Economic impacts of a glacial period: a thought experiment to assess the disconnect between econometrics and climate sciences

Anthropogenic climate change raises growing concerns about its potential catastrophic impacts on both ecosystems and human societies. Yet, several studies on damage induced on the economy by unmitigated global warming have proposed a much less worrying picture of the future, with only a few points of decrease in the world gross domestic product (GDP) per capita by the end of the century, even for a global warming above 4 C. We consider two different empirically estimated functions linking GDP growth or GDP level to temperature at the country level and apply them to a global cooling of 4 C in 2100, corresponding to a return to glacial conditions. We show that the alleged impact on global average GDP per capita runs from −1.8 %, if temperature impacts GDP level, to +36 %, if the impact is rather on GDP growth. These results are then compared to the hypothetical environmental conditions faced by humanity, taking the Last Glacial Maximum as a reference. The modeled impacts on the world GDP appear strongly underestimated given the magnitude of climate and ecological changes recorded for that period. After discussing the weaknesses of the aggregated statistical approach to estimate economic damage, we conclude that, if these functions cannot reasonably be trusted for such a large cooling, they should not be considered to provide relevant information on potential damage in the case of a warming of similar magnitude, as projected in the case of unabated greenhouse gas emissions.

o Clarifications of our climate change scenario and acknowledgment of the inconsistencies implied by the absence of the northern ice sheets. We also acknowledge that the response of the Earth to a cooling stimulus would be different from the LGM.
o A paragraph on the hypotheses made on the climatic conditions over the area covered by the ice sheets during the LGM.
o Additional elements on climatic conditions over Europe and Asia. o A new paragraph on the issue of potential compensation of precipitation decrease by the reduction of evaporation.
o Additional elements on dust sources.

Section 6:
o New section 6.3 discussing the symmetry or asymmetry of a cooling vs. a warming scenario.
o New elements in section 6.4 (and reorganization with bullet points) on the different general issues of the econometric approach.
We also corrected the typos indicated by referee#2 and added the article Pezzey (2019) to the references.
The complete web address to download Newell et al. (2018) has been added as a footnote. We have also added the LGM temperature data and the code modified from the replication data provided by Burke et al. (2015) as supplementary material. We provided only the scripts that were modified in our work compared to Burke et al. (2015). Other input data or scripts required for full replication are to be found in the original replication data of Burke et al. (2015).
We hope this revised version of our manuscript will meet your expectations, Best regards,

Marie-Noëlle Woillez
-The main advantage of the enumerative approach is to be based on natural sciences experiments, models and data (Tol, 2009). 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 70 and therefore a major source of uncertainty in the projections. This method also implies to be 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, nor price changes induced by changes in demand or supply (Tol, 2018).
-The statistical approach has the major advantage of relying on aggregates such as GDP per capita. There is no need to 75 identify the different types of impacts for each economic sector and to estimate their specific costs. They rely on a limited number of climatic variables, such as temperature and precipitation, which are used as a proxy for the different climatic impacts. Adaptation is also implicitly taken into account, at least to the extent that it already occurred in the past. But as acknowledged by Tol (2018), one of the main weakness of some statistical approaches is that they use variations across space to infer climate impacts over time. This method also shares with the enumerative one the disadvantage of using only data from the recent past, and hence from a period with a small climate change. The issue of future climatic impacts outside the calibration range of the function still holds.
Despite different underlying methodological choices, a large number of studies investigating future climatic damages conclude that global warming would cost only a few points of the world's income (Tol, 2018). A 3 • C increase of the global average temperature in 2100 would allegedly lead to a decrease of the world's GDP by only 1-4%. Even a global temperature 85 increase above +5 • C is claimed by certain authors to cost less than 7% of the world's future GDP (Nordhaus, 1994a;Roson and Van der Mensbrugghe, 2012).
Some statistical studies looking at GDP growth (e.g. Dell et al., 2012;Burke et al., 2015) emphasize the long-run consequences and lead to higher damage projections than those aforementioned. In particular, Burke et al. (2015) (hereafter BHM) evaluated the impact of global warming on growth at the country scale, using temperature, precipitation and GDP data for 165 90 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 the Shared Socio-economic Pathway 5 (SSP5, high growth rate, Kriegler et al., 2017). 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 global GDP would still be higher than today. It must be noticed 95 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 (Pindyck, 2013). There is however no consensus on the matter.

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In a recent work, Newell et al. (2018) (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 non-linear 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 damages to the global economy usually do not pretend to account for all possible future 105 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. Nordhaus (2006) for instance gives three major caveats to his statistically-based projections of climate change damages: 1) the model is incomplete; 2) estimates do not incorporate any non-market impacts or abrupt climate change, especially on ecosystems; 3) the climate-economy equilibrium hypothesis used is highly simplified. Burke et al. (2015) also acknowledge that their econometric model only captures effects for which historical temperature has 110 been a proxy. Yet, despite these major caveats, results from both approaches are widely cited as "climate change" damages estimates (Carleton and Hsiang et al., 2017), 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 (Tol, 2018). 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 specific chosen proxy variable. 115 In our view, in addition to these common semantic confusions, at least two of the aforementioned caveats are highly problematic: 1) extrapolating relationships outside their calibration range (which concerns both the enumerative and the 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 damages 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 human history, with growing concerns on the potential non-linearities in the way the Earth system as a whole may evolve: ecosystems have tipping points (e.g. Hughes et al. (2017); Cox et al. (2004)); the ice loss from the Greenland and Antarctic ice sheets has already clearly accelerated since the middle of the 2000s (Bamber et al., 2018;Shepherd et al., 2018); the projected wet-bulb temperature rise in the tropics could reach levels that do not occur presently on Earth and 125 which would simply be above the threshold for human survival (Im et al., 2017;Kang and Eltahir, 2018 The choice of these two functions was based on the following considerations: -While there might be controversies regarding the paper of Burke et al. (2015) 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 135 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. Burke et al., 2018;Diffenbaugh and Burke, 2019).
-The function of Newell et al. (2018) has not been published in a peer-reviewed journal 4 , but we considered it anyway because: 1) it belongs to the family of damage functions assuming an impact of climate on GDP level rather than 140 growth, leading to very small damages; 2) it is based on the same data and methodology than Burke et al. (2015), hence simplifying the exercise.
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/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 in IPCC reports. Therefore, we believe it is important to add new elements to the existing critics. 4 The paper can be downloaded here: https://media.rff.org/archive/files/document/file/RFF%20WP-18-17-rev.pdf

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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 150 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).

Material and Methods
In order to assess the economic damages of a hypothetical return to an ice age, we compute the evolution of average GDP per 155 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 in their manuscript, or the preferred specification of 160 NPS (temperature impacts GDP level, best model by K-fold validation, full details in Newell et al., 2018).
-Our climate change scenario corresponds to a global cooling of 4 • C, based on LGM temperature reconstructions and assuming a linear temperature decrease, instead of the climate projections for the RCP8.5 scenario. Following BHM, who consider only temperature projections for the assessment of future damages, we do not use LGM precipitation reconstructions.

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Criticism of potential mathematical, variable choices or data issues in 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 socio-economic scenario SSP5 as a benchmark of 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.

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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: where ∆ln(GDPcap i,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 (T i,t ) is a function of the mean annual temperature, g(P i,t ) a function of the mean annual 175 precipitation, µ i a country-specific constant parameter, ν t a year fixed effect capturing abrupt global events, and h i (t) a countryspecific function of time accounting for gradual changes driven by slowly changing factors. BHM control for precipitation in equation 1, 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 (T i,t ) is defined as: Based on historical data, they determined the coefficient values to be α 1 = 0.0127 and α 2 = −0.0005.
Future evolution of GDP per capita in country i and year t between 2010 and 2100 is then given by: with η i,t the business as usual country growth rate without climate change, according to SSP5 (taking into account population 185 changes), and δ i,t the additional effect of temperature on growth when the mean annual temperature differs from the reference average over 1980-2010, T i,ref : It should be noticed 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 T i,t , with an optimum temperature around 13 • C 190 ( Fig.1). Therefore, for a country with a reference mean annual temperature below this GDP per capita-maximizing value (e.g. Iceland), the annual growth rate increases (resp. decreases) when the mean temperature increases (resp. 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 will move them away from this optimum and 195 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:
Using this formula, the future GDP per capita with climate change for the 21 st century, GDPcap i,t , is expressed as: with GDPcap * i,t being the GDP per capita of the country without climate change, according to SSP5: 205 The NPS GDP-temperature relationships is also a concave functions of T i,t , with an optimum temperature around 13 • C ( Fig.1). 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 η i,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.

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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: with ∆T i the population-weighted temperature anomaly of country i at the LGM computed from Annan and Hargreaves (2013) 215 (Fig.2) .
Similarly to Burke et al. (2015) who cap T i,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 T i,t at the lower bound of observations (−5 • C).

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All results are expressed as changes of average potential GDP per capita, based on the baseline SSP5 scenario which assumes no climate change. The impact on global average GDP per capita is a population-weighted average of country-level impacts.
Using the NPS specification, 34% of the countries see a lower income per capita than it would be without glacial climate change, but no country is poorer than today. The strongest impacts on GDP are projected on Northern countries: Canada and Norway for instance exhibit a potential GDP loss of about 8% in 2100. But at the global scale, the GDP loss projected in 225 Northern countries is more than compensated by 1-2% GDP gain in most Southern countries ( Fig.4(a)). All in all, the impact of the temperature decrease on the world's potential GDP is very limited, only about -1.8% in 2100 (Fig.3).
With 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%, i.e. the impact of temperature on potential GDP growth is so large that it leads to a complete economic collapse ( Fig.4(b) and Fig5). Similarly, stronger positive effects are 230 projected in Southern countries, with large GDP increases for most of them in 2100 ( Fig.4(b)): e.g. +254% in Gabon, +314% in Ghana, +267% in India, +300% in Laos, +366% in Mali or +400% in Thailand. China is the sole country where potential GDP remains roughly unchanged with impacts smaller than 1%. Globally 31% 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's GDP during the first half of the century, with maximal global damages around 2050, at about -4%. In the second 235 half, however, positive impacts in Southern countries more than over-compensate damages 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.3).

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To assess the credibility of these results we now survey the environmental conditions that human beings would have to face on our planet under our theoretical scenario, taking what is currently known of the LGM as a reference and considering 240 both climate and ecosystem changes. Ecosystem changes where then driven by both climate change and the impacts of low atmospheric CO 2 concentrations on photosynthetic rates and plant water-use efficiency (Jolly and Haxeltine, 1997;Cowling and Sykes, 1999;Harrison and Prentice, 2003;Woillez et al., 2011) 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 at that time are available (Kucera et al., 2005;Bartlein 245 et al., 2011;Prentice et al., 2011;Nolan et al., 2018;Clark et al., 2009), as well as numerous modeling exercises (Braconnot et al., 2007;Kageyama et al., 2013;Annan and Hargreaves, 2013;Kageyama et al., 2018). Despite remaining uncertainties and discrepancies, data-based reconstruction and modeling results provide a fairly good picture of the Earth during the LGM.
The most striking feature of the last glacial world was the existence of large and thick ice sheets in the northern hemisphere (Peltier, 2004;Clark et al., 2009). Of course, reaching the full extent of the LGM ice sheets, which depends on both static snow 250 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 we have reached the LGM climate equilibrium, except for the ice-sheet thickness and extent and associated sea-level drop, since the timing is obviously too short. Such a simplification implies some inconsistency, since the LGM climate also depends 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, 255 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-inter glacial changes that occurred naturally during the last 800,000 years: about 65 times as fast as the average warming during the last deglaciation (Nolan et al., 2018). Besides, the level of warming in 2100 for the RCP8.5 scenario might exceed +4 • C, especially if strong positive feedback loops lead 260 to the crossing of planetary thresholds hence driving Earth in a "hothouse" state (Steffen et al., 2018;Schneider et al., 2019).
Accordingly, using the LGM-to-present environmental changes as an index of future changes might even be considered as conservative.
With these caveats in mind, let us now take a closer look at the most obvious consequences of our scenario for human societies.

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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 cm per year (e.g. Calov et al., 2005). Therefore, in our thought experiment, snow accumulation on regions corresponding to the LGM icesheet extent would reach a few meters at the end of the century. Moreover, in the most central regions, the decrease of the mean annual temperature would be greater than 20 • C (Fig.2) and the cold would be hard to cope with. We presume that regions 270 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 and the Great Lakes region of the United States, the states north of 40 • N on the East coast, the Scandinavian countries, the northern part of Ireland and of the British islands, half of Denmark, the northern parts of Poland and the north-east territories of Germany, all of the Baltic countries as well as the north-eastern part of Russia. We assume that alpine regions that were widely covered by 275 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 280 (Gersonde and De Vernal, 2013) and calving icebergs.
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.2). 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 285 10 − 20 • C (Ramstein et al., 2007) and the mean annual precipitation would decrease by about 300 mm/year . about 10% of the national production (Clauss et al., 2016), would no longer be possible, among other crops. 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 (Cao et al., 2010), questioning current hydroelectricity production. In short, current livelihoods in these regions would no longer be sustainable 300 and 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 Annan and Hargreaves, 2013) (Fig.2). This temperature decrease might be considered as good news, and is indeed the driver of the GDP increase simulated in tropical countries with both specifications we considered (Fig.4). However, tropical temperature decrease would come with strong changes in the hydrological cycle, casting some doubts on such an optimistic view. The inter-annual 305 rainfall variability in East Africa would be reduced (Wolff et al., 2011), but so would be the mean rate; the Southwest Indian monsoon system would be significantly weaker over both Africa and India (Overpeck et al., 1996); the Sahara desert and Namib desert would both expand (Ray and Adams, 2001); annual rainfall over the Amazon basin would strongly decrease (Cook and Vizy, 2006). Compared to their modern extension, the African humid forest area might be reduced by as much as 74%, and the Amazon forest by 54% (Anhuf et al., 2006).

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Globally, the planet would appear considerably more arid (Kageyama et al., 2013;Ray and Adams, 2001;Bartlein et al., 2011). However, this widespread increase in aridity is debated since the reduction of the atmospheric demand for evaporation because of lower temperatures could compensate the precipitation decrease and drier places in terms of precipitation at the LGM were not always drier in terms of hydrology McGee, 2020). As already mentioned previously, vegetation changes are also driven by the decrease in atmospheric CO 2 , which can bias aridity increase inferred from pollen 315 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 desert for instance is estimated to 300-450 km (Lioubimtseva et al., 1998). For India, LGM data are rather sparse. Simulations results suggest that there was indeed a large decrease in runoff across monsoonal Asia (Li and Morrill, 2013), in agreement with marine proxy data from the Bay of Bengal suggesting a reduction in fluvial discharge . This could mean less flooding during the monsoon season, but also a decrease 320 of water resources during the dry season, in areas where droughts are already an issue nowadays. In regions already dry today, like Pakistan or north-western India, it seems that the last glacial conditions were even more arid .
In Indonesia, simulations results show a decrease in the precipitation minus evaporation  but vegetation changes depends on the location , and we cannot really inferred potential impacts for human populations.
The planet would also appear much dustier than today, with probably more frequent and/or intense dust storms which would Thus, overall, postulating that cooling would drive a large GDP surge in tropical countries, as simulated with BHM specification, is highly questionable.

Discussion
In summary, our hypothetical ice-age scenario corresponds to strong and widespread changes in climatic conditions, not only in temperature, driving major environmental changes (Nolan et al., 2018). In such conditions, neither the results obtained with the BHM and NPS functions nor the baseline GDP scenario (SSP5) appear as plausible projections.
6.1 Temperature-GDP level relationship 335 We argue that the disruptions in the living conditions on our planet, as briefly described above, cannot plausibly result in a small decrease of less than 2% in the world potential GDP per capita in 2100, as inferred from the NPS specification. According to these results, Canada would experience only a 8% decrease in its potential GDP per capita, despite its infrastructure being buried under snow, its natural resources being inaccessible or disappeared and tremendous frost. Such estimations of climate damages remain utterly unrealistic even if we were ready to consider optimistic adaptation skills of human societies that would 340 prevent them from social calamities such as revolutions, famines or wars. Our results illustrate how the idea that climate influences only the level of economic output and has no impact on economic growth trajectory is not appropriate for a large climate change. The complete failure of this approach to provide plausible results for a cooling discredits its reliability to account for the impact of a global warming of similar magnitude, which would without doubts drive environmental changes as huge as the one we listed above for the LGM. The BHM specification gives somewhat more plausible results for Northern countries, with the projection of a complete collapse of their economies, in agreement with the prospect of permanent snow accumulation, very low temperatures and large ecosystem shifts. However, we have serious doubts on the (very) large GDP per capita increase predicted in tropical countries, given the strong decrease in precipitations in many places and global desert expansion, threatening in particular water resources 350 and agriculture. How can we reconcile, for instance, the projection of a GDP increase of more than 300% in sahelian countries with a southward expansion of the Sahara desert of about 400 km? The BHM set-up focuses on damages driven by temperature change only (or changes for which temperature is a proxy) and does not take into account precipitation changes for climate change projections. The author's study did not find that mean annual precipitations had a significant effect on the economy in the last decades, a result rather surprising, considering the strong impacts that droughts or extreme precipitations may have.

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This could be due to the fact that the mean precipitation at the country scale is not an appropriate variable, since it does not necessarily capture correctly seasonality changes or extreme events for instance. In any case, should precipitation effects be negligible for the recent past, they cannot be ignored in the case of major hydrological changes that would also drive radical ecological shifts.
Similarly, the absence of damages in China can hardly be conceptually reconciled with both deserts and permafrost expan-360 sion, which should very probably have strong negative impacts on agriculture in the north and north-east of the country, or the strong decrease in fluvial discharge.
Moreover, the complete collapse of (at least) the northern nations, including expected massive migrations of millions of people outside these regions, would be expected to have serious economic and geopolitical consequences at the global scale, that we can hardly imagine being very positive. The statistical method of BHM capture the present-day political and economic re-365 lationships between countries, but it cannot account for future changes in these relationships, a major deficiency in a globalized world.
It is difficult to imagine how the world could be globally much wealthier than it would have been without such disruptions in climatic and ecological conditions, especially if most places are no longer suitable for agriculture, as it may have been the case during the Pleistocene (Richerson et al., 2001). Agriculture may account for only a few percentages of GDP in present-day 370 developed countries, but food production is obviously the first need of any society. We therefore conclude that, despite its endeavor toward realism, the BHM function does not provide results more convincing than the NPS one.
6.3 Cooling vs warming: symmetry or asymmetry of impacts ?
From a physical point of view, there is no a priori reason to postulate that a global warming and cooling of similar magnitude would have similar huge impacts. However, the symmetry is implicitly assumed by the GDP-temperature relationship itself:

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it was built on both negative and positive temperature anomalies and therefore, by design, it cannot be assumed that such a function could provide relevant damage estimates for a warming, but not for a cooling (or the other way around). Moreover, when considering some of the most dramatic climate projections for the RCP8.5 scenario at the end of the century, it seems rather plausible that such a warming would have similar strong impacts as a cooling of similar magnitude: -On the one hand, as discussed in section 5, for our LGM scenario large parts of North America and Europe would become -On the other hand, for global warming, the number of people currently living in areas which may be exposed to permanent inundation for a sea level rise of 1.46 m in 2100 has been estimated to 340 millions (Kulp and Strauss, 2019), a number that would be further increased for higher sea level rise values . But the most alarming projections

General issues 395
Whether temperature changes impact the GDP growth or level is actually a debate of little relevance. In both cases, the use of the mean temperature at the country scale as a proxy for climate effects turns out to provide a highly insufficient picture in the case of a large climate change and leads to a large underestimation of the risks to lives and livelihoods.
This failure can be attributed to different issues of such statistical approaches: -To our knowledge, there is currently no publications on potential issues in the statistical model itself. To this respect, 400 comments made by one anonymous referee regarding stationarity and the use of control variables (see the public discussion of this paper as well as section B.2 of the supplementary information of Burke et al. (2015)) seem interesting and worth investigating. As these considerations fall outside the scope of this paper, we leave them for further research.
Beyond any purely mathematical consideration, it is interesting to note that both BHM and NPS considered only the proxies for climatic variables that would have strong economic impacts, such as seasonality, extreme precipitation events, droughts or heatwaves.
-As mentioned in section 2, one of the serious limitation of these statistical approaches is that they rely on climatic variations over space to extrapolate over time. Indeed, BHM argue that, for most countries in their sample, a global warming of 4 • C takes them out of their own historical range of temperature, but that they still remain within the worldwide dis-410 tribution of historical temperatures. For that reason, they consider that there is no extrapolation out of sample for these countries. If a country gets warmer, the economic impacts can be deduced, they assumed, from past observations in another country whose past temperature was similar. Only a few hottest countries would reach temperature outside the worldwide historical range, and for this category they chose not to extrapolate but to cap future temperature at the upper bound observed in the sample period. As already pointed out by Pezzey (2019), such assumption is actually untestable.

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One could argue that human adaptation capacities would succeed in maintaining climate-economy equilibrium even in a changing climate. This hypothesis would be very doubtful in the case of long-living infrastructures facing rapid climate change and certainly does not hold for ecosystems, one of the channels through which climate change impacts the economy. Ecosystems simply cannot adapt quickly enough to a climate change as fast as +4 • C in a century. The speed of forest migration for instance is a few hundreds of meters per year (e.g. Brewer et al., 2002) while temperature 420 change in 2100 according to the RCP8.5 scenario would correspond to a displacement of more than 1000 km of current temperature zones. The ecosystem-climate equilibrium is not valid on the timescale of a century and therefore, we argue that this issue is in itself sufficient for the extrapolation from space to time to be unwarranted.
-BHM and NPS functions are based on economic data from societies adapted to their current environment. The alleged statistical relationship between GDP per capita and temperature is established for stable ecological conditions and is 425 therefore hardly relevant to assess damages on societies who will experience decades of drastic changing climate and ecosystems and having to re-adapt endlessly to ephemeral new living conditions. It should also be stressed that, as illustrated in Burke et al. (2015), the results obtained with their methodology strongly depends on the assumed reference GDP growth rate without climate change. There are evidences that economic growth rates are path-dependent (Bellaïche, 2010), therefore in this case it makes no sense to apply a correction to a baseline growth rate which remains unaffected 430 by the damages that occurred the previous years.
-What econometrics maybe show is that, for the few last decades, with a still relatively stable climate, interannual weather thawing permafrost, stronger tropical cyclones, ocean acidification and ecosystem shifts. It is therefore very misleading to consider that they allow to quantify "climate change" economic damages. At best, they might give an insight of damages for which temperature has been historically a proxy, and this is highly insufficient, conveying a false picture of the potential risks.

445
Should GHG emissions continue unabated, the climate change expected for the end of the century will be of similar magnitude than the last deglaciation, which did not occurred 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 damages 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 We can therefore conclude that temperature only is a very bad proxy to estimate damages of 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 460 damages 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 assess quantitatively future economic damages. 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 damages at regional, rather than global, scales 465 where 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 the introduction. 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 damages just as aggregated statistical method do. Instead, they should account for tipping points or potential cascading effects already pointed out by Pezzey (2019) 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" (

The comments of Mikhail Verbitsky are reproduced below in black. Our responses are in blue.
The authors endeavor to study the limitations of some quantitative methods of assessing future economic damages using "an ad absurdum example of a hypothetical cooling of climate at speed and magnitude equivalent to what the business-as-usual scenario of the IPCC announces." Though ad absurdum examples are always entertaining and occasionally useful, the "degree" of absurdity should be constrained by the laws of physics. From this standpoint, fast cooling of the planet toward the end of this century, though hard to imagine, is not precluded by physics. The real absurdity, which is not supported by physics and therefore invalidates the study, appears elsewhere. The authors suggest that "…the regions covered by ice at the LGM would in our scenario be buried under several meters of snow at the end of the century…The impacted regions would be: Canada, Alaska and the Great Lakes region of the United States, the states north of 40N on the East coast, the Scandinavian countries, the northern part of Ireland and of the British islands, half of Denmark, the northern parts of Poland and the north-east territories of Germany, all of the Baltic countries as well as the north-eastern part of Russia, Switzerland and half of Austria". It appears that the authors think that an ice age begins immediately and simultaneously on 50 mln square kilometers when the winter snow is not completely melted during the summer and over time becomes what we know as Laurentide and Scandinavian ice sheets. This is not how ice-age physics works. The timing of the ice ages is defined by the speed of the moving horizontal boundary of the spreading viscous ice media, not by the snow growth from the ground.To spread all over the areas mentioned above, would take about 100,000 years, not 1,000 years as the authors suggest. Therefore, though the authors call this vast permanent snow coverage the "most obvious consequences for human societies", it is in fact far from obvious and all of these regions may be permanent-snow-free for a very long period of time.
Even the emergence of smaller, nucleus, glaciers (that do grow from the ground) is not granted because the cooling may reduce snow precipitation rates in polar regions instead of increasing them. In short, the climate system is non-linear; the ice ages begin when the global temperature is high and end when it is low.
Thank you for your comment; we agree that ice sheets do not grow only because of static snow accumulation and the role of the viscous spreading should indeed be mentioned in the text. We also perfectly acknowledge that reaching the last glacial maximum northern ice sheets geometry would not be possible within 100 years, as stated L. 214 of our paper. By "millennia" we meant "thousands of years", the text should be modified for greater clarity. L.214 would then be modified as follows (in italics): "Of course, the growing and spreading of large ice sheets actually requires thousands of years, not a century." We also agree that ice sheets do not build quickly as soon as snow accumulates on the ground. However, according to the Milankovitch theory, ice ages are triggered by the reduction of summer insolation at high latitudes, which allows winter snow to persist in summer and then eventually, because of various positive feedbacks (e.g. Khodri et al., 2001;Calov et al., 2005), to the ice-sheet build-up and full glaciation. Snow accumulation is not sufficient to build an ice sheet, but it is necessary. Indeed, the last ice age was drier than present-day climate (e.g. Kageyama et al., 2020) and precipitation decrease could prevent snow accumulation on the areas listed in our paper.
However the LGM simulations of Calov et al. (2005) show that the area of positive annual mass balance correspond to the area of the ice sheets (except on the edges of the Fennoscandian ice sheet). In another context, Robock et al. (2009) also simulated the persistence of snow in the midlatitudes of the North hemisphere in response to a massive volcanic eruption, because of very low temperatures. Therefore, our assumption does not seem utterly unreasonable, even if it is of course a rough first-order estimate.
Moreover, the direct comparison between the timing of the last glacial cycle and our thought experiment is not possible since the slow ice-sheet build-up during the last glacial period was triggered by the slow evolution of the orbital forcing. Their evolution was far from linear during the ~100 ky between the last interglacial and the LGM: proxy data show a fast growth of the ice sheets between 120-110 ky, with a 30-60 m of sea level drop. Simulations of the glacial inception by Calov et al. (2005) show that "Between 118 and 117 kyr BP the land area covered by ice increases by more than 4.10 6 km 2 in just a few hundred years, reaching approximately 30% of the area of LGM ice sheets in North America". The temperature decrease during the LGM compared to present-day would be a much stronger driver than the orbital forcing at the last glacial inception, and the ice-sheet growing and spreading could then be much faster than what was observed for the last glacial inception. However, to our knowledge, no modelling study is currently available in the literature to test this hypothesis. The closest comparison could be with the strong cooling induced by a massive volcanic eruption (Robock et al., 2009) or a nuclear war (Robock et al., 2007), but in such cases the pattern of temperature and precipitation changes is different from the LGM and lasts only a few years.
In any case, the estimated -4°C of global cooling during the LGM corresponds to a climate more or less at equilibrium, where all feedbacks had enough time to act (snow and ice albedo , decrease of greenhouse gases, vegetation changes, elevation of the ice sheets…etc). In our work, we chose to assume equilibrium as a simplification for the sake of the demonstration and to have a known period to estimate the plausibility of econometrics projections. The only exception to this assumption are the ice sheets and associated sea level drop, as the timing is obviously too short. The LGM ice-sheet extension is used as a rough constraint for the location of the areas where snow accumulation would occur, not taking into account the role of ice dynamics during the LGM, which should be mentioned in the text for more clarity. But we cannot constrain the hypothetical rate of snow accumulation, (taking into account a drier climate) without ad hoc experiments with a climate model, which is beyond the scope of the paper. In any case, even if some of the regions listed in our paper would remain snow-free for a long time, the cold would anyway be a strong constraint to economic activities, even if not as dramatic as with a thick permanent snow cover. By comparison, currently most of the high northern latitudes have a very low population density (see also the recent work by Xu et al. 2020 on human ecological niche).
We suggest adding at L.227 the following sentence (in italics): "We presume that the regions covered by ice at the LGM would in our scenario be buried under several meters of snow at the end of the century. This is a rough first-order estimate, not taking into account the role of ice dynamics in the spreading of the ice-sheets over the north hemisphere during the last glacial period".
Anthropogenic global warming, if extended, may preclude next ice age; it doesn't necessarily mean that anthropogenic global cooling would "instantaneously" generate one. I understand that this paper is not about ice-age physics, and the authors want to make a (probably valid) point about the inconsistency of some economic models, but their choice of the thought experiment is very unfortunate. As economists, they want to ": : :conclude that temperature only is a very bad proxy to estimate damages of a major climate change at a country scale or at the global scale and should not be used for that purpose" but, as climatologists, they make exactly the same mistake, assuming that temperature only (-4°C) would bring our climate exactly where it was 20,000 years ago.
We do not assume that such a cooling would be of anthropogenic origin. Actually, we do not propose any physical mechanism. We make the hypothesis of a return to the LGM, even if physically implausible, and merely have a look at what the consequences would be according to econometrics. Our main focus is on highlighting the unrealistic results obtained with statistical damage functions for a climatic change symmetrical to the RCP8.5 (when looking only at the mean temperature), not to discuss the physical mechanisms that could trigger such a change. Although not fully comparable, our approach is inspired from Nolan et al. (2018), who use the ecosystem changes during the last glacial-to-interglacial transition as a proxy to assess the risk of future major ecosystem transformations worldwide in the case of unabated greenhouse gas emissions.
However, our working hypothesis probably needs to be clarified in the introduction. We do not assume that temperature change would trigger a return to a glacial climate. Rather, we assume a return to the last glacial maximum, with all its consequences (including precipitation and ecosystem changes for instance), and use it as a benchmark to test econometric models based on mean annual temperature, to illustrate that looking at temperature changes only leads to unrealistic impacts on GDP. Therefore, we did not consider only temperature changes to quantitatively estimate the impacts, but also precipitation, vegetation, permafrost or desert area changes, since lower temperatures and large ice sheets are not the only features of the last ice age. This could be clarified in the text by modifying L.37 as follows: "Therefore, we can try them for a hypothetical return to the LGM, corresponding to a cooling of 4°C in 2100". In the conclusion, L.353 could also be modified as follows: "In order to strengthen this point, Thank you for your response. Your explanations are helpful, and the modifications to the text you propose will definitely improve it.
The only concern I still have relates to your following statement: "We make the hypothesis of a return to the LGM, even if physically implausible, and merely have a look at what the consequences would be according to econometrics. Our main focus is on highlighting the unrealistic results obtained with statistical damage functions for a climatic change symmetrical to the RCP8.5 (when looking only at the mean temperature), not to discuss the physical mechanisms that could trigger such a change." is implausible in 2100, then all your arguments regarding the economic impact are also implaus Frankly, I have a difficulty to imagine a situation where physically implausible arguments would have any value. If the LGM ible. How can we judge that the statistical damage function is unrealistic if you compare it with unrealistic world? Again, the absurdity must be measured against physical laws. The econometrics you challenge may be absurd (unrealistic) only if physics tells us that, for example, in 2100 North America and Europe will be covered by ice. But if it is not physically plausible, then the econometrics seems to be valid. If physically implausible arguments are admitted, one may come up with multitudes of equally implausible scenarios that support the econometrics you contest. Therefore, plausibility of a scenario should always be a concern. Let us estimate it from very general scaling considerations. The empirical energy density spectrum of Huybers and Curry (2006) has a frequency slope of roughly B _ 1.64 in northern latitudes. Since the energy density slope B relates to the fluctuation amplitude slope b as B=2b+1, B _ 1.64 corresponds to b = 0.32. Therefore, the amplitude of the climate system response to 0.1-kyr forcing relates to the amplitude of the 100-kyr response as10ˆ(-0.96) = 0.11. Thus, regardless of the physical nature of the centennial forcing you want to invoke for your scenario, in 2100 you may count at best on _10% response relative to LGM. Perhaps it is enough to make a case regarding the validity of the econometrics. Otherwise, to discredit the econometrics, one needs to come up with a justification of the centennial forcing amplitude which is 10 times stronger than it was observed in the past.
One of the issues concerning current climate change is that there is no analogue in the « recent » past of our planet of such a change. There are similar changes in magnitude, but not in rate. As pointed out by Nolan et al. (2018) in their study, "under the RCP8.5 scenario the rate of warming will be on the order of 65 times as high as the average warming during the last deglaciation".
Therefore, to illustrate the disconnect between climate sciences and econometrics, two options can be considered: 1) Carefully list all the expected climate and environmental changes according to climate models at the end of the century (including extreme events, sea level rise…etc) that are not accounted for by statistical damage functions and show that they would have an impact far above the projections from these functions. This was the approach of DeFries et al. (2019). This option relies on current Earth system models, and there are still many uncertainties. 2) Apply these functions to a different, but rather well-known, climate change that has occurred in the past. We chose the LGM because it is the most recent past period representing a climate change of the same magnitude than what may be our future (RCP8.5). This period is actually often used in climate communication to illustrate the fact that a difference of 4°C in the global mean temperature is by no mean a small change but corresponds to a completely different world. As mentioned previously, the comparison between the LGM and the RCP8.5 has already been made by Nolan et al. (2018) to assess ecosystem changes.
On the one hand, going back to exactly the same climate state than the LGM would require following exactly the same path than for the last glacial period, with the same forcings. By definition, this is not possible (even the different glacial periods of the Pleistocene have their own climate and ice-sheet patterns). In this regard, our scenario is implausible.
But on the other hand, the glacial climate state itself is not physically implausible, since it has already occurred in the past. We excluded the ice sheets from our equilibrium assumption, because considering that the LGM extent and thickness of the Laurentide and Fennoscandian ice sheets is reached would be like assuming more than 20 m of sea level rise in 2100 for the RCP8.5, by comparison with the mid-Pliocene estimates.
Looking at the surface mass balance over the Laurentide and Fennoscandian ice sheets at the LGM, as simulated with the IPSL_CM4 climate model, it appears that the balance is positive over most of the ice sheets (except on the edges), with values above 40 cm/year on the southern edges (outside the ablation zone) and 10-20 cm/year more in the center (Woillez et al., 2012). But the spatial resolution of this simulation is rather coarse. Other simulations from Ullman et al. (2015) for the Laurentide ice sheet actually show that the accumulation rate is above 50 cm/year on the edges, but very low in the center, as you suggested it could be because of the drier glacial climate.
Based on these elements, I consider that, in our thought experiment, snow accumulation on the regions corresponding to the edges of the LGM northern ice sheets would be of a few tens of cm/year in the last decades of the scenario, which would lead to an accumulation of a few meters of snow. The total thickness would of course depend on when the threshold for accumulation is crossed, depending on temperature and precipitation evolution. In the more central regions, it is difficult to provide an estimate based only on published surface-balance maps for the LGM. Yet, for these regions, the decrease of the mean annual temperature is greater than 20°C, which makes them rather unsuitable for significant human activities anyway.
To summarize, a better assessment of what snow accumulation would be at the end of the century would require performing ad hoc simulations using our hypothetical climate scenario as an input for a surface model including a snow model. But we can consider that on the areas corresponding to the LGM ice sheets there would be either a permanent snow layer of a few meters and/or that the climate would be much too cold for human activities. In both cases, we cannot expect the current level of economic activities to be maintained, even less so to grow. Therefore, we do not think that this issue of ice sheets invalidates our demonstration, but we suggest that 1) the above arguments should be added in the manuscript; 2) given the uncertainties on the snow accumulation rate without new simulations we cannot constrain the rate of sea level drop and whether it would be fast enough to really have a significant economic impact, therefore it would be better not to consider these impacts. Moreover, the inconsistency of the GDP projections for southern countries remain: if the damage functions of Burke et al. (2015) manage to simulate a collapse of northern countries because of cold temperatures, the results obtained for southern countries (large positive impacts on GDP) appears unrealistic compared to the climate and ecosystem changes (sahelian countries for instance). Woillez, M. N., Krinner, G., Kageyama, M., & Delaygue, G. (2012). Impact of solar forcing on the surface mass balance of northern ice sheets for glacial conditions. Earth and Planetary Science Letters, 335, 18-24. Ullman, D. J., Carlson, A. E., Anslow, F. S., LeGrande, A. N., & Licciardi, J. M. (2015). Laurentide ice-sheet instability during the last deglaciation. Nature Geoscience, 8 (7), 534-537.

The comments of referee#2 are reproduced below in black. Our responses are in blue.
This is an interesting article. While I see the point (raised by an earlier reviewer and editor) that it does not generate much knowledge on the real (warming) world, I believe it neatly summarises and illustrates issues with climate damage function, with an original twist of argumentation. The current article could stimulate discussion on the merits, limitations, and validation of damage functions, which would be a valuable contribution to the scientific discourse around climate change.
I therefore think that the article should be published. However, there are some issues which require clarification, as listed below.
 Thank you for your positive comments on our work. Indeed, our main goal is not to generate knew knowledge on future climate change and its impacts but to question the relevance of (some) current damage functions.

Major Comments
Inconsistency: "known" cooling vs "unknown" warming scenario An important line of argumentation seems to me that while we don't know what a warming world looks like, we can form an idea about a cooling of similar magnitude by looking at the ice age data. However, in fact, the paper does not assume a full transition to an ice age (which would involve long-term equilibration of ice sheets etc) but a quick cooling, i.e. a scenario for which we have no data. The uncertainty may involve the question of snow accumulation, raised by an earlier interactive comment, and effects depending on it (e.g. circulation changes due to the albedo effect of the snow), but also changes in ocean circulations (how does the AMOC react to the cooling?). The fast cooling scenario may thus differ form an ice age in more respects than the presence or absence of ice caps. So, is the damage in a fast cooling scenario just as speculative and difficult to assess than in a warming scenario?
There are in fact two types of uncertainty here, 1. what would the state of the climate system be like under fast cooling, 2., what would be the impacts for society?
In my view, there are two ways to deal with the first issue.
• Simply define that your cooling scenario is "an ice age except that ice sheets are not there yet". You would have to explicitly acknowledge that this may not be the actual response of the Earth system to a cooling stimulus (such as rapid greenhouse gas depletion), but you could still analyse the potential (societal) impact of such a hypothetical climate.
• Or perform a model simulation (/team up with a modelling group) of a 4degree cooling in 100 years, either by dropping GHG concentrations or a reduction in solar irradiation.
I strongly encourage you to consider the second option.
Once you clarified your climate scenario, you can argue, as you do now, that the impact of society would be severe (with higher certainty than the severity of an equivalent warming?).
 Your comment is quite similar to the previous interactive comment of M. Verbitsky and we agree that we should clarify our climate change hypothesis: we assume a return to the last glacial maximum, except for the ice sheets. The hypothesis includes ecosystem changes, which were triggered not only by temperature and precipitation changes but also by lower CO2. Of course, this hypothesis implies some inconsistency, as the LGM climate takes into account the albedo and elevation impact of the ice sheets. We acknowledge that 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. A short discussion on that issue will be added to the manuscript. Please also refer to the response to M. Verbitsky for the other modifications that would be implemented in our manuscript to clarify this issue.
Performing some ad hoc climate modelling to simulate a cooling of 4°C by 2100 would indeed allow avoiding the above mentioned issue. However, it would, in our view, raise at least two new issues: 1) Unrealistic forcing mechanism: As you mentioned, the forcing mechanism could be either a strong reduction in solar irradiation or a drop in GHG concentrations. But to reach -4°C, the decrease in solar irradiation would have to be much stronger than the natural changes currently reconstructed for the past millennia and a decrease of GHG would have to be even larger than for the LGM (since GHG drop alone during the LGM is not sufficient to simulate a full glacial climate, e.g. Kim, 2004.), which could not be reached within a century with natural mechanisms. Therefore, we would have to assume some anthropogenic factors, like massive atmospheric CO2 pumping and storage, which would be unrealistic. The last option would be a massive volcanic eruption, but it would have to last continuously for several decades, which would be a very questionable hypothesis. 2) Most importantly, the climate scenario would then rely on climate modelling only, with only one model, with all the associated uncertainties, especially concerning ecosystem changes. Therefore, confronting the climate projections with the damage projections would not be different from doing the same exercise in the case of a warming scenario (which of course remains a valid option to illustrate the inconsistency of climate damages projections). In our view, the main interest of using the LGM as a benchmark to test econometric models based on mean annual temperature is to have not only climate simulations but also various proxy data on the climate and ecosystem at that time. This is why we decided to stick with the first proposed solution of clarifying our climate change hypothesis.
Asymmetry warmingcooling The ice-age scenario obviously contains very severe impacts for human activities, many of which cannot be captured by looking at recent data, as the ice-age Earth might be a qualitatively different place from our current world.
However, this does not automatically imply that a warming of equal magnitude would have similarly huge impacts.
This does not invalidate your main argument, that (statistical) damage functions may well overlook major impacts of climate change which current data cannot capture, but I would like this asymmetry to be acknowledged explicitly. Even better, if possible, would be to include a brief discussion on whether it is plausible/impossible to know/implausible that warming has similarly strong impacts as cooling. For example, how does the area (or number of inhabitants, or value of infrastructure) threatened by sea level rise under 4 degree warming compare to the area (or number of people/ amount of wealth) threatened by snow under 4 degree cooling? Obviously, uncertainties are huge, but maybe something meaningful can still be said about the issue?
We agree that this point should be acknowledged explicitly.
When looking at some of the most dramatic climate projections for RCP8.5 at the end of the century, it seems rather plausible that warming would have similar strong impacts as a cooling of similar magnitude: -On the one hand, at the LGM, large parts of North America and Europe would become rather unsuitable for large human populations and most modern economic activities. Currently 37 millions of people live in Canada and about 30 millions in northern Europe, where we can reasonably assume that only a small population could remain. Maintaining a total population of more than 700 millions of people in Europe despite the very cold temperature in winter and permafrost expansion is doubtful, even if the number of people that could still live there (probably mostly in southern Europe) remains speculative. Similarly, in India, data suggests that the north-western part of the continent experienced extreme desert conditions during the LGM , which would probably have strong negative impact for its current 70 millions of inhabitants. -On the other hand, the number of people currently living in areas which may be exposed to permanent inundations for a sea level rise of 1,46 m in 2100 was recently estimated to 340 millions (population growth and migration not taken into account, Kulp & Strauss 2019), a number that would be further increased for higher SLR values (SLR>2,4m has 5% probability according to . But the most alarming projections are maybe the ones concerning future heat stress: according to , temperature and humidity conditions above potentially deadly threshold could occur nearly year-round in humid tropical areas, including some of the most densely populated areas, threatening hundreds millions of people. How people could adapt to such unprecedented climatic conditions remains an open question. However, while we agree that from a physical point of view there is no a priori reason to postulate that warming and cooling of similar magnitude would have similar huge impacts, it should be noticed that this issue of symmetry between a warming and a cooling is implicitly assumed by the damage function itself: it was built on both negative or positive temperature anomalies. Therefore, by design, it cannot be assumed that such function would provide relevant damage estimates for a warming but not for a cooling (or the reverse).
A paragraph explaining the above points will be added in the general discussion.
Enumerative vs. data-driven damage function You use two damage functions of the statistical kind and none of the enumerative kind. Is this a conscious choice, and could you please motivate it? For example, did you make this choice because statistical damage functions inherently include the (statistical) effect of both cooling and warming, whereas the enumerative ones primarily look at warming (e.g. they may include a term for heat stress on maize plants, but not for frost stress...)?
In particular, it seems to me that your argumentation shows that capturing climate damage exhaustively with a statistical approach is impossible, whereas an enumerative approach could work in principle (but maybe not in practice). Please clarify.
 Yes, this is a conscious choice, which will be justified briefly in section 2. As you pointed it out, enumerative damage functions are designed for a warming and we could not have applied them to a cooling. They may lead to implausible results as well (especially at a global scale), because some impacts are not accounted for or because the sectorial impacts are generalized based on evidence limited to a short time period or small spatial scale for instance. In that case, illustrating the disconnect with climate sciences would have required a different approach (e.g. questioning their assumptions, sector by sector, or providing damage estimates for impacts usually not taken into account, like extreme events).  We consider that the enumerative approach could work in principle, providing that the potential cascading effects could be taken into account, but we doubt that this could actually be done at the global scale. Damage projections may be possible, to some extent, at region or country scale, but it remains a complex and challenging work and it is highly probable that high levels of uncertainties will remain, as very well pointed out in the article of Pezzey that you have indicated. A short paragraph will be added in the conclusion, to further discuss this point, including some of the issues raised by Pezzey (2017).

Minor Comments
• Line 253: "these regions would be about as suitable for humans as present day Arctic is"... Instead of this picturesque metaphor, I suggest to specify the conditions (how cold and dry? unsuitable for any form of present-day agriculture, forestry, even Sami-style animal husbandry?).
Please find below in red some additional information, which will be added to the text: "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.2). 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 (Ramstein et al., 2007) and mean annual precipitation would decrease by about 300 mm/year . Forests would be highly fragmented, replaced by steppe or tundra vegetation (Prentice et al., 2011). The southern limit of the permafrost would approximately reach 45°N, i.e. the latitude of Bordeaux (Vandenberghe et al., 2014). In such a context, maintaining European agriculture at its current 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 it is doubtful that Europe could still 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 to 8°C over most Chinese regions for instance ( Fig.1) The boreal forest would progressively vanish, replaced by steppe and tundra (Prentice et al.,2011). Permafrost would extend in the North-East and North China, up to Beijing, as well as in the west of the Sichuan (Zhao et al., 2014). As a result, rice cultivation in the northern province of Heilongjiang, currently >20.10 6 tons/year, i.e. about 10% of the national production (Clauss et al. (2016), 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 (Cao et al., 2010), questioning current hydroelectricity production. In short, current livelihoods in these regions would no longer be sustainable and population would probably be much lower than today. In short, these regions would be about as suitable for humans as present-day Arctic is." • Line 266ff: "Most places would become unsuitable for agriculture and water resources would largely decrease. Drier regions include ...India and Indonesia".
Would drying be a severe concern in regions that are currently wet (like Indonesia and parts of India)? And even if rainfall decreases, could it not be that the reduction of evaporation due to cooling compensates the effect, leading to no severe increase in drought? Note that several regions, including the Mediterranean, and parts of South Africa, are threatened by drought under global warming (for example because of poleward expansion of the ITCZ system and hence the subtropical deserts). Of course, drought needn't be linear in global mean temperature, but possibly these regions would get less drought-prone under global cooling.
It is indeed important to take into account temperature, whose decrease could compensate for the precipitation decrease. Compilations of lake levels at the LGM indeed show that some were higher at the LGM whereas other where lower (McGee, 2020) and climate models show that drier places in terms of precipitation were not always drier in terms of hydrology . This point, which has not been discussed in our manuscript, will be added in section 5.
Concerning Indonesia, you are right. Data for that region are rather sparse, and showing spatial variability: for Borneo for instance it seems that the vegetation cover was broadly similar during the Holocene and the LGM, suggesting that there was no pronounced dry season, whereas for Sumba, pollen data suggest enhanced aridity and water stress during the dry season . Thus, it seems actually difficult to make hypotheses on the potential impact for human populations and the reference to Indonesia will either be suppressed or the uncertainties will be explained.
For India, data are also rather sparse. Analyses of a marine core in the Bay of Bengale suggest that fluvial discharge was reduced during the LGM, but the decrease is not quantified . Looking at simulation results, it seems that there was a decrease in P-E ) and a large decrease in runoff across monsoonal Asia, including India and south-east Asia (Li et al., 2013), suggesting that the decrease in temperature did not compensate for the decrease in precipitation. This could mean less flooding during the monsoon season, but also a decrease of water resources during the dry season, in areas where droughts are already a problem at present-day. Unfortunately, to our knowledge, there is no publication on the seasonality of runoff during the LGM. In regions already dry today, like the Pakistan or north western India, it seems that conditions were even more arid during the last glacial . These references will be added in section 5.
• This reference could be interesting for the general discussion on damage functions: JCV Pezzey, "Why the social cost of carbon will always be disputed", https://onlinelibrary.wiley.com/doi/full/10.1002/wcc.558,  Thanks for this reference, which will be added to the general discussion on damage functions. It nicely (and sometimes provokingly) summarizes the different issues, including for the statistical approach. It could also be cited in the conclusion, since it questions the very social/political utility of damage functions.