconomic scenario SSP5 as a benchmark for future GDP per capita growth per country. SSP5 is supposed to be consistent with the GHG emission scenario RCP8.5, but it does not include any climate change impact, even for high levels of warming. Therefore, we can still use it in our glacial scenario without inconsistency.

The base case of BHM links the population-weighted mean annual temperature to GDP growth at the country level. Their model uses the following functional form: 1Δln⁡GDPcapi,t=fTi,t+gPi,t+μi+νt+hi(t)+εi,t, where Δln⁡(GDPcapi,t) denotes the first difference of the natural log of annual real GDP per capita, i.e., the per-period growth rate in income for year t in country i, f(Ti,t) is a function of the mean annual temperature, g(Pi,t) a function of the mean annual precipitation, μi a country-specific constant parameter, νt a year fixed effect capturing abrupt global events, and hi(t) a country-specific function of time accounting for gradual changes driven by slowly changing factors. BHM control for precipitation in Eq. () because changes in temperature and precipitation tend to be correlated. Rather surprisingly, their study does not show a statistically significant impact of annual mean precipitation on per capita GDP.

In their base case model, f(Ti,t) is defined as 2fTi,t=α1×Ti,t+α2×Ti,t2. Based on historical data, they determined the coefficient values to be α1=0.0127 and α2=-0.0005.

Future evolution of GDP per capita in country i and year t between 2010 and 2100 is then given by 3GDPcapi,t=GDPcapi,t-1×1+ηi,t+δi,t, with ηi,t the business-as-usual country growth rate without climate change, according to SSP5 (taking into account population changes), and δi,t the additional effect of temperature on growth when the mean annual temperature differs from the reference average over 1980–2010, Ti,ref: 4δi,t=α1×Ti,t-Ti,ref+α2×Ti,t2-Ti,ref2. It should be noted that BHM do not take into account precipitation changes in their projection of future GDP.

The income growth–temperature relationship is a concave function of Ti,t, with an optimum temperature around 13 ∘C (Fig. ). Therefore, for a country with a reference mean annual temperature below this value that maximizes GDP per capita (e.g., Iceland), the annual growth rate increases (decreases) when the mean temperature increases (decreases). This relationship is reversed for countries with a reference temperature above the optimum value (e.g., Nigeria). Note that for countries already close to the optimum temperature (like France), a small temperature change will have a very limited impact on per capita GDP growth, but any major temperature change of several degrees, whatever the sign, will move them away from this optimum and have a negative impact on per capita GDP growth.

The preferred model of NPS links the mean annual temperature to the per capita GDP level based on the same historical sample as BHM and excludes any precipitation component. It links GDP in country i at year t to a polynomial function of mean annual temperature: 5ln⁡GDPcapi,t=β1×Ti,t+β2×Ti,t2+…. Based on historical data, the authors determined the coefficient values to be β1=0.008141 and β2=-0.000314.

Using this formula, the future GDP per capita with climate change for the 21st century, GDPcapi,t, is expressed as 6GDPcapi,t=GDPcapi,t*×exp⁡β1×Ti,t-Ti,ref+β2Ti,t2-Ti,ref2, with GDPcapi,t* being the GDP per capita of the country without climate change, according to SSP5: 7GDPcapi,t*=GDPcapi,t-1*×1+ηi,t.

The NPS GDP–temperature relationship is also a concave function of Ti,t, with an optimum temperature around 13 ∘C (Fig. ). The shape is therefore similar to BHM, but the function is conceptually different since the impact of temperature is on the GDP level instead of its growth rate. The SSP5 growth rate ηi,t remains unaffected by climatic conditions, and any negative temperature impact on year t has no impact on the GDP per capita level at year t+1, which depends only on the underlying SSP5 scenario and on the temperature at year t+1.

To build our “glacial” scenario, we assume a linear decrease in temperature between 2010 (the end of the reference period) and the glacial state projected for 2100. For any year t>2010, the country-specific mean temperature is therefore computed as 8Ti,t=ΔTi×t-20102100-2010+Ti,ref, with ΔTi the population-weighted temperature anomaly of country i at the LGM computed from (Fig. ).

Similarly to , who cap Ti,t at 30 ∘C, the upper bound of the annual average temperature observed in their sample period, to avoid out-of-sample extrapolation, we cap the minimum possible value of Ti,t at the lower bound of observations (-5 ∘C).

All results are expressed as distance from the baseline potential GDP based on the baseline SSP5 scenario, which assumes no climate change. The impact on world average GDP per capita is a population-weighted average of country-level impacts.

Using the NPS specification, in 2100, 34 % of the countries have a lower income per capita than without glacial climate change, but no country is poorer than today. The strongest impacts on GDP are projected in northern countries: Canada and Norway, for instance, exhibit a potential GDP loss of about 8 %. But at the global scale, the GDP loss projected in the northern countries is more than compensated for by a 1 %–2 % GDP gain in most of the southern countries (Fig. a). All in all, the impact of the temperature decrease on the world potential GDP is very limited, only about -1.8 % in 2100 (Fig. ).

With the BHM specification, projected impacts are much more severe in northern countries: in the United States, Canada, Russia, and most of Europe GDP decreases range from 80 % to nearly 100 % in 2100; i.e., the impact of temperature on potential GDP growth is so large that it leads to a complete economic collapse (Figs. b and ). Similarly, stronger positive effects are projected in southern countries, with a large increase in GDP for most of them in 2100 (Fig. b): e.g., +254 % in Gabon, +314 % in Ghana, +267 % in India, +300 % in Laos, +366 % in Mali, and +400 % in Thailand. China is the sole country where potential GDP remains roughly unchanged, with impacts smaller than 1 %. Globally, 31 % of countries exhibit lower income per capita than projected without climate change and 17 % are poorer than today. Losses in northern countries drive a decrease in the world GDP during the first half of the century, with maximal global damage around 2050 at about -4 %. In the second half, however, positive impacts in southern countries more than overcompensate for damage in the north, and as a consequence average potential GDP per capita gains 36 % in 2100 at the world level with respect to the baseline scenario (Fig. ).

To assess the credibility of these results we now survey the environmental conditions that human beings would have to face on our planet in 2100 under our theoretical scenario, taking what is currently known of the LGM as a reference and considering both climate and ecosystem changes. Ecosystem changes were then driven by both climate change and the impacts of low atmospheric CO2 concentrations on photosynthetic rates and plant water-use efficiency , but, in order to simplify our argument, we do not distinguish between these two effects in our description of a world cooled by 4 ∘C.

Many reconstructions of the climatic and environmental conditions during the LGM are available , as are numerous modeling exercises . Despite remaining uncertainties and discrepancies, data-based reconstruction and modeling results provide a fairly good picture of the Earth at that time.

The most striking feature of the last glacial world is the existence of large and thick ice sheets in the Northern Hemisphere . Of course, reaching the full extent of the LGM ice sheets, which depends on both static snow accumulation and ice viscous spreading, would require tens of thousands of years, not a century. Therefore, as a simplification for the sake of the demonstration, we assume the LGM climate equilibrium is reached in 2100, except for the ice sheet thickness and extent as well as associated sea level drop, since the timing is obviously too short. Such a simplification implies some inconsistency, since the LGM climate also depended on the albedo and elevation feedbacks from the ice sheets. We also acknowledge that (1) the response of the Earth system to a forcing that would lead to a 4 ∘C cooling in 2100 would be different from the LGM, depending on the type of forcing, and therefore the LGM is not a perfect reverse analog of a future at +4 ∘C; (2) it took much more than a century to move from the LGM to the Holocene, our current interglacial period. However, the projected rate of global warming for the RCP8.5 scenario is actually faster than any glacial–interglacial changes that occurred naturally during the last 800 000 years: about 65 times as high as the average warming during the last deglaciation . Besides, the level of warming in 2100 for the RCP8.5 scenario might exceed 4 ∘C, especially if strong positive feedback loops lead to the crossing of planetary thresholds, hence driving the Earth in a “hothouse” state . Accordingly, using the LGM-to-present environmental changes as an index of future changes might even be considered conservative.

With these caveats in mind, let us now take a closer look at the most obvious consequences of our scenario for human societies.

Results from climate models show that the surface mass balance of the northern LGM ice sheets was positive over most parts, outside the ablation zones on the edges, with annual accumulation rates of water equivalent of a few tens of centimeters per year e.g.,. Therefore, in our thought experiment, snow accumulation on regions corresponding to the LGM ice sheet extent would reach a few meters at the end of the century. Moreover, in the most central regions, the decrease in the mean annual temperature would be greater than 20 ∘C (Fig. ) and the cold would be hard to cope with. We presume that regions experiencing either such low temperatures and/or being buried under a thick permanent and growing layer of snow would become rather unsuitable for most modern economic activities. The impacted regions would be Canada, Alaska, the Great Lakes region of the United States, the states north of 40∘ N on the east coast of the United States, the Scandinavian countries, the northern part of Ireland and of the British islands, half of Denmark, the northern parts of Poland, the northeast territories of Germany, all of the Baltic countries, and the northeastern part of Russia. We assume that alpine regions that were widely covered by glaciers during the LGM, i.e., Switzerland and half of Austria, would in our scenario also experience several meters of snow accumulation. All these regions would become unsuitable for most of the millions of people who currently live there, and access to their present natural resources would be very difficult, if not impossible. By comparison, nowadays regions with a mean annual temperature below about 5 ∘C have a very low population density . Shipping routes in the North Atlantic would also be disrupted by the southern expansion of sea ice up to 50∘ N in winter .

In Europe, the mean annual temperature would decrease by 4–8 ∘C in the Mediterranean region, by 8–12 ∘C over the western, central, and eastern regions, and by more than 12 ∘C over northern countries (Fig. ). For France, for instance, whose current mean annual temperature is about 11 ∘C, the temperature decrease would thus correspond to a shift to the current mean temperature of northern Finland. Over western Europe, the mean temperature of the coldest month would decrease by 10–20 ∘C and the mean annual precipitation would decrease by about 300 mm yr-1 . Forests would be highly fragmented and replaced by steppe or tundra vegetation . The southern limit of the permafrost would approximately reach 45∘ N, i.e., the latitude of Bordeaux . In such a context, maintaining European agriculture at its present state, among other human activities, would be a costly and technically highly demanding challenge. Energy needs for heating would tremendously increase, current infrastructures would be damaged by severe frost, and there is no doubt that Europe would no longer sustain its current population on lands preserved from permanent snow accumulation.

In Asia, similar problems would occur, with a decrease in mean annual temperature between 4 and 8 ∘C over most Chinese regions, for instance (Fig. ). The boreal forest would have vanished and been replaced by steppe and tundra . Permafrost would extend in the northeast and North China, up to Beijing, as well as in the west of the Sichuan . As a result, rice cultivation in the northern province of Heilongjiang, for instance, which is currently above 20×106 t yr-1, i.e., about 10 % of the national production , would no longer be possible. Permafrost would not stretch out to the whole densely populated North China Plains, but the cold and dry climate there would nonetheless prevent rice cultivation. The discharge of the Yangtze River at Nanjing would be less than half its present-day value , questioning current hydroelectricity production. In short, current livelihoods in these regions would no longer be sustainable and the population would probably be much lower than today.

Temperature changes in the tropics would be rather moderate, with a cooling of 2.5–3 ∘C (Fig. ). This temperature decrease might be considered good news and is indeed the driver of the GDP increase simulated in tropical countries with both specifications we considered (Fig. ). However, tropical temperature decrease would come with strong changes in the hydrological cycle, casting some doubts on such an optimistic view. The interannual rainfall variability in East Africa would be reduced , but so would be the mean rate; the southwest Indian monsoon system would be significantly weaker over both Africa and India ; the Sahara and Namib would both expand ; annual rainfall over the Amazon basin would strongly decrease . Compared to their modern extension, the African humid forest area might be reduced by as much as 74 % and the Amazon forest by 54 % .

Globally, the planet would appear considerably more arid . However, the widespread increase in aridity at the LGM is debated since the reduction of the atmospheric demand for evaporation because of lower temperatures could compensate for the precipitation decrease, and drier places in terms of precipitation were not always drier in terms of hydrology . As already mentioned, glacial vegetation changes were also driven by the decrease in atmospheric CO2, which can bias aridity increase inferred from pollen proxy data. Yet, many places were indeed hydrologically drier at the LGM, including some currently densely populated areas. The southward spread of the extra-arid zone of the Sahara, for instance, is estimated to 300–450 km . For India, LGM data are rather sparse. Simulation results suggest that there was indeed a large decrease in runoff across monsoonal Asia , in agreement with marine proxy data from the Bay of Bengal, suggesting a reduction in fluvial discharge . For our scenario, this could mean less flooding during the monsoon season, but also a decrease in water resources during the dry season, in areas where droughts are already an issue. In regions already dry today, like Pakistan and northwestern India, it seems that the climatic conditions would indeed be even more arid . In Indonesia, LGM climate simulations show a decrease in the precipitation minus evaporation , but vegetation changes depend on the location . Therefore, for that region, we cannot really infer potential impacts of our glacial scenario for human populations.

The planet would also appear much dustier than today, with probably more frequent and/or intense dust storms that would impact soil erosion rates, health, transportation, and electricity generation and distribution . A potential increase in dust source areas would include northeast Brazil, central and southern South America, southern Africa, central Asia and the Middle East, Australia, China, and southeastern Asia .

In summary, our hypothetical ice age scenario corresponds to strong and widespread changes in climatic conditions, not only in temperature, driving major environmental changes . In such conditions, neither the results obtained with the BHM and NPS functions nor the baseline GDP scenario (SSP5) appear to be plausible projections.

Should GHG emissions continue unabated, the climate change expected for the end of the century will be of similar magnitude as the last deglaciation, which did not occur in a century but in about 10 000 years. Such a rapid change has no equivalent in the recent past of our planet, even less so in human history. Trying to establish a robust assessment of future economic damage based on aggregate statistics of a few decades of GDP and climate data, as attempted by econometric approaches, is probably doomed to failure, even more so when considering only mean annual temperature as a proxy for climate change. Such methodologies seem irrelevant for what lies ahead, since they fail to account for the largest potential impacts of climate change, as was already pointed out by . In order to strengthen this point, we have used an ad absurdum example of a hypothetical return to the climatic and environmental conditions of the LGM by the end of the century, except for the presence of the northern ice sheets and associated sea level drop, corresponding to a global cooling at a speed and magnitude equivalent to what the business-as-usual scenario of the IPCC announces. The comparison between the results obtained with two different statistical temperature–GDP relationships for our scenario and what we know of the Earth during the LGM suggests that both approaches severely underestimate the impact of climate change. We can therefore conclude that temperature only is a very bad proxy to estimate damage due to a major climate change at a country scale or at the global scale and should not be used for that purpose. More generally, several issues inherent to statistical approaches cast strong doubts on potential significant improvement. In this context, empirically estimating the aggregated relationship between economic activity and weather variables to project future damage is at best useless, at least from a policy point of view. Economists should hence refrain from using existing statistical damage functions to infer the global impacts of climate change or to compute optimal policy.

To summarize, our work has proven by absurdum the strong limitations of statistically based methods to quantitatively assess future economic damage. In our view, a more modest and realistic ambition could be endorsed by integrated assessment scenarios, namely that of making an educated guess on the lower bound of such damage at regional, rather than global, scales at which the uncertainty surrounding prospective estimations may be more easily dealt with. This alternate kind of approach would be closer to the enumerative one mentioned in Sect. . This ideal approach should, however, not merely use sectorial statistical relationships established for the recent past, as is often currently done. They would otherwise underestimate damage just as aggregated statistical methods do. Instead, they should account for tipping points or potential cascading effects and should definitely be consistent with the future described by climate and ecological sciences . But as already pointed out by , it is highly probable that high levels of uncertainties will remain and some risks “are currently impossible to assess numerically, which economists need to acknowledge with greater openness and clarity” .