Fabien Candau
email: fabien.candau@univ-pau.fr

Charles Regnacq

Julie Schlick

Ariel Dinar

Gwenolé Le Velly

José De Sousa

Jaime De

CLIMATE CHANGE, COMPARATIVE ADVANTAGE AND THE WATER CAPABILITY TO PRODUCE AGRICULTURAL GOODS

Keywords: Q17, Q25, Q56, F18

This article analyzes how climate change inuences the capabilities to export agricultural goods and the specialization of nations (e.g., comparative advantages) by altering farmers' capability to use available water. Our main contribution is methodological since we present the rst attempt to link precisely the micro-determinants of production to the macro-determinants governing the specialization of countries. We use a rich set of data both locally (at the crop level analyzing thousand elds that cover the Earth's surface) and at the global level (analyzing bilaterally the international trade of nations). At the local level, we estimate the elasticity of production to the thermal and hydrologic conditions (including blue and green water as well as groundwater storage) along with xed eects (at country-product and at the crop level) to control for omitted variables. At the global level, we use the predicted value of these elasticities to compute an indicator of the water capability to export agricultural goods, which is then used in a trade gravity equation to control for trade costs that also shape the specialization of countries. From these estimates, we nally build an indicator of comparative advantage in agricultural goods and analyze how these relative advantages are aected by climate change in 2050. We present unexpected results at rst sight, that are however in line with the Ricardian theory, such as cases where a deterioration of the local conditions to produce a good does not prevent an improvement in the comparative advantage to produce it (representing 32.51% of cases in our simulation), or the reverse, when the improvement of the local conditions happens simultaneously with a deterioration of the comparative advantages (representing 18.16% of cases in our simulation).

Introduction

Climate change will have a myriad of eects on the productions of agricultural goods (IPCC (2007)).

The most obvious, is that by deteriorating the natural conditions of plant growth, it will lead to less production. A more subtle consequence is that climate change will aect dierently the relative costs of production of dierent crops [START_REF] Costinot | Evolving Comparative Advantage and the Impact of Climate Change in Agricultural Markets: Evidence from 1.7 Million Fields around the World[END_REF]. Then, apparently unexpected results can arise, such as the production of goods that are not fully adapted to the new climate but which are possible because climate change will have even worse consequences on other outputs in this country relatively to what occurs elsewhere, leading producers to focus their investments and resources on these less aected agricultural products. In case of a positive shock, the same mechanism holds, not all the favoured products by climate change are going to be produced, but only those with the lowest relative costs of production in comparison with foreigner competitors. This is at least what can be expected in a globalized world according to the theory of comparative advantage of [START_REF] Ricardo | On the Principles of Political Economy and Taxation[END_REF]: the specialization of countries is based on a comparison of their relative productivity dierences. In this paper, we analyze to what extent the utilization of an essential factor of production, water, explains the specialization of countries on dierent agricultural products. Then, we study how climate change, by aecting this resource, can destabilize the current comparative advantages of all the countries in the world. 1

We dene the water capability to produce as all the conditions related to water that enable to grow a plant. We thus build an indicator that includes the availability of all sources of water (such as river's runo, groundwater and precipitation), taking into account the water use competition between the dierent crops (as well as the competition with municipal and industrial consumption). We also consider the climatic constraints that impact the eciency of the available water in the production of agricultural goods. Indeed the evapotranspiration of plants (depending of their location), and the temperature requirement of each crops determine whether there is enough water to sustain production.

2

Finally, we build an indicator that measures the cost of using water for a particular crop relatively to all other production that are possible according to the climate and hydrologic conditions.

We focus on this water capability to produce, for two reasons.The rst and the most obvious is that the utilization of water is an essential component of the agricultural production and thus worth of interest regarding the essential role of agriculture for human development. 3 The second reason is that many researches have been done by hydrologists and agronomists on water, enabling to have an accurate measure of the current water capability to produce at a very disaggregated spatial level and for dierent agricultural products all over the world. We then build an indicator of water capability at the scale of a 30 arc-minute worldwide grid or approximately 55 kilometers at the equator. This spatial disaggregation at the grid scale, which is then ner than a regional or even a communal scale, is important to observe where the specialization of countries comes from. Hence our detailed analysis enables to locate the development and crisis related to water for the production of agricultural inside each country. Furthermore, the product disaggregation of the water capability to produce dierent goods is also critical for our research question, because it enables to determine the water productivity of a location for all agricultural activities, and not just those in which it is currently employed. This allows to study how dierent lands can be converted to develop new types of products in front of climate change.

Why does it matter to take into account international trade in this analysis of the eect of climate change? After all, why exchange is so important, and not only internal food production? As stated earlier, from the theoretical framework from which the current analysis is based, namely the comparative advantage of [START_REF] Ricardo | On the Principles of Political Economy and Taxation[END_REF], it is the process of international exchange that drives the specialization of nations. Such an emphasis on the importance of trade integration to explain the 1 We focus here on how climate change by increasing water scarcity has a signicant negative eect on agriculture production and then specialization. Obviously, climate change also aects agriculture via other channels, for instance, by enhancing the probability of oods, it would equally damage crops (e.g. [START_REF] Bronstert | Floods and Climate Change: Interactions and Impacts[END_REF][START_REF] Su | Long-term Flood Risk Assessment of Watersheds under Climate Change Based on the Game Cross-Eciency DEA[END_REF]. We do not consider here the eects of climate change on ooding, which would require a dierent analysis that is left for future research.

2 More concretely, data on precipitation, runo and evapotranspiration come from the AQUAMAPS data of the FAO, which are merged with data of the Global Agro-ecological Zones v3.0 (GAEZ) to take into account the thermal regime (including the crop suitability of the local thermal regime), the soil quality, the terrain slope, the share of land covered with building and other natural coverage (lake, forest or ice). These variables are then used to explain the agriculture production (available from MIRCA2000) to build our new indicator of the local water capability to produce agricultural goods. specialization of nations is not solely at the heart of the modern Ricardian theory (e.g. [START_REF] Eaton | Technology, Geography, and Trade[END_REF], [START_REF] Costinot | What Goods Do Countries Trade? A Quantitative Exploration of Ricardo's Ideas[END_REF]) but it is a common feature of all analysis in international economics.

4 Moreover the relative cost of production inside a country is not enough to determine its specialization, international trade costs also matter. For instance, the relative productivity advantage due to water in one country, can be outweighted by the high trade costs to export agricultural goods from this country (relatively to other countries). In brief, locational (dis)advantage also explains the specialization of nations. From that stand point, it would be illusive to analyze the specialization of countries without taking into account international trade. In this paper, we use international trade ows, to measure trade costs (via a trade gravity equation) and then to reveal the comparative advantage of countries (via the [START_REF] Balassa | Trade Liberalisation and 'Revealed' Comparative Advantage[END_REF] index, aptly named the Revealed Comparative Advantage index, hereafter RCA).

5 Then, by studying how climate change aects the water capability to export agricultural goods, we are able to predict how the agricultural RCA can evolve. 6 Furthermore, by considering the implications for the world development, analyzing climate change in an open economy also enables to study the conditions under which international trade can mitigate the consequences of climate change via agricultural reallocation of production between countries.

Our ndings concerning the production of agricultural goods measure the importance of the thermal and hydrologic conditions and the essential role of groundwater storage. Indeed, our estimates show that having insucient renewable water resources available to fulll the needs of plants may induce a minimum loss of capability to produce agricultural goods by approximately 4%. Yet, such a loss may be attenuated by pumping water from the underground as we nd that an increase of groundwater stock by 1% could potentially help to increase this capability by approximately 0.03% in the localities with insucient renewable water resources. When simulating the eects of climate change, we nd that 64.2% of agricultural lands may experience a decrease in their capabilities to produce. The most vulnerable countries to climate change will likely bear the most of these negative changes with a total loss of almost 17% of agricultural lands. 7 Regarding the international trade of agricultural products, we nd that the water elasticity to export 8 is the smallest for the most vulnerable countries. This nding that exports of the most vulnerable countries are less sensitive to the water conditions seems to be a good new, indicating a specialization in the production of goods that are less intensive in water.

However, these specializations seem to be insucient to cope with climate change as we nd that these countries could experience a drop of their exports by 14 % partly due from a strong decrease in their capabilities to use water for producing agricultural goods at the local level (-17 %) and partly due to a relatively low access to international markets (less than 10% of global trade in 2050). 9 This indicates a relative increase in the cost to produce agricultural goods and an increase in the marginalization of these countries to the world exchange. This may be particularly problematic for the development of these countries where exports of agricultural goods may have spillover eects in terms of productivity and explain the agricultural-demand-led industrialization [START_REF] Adelman | Beyond Export-Led Growth[END_REF][START_REF] De Pineres | Externalities in the Agricultural Export Sector and Economic Growth : A Developing Country Perspective[END_REF][START_REF] Bustos | Agricultural Productivity and Structural Transformation: Evidence from Brazil[END_REF]. 10 Therefore, our analysis going from the micro geographical scale of the crop to the macro analysis of countries specialization enables to determine where the deterioration of the local conditions could lead to a deterioration of the comparative advantages (e.g. for cassava in Africa), as well as the reverse, namely the identication of locations where the improvement of the local conditions could lead to an improvement of the comparative advantages (this represents approximately half of the cases). We also present less intuitive results, such as cases where the deterioration of the local conditions to produce a good leads to an improvement in the comparative advantages to trade it (representing 32.5 % of cases, e.g. potatoes in the mediteranean countries), or when the improvement in the conditions to produce a good leads to a deterioration of the comparative advantages to trade it (representing 18.2 % of cases, e.g. rice in India).

Our analysis is related to dierent elds. Our concept of the water capability to produce agricultural goods is related to an emerging array of research on the link between water scarcity and the supply of crops. For instance, [START_REF] Vallino | Measuring Economic Water Scarcity in Agriculture: A Cross-Country Empirical Investigation[END_REF] propose to use an indicator of management of domestic and transboundary water resources to approximate the economic water scarcity and show that this indicator explains the agricultural productivity of countries. Interestingly they nd that their indicator is not always associated to high country's income or to the hydrological water scarcity. [START_REF] Rosa | Global Agricultural Economic Water Scarcity[END_REF] also propose an indicator of agricultural economic water scarcity, dened as the lack of irrigation due to limited institutional and economic capacity. They identify agricultural economic water scarce lands where investments in sustainable irrigation have the possibility to increase food production (e.g. in Sub-Saharan Africa). In comparison, our study does not analyze the role of institutions and governance of water, but better captures the hydrologic constraints and physical opportunities to produce agricutural goods.

Hydrologists have also developed models of the determinants of agricultural production linked to the water availability at the local level, such as the LPJmL (Lund-Potsdam-Jena managed Land, developed by [START_REF] Bondeau | Modelling the Role of Agriculture for the 20th Century Global Terrestrial Carbon Balance[END_REF]), a dynamic global vegetation model designed to simulate vegetation composition and distribution for natural and agricultural ecosystems. However, such type of models have not only the major drawback of being very dicult to handle due to the complexity of the computation, 11 but also often failed to analyze the economic consequences such as the impact of the economic water scarcity of the agricultural specialization of nations. Economists on the other side, investigate in details how comparative advantages evolve [START_REF] Costinot | Evolving Comparative Advantage and the Impact of Climate Change in Agricultural Markets: Evidence from 1.7 Million Fields around the World[END_REF][START_REF] Coniglio | On the Evolution of Comparative Advantage: Path-Dependent versus Path-Defying Changes[END_REF], but neglect the detailed hydrological information at the local level to understand the role of water in the production of agricultural goods. For instance, [START_REF] Murphy | The World's Water 20082009: the Biennial Report on Freshwater Resources[END_REF] and [START_REF] Afkhami | Virtual Water Trade: The Implications of Capital Scarcity[END_REF] capture the availability of water with annual runos and groundwater recharges in the exporting country.

These indicators are problematic because the sole water endowment aggregated at the country level is misleading as some regions inside a nation can have sucient water resources but not the temperatures or soil quality required to produce.

12 Our value added is thus to propose an indicator richer than the one used by economists, but simpler and more transparent than those presented by hydrologists in order to understand how the specialization of nations in dierent agricultural goods.

Our contribution can also be discussed at the light of a large literature on virtual water trade, 10 There are many researches and debates on the conditions under which exports of agricultural goods stimulate growth. [START_REF] Bustos | Agricultural Productivity and Structural Transformation: Evidence from Brazil[END_REF], for instance, show the introduction of genetically engineered soybean seeds in Brazil in the context of a high level of trade openess has led to industrial growth in this country because this new technology was strongly labor-saving.

which measured the volume of water used in production of goods that are traded at the global level. [START_REF] Debaere | The Global Economics of Water: Is Water a Source of Comparative Advantage?[END_REF] nds that relatively water abundant countries export more water intensive products. [START_REF] Delbourg | The Globalization of Virtual Water Flows: Explaining Trade Patterns of a Scarce Resource[END_REF] demonstrate that arid countries use trade in order to alleviate their problem of water scarcity. They also show that some countries with abundant factors (land and labor) use water with less eciency. A lively debate has however being at the center of this literature, since numerous authors have found opposite results, such as the fact that some water scarce countries actually export water-intensive crops (and vice versa). 13 [START_REF] Vallino | Trade of Economically and Physically Scarce Virtual Water in the Global Food Network[END_REF] improve these analyses by weighting the global virtual water trade with a new composite water scarcity index that combines physical and economic water scarcity. They nd that almost half of water volumes traded comes from countries that are worse-o than their partners regarding their composite water scarcity and their economic wealth. While this literature considers that governance, institutions and economic development at the local level can explain the conict between the comparative (dis)advantage of countries and their specialization in agricultural goods, we pursue another explanation by considering that the unequal access to international markets for exporters from dierent countries can contradict the comparative advantage dened at the local/national level. By considering this, our article proposes a new contribution to the literature on the interaction between specialization and trade costs. To date, the most signicant ndings in this literature have been theoretical. [START_REF] Venables | Geographical Disadvantage: a HeckscherâOhlinâvon ThÃ×nen Model of International Specialisation[END_REF] rst propose a theoretical model to demonstrate that the equilibrium pattern of specialization involves a trade-o between comparative production costs and comparative transport costs.

14 [START_REF] Deardor | Local Comparative Advantage: Trade Costs and the Pattern of Trade[END_REF] also shows that this trade-o matters and develops a concept of local comparative advantage (dened as autarky prices in comparison to nearby countries) to explain the specialization of countries. While some empirical analysis have been done from these theoretical foundations (e.g. [START_REF] Harrigan | Airplanes and Comparative Advantage[END_REF], we propose here a new methodology to reconciliate the local comparative advantage (linked to water) to international trade costs in order to determine the comparative advantage at the national level.

Finally, the consequence of climate change on agricultural trade have been at the core of many studies in the last decade [START_REF] Huang | Climate Change and Trade in Agriculture[END_REF][START_REF] Costinot | Evolving Comparative Advantage and the Impact of Climate Change in Agricultural Markets: Evidence from 1.7 Million Fields around the World[END_REF], [START_REF] Gouel | The Crucial Role of Domestic and International Market-Mediated Adaptation to Climate Change[END_REF]).

The conclusion is optimistic, international trade can mitigate the consequences of climate change via agricultural reallocation of production inside and between nations. Climate change will also induce yield changes and large price movements fostering incentive to adjustments. In comparison with this literature, we propose a very dierent methodology which is based on estimations and not on numerical simulations of Computable General Equilibrium models (CGE). We also provide a new analysis of the hydrological conditions at the source of the comparative advantage of nations. Our results also dier and are less optimistic, for example, we present many cases where the reallocation of production inside nations fails to sustain the comparative advantage of countries.

The reminding part of this article includes the following sections. In Section 2, data on precipitation, runo, groundwater storage, evapotranspiration and the thermal regime are used to explain the agricultural production at the local level. Then, the predicted values of this estimation are at the basis of our new indicator of the local water capability to produce agricultural goods. In Section 3, this indicator is used to explain bilateral trade between countries.

15 We also study how this water 13 See [START_REF] Fraiture | Does International Cereal Trade Save Water? The Impact of Virtual Water Trade on Global Water Use[END_REF] and [START_REF] Kumar | Virtual Water in Global Food and Water Policy Making: Is There a Need for Rethinking?[END_REF] for early critical analyses of virtual water trade. See also [START_REF] Ramirez-Vallejo | Virtual Water Flows and Trade Liberalization[END_REF] who show that virtual water trade ows are independent of water resource endowments in contradiction with one standard theory of international trade (the Heckscher-Ohlin Theory). [START_REF] Verma | Going against the Flow: A Critical Analysis of Inter-State Virtual Water Trade in the Context of India's National River Linking Program[END_REF] quantify and critically analyze inter-state virtual water ows in India. [START_REF] Han | Virtual Water Output Intensies the Water Scarcity in Northwest China: Current Situation, Problem Analysis and Countermeasures[END_REF] show that virtual water trade intensies the water scarcity in Northwest China. capability to produce agricultural goods inuences dierently the exports of dierent groups of countries distinguished by their degree of vulnerability to climate disruption (and endowment in capital).

In Section 4, we build an index of the revealed comparative advantage that takes into account this variable of water and all the determinants of trade (including trade costs). All this analysis enables to follow the eect of climate change on water conditions at the local level, and then on production and trade to analyze the specialization of countries. Finally, Section 5 concludes with some avenues for future research.

2 Agricultural production and water at the crop level, a world analysis

The agricultural production depends on water but obviously depends on many other determinants, that need to be taken into account to isolate the productive eect of water on agricultural specialization.

Some determinants are related to water and are often dened at the micro-spatial level (e.g. at the crop level where the water is available). Other determinants that depend, for instance, on the agricultural technology and/or on the global market access of producers are dened at the national and/or even at the international level. Our analysis is thus divided in two parts. In this section we lead a substantial investigation at the crop level to measure all the micro-constraints encounter by agricultural to produce. These micro-level constraints refer to the capability of producers to transform the available water resources into agricultural goods at the local level, they depend on temperature, soil quality, and so on. At this micro-spatial level we measure the relative costs of using water for a particular product relatively to all other products that can be produced (namely in the spirit of the Ricardian theory of comparative advantage). In the next section, we use a trade gravity equation to capture all the determinants that limit the capability to export. Among these constraints, trade costs between countries, 16 and dierences in technology are taken into account.

Supply of crop at the micro-geographical level

To infer the impact of local water availability upon the capabilities to grow dierent type of crops, it is possible to follow a rich literature 17 that denes the behavioral rules of farmers regarding the crop acreage choice subject to agronomic and climatic constraints. On that matter, dierent models have been proposed such as multicrop production models with multinomial logit acreage shares presented in [START_REF] Carpentier | Multicrop Production Models with Multinomial Logit Acreage Shares[END_REF] or the Ricardian model of trade in [START_REF] Costinot | Evolving Comparative Advantage and the Impact of Climate Change in Agricultural Markets: Evidence from 1.7 Million Fields around the World[END_REF]. However, we do not use a formal model from this literature, as we aim to develop an indicator that does not depend on the expected gross margins per hectare of crop, on the price of the good produced or on the intermediate goods used. Our aim is to determine the supply of crops related to water that depends on natural determinants such as precipitations, the surface of waters, groundwaters and the water requirement of the dierent crops. This point matters to alleviate an endogenous bias in our empirical investigation (due to reverse causality between production and export). Indeed since our indicator is used to explain exports, we need an index that is not based on the current production choice of farmers but on a hypothetical choice based on the water endowment of locations. In other words, we do not compute an indicator on the types of products that are produced at a location l (depending of prices, fertilizers and so on), but rather on the types of products that could be produced in l given various exogenous conditions. In that respect, our work is based upon the idea of capabilities to transform the available natural resources into valuable goods given local natural constraints that can be traded on the international markets.

for the competitiveness of exporters, demand eects, and changes occuring in other nations (what's the literature called the multilateral resistances).

16 These trade costs, that can be decomposed in four components, called the four Ts by [START_REF] Spulber | Global Competitive Strategy[END_REF], are trans- action costs (due to customs, business practices, and legal environments), tari and non-tari trade barriers (including environmental regulation and anti-dumping practices), transport costs and time costs.

17 See Carpentier et al. (2015) for a literature review.

Furthermore, we follow the core principle of these aforementioned models by analyzing the relative capability to produce agricultural goods instead of an absolute value. Thus, similar to [START_REF] Carpentier | Multicrop Production Models with Multinomial Logit Acreage Shares[END_REF] or [START_REF] Costinot | Evolving Comparative Advantage and the Impact of Climate Change in Agricultural Markets: Evidence from 1.7 Million Fields around the World[END_REF], we dene our local capability to use water for producing a specic crop in comparison to the capabilities to use water to produce other crops and/or to fulll non-agricultural needs.

Formally, we divide the world into gridded cells of 30 arc-minutes each representing localities l in which farmers can grow multiple crops, indexed by k. The categorization of these crops will follow the international nomenclature of the Harmonized Commodity Description and Coding Systems (called HS4 later in the text).

18 In such a setting, the heterogeneity of farmers comes from the fact that farmland does not match the cells such that multiple farmers may be within each locality l and the farmland of one farmer may overlays multiple localities. In that respect, dierent behaviors may arise within each locality leading to a certain diversity of crop acreage in l.

Following [START_REF] Carpentier | Economic Modelling of Agricultural Production: Past Advances and New Challenges[END_REF], local constraints to grow a given crop k in locality l can be decomposed into two broad categories: the land use choice variables and the acreage choice variables.

The land use choice describes the individual choice to produce agricultural production in a given locality. Among the variables that determine this choice, there are, for instance, the soil quality, the thermal regime, the hydrologic conditions. These variables are important determinants of the average productivity of land for agricultural use in the broad sense. They are also useful to dene localities l where agricultural production is not possible for any type of crop k. This last point is particularly important once we consider climate change, since the land use choice to produce agricultural goods can be hindered by a deterioration of these variables (IPCC, 2007).

Acreage choice describes the choice of farmers to produce a particular good among the dierent types of crop k that can be grown in each locality l. This choice depends on a vector of variables, hereafter denoted C k l , that are dened at the crop level, such as the crop specic suitability of hydro- logic conditions and of the thermal regime at the cell level. In other words, this vector of variables encompasses all the agronomic factors that aect directly the capability of farmers to use water for agricultural production which will be more precisely dene in the next section. This choice is also done by a comparative analysis: the incentive to produce a particular product depends on its suitability to the natural conditions compared to the suitability of all other goods that can be produced under these conditions ( k C k l ) (Carpentier and Letort, 2013; Costinot et al., 2016). This choice also depends on the alternative uses of water (namely water not used for the agricultural production), that reduce the water available to grow the crop k [START_REF] Flörke | Water Competition between Cities and Agriculture Driven by Climate Change and Urban Growth[END_REF]). These alternative uses (e.g. water for consumption in cities) are denoted W mun l . The higher W mun l , the smaller the share of a eld l allocated to any given crop k that can benet from water, and then the smaller the production at this location.

To summarize, we aim to capture here the relative cost to use water for a particular k in comparison with other use of water (agricultural and non-agricultural).

We combine these elements 19 to build an indicator of the production of a given crop k in locality l, L k l , that may be interpreted as a measure of the local water capability to produce agricultural goods such as:

L k l = Land U se l × C k l W mun l + k C k l Acreage Choice (1)
This expression (1) takes a similar form than the one presented in [START_REF] Costinot | Evolving Comparative Advantage and the Impact of Climate Change in Agricultural Markets: Evidence from 1.7 Million Fields around the World[END_REF] (Equation 8) where farmers allocate their xed land inputs to multiple crops with land share assigned to each 18 A list of all products we consider in our analysis can be found in table (4) in the Appendix and a detailed explanation of these dierent classication can be found at http://www.fao.org/statistics/standards/en/ 19 See the data section 2.2 where we further expand the explanation and computation of these dierent variables.

crop being somewhat proportional to its relative productivity. Here, we solely substitute the concept of productivity by the one of capability.

Data and Empirical Strategy

In this section, we present the data and the dierent steps necessary to build our indicator of the local water capability to produce agricultural goods in the next section. Since this involve a complex methodology, we breakdown the procedure into two dierent steps which are dedicated to the vector of variables C k l where we rst present the data and computation used to dene each variable included in C k l and in the second step, we estimate the weight of each of this variable through a structural estimate of equation ( 1) allowing us to build a set of values C k l for each locality l and crop k.

2.2.1

Data and Computation of the Variables in C k l

The vector of variables that dene the acreage choice concerning C k l is dened hereafter.

The crop specic thermal regime (T k l ) is the temperature constraint factor from the Global Agroecological Zones v3.0 (GAEZ) to dene the suitability of each cell l for growing any specic crop k. Here, the monthly prole is not necessary as the variable given by GAEZ already accounts for the adequation of temperatures in the growing period of each crop. This variable is expressed in percentage and thus ranges from 0 to 1 (where 0 implies the thermal regime of the locality l being unsuitable for the crop k and 1, the locality l being perfectly suitable for growing the crop k).

The crop specic suitability of local renewable hydrologic supplies (RW k l ) is computed as the monthly average of the ratio between the local renewable water availability and the local crop water requirement. On the one hand, the local renewable water availability in locality l for each month m is the sum of soil moisture dened as R SM lm (data taken from the C3S Soil Moisture developed within ESA's Climate Change Initiative Soil Moisture Project), surface water runo dened as R SR lm (data taken from the Global Composite Runo Fields, CSRC-UNH and GRDC, 2002) and groundwater recharge dened as R GR l (data taken from the Groundwater Resources of the World, WHYMAP GWR). Finally, since ground and surface water resources can be interconnected, the simple sum may induce some double counts. To avoid that, we follow the FAO guidelines (FAO ( 2003)) to calculate a common water variable at the local level (C W l ) that will be subtracted from the calculation to avoid the double counting of the amount of water available in each cell l. On the other hand, the crop specic water needs (dened as D k lm ) can be approximated by the evapotranspiration in each cell l for the month m and the crop k using the monthly potential evapotranspiration from the Global map of monthly reference evapotranspiration, AQUAMAPS-FAO which is multiplied by a crop coecient given in the Chapter 6 of [START_REF] Allen | FAO Irrigation and drainage paper No. 56[END_REF] (for each crop, we build a Kc curve which calculates the amount of water required depending of the growing stage of the plant, allowing to calculate an accurate monthly water requirement for agricultural production). More formally, D k lm = c k × P ET lm with c k , the crop coecient for k and P ET lm , the potential evapotranspiration in l for the month m. Thus, the computation of RW k l is as follow:

RW k l = 1 M k l m 1 D k lm R SM lm + R SR lm + R GR l -CW l M k l
Where M k l is the number of months of the growing period of the crop k in locality l. We divide the adjusted groundwater recharge by this variable because data are only on annual basis such that we transform these yearly values into monthly ones with the assumption that farmers may capture the full yearly recharge to use it during the sole growing period.

20 Interpretation of RW k l is relatively straightforward: if RW k l < 1, the amount of renewable water in locality l is insucient to fulll the needs of the crop k but if RW k l ≥ 1, then the crop k in locality l is not limited by water resources.

20 We are thankfull to the anonymous referee for pointing out this aspect.

The supplemental quantity of non-renewable water (NRW k l ) is dened as underground non-renewable water that can be used by farmers in case of insucient renewable water. The groundwater storage, noted R GS l is taken from the study of [START_REF] Gleeson | The Global Volume and Distribution of Modern Groundwater[END_REF] who estimate the volume and the spatial distribution of modern groundwater storage with several methods. We choose to use the method that matches recharge and water table in our calculation (we also test with another method that matches recharge and porosity and found only very marginal changes). We then assume that this water storage is only used when the renewable water in locality l is insucient to fulll the needs of crop k (pumping non-renewable underground being often costlier than the surface water, this resource is generally used in last resort, [START_REF] Siebert | Quantifying Blue and Green Virtual Water Contents in Global Crop Production as Well as Potential Production Losses without Irrigation[END_REF]; [START_REF] Wada | Nonsustainable Groundwater Sustaining Irrigation: A Global Assessment[END_REF]). In that respect,

N RW k l = R GS l 0 if RW k l < 1 otherwise 2.2.2 Estimation of the Variables in C k l
We estimate a Log-linearization of Equation ( 1) that takes the following form:

ln L k l = c L + θT ln T k l + θRW ln RW k l + 1 {RW k l <1} θNRW ln R GS l + η ln C k l + f l ln land use l W mun l + k C k l +f k o +ε k l (2)
where the variables that dene C k l (namely T k l , RW k l and R GS l ) are introduced additively. Following + Cl ]) and we also add a second set of xed eect at the country-product level (named f k o ) intended to capture the macroeconomic eects (national policies, international trade, ...).

21

The coecient θT , θRW and θNRW represent the estimated elasticities of the crop thermal regime suitability, the crop suitability of local renewable hydrologic supplies and the supplemental quantity of non-renewable water respectively. When θT ( θRW ) is higher, the supply is more sensitive to changes in the thermal regime (renewable water available). The indicator variable 1 {RW k l <1} takes the value 1 if the quantity of renewable water is insucient to fulll the need of the crop k (RW k l < 1) and is factorized with the groundwater storage (R GS l ) to correspond to the variable N RW k l . Finally, the estimated parameter η captures potential heterogeneity of θRW in localities with a low quantity of renewable water supplies (as such, this coecient is also factorized with the indicator variable the IRWR variable alone has now the expected negative sign, showing that places with relatively low quantity of water have a signicant tendancy to produce less. We also observe that the coecient of hydrologic condition is smaller than in the previous estimation, indicating that the bias of omitted variables is now partly corrected. Comparing the estimated coecients of thermal regime suitability with the one of renewable water suitability, we can see that the former is much larger than the latter (0.863 for the thermal suitability and 0.0203 for the renewable water suitability). This dierence can be partly explained by the dierence in magnitude of the two variables (the thermal suitability is bounded to 1 but not the renewable water suitability) but also validates the core idea that the capability to use water at the local level matter a lot to produce. This also implies that taking only water resources available at the national level as many researches in economics have done (e.g. [START_REF] Debaere | The Global Economics of Water: Is Water a Source of Comparative Advantage?[END_REF] does not allow to account for heterogeneous thermal regime inside countries. Putting dierently, using the water endowments at national level largely overestimate the potential to eectively use this water for producing agricultural goods. Since the explanatory power of this last estimation is much higher than the previous ones (R 2 adj = 0.75), we consider that the model is suciently controled for a various range of external eects and we use these estimated parameters in the rest of the paper. Obviously, this approach using xed-eects is valid for obtaining the mean value of these elasticities but does not take into account that these elasticities are likely to be non-linear and location specic.

1 {RW k l <1} ).

Indicator

This section presents the computation our indicator L k l from Equation (1) using the set of values C k l estimated in the previous step in combination with the Land U se l and W mun l variables.

Using the previous estimates, we can now compute the explicit form of C k l as:

C k l = T k l θT RW k l θRW exp 1 {RW k l <1} θNRW ln R Gs l + η
Introducing this expression in Equation (1) gives then:

Lk l = Land U se l × T k l θT RW k l θRW exp 1 {RW k l <1} θNRW ln R Gs l + η W mun l + k T k l θT RW k l θRW exp 1 {RW k l <1} θNRW ln R Gs l + η (3)
Concerning the water demand for municipal and industrial uses, W mun l , we use the country average municipal and industrial water consumption per capita (data taken from AQUASTAT of the FAO) 23

multiplied by the population density per square kilometer of the location l (given by the SEDAC).

Using the population density instead of population count allows to convert to the same unit as the other variables (cubic-meter per surface area). We then compute the ratio between this water demand and the yearly surface river runo in locality l dened as R S l = m R S lm (data taken from the Global Composite Runo Fields, CSRC-UNH and GRDC, 2002).

To take into account determinants of the land use choice, Land U se l , presented in (3), we consider the following multiplicative form:

Land U se l = A l S l Tl Wl (4)
where A l is the area of each locality. These values are directly taken from the Socioeconomic Data and Applications Center (SEDAC) which account for the reduced area of cells along the coast lines (the delimitation of each cell being arbitrary, it often overlaps with seas and oceans for cells along the coast lines). The unit of this variable is in km².

S l represents the suitability of land for agricultural production. This variable is built from the multiplicative combination of four variables given by the Global Agro-ecological Zones v3.0: the soil quality (s soil l

), the terrain slope (s slope l

), the share of the land covered with buildings (s built l

) and if other natural coverage (such as lake, forest or ice) limit the development of agricultural production (s land l

). All of these four variables have values ranging from 0 (unsuitable) to 1 (perfectly suitable) and the calculation is:

S l = s soil l × s slope l × s built l × s land l
(if one of the four variables equals to 0, then S l also equals to 0).

To measure the mean value of local thermal regime suitability, Tl , we compute the average value of the crop specic temperature constraint factors (T k l ) to dene a general thermal regime suitability of each cell l irrespective of any specic crop k. The initial value given by GAEZ ranges between 0 (unsuitable) and 1 (perfectly suitable), thus the average value that we use here also ranges between 0 and 1 with identical interpretation.

Finally, to approximate the mean value of local hydrologic condition suitability, Wl , we compute the average value of the crop specic suitability of local renewable hydrologic supplies (RW k l ) and restrict the limit denition of this average value from 0 to 1 (any average value superior to 1 implies that renewable water is sucient to fulll the need for at least one crop).

By inserting (4) in (3), we get our indicator, Lk l . The following map depicts the value of this indicator all around the world (to represent this variable with an unique gure, we compute the sum over the product k of our indicator or more formally:

L l = k L k l ).
Figure 1: Predicted local water capability to produce agricultural goods (in km²)

After aggregating at the country level, this variable is used in the next section to estimate the impact of water resources on the agricultural trade. We used the third column of the estimation to compute the indicator.

The Water Capability to Export

As stated earlier, the macro-level capability is dened by the dierent constraints, typically trade costs, which limit the potential trade of agricultural goods and inuence the specialization of countries. In particular, [START_REF] Venables | Geographical Disadvantage: a HeckscherâOhlinâvon ThÃ×nen Model of International Specialisation[END_REF] and [START_REF] Deardor | Local Comparative Advantage: Trade Costs and the Pattern of Trade[END_REF] the exporter o, to the destination, namely the importer d, for the product k over the time period from 1995 to 2005, noted X k od . The equation to be estimated is thus:

X k od = exp c + λ o ln Lk o + λ d ln Lk d + δ d + δ od + δ o + δ k + ε k od (5)
We control for the bilateral frictions, importer, exporter and product characteristics with xed eects, respectively noted δ od , δ d , δ o and δ k . Adding an exporter xed eect allows to control for the capital stock and thus, the capability to mitigate the unfavorable natural conditions for growing crops in a country through technology. These individual xed eects (exporter xed eects δ o , but also importer xed eects δ d ) enables to take into account all the multilateral trade resistances, 24 the dierence in agricultural technologies (δ o ) and in demand size (δ d ) between countries that inuence bilateral trade ows (see [START_REF] Head | Gravity Equations: Workhorse, Toolkit, and Cookbook[END_REF] for theoretical models that lead to this so called 'structural' gravity equations). Finally the two-way xed eects δ od , capture trade costs between countries.

Taking into account this rich set of xed eects enables to get an unbiased estimate of λ o and λ d . The elasticities estimated, λo and λd , represents the sensitivity of export to the water capacity to produce in o ( Lk o ) and in d ( Lk d ), purged to all other variables dened at the origin of the ow, at the destination, or both.

The main coecient of interest is λ o . We expect that exporter with a high level of water capacity to produce goods k (relatively to other goods), Lk o , are going to export these goods more than other countries, but however not to all destinations, and in particular not to countries with good water capacity to produce them, Lk d . In other terms, we expect that λo > 0 and λd < 0.

One drawback of this estimation is that it is implicitly assumed that the trade elasticity of water is homogeneous across space, which is questionable. To take into account the fact that countries may react dierently to change in their endowment of water, we estimate again this gravity equation by dividing up our whole set of countries into four categories n = {1, 2, 3, 4} in order to estimate these trade elasticities for dierent types of countries. Such groups of countries are delineated according to their vulnerability to climate change (this is more precisely detailed in the next section).The new estimation is given by:

X k od = exp c + λ o ln Lk o + 4 n=1 λ n o 1 {o⊂n} ln Lk o + λ d ln Lk d + δ d + δ od + δ o + δ k + ε k od (6)
24 Multilateral trade resistances may be understood by considering them as a price index of all the goods that are consumed/imported in one country. This price index in a country d depends on the trade costs between the partner o and d, but also of all other trade costs of goods that are imported in d from other countries. Thus a change in trade costs from these external countries (external in a sense that they are external to the bilateral trade considered between o and d), can have an eect on the exchange between o and d by modifying the price index. These resistances are sometimes called third country eects.

where the variable 1 {o⊂n} is an indicator variable taking the value one if the country o is in the group n and zero otherwise. We consider several indicators to split our sample that are related to the level of capital endowment in dierent countries, to the readiness of countries to climate change and to the vulnerability of countries to climate disruption. For each indicator (described in the data section), interpretation of elasticities is for any category n: λ o + λ n o .

To deal with zero trade ows and problems of heteroskedasticity we follow a large strand of the literature by assuming that the distribution of the errors are of a Poisson type (hence, the exponential form of the equation) and for that reason we use the PPML estimator. 25

Data at the Macro-Geographical Level

At the macro-geographical level, we use classical trade data for the gravity estimations in addition to the less classical specication of dividing the country set into categories. We focus our estimation on a large subset of 114 countries and a total of 30 products (at the 4 digit of the Harmonized Commodity Description and Coding Systems, called HS4) including major crops such as rice, maize.

Trade data (X k od ) comes from the Base pour l'Analyse du Commerce International (named BACI) developed by CEPII [START_REF] Gaulier | BACI: International Trade Database at the Product-Level. The 1994-2007 Version[END_REF]). It contains annual bilateral ows on the period 1995-2017 highly disaggregated for an important number of countries. It covers more than 5000 products and 200 countries. This dataset is appealing for the estimation of gravity equation because authors have been employed an approach to reconcile the original data (COMTRADE database of the United Nations Statistics Division) where the information between imports and exports for a same ow can be dierent. This procedure allows to correct some errors and to obtain reliable data. It is important to note that we do two modications to these data. The rst one relates to South Africa which encompasses in BACI the trade ows of Namibi, Botswana, Lesotho and Swaziland in addition to the South Africa country. As it is not possible to delineate trade ows from each of these countries, we combine the ve countries in one and perform the estimates on this group of countries. The second modication relates to exports products from prior imports which cannot be separate from the exports of products from production within countries (e.g. Finland exporting a substantial amount of coee while not being able to produce it). We attempt to reduce the biases by setting trade ows to zero when the exporter country cannot produce the good (when Lk o = 0 then X k od = 0).

The four categories are dened as quartils based upon an indicator of physical vulnerability to climate change built by [START_REF] Feindouno | The Physical Vulnerability to Climate Change Index: An Index to Be Used for International Policy[END_REF]. This indicator, called Physical Vulnerability to Climate Change Index (PVCCI) is an index of exogenous vulnerability, namely not inuenced by the present policy of the countries concerned. It takes into account the risk of ooding from the rise of sea level, the risk of increasing aridity, the risk of increasing recurrent shocks (storms and typhoons).

This indicator is computed for 191 countries and the score obtained is between 0 and 100. The higher is the score, the more vulnerable is the country. To dene our four categories, we simply break down the whole set of countries into four equal parts with the category 4 being 25th percent of the countries with the highest value of vulnerability while the category 1 gathers the 25th percent of countries with the lowest value. The following map shows the countries with their respective category.

25 This estimator is the most used in the literature. See Santos [START_REF] Silva | The Log of Gravity[END_REF] and [START_REF] Head | Gravity Equations: Workhorse, Toolkit, and Cookbook[END_REF] for a discussion. Our estimations need substantial xed-eects (bilateral, importer, exporter and product), the PPML command in Stata leads to estimations which are very long. To overcome this problem, we use a recent Stata module to implement Pseudo Poisson Maximum Likelihood including multiple high-dimensional xed-eects, called ppmlhdfe developed by [START_REF] Correia | PPMLHDFE: Stata Module for Poisson Pseudo-Likelihood Regression with Multiple Levels of Fixed Eects[END_REF]. The speed of estimations can be explain by two elements. Firstly, the using of iterative reweighted least square algorithm allows to reduce the dimensionality problem. Secondly, this command uses the advantage of reghdfe command allowing to reduce some computations which are performed once and so it is not necessary to perform these computations for each iteration.

The Elasticity of the Water Capability to Export

We study here the water determinants of bilateral trade as presented in Equation (5). Our indicator of water capability to produce a product k in countries o, signicantly explains the exports of these products toward all the partners d on average (Column 1, Table (2)). However a high level of water capability at the destination countries d seems to reduce these exports (Column 2). In other terms, our estimation shows that a high capability to produce in d makes the demand less dependant of the supply of agricultural goods coming from outside. Finally, by considering how bilateral trade is explained both by the water capability to produce of the exporter and of the importer, we conrm these results (Column 3). This contributes to account for the importance of good water conditions to sustain the international trade of agricultural goods.

To evaluate the performance of our measure of water to explain the exportation of agricultural goods, we compare our results with those obtained with a more classical indicator of water endowment, the Total Renewable Water Resources, hereafter TRWR (see for instance [START_REF] Debaere | The Global Economics of Water: Is Water a Source of Comparative Advantage?[END_REF][START_REF] Fracasso | A gravity Model of Virtual Water Trade[END_REF]or [START_REF] Afkhami | Virtual Water Trade: The Implications of Capital Scarcity[END_REF]). This indicator is computed on both exporter and importer side from the total renewable water resources (which include rainfalls, runos and groundwaters) at the country level divided by the country population (in order to get the water availability per capita) and multiplied by a sectoral water intensity. This computation gives a variable at the country-product dimension (we use here exactly the methodology and the data of Debaere ( 2014)).

with our approach, water intensities are not directly related to evapotranspirations, temperatures or crop coecients such that any changes in those variables, for instance due to climate changes, implies a problematic discrepancies between the value of water intensities and the real water needs of crops.

Maybe in reason of this lack of accuracy, or in reason of a problem of endogeneity, this indicator performs poorly as demonstrated by the next table. More precisely, the last three columns in Table (2) present the previous estimation with the TRWR respectively for the exporter, the importer and both. Signs are the reverse of what can be expected (negative for exporter and positive for importer), which is, to say the least, a dubious result.

Two reasons may explain the dierence between our results and those obtained with the TRWR.

The rst one is that our indicator is more accurate than the TRWR because it takes into account many local factors at the grid level that explain whether the endowment of water is used or not. 28 A second explanation is that the estimation using the TRWR represents an application of the absolute advantage to have a high endowment of water, but it well known from [START_REF] Ricardo | On the Principles of Political Economy and Taxation[END_REF] to [START_REF] Eaton | Technology, Geography, and Trade[END_REF] that what matters to explain exports is the relative advantage of production and not the absolute one. Our indicator is based on this idea, since it measures the water capability to produce a product k relatively to the water capability to produce all other products (see the denominator of Equation 3), which may explain why our results are in line with what is expected (in theory at least).

These rst results give the average eect of water on trade by treating the heterogeneity of our sample thanks to xed eects. However, to take into account the heterogeneity of the utilization of water to exports agricultural goods in dierent countries, we estimate the gravity equation again by dispatching the dierent countries according to their endowment in capital per capita (Gross Capital Formation on population) and to their physical vulnerability to climate change.

28 In many locations l inside a country, one can have an endowment of water that cannot be used to produce a product k due for instance to thermal conditions. In that case, our variable T k l equals zero and thus the water located in l is not taken into account for the production of these goods. In contrast, many indicators dened at the national level, such as the TRWR, take into account the total endowment of water, including these unusable waters, and thus over-estimate the amount of water that is really available. In all specications, the dependent variable is the mean of bilateral ows between 1995 and 2005.

The capital indicator is Gross Capital Formation per inhabitant.

The Exp. Indic is dierent for each columns and is indicated in the header of column (PVCCI,

Readiness, and Capital).

A general result is that our water capability to export indicator is signicant and positive in almost all specications, implying that water do impact the ability to trade water intensive products. Looking at the Colomn (1), we also nd from these estimates that the more vulnerable the countries are, the less they export. However, the eect of water on exports is decreasing with the level of vulnerability.

Countries that are the less vulnerable have a trade water elasticity of 1.083 (Group 1 and 2), while countries with intermediate of vulnerability (Group 3) have an elasticity of 0.721 (=1.083-0.362), and nally in countries with the worst score (Group 4), the eect is equal to 0.484 (=1.083-0.599).

Obviously, the explanations behind the results obtained for vulnerable and not vulnerable countries dier. The most vulnerable countries are maybe less dependent on water conditions in reason of their specialization in products that are less water intensive. The high coecient obtained for the less vulnerable countries (Group 1 and 2) may reect that among these countries, there are some high income countries that in reason of their technology, export more agricultural goods than other countries. We verify this result in Column (2) where we distinguish countries along their capital endowment (Gross Capital Formation on population). The indicator of readiness (Column (3)), which measures the ability of countries to leverage investments to adaptation actions, is relatively dierent but conrms the results obtained so far. For instance, exporters from countries with the lowest level of readiness are also less sensitive to their water conditions (0.703=0.385+0.318) than countries with the highest level of readiness (0.999=0.385+0.606), conrming the hypothesis that these countries are already specialized in water intensive goods.

4 Illustrative Application: Forecasting the Eects of Climate Changes on the Water Comparative Advantage

In the previous section, the gravity equation enables to distinguish the determinants of trade ows that depend on water to other determinants dened at the macro level (e.g. trade costs). This oers the possibility to analyze how climate change by aecting this water capability can aect the international trade of nations and the specialization of countries via the formula of the Revealed Comparative Advantage (RCA) of [START_REF] Balassa | Trade Liberalisation and 'Revealed' Comparative Advantage[END_REF]. Finally, we analyze how climate change by aecting the water capability to produce aects these RCAs.

Methodology

To update our indicator of water capability to produce with the potential variations of climatic variables following climate change, we take several key variable's predictions from multiple sources which is based on the specic scenario A2 from the model 3 of the Hadley centre, UK Meteorological Oce (see the data section for more details) but we do not change the logic of calculation as expressed in Section 2.

29 In that respect, we compute a new local capability indicator based upon these forecast values of climatic variables for the years around 2050, noted L k l,t . The changing variables composing this indicator are also denoted with the lowerscript t ′ which are the temperatures T k l,t ′ , the water resources R lm,t ′ , the pseudo-demand for water by crops D k lm,t ′ and the demand of water for municipal and industrial uses W mun l,t ′ (the methods and data for computing these new variables for the years 2050's are presented more deeply in the Section 4.2). The computation of L k l,t ′ is thus as follow:

L k l,t ′ = A l S l Tl,t ′ Wl,t ′ T k l,t ′ θT RW k l,t ′ θRW exp 1 {RW k l <1} θNRW ln R Gs l + η W mun l,t ′ + k T k l,t ′ θT RW k l,t ′ θRW exp 1 {RW k l <1} θNRW ln R Gs l + η (7)
From this indicator of local water capability in 2050, we can compute the future trade ows of agricultural goods by using the elasticities λo , λn o , λd and the xed eects δod , δo , δd and δk estimated from the specication using the categorization from the PVCCI (Column 1 of Table 3) in the previous section. We assume that the trade elasticities of water capability to export are constant over time between the 2000's and the simulations in the 2050's (where we are using these elasticities to compute new trade ows).

30 This is a strong assumption but to date, there is no research allowing to determine how climate change is going to aect this trade elasticity in the 2050's. We thus get the predicted trade X k od,t ′ by the following equation:

29 However, we need to drop one country with this simulation (the Serbia-Montenegro) as data are not available.

X k od,t ′ = exp ĉ + λo ln L k o,t ′ + 4 n=1 λn o 1 {o⊂n} ln L k o,t ′ + λd ln L k d,t ′ + δd + δod + δo + δk (8)
It may be interesting to observe that in addition to the variables of the water capability to produce agricultural goods (representing here a local comparative advantage), we have bilateral xed eects that capture the relative dierence in trade costs between countries. Our calculation of this predicted value of trade is thus in the spirit of the theoretical literature on specialization and trade costs which emphasizes that the advantage in the cost of production can be contradicted by a bad market access [START_REF] Venables | Geographical Disadvantage: a HeckscherâOhlinâvon ThÃ×nen Model of International Specialisation[END_REF][START_REF] Deardor | Local Comparative Advantage: Trade Costs and the Pattern of Trade[END_REF].

A comparison between the country international trade simulated in the 2050's (X k

o,t ′ = d X k od,t ′ )
and the country predicted trade in the 2000's shows that both values are closely correlated (with a correlation coecient of 0.95) with 50% of trade ows which are decreasing and 12.5% of trade ows that are reduced by half.

Turning to the computation of the comparative advantages, we use the Balassa's revealed comparative advantages [START_REF] Balassa | Trade Liberalisation and 'Revealed' Comparative Advantage[END_REF]) :

RCA k o,t = X k o,t o X k o,t / k X k o,t o k X k o,t (9)
Where X k o,t = d X k od,t , with t = 2000, 2050.

By using the predicted value of exports, the advantage of this computation is that we take into account all the determinants of trade that are captured by the gravity equation, including dierences in productivity between countries (exporter xed eects) and products (product xed eects) or specic bilateral relationship due to distance or to political links (bilateral xed eects). This matters because the water capability to produce should be somewhat weighted by all other variables that explain trade to compute its impact. One drawback of this approach is that these RCAs are based on the initial linear regression of agricultural production (Equation 2), then by not taking into account in our indicator of water capability that the elasticities of production are not linear with respect to water resources (e.g. that reducing the water resources is likely to reduce crop suitability more in water-scarce parts of the world than in water-rich parts of the world) we make a strong assumption that may inuence our result on RCA. Not reported here, we have however led several sensitive tests by taking dierent elasticities for dierent types of countries according to their level of water resources and we have found that our results on RCAs are very similar to those presented in this section 31 . The scenarios of the B's category focus on less environmental (with a dierence in the im-the population, with signicant dierences growth rates of GDP per capita and technological changes between regions of the world. The use of this scenario is interesting because it allows to apprehend the consequences of inaction: few decisions are taken regarding climate change. We enumerate new sources for each variable (spatial and volumetric units stay unchanged for simulations).

Data for

The crop specic suitability of local renewable hydrologic supplies (RW k l,t ′ ): part of the variable is re-computed to account for the change in 2050 using exactly the same methodology as for the computation of the crop specic suitability of local renewable hydrologic supplies in the 2000's. For the renewable water resources available: the soil moisture (R SM lm ) and surface water runos (R SR lm ) are both predicted from the future precipitation (R P lm,t ′ ) taken from the Climate Change, Agriculture and Food Security 33 (CCAFS). We keep the same distribution of these precipitations within each basin.

For the crop requirement (D k lm,t ′ ), we compute the monthly potential evapotranspiration with two methods in using the predicted monthly temperatures. For both method, SPEI package (Vicente-Serrano et al. ( 2010); Beguería et al. ( 2014)) of R software has been used. This package allows several methods of calculation of evapotranspiration according to the available climatic data. We base on the [START_REF] Hargreaves | Dening and Using Reference Evapotranspiration[END_REF] equation which requires the minimum and maximum temperatures as well as latitude (this variable is used as proxy for the mean external radiation). 34

The supplemental quantity of non-renewable water (NRW k l,t ′ ): we do not compute new value for the groundwater storage (R Gs l ) because this would implies to predict the rate of extraction over the years from the 2000's to the 2050's which would add a lot of complexities. However, we re-compute the indicator variable 1 {RW k l,t <1} (taking the value 1 for localities that suer from insucient renewable water resources and 0 otherwise). Thus, we use the updated variable RW k l,t ′ as explained above and calculate a new indicator variable 1 RW k l,t ′ <1

for the year 2050 that will account for localities with insucient renewable water in 2050.

The water demand for municipal and industrial uses (W mun l,t ′ ): this variable is based on three parts : municipal, industrial water consumption and the density of population. It doesn't exist data about the future water consumption for industrial and municipal purposes. Morethan, the estimation is complicated. So we conserve these data. But it exists data about the projections of population for 2050. This part is very important, because the scenario used, as explained previously, is based on important increasing in population. The projections of population for 2050 data come from the same source as previous population data, that is, from SEDAC.

The thermal regime (T k l,t ′ ): as previously, we use the temperature constraint factor for 2050 from the Global Agro-ecological Zones v3.0 to dene the suitability of each cell l for growing any specic crop k. As explained above, we take data obtained with the climate model 3 and scenario SRES A2

for consistency reason between data used in the indicator.

The suitability of land (S l ): given the impossibility to obtain data about this indicator, we assumed no changes and reused the same data. This hypothesis is obviously strong and in particular regarding forests (think to deforestation in the Amazon, and elsewhere in the world), but predicting forest change and management is such a signicant work, that we follow the literature in international economics by postponing this task to a future work (see also [START_REF] Gouel | The Crucial Role of Domestic and International Market-Mediated Adaptation to Climate Change[END_REF]).

Results

Export Flows and Specialization

Based on computable general equilibrium models (see [START_REF] Dellink | International trade consequences of climate change[END_REF] to produce a good k on the territory l in the country o. Because we cannot present this analysis for all products, we chose idiosyncratically some commodities, among which maize, wheat, coee, soya beans and potatoes to illustrate our nding for dierent part of the world. Four situations are studied:

A deterioration of the local conditions to produce a good but an improvement in the comparative advantages to trade it (country in green with localities in red triangle shaped symbols).

This result that bad conditions to produce a good can lead to an increase of its exports may seem puzzling, but it is not and can be explained by an environment that becomes even more hostile (costly) to other productions. This mechanism is at the heart of the theory of comparative advantage that concerns relative costs of production. Such a case occurs in Europe for the production of potatoes, for instance, in Ukraine, Romania and Hungary (see Figure ( 4)). Adaptation by farmers in this production is an example on how the negative eects of global warming can be mitigated and at the source of new comparative advantages.

Another mechanism that explains these opposite variations between RCA and the local water resources is the spatial reallocation of production. Indeed, the losses in one part of the country can be more than compensated by an improvement in another place of the country, leading this country to develop an advantage. This is typically what could occur in the USA for the production of wheat and meslin (see Figure ( 5)) which are going to become harder to produce in 2050 in the West and in the East of the Corn Belt but easier in its center leading to improve the yields of this crop. This case turns the previous one on its head but follows the same reasoning. Despite an improvement in the water capability to export a good, the comparative advantage in this production is reduced because other goods are even more adapted to the new local conditions. The production of maize in the core of the Corn Belt in the U.S. follows this pattern. This production that is water intensive may nd a more protable substitute due to climate change (e.g. wheat).

In Asia, many countries could suer a decrease in their comparative advantages for rice despite an increase in local capabilities in many places (see Figure (6)). For example, our simulations suggest that India will see a widespread increase in local capability for rice production but these changes are not enough to prevent a loss in term of RCA.

In South-America, the production of soya beans is in a similar situation of a decreasing RCA despite an improvement of the hydrological conditions for this crop (see Figure ( 8)). 7)). In some countries, such as in Ghana or Nigeria, there are some possibilities to relocate this production, but even with this spatial reallocation, the decline of the RCA in cassava seems inevitable. Yet, only countries along the Equator may be aected by a negative variation of their RCAs since countries in the Maghreb and South of the Equator may gain some comparative advantages in cassava. However, almost all countries in Africa may experience a decrease of their comparative advantage for the maize often due to strong decrease of local capabilities (despite some localities having still a gain in local capability). 7)). In Angola, the predicted strengthening of the comparative advantage of exporting cassava is due to an increase in the local water capability to produce this good in the center of this country (that compensates the losses along its southern border).

Considering now coee and soya beans in the South American continent (see Figure ( 8)), it is interesting to observe that among the main traditional exporters of Coee (Columbia, Venezuela and Brazil), our simulations suggest that only Brazil will improve its comparative advantage. This improvement is associated to a reallocation of the local capabilities to produce this coee toward the southern part of the country. Then, from these three steps that go from the production, to exports and comparative advantages, we nd several results. First, we nd that groundwater sustains the production of goods that suers of the insuciency of renewable water resources. Since a part of these groundwater are non-renewables, this poses a particular challenge in front of climate change. Second, the physical vulnerability to climate change is already detrimental for exports, however agricultural exports from vulnerable countries could be less sensitive to water conditions than those from other countries. Vulnerable countries may be more specialized in the production of agricultural goods that are less intensive in water. Our simulation shows a general resilience of the comparative advantages of nations but also reveals signicant changes within countries and for dierent sectors. At the local scale, these changes may have dramatic consequences for farmers which call policy makers to implement mitigation strategies in territories under water pressure. While in some countries climate change leads to a deterioration of important agricultural production without alternative solution (e.g. Coee in Argentina), there are also places where crops of substitution remains available (e.g. maize in the USA).

The limitations of our studies are obviously numerous. Our indicator of local capabilities takes into account the climatic conditions under which a good can be produced, and not the real behavior of farmers. There is no certainty that the possibilities of new productions are going to be taken into account by farmers in 2050. Consequently, the improvement in trade, and implicitly the capability of producers to adapt their production, is certainly overestimated in the northern hemisphere. 35 Similarly, the forecasted value of trade ows only evolves in our model in reason of the relative costs to produce dierent goods under climate change, and takes as given the technology and the possible change in the demand of consumers. Our results may also be sensitive to some specic assumptions, for instance, by lumping together the elasticity of crop production to water for all countries, we do not take into account the non-linearity of these elasticities at the local level that certainly drive partially changes in RCAs because they aect the relative changes in crop production.

Finally, our analysis does not pay enough attention to how the water resources is shared. Our computation at the national level is simply the sum of the indicator computed at the local level, which is a too simple manner to take into account the political and hydrological dynamics of the localities within countries. A better implementation of the local institutions upon which rely most of the water allocation can be particularly helpful in devising a more accurate indicator of water availability.

In that respect, this article is an only rst step toward a deeper analysis into the relationship between the eective water endowment and the international trade of agricultural goods in the wake of climate change.

6 Appendix 7.2 How RCA could change in 2050?

We present here the revealed comparative advantages concerning the predictions for the years 2000's (horizontal axis) against the simulations for the years 2050's (vertical axis) for six crops, namely maize, wheat, manioc, potatoes, tomatoes and citrus. The 45°line represents a situation where the RCA has not changed over the period. Countries below this line have faced a decrease in their comparative advantages (this does not mean that these countries have initially a strong comparative advantage on the product studied) and vice-versa. We also dierenciate the four categories of countries based on the PVCCI index to derive some more accurate trends. For many products, the conclusion of the literature seems well veried, many countries have their RCA clustered around the 45°line, indicating few changes in their specializations due to climate change.

However, such a general conclusion does not hold for all countries and products. Some exceptions exist as we can see for citrus product, some countries move away from the 45°line which are countries mainly considered as more vulnerable to climate change (Mexico, Australia, Kenya, ...). Even if Figure ( 12) depicts an average tendency of small change, we can note some dierence in function of products.

For maize, the majority of countries are close to the line but have a slightly negative impact on the RCA and we can note the reverse situation in the case of Manioc.

40

Figure 12: Comparison of Revealed Comparative Advantages between the 2000's and the 2050's q q q q q q q q q q q q q q q q q q q q q q q q q q q q 0 1 2 3 0 1 2

Categories q

High Vulnerability Low Vulnerability

Medium-High Vulnerability Medium-Low Vulnerability Maize q q q q q q q q q q q q q q q q q q q q q q q q q q q q 0 1 2 Wheat and meslin q q q q q q q q q q q q q q q q q q q q q q q q q q q q 0 1 2 q q q q q q q q q q q q q q q q q q q q q q q q q q 0 1 2 0 1 2 3

Categories q

High Vulnerability Low Vulnerability

Medium-High Vulnerability Medium-Low Vulnerability Potatoes q q q q q q q q q q q q q q q q q q q q q q q q q q q q 0.0 0.5 1.0 0.0 0.5 1.0 1.5

Categories q

High Vulnerability Low Vulnerability

Medium-High Vulnerability Medium-Low Vulnerability Tomatoes q q q q q q q q q q q q q q q q q q q q q q q q q q q q 0.0 Not reported here to save space, 36 we have also reproduced this analysis for all the products of our database, namely for 24 additional crops. We found the same general trend of small changes around 36 These results are however available on request.

  [START_REF] Morais | Using Compositional and Dirichlet Models for Market Share Regression[END_REF], we add a locality xed eect, noted f l that captures all variables of the land use choice of Equation (1) and of the crop independant variables in the acreage choice (more formally, f l = ln[land use l / W mun l

  have presented theoretical models in which the comparative advantage of production can be reverted by a comparative disadvantage in trade costs.[START_REF] Harrigan | Airplanes and Comparative Advantage[END_REF], while working on a dierent subject (comparative advantage and the cost of shipping goods by airplanes), nds empirical evidences of this result. To link our measure of the local capacity to produce, which represents a local comparative advantage, to the macro-level that takes into account trade costs, we propose to undertake two further steps. The rst one is to aggregate our indicator of water from the cells level to the country level. For the sake of simplicity, we take the sum of our indicator Lk l at the country level o : Lk o = l Lk l with l ∈ o. Similarly, we compute for the importer side as Lk d = l Lk l with l ∈ d. These values are computed for the years around 2000's because all the data required are not available on a more recent period. The second step is to estimate the bilateral trade frictions using a gravity equation. We take the average bilateral trade ows from the origin, i.e.

Figure 2 :

 2 Figure 2: Map Depicting Countries according to the index of physical vulnerability (PVCCI)

  Simulating Trade in the 2050's To recompute our indicator for 2050, we use dierent data sources. To keep a certain consistency within these new datasets of predicted values for the years 2050's, we use data from the climate model 3 from Hadley centre, UK Meteorological Oce. Regarding the scenario, we consider the SRES (Special Report on Emissions Scenarios) A2 scenario as dened by the Intergovernmental panel on Climate Change (IPCC). 32 This scenario depicts an heterogeneous world with increasing demographic rate of 31 The sensitive tests are available in the supplementary analysis at https://github.com/fcandau/Water-Comparative- Advantage 32 It exists four scenarios (A1, A2, B1 and B2) each of these are based are three main features: population predictions, economic development as well as structural and technological changes. The scenarios of the A's category focus on economic development (with a dierence about globalisation development (A1) and regional development (A2)).

  ,[START_REF] Gouel | The Crucial Role of Domestic and International Market-Mediated Adaptation to Climate Change[END_REF]), a standard results that developed countries generally gain in term of agricultural export from climate changes in comparison to developing countries, mainly because they are better prepared to mitigate the disruptive eects of climate changes (due to technologies and capital) and because the global raising temperature will induce a more favorable climate for number of crop varieties in these countries (at least those located southern of the Capricorn Tropic and northern of the Cancer Tropic). Our results based on the variation of exports (see Appendix 7) conrm these analysis. According to our computation (and then assumptions) countries which are the less vulnerable to climate change (in Group 1 and 2) register an increase in their total exports (e.g. Canada, France, Germany, but also Peru and to a lesser extent Russia). In contrast many countries in Africa and in the Middle East experience a sharp decrease in their exports (such as Egypt, Yemen, Libya and Senegal). Many of these countries are considered among the most vulnerable to climate change in the PVCCI index (category 4 in our estimations), all of them are ranging from the 24th to 38th country the most vulnerable.While these eects on exports are already known, the consequence of climate change on the comparative advantages of nations remains a very active line of research with no denitive conclusion (see the discussion in the Introduction). To provide the most exhaustive presentation of our results on RCA, which is made dicult by the high number of countries and products, we present in Appendix 7 the revealed comparative advantages with the predictions for the years 2000's against the simulations for the years 2050's for dierent crops. The overall picture is that, in general, RCA are not radically modied by the climate change in 2050. However such a general conclusion does not hold for all countries and products.To illustrate the losses of competitiveness in the agricultural production at the country level, Figure(3) presents the share of product with a strong negative variation in RCA. These results show that in several vulnerables countries the decrease in export is linked to a decrease in comparative advantage (e.g. in Africa), but the most interesting result of this Figure(3) is that even in countries where the total volume of exports is not aected (or even improved), a loss of comparative advantage is also at play due to climate change (for instance in Belgium, France, Finland, India or Peru).

Figure 3 :

 3 Figure 3: Share of Product with a Negative Variation of RCA

Figure 4 :

 4 Figure 4: Variation of Local Comparative Advantage in Europe for several products

Figure 6 :

 6 Figure 6: Variation of Local Comparative Advantage in Asia for Rice

Figure 7 :

 7 Figure 7: Variation of Local Comparative Advantage in Africa for Manioc and Maize

Figure 8 :

 8 Figure 8: Variation of Local Comparative Advantage in South America for Coee and Soya Beans

Figure 9 :

 9 Figure 9: Variation of Local Capabilities and RCA

Figure 10 :

 10 Figure 10: Variation of Total Exports by Country

Figure 11 :

 11 Figure 11: Trade Variation by Category of Vulnerability to Climate Changes

Figure 13 :

 13 Figure 13: Comparison of Revealed Comparative Advantages between the 2000's and the 2050's

  Table (1) presents estimates of coecients θT , θRW , θNRW and η from the Equation (2). has a positive eect which may come from the lack of control regarding the specialization of agricultural producers. To address this issue, we add country-product xed eects in Column (3). The positive eect of groundwater on production in locations where there is not enough renewable water is conrmed (see the coecient of the interaction between groundwater and IRWR), indicating that farmers rely on this non-renewable water resource when necessary. Quite logically, locations with not enough renewable water and without groundwater are negatively aected, we indeed observed that

		Table 1: Micro-geographical Level Capabilities Estimations
			(1)		(2)	(3)
			Production	Production	Production
	Thermal Regime Suitability	0.763	* * *	1.123 * * *	0.863 * * *
	-θ T		(0.0251)	(0.0208)	(0.0358)
	Renewable Water Suitability	0.148	* * *	0.283 * * *	0.0203 * *
	-θ RW		(0.00707)	(0.00984)	(0.00884)
	Groundwater	-0.0598 * * *
	-log(R	Gs l )	(0.00569)
	Insucient Renewable Water Res.	-0.218	* * *	0.0899 * * *	-0.0399 *
	-η		(0.0287)	(0.0342)	(0.0224)
	Insucient Renewable Water Res. × Groundwater	0.296	* * *	0.000812	0.0261 * * *
	-θ N RW	(0.00911)	(0.0122)	(0.00789)
	Constant	0.0230	-0.0152	0.0322	* * *
			(0.0171)	(0.0115)	(0.00836)
	Localities FE	No		Yes	Yes
	Country-Product FE	No		No	Yes
	Observations	256378	255446	255336
	Log-Likelihood	-678966.2	-602176.6	-483199.0
	R2 ajusted	0.0120	0.366	0.748
	Column (1) explains the production of agricultural goods by considering the thermal and hydrologic
	conditions, the groundwater storage and our indicator of Insucient Renewable Water Resources, here-
	fater denoted IRWR. Thermal and hydrological conditions have the expected sign and the groundwater
	variable has a positive signicant eect in locations where the renewable water resources are insucient
	(0,2362=0.296-0.0598). The lack of controls in this estimation is however problematic due to the bias
	of omitted variables. Column (2) introduces locality xed eects and presents similar results notably
	concerning the suitability of the thermal regime and of water conditions. 22 Surprisingly, the IRWR

21 These xed eects are only used to control the estimation and are not used in the calculation in the rest of the computation.

Standard errors in parentheses. * p < 0.10, * * p < 0.05, * * * p < 0.01 variable

Table 2 :

 2 Gravity Equation Regression by Group

		(1)	(2)	(3)	(4)		(5)	(6)
		Flow	Flow	Flow	Flow	Flow	Flow
	Exp. Water Indic.	0.820 * * *		0.771 * * *
		(0.0349)		(0.0434)
	Imp. Water Indic.			-0.130 * * *	-0.111 * * *
				(0.0133)	(0.0161)
	Exp. TRWR					-0.529	* * *		-0.408 * * *
						(0.130)		(0.126)
	Imp. TRWR							0.0497	0.0582
								(0.117)	(0.120)
	Constant	3.007	* * *	11.06 * * *	3.550 * * *	10.62 * * *	10.27 * * *	9.882 * * *
		(0.301)	(0.0771)	(0.357)	(0.201)	(0.124)	(0.214)
	Importer FE	No	Yes	Yes	No		Yes	Yes
	Exporter FE	Yes	No	Yes	Yes	No	Yes
	Product FE	No	No	Yes	No		No	Yes
	Bilateral FE	Yes	Yes	Yes	Yes

Table ( 3

 ( ) provides the main results of the estimation with dierent categorizations.

	Table 3: Gravity Equation Regression by Group (Vulnerability Indicator)
		(1)		(2)	(3)
		PVCCI	Capital	Readiness
	Exp. Water Indic.	1.061	* * *	0.419 * * *	0.386 * * *
		(0.0954)	(0.0683)	(0.0801)
	Exp. Indic=2 × Exp. Water Indic.	-0.0540	0.00473	0.237	* *
		(0.131)	(0.0873)	(0.108)
	Exp. Indic=3 × Exp. Water Indic.	-0.364	* * *	0.264	0.159
		(0.100)	(0.216)	(0.151)
	Exp. Indic=4 × Exp. Water Indic.	-0.591	* * *	0.560 * * *	0.551 * * *
		(0.194)	(0.0928)	(0.0932)
	Imp. Water Indic.	-0.113	* * *	-0.112 * * *	-0.112 * * *
		(0.0162)	(0.0166)	(0.0162)
	Constant	3.279 * * *	3.142 * * *	3.492 * * *
		(0.334)	(0.457)	(0.328)
	Importer FE	Yes	Yes	Yes
	Exporter FE	Yes	Yes	Yes
	Product FE	Yes	Yes	Yes
	Exporter-Product FE	No		No	No
	Observations	243570	236520	243570
	Log-Likelihood	-123488348.8	-122326321.7	-123165063.3
	Pseudo R2	0.732	0.733	0.733

Standard errors in parentheses. * p < 0.10, * * p < 0.05, * * * p < 0.01

Table 4 :

 4 of plants (including seeds and fruits), of a kind used primarily, in perfumery, in pharmacy or for insecticidal, fungicidal or similar purposes 1212Locust beans, seaweeds and other algae, sugar beet, sugar cane, fresh, chilled, frozen or dried, whether or not ground;fruit stones, kernels and other vegetable products (including unroasted chicory roots) used primarily for human consumption 1214 Swedes, mangolds, fodder roots, hay, lucerne (alfalfa), clover, sainfoin, List of HS4 Products

	HS4 Code	Entitled of HS4
	701	Potatoes
	702	Tomatoes
	703	Onions, shallots, garlic, leeks and other alliaceous vegetables
	706	Carrots, turnips, salad beetroot, salsify, celeriac, radishes and similar edible roots
	709	Other Vegetables
	713	Leguminous Vegetables
	714	Manioc, arrowroot, salep, Jerusalem artichokes, sweet potatoes
		and similar roots and tubers with high starch or inulin content
	801	Nuts, coconuts, Brazil nuts and cashew nuts
	803	Bananas, including plantains
	805	Citrus fruit
	806	Grapes
	901	Coee
	902	Tea
	1001	Wheat and meslin
	1002	Rye
	1004	Oats
	1005	Maize
	1006	Rice
	1007	Sorghum
	1008	Buckwheat, millet and canary seeds
	1201	Soya beans
	1202	Groundnuts
	1205	Rape or colza seeds
	1206	Sunower seeds
	1207	Oil seeds and oleaginous fruits
	1211	Plants and parts forage kale, lupines, vetches and similar forage products
	1801	Cocoa beans
	2401	Tobacco
	5201	Cotton
	5301	Flax

Table 8 :

 8 Countries included in category 4 for each variable

	Vulnerability Indicator	Capital per inhabitant Indicator	Readiness Indicator
	Afghanistan	Argentina	Australia
	Algeria	Australia	Austria
	Australia	Austria	Belgium

According to[START_REF] Bairoch | Agriculture and the Industrial Revolution 17001914[END_REF] and to a more recent literature in economic growth (see[START_REF] Ashraf | Dynamics and Stagnation in the Malthusian Epoch[END_REF] success- ful productivity growth in agriculture has been the source of early structural transformation leading to industrialization, urbanization and development in most of today's high income countries.

In the neo-classical analysis of comparative advantage based on factor endowments (the Heckscher-Ohlin model), openness leads countries to specialize their production in goods that use the most intensively the most aboundant factor.According to the new theories of trade, openness fosters a specialization in the production of goods which have the largest domestic market (the so-called home market eect, see[START_REF] Costinot | The more we die, the more we sell? a simple test of the home-market eect[END_REF]) or drives the resource toward the most productive rms[START_REF] Melitz | The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity[END_REF].

The RCA is an index used in international economics for calculating the relative advantage or disadvantage of a certain country in a certain class of goods as evidenced by trade ows. See[START_REF] French | Revealed Comparative Advantage: What Is It Good For[END_REF] who shows why this index is appropriate to uncover countries' fundamental patterns of comparative advantage.

In what follows, we often use the term comparative advantage instead of revealed comparative advantage or RCA because it is more telling and convenient but all our analysis of comparative advantages is based on the RCA.

In our analysis, we distinguish 4 group of countries depending upon their vulnerability to climate change (using an index developped by the FERDI).

The water elasticity of trade is a measure of how sensitive the export from one country to another is to its water capability to produce agricultural goods. The term strong elasticity means that changes in the water capability to produce have a relatively strong eect on exports.

We also present a substantial reallocation of production at the benet of the less vulnerable countries that could experience a rise of their export by around +72% (with a strong increase of their comparative advantages: +59.5% on average) despite a drop of their average capabilities to use water for producing agricultural goods at the local level.

The use of these models are challenging for non-hydrologist scientists who may consider them as black boxes.Furthermore, these models also turn-out to be sometimes inadequate for economic studies as key parameters are generally estimated through country xed eects (which induces major concerns about endogeneity bias when this indicator is used as an explanatory variable in a regression that also introduces xed eects).

In fact, authors implicitly assume that a surplus of water in one location can be transferred to another part of country where water is missing, but unlike other types of production factors such as capital, water resources cannot always be moved easily from a water-abundant region where production is not possible to a water-scarce one where other conditions to produce are located.

The literature called the New Economy Geography summarized in[START_REF] Fujita | The Spatial Economy: Cities, Regions, and International Trade[END_REF] and[START_REF] Candau | Entrepreneur' Location Choice and Public Policies: A Survey of the New Economic Geography[END_REF] has analyzed how increasing returns and transport costs interact to explain the agglomeration of activities, and then indirectly explains how trade costs aect the trade patterns, however few analysis have been done on comparative advantage (see however[START_REF] Ricci | Economic Geography and Comparative Advantage:: Agglomeration Versus Specialization[END_REF].

Trade decisions are obviously complex and not completely determined by changes in production patterns, they depend on prices, policies, and changes occurring in other nations. To take into account all these elements, and then to isolate the role of our water variable, we use the best practice in the literature of international trade (see[START_REF] Head | Gravity Equations: Workhorse, Toolkit, and Cookbook[END_REF] for a survey), that consists to explain trade ows via a gravity equation with bilateral xed eects to control for all the bilateral relationships between partners (e.g. trade agreements), country eects and product eects that control

The eect of groundwater storage is not estimated (and the interaction of this variable with IRWR is no longer signicant) due to the colinearity with xed eects that are dened at the same locality level.

We do not have these informations for some countries in our data, we thus decide to ll in missing values by the world average (testing for dierent method of ll in values does not change signicatively the results).

Data and replication codes are available at https://data.mendeley.com/datasets/s468kpnvx8/1

The methodology is to log-transform the total amount of renewable water resources per capita of a country and multiply this log-value by a water sectoral intensity.

While this ceteris paribus analysis, may be justied for some variables, for instance, the eect of distance on trade has been surprisingly stable for the past fty years (see[START_REF] Disdier | The Puzzling Persistence of the Distance Eect on Bilateral Trade[END_REF], there are obviously many determinants of trade that are going to change by 2050.

plementation of global climate measures (B1) and regional measures (B2)).For more details about dierent SRES scenarios, please read the Special Report on Emissions Scenarios from IPCC at the following web link : https://www.ipcc.ch/site/assets/uploads/2018/03/emissions_scenarios-1.pdf 33 http://ccafs-climate.org/data_spatial_downscaling/ 34 We compute potential evapotranspiration as[START_REF] Thornthwaite | An Approach toward a Rational Classication of Climate[END_REF] equation for which the computation used the monthly mean temperatures and used proxy from the literature for the rest of variables (we use the predicted mean temperatures which are describe below) and latitude. The both method lead to similar results for the evapotranspiration.

However, the advantage of this strategy is that in vulnerable countries our indicator is certainly more realistic since it presents the physiological constraints of ecosystems to produce particular crops.

 10). Some notable exceptions arise with the USA that decrease their exports by 7 % while Peru, Argentina and Niger increase their export by 32.18 %, 0.37 % and 4.54 % respectively. Looking by continent, North America may see their export increase by 13.78 % largely driven by the Canada (+ 28.4 %) followed by Europe with an increase of 7.66 %. All other continents may see a drop of their exports with Oceania, Asia and Africa experiencing the most important decrease (-24.57 %, -17.04 % and -14.59 % respectively) while the South and Central America may be the least aected with a drop of 12.21 % of their exports.

the 45°line, but with however some interesting rise and fall of RCAs such as a loss of specialization in sunower seeds in Russia, manioc in South-Africa, vegetables in Mexico or ax in Canada and a potential improvement in grapes for Italy (and for African countries such as in Uganda and Ethiopia), groundnuts for Kenya and tobacco for Poland among many other results. All these results are obviously conditioned by the assumptions done in this paper.