Emmanuelle Lavallée
email: lavallee@dial.prd.fr

Vincent Vicard
email: vincent.vicard@banque-france.fr

Adeline Bachellerie

Pierre-Philippe Combes

Lionel Fontagné

Luke Haywood

Philippe Martin

Thierry Mayer

National borders matter...where one draws the lines too *

Keywords: JEL classification: F1, N70. Keywords: Trade, Borders, Political disintegration, Trade statistics. Résumé F1, N70. Mots clés: Commerce international, Frontières, Désintégration politique, Statistiques commerciales

The fact that crossing a political border dramatically reduces trade flows has been widely documented in the literature. The increasing number of borders has surprisingly attracted much less attention. The number of independent countries has indeed risen from 72 in 1948 to 192 today. This paper estimates the effect of political disintegration since World War II on the measured growth in world trade. We first show that trade statistics should be considered carefully when assessing globalization over time, since the definition of trade partners varies over time. We document a sizeable resulting accounting artefact, which accounts for 17% of the growth in world trade since 1948. Second, we estimate that political disintegration alone since World War II has raised measured international trade flows by 9% but decreased actual trade flows (including inter-regional trade) by 4%.

I Introduction

International trade has grown almost twice as fast as world income since World War II, leading to an increase in the trade to GDP ratio from 24% in 1960 to 48% in 2003. The causes of economic globalization remain surprisingly disputed [START_REF] Krugman | Growing World Trade: Causes and Consequences[END_REF]. The usual suspects put forward in the literature are decreasing transport costs and the removal of tariffs and non-tariff barriers to trade. [START_REF] Hummels | Transportation Costs and International Trade in the Second Era of Globalization[END_REF] nevertheless finds little systematic evidence documenting the decline in transport costs. He shows that, whereas air shipping experienced a sharp cost reduction between 1955 and 2004, ocean shipping, which accounts for 99% of world trade by weight, did not register such a decline. 1These explanations relate to the dissolution of national borders, either because of technological progress in transport and communication or of the worldwide implementation of free trade policies. A third explanation relates to the drawing of political borders. As stated by Krugman (1995, p.340), "if international trade only includes shipments that cross the borders, it is clear that the volume of trade depends quite a lot on where one draws the line". In this respect, an outstanding feature of the past five decades is the increasing number of sovereign nations. The number of countries has indeed increased from 72 in 1948 to 192 today, thanks in particular to the decolonization process and the break-up of the Soviet Union. Figure 1 clearly suggests that the number of independent countries and global trade openness measured by export plus imports over GDP are correlated. 2The aim of this paper is to investigate how and to what extent political disintegration has affected the volume and geography of world trade since World War II.

The break-up of nations affects international trade through three channels. On the one hand, former intra-national trade flows become international trade flows. Since these shipments existed before independence, recording them as international flows creates an accounting artefact in the measurement of international trade over time. Moreover, pairs of countries ever in a colonial relationship or former members of the same country share linkages and economic, cultural and institutional characteristics that make them trade more than average pairs of countries [START_REF] Rose | One money, one market: the effect of common currencies on trade[END_REF][START_REF] De Sousa | Does political disintegration lead to trade disintegration?[END_REF][START_REF] Head | The erosion of colonial trade linkages after independence[END_REF]. On the other hand, the creation of political borders change relative trade costs. It creates impediments to trade -tariffs as well as non-tariffs barriers to international flows such as independent currencies or different standards and competition policies [START_REF] Anderson | Trade Costs[END_REF]) -that dramatically reduce international trade in comparison to 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 [START_REF] Mccallum | National Borders Matter: Canada-U.S. Regional Trade Patterns[END_REF][START_REF] Anderson | Gravity with Gravitas: a Solution to the Border Puzzle[END_REF]. Finally, since bilateral trade flows depend on relative trade costs [START_REF] Anderson | Gravity with Gravitas: a Solution to the Border Puzzle[END_REF], creating border barriers with some partners should increase trade with other partners.

For instance, the Czech Republic would be expected to trade less with Slovakia after the break-up of Czechoslovakia, but more with any third country.

The contribution of this paper is threefold. We first provide an assessment of the growth in international trade since World War II due to the variation over time in the sample of countries recorded in the international statistics. We show that this accounting artefact is sizeable and accounts for one sixth in the growth of measured international trade since World War II. Part of the accounting artefact comes from the fact that the trade flows of some former colonies were not recorded at all in international statistics (neither independently nor as part of their colonizer's trade) up to their independence. Second, we investigate the impact of the creation of new political borders alone on the volume and geography of world trade since World War II. Based on a theoretically motivated gravity model of trade, we estimate world trade flows in 2005 and in a counterfactual world in 2005 with 1945 borders. We show that newly independent states trade less with former members of the same country (or their former colonizer) but trade more with the rest of the world. Overall, our empirical results suggest that political disintegration has increased measured international trade flows by 9% but decreased actual (including inter-regional) trade flows by 4%. Third, we show that the distribution of GDP abroad affects a country's trade to GDP ratio; a country's trade openness increases when GDP abroad is distributed among a larger number of trade partners.

Several papers investigate the causes of the growth in world trade as a share of GDP. [START_REF] Estevadeordal | The rise and the fall of world trade, 1870-1939[END_REF] study the causes of the rise and fall of the trade to output ratio during the 1870-1939 period. They show that the driving forces of trade globalization were a fall in transport costs and the rise of the gold standard. [START_REF] Rose | Why has trade grown facter than income?[END_REF] and [START_REF] Baier | The growth of world trade: tariffs, transport costs, and income similarity[END_REF] focus on the second wave of globalization after World War II. They both work on a sample of OECD countries. [START_REF] Baier | The growth of world trade: tariffs, transport costs, and income similarity[END_REF] show that two thirds of the growth in trade between the late 1960s and the late 1980s can be explained by income growth, 25% by a reduction in tariffs and 8% by a decline in transport costs. 3All these papers investigate the determinants of international trade growth on a subset of countries, i.e. they investigate the intensive margin of the growth in international trade.

They cannot address the effect of the change in underlying features of the data such as the distribution of GDP among an increasing number of potential trading partners, i.e. the extensive margin of the growth in international trade. Yet world trade has increased by a factor of 30 between 1948 and 2007, while over the same period trade between OECD countries4 has increased by a factor of only 20. At the same time, the international trading system has expanded from 72 × 71/2 = 2556 potential bilateral trade relationships in 1948 to 192 × 191/2 = 18336 today. Assessing the contribution of this extensive margin to the growth in international trade requires a structural estimation of a theoretically motivated gravity model.

The paper proceeds as follows. The next section provides evidence and estimates of the accounting artefact related to variations over time in countries reported in international trade statistics. The third section presents a theoretically based gravity framework allowing the estimation of the impact of border changes on the geography and volume of world trade flows. Section 4 reports the estimation results.

II An assessment of the accounting artefact

The assessment of globalization through measured world trade depends crucially on the number of trade partners considered:

M W = i∈N j∈N,j =i M ij (1)
where M W denotes world imports and M ij imports of i from j. Aggregate international trade depends on the set of declaring exporters and importers N . In this section, we estimate how variations over time in the sample of trade partners affect measured trade growth since World War II.

We use the declared imports in the Direction of Trade Statistics (DOTS) database of the International Monetary Fund, which provides data on bilateral merchandise trade over the period 1948-2007. The DOTS database is the main source of international trade data available over a long time span.

1 Independent states and trade partners in the DOTS

The DOTS database reports trade flows between "entities" that are not necessarily independent countries as defined by international law and practice. As put forward by [START_REF] Russett | National Political Units in the Twentieth Century: A Standardized List[END_REF] and Small and Singer (1982, p38-46), in order to be registered as a state member of the international system, "the entity must be a member of the United Nations or League of Nations, or have population greater than 500,000 and receive diplomatic missions from two major powers". 5 Trade partners in the DOTS database include some territorial entities that are not independent states, and some independent states are not considered as trade partners.

Figure 2 illustrates the discrepancy between the number of independent states and the number of trade partners in the DOTS. For instance, in 2000, 191 states were recognized as sovereign nations, while 195 trade origins (i.e. entities reporting imports) were recorded in the DOTS. This discrepancy is due to the fact that some independent countries (Taiwan, Monaco, Andorra, Liechtenstein, Botswana, Lesotho, Namibia and Swaziland 6 ) were not taken into account whereas some territorial entities, that were not sovereign states, were. 7

In addition, Figure 2 underlines that the DOTS matrix is not squared, since the number of declared trade partners varies by trade origin and increases over time.

From 1948 to 2007, 120 countries became independent but only 102 new trade origins were created (Figure 2). The size of the DOTS matrix therefore depends to a large extent on changes in political borders over time. New independent countries, however, did not necessarily enter the DOTS in the years following their independence. Some colonies were already taken into account in the DOTS in 1948 (see Table 1). Subsequently, in half of the cases, a new independent country was recorded as a trade origin before its independence. Since 1948, the number of effective (positive) bilateral trade flows has been continuously growing and has increased more than six-fold over the period. New trade flows (i.e.

involving a new trade origin and/or partner) represent an increasing share of bilateral five French overseas departments (Guadeloupe, Guyana, Martinique, Reunion and French Guiana) were considered as distinct trade origins even if they were (and still are) part of France. On the contrary, Belgium and Luxembourg were recorded as a single trade partner from 1948 to 1996.

trade flows, from 4% in 1950 to 55% in 2007 (see Figure 3 and Table 2).9 In comparison, the share of trade flows between countries that used to belong to the same statistical entity made up 1% of world trade transactions in 2007 (see table 2). The value of trade flows involving new entities has also increased dramatically, to stand at 28% in the 2007. In the general case of a country break-up, former inter-regional trade flows become international flows because former regions of the same country become sovereign nations.10

For instance, the break-up of Czechoslovakia in 1993 resulted in the creation of two new countries: the Czech Republic and Slovakia. Czechoslovakian trade, however, included the trade of all its regions with the rest of the world. In this case, we thus define trade flows between the Czech Republic and Slovakia (i.e. USD 4882 millions in 1993) as a statistical artefact since they existed before independence but were not recorded in the DOTS.

A country's independence may nevertheless have more severe consequences on the measurement of international trade. The trade of some independent states, territories or colonies was simply not recorded at all in international trade statistics before their independence or their creation as a trade origin. In this case, all trade flows of these countries contribute to the accounting artefact since they existed but were not recorded in 1948 and appeared in international statistics between 1948 and 2007. To illustrate the relevance of this second source of accounting artefact, let's consider the case of the former French West and Equatorial African colonies, whose trade flows were simply not included in the DOTS database even as part of the French imports or exports.11 Table 3 shows that in 1962 these countries represented 4.25% of French foreign trade and that, from 1959 to 1962, their independence and creation as a trade origin accounted for 13.4% of the increase in French trade. In addition, although they represented less than one percent of world trade in 1962, their creation accounted for almost 4% of the increase in the value of world trade flows between 1959 and 1962.

The accounting artefact is sizeable also at the world level. In order to assess the bias introduced in world trade statistics by the creation of new trade origins and trade partners, we compute the share of the growth in world trade due to flows that were not recorded as international trade flows in 1948. More precisely, we subtract from the total value of imports recorded in the DOTS since 1948 the total value of trade between country pairs that were not recorded in the DOTS trade matrix in 1948. Our definition includes country pairs that used to belong to the same country (e.g. Czech Republic and Slovakia) and country pairs that were not recorded in 1948 either because the importer was not recorded as a trade origin in the DOTS in 1948 (e.g. Afghanistan, Mali) or because the exporter was not declared as a trade partner by a particular trade origin. Note that our definition of the accounting artefact is restrictive since we consider as existing all country pairs recorded in the DOTS in 1948, including those for which a zero or missing value is reported in 1948 (79% of observations).12 Accordingly, our quantification of the accounting artefact excludes the 'real' extensive margin, i.e. zero trade flows between existing country pairs in 1948 that subsequently turned positive.

Results in Table 4 confirm that the accounting artefact is sizeable: it accounts for more than one sixth of the growth in world trade since World War II. The accounting artefact was particularly significant in the 1950s and 1960s due to the decolonization process and in the 1990s due to the break-up of the Soviet Union. 13 Overall, 17% of world trade growth since 1948 is related to the inclusion of new trade origins in the DOTS database.

This section shows that variations over time in the number and definition of trade origins and partners in international trade statistics inflate the measured growth in international trade. As underlined above, the creation of a new trade origin does not necessarily reflect the recognition of a new sovereign state. Moreover, changing political borders may affect trade with third countries. Fully quantifying the contribution of changing political borders on the growth in world trade therefore requires to go beyond simple descriptive statistics and to structurally estimate a trade model. In the next section, we investigate the impact of changing political borders on the volume and geography of world trade based on a micro-founded gravity model of trade à la [START_REF] Anderson | Gravity with Gravitas: a Solution to the Border Puzzle[END_REF].

III The gravity model and borders

The gravity model of trade is based on two building blocks [START_REF] Anderson | Gravity with Gravitas: a Solution to the Border Puzzle[END_REF]. Consider first N countries/regions each specialized in the production of one good differentiated by place of origin. We assume the supply of each good to be fixed. Let then add identical, homothetic preferences represented by the following CES utility function:

U j = i∈N c (σ-1)/σ ij (2)
where c ij is consumption of goods produced in country i by consumer of country j and σ is the elasticity of substitution between all goods. Country j's consumers maximise (2) subject to the budget constraint:

i∈N p ij c ij = y j (3)
where p ij is the price of goods produced in country i for country j's consumers and y j is country j's nominal income.

Let t ij be the variable trade costs on exports from i to j. Then p ij = p i t ij where p i is country i's supply price. The value of exports from country i to country j is

x ij = p ij c ij and total income of country i is y i = j∈N x ij .
Maximization of (2) subject to (3) yields:

x ij = p i t ij P j 1-σ y j ( 4
)
where P j is given by:

P j = i∈N (p i t ij ) 1-σ 1/(1-σ)
.

(5) Market clearance implies:

y i = j∈N x ij = p 1-σ i j∈N t ij P j 1-σ y j . ( 6
)
Following [START_REF] Anderson | Gravity with Gravitas: a Solution to the Border Puzzle[END_REF], using [START_REF] Fidrmuc | Disintegration and Trade[END_REF] to solve for the unknown prices p i together with ( 4) and ( 5), we obtain:

x ij = y i y j y w t ij Π i P j 1-σ (7)
where

Π 1-σ i =   j y j y w t ij P j   1-σ (8)
P 1-σ j = i y i y w t ij Π i 1-σ . ( 9
)
1 World openness under free trade

Under free trade, i.e. without transport costs or tariffs so that prices are identical for all countries, bilateral trade is determined by the product of the two countries' GDPs. The analysis of world trade is then straightforward: global trade openness depends only on the size distribution of countries. Since prices are identical for all countries, we normalize them to unity: p ij = 1∀i, j. We thus have:

x ij = y i y j y w = x ji . ( 10
)
In this framework, [START_REF] Helpman | Imperfect competition and international trade: Evidence from fourteen industrial countries[END_REF] shows that, for a group of countries A, the fraction of GDP traded inside the region is defined by:

T A Y A = s A 1 - i∈A (s iA ) 2 (11)
where T A is the volume of intra-regional trade, Y A is the regional GDP, s A is the share of region A in world GDP and s iA are the share of region A's GDP of each country i in region A. At the world level, Helpman (1987)'s equation yields:

T W Y W = 1 - i∈N (s i ) 2 (12)
where T W is the volume of world trade, N is the total number of countries in the world and s i is i's share of world GDP. The last term on the right hand side of ( 12) is a "size dispersion index". The latter is minimized for N identical countries whose share of world GDP is 1 N . Hence, under free trade, the relationship between global trade openness and the number of independent countries is straightforward: an increase in the number of countries increases the share of world production traded internationally by decreasing the "size dispersion index".

Gravity with trade barriers

With transport costs, the analysis is less straightforward since bilateral trade depends on relative trade costs [START_REF] Anderson | Gravity with Gravitas: a Solution to the Border Puzzle[END_REF]. Any change in bilateral trade costs between two countries therefore affects the trade flows of each country with its other partners. A country break-up creates border barriers between former regions of the same country. This has two effects on international trade. First, it reduces actual trade flows between the two new independent countries but increases recorded international trade flows since trade between regions is not recorded as international trade before independence.

Second, it increases the average trade barriers that new countries face with all their trading partners. A new independent country should thus trade less with the former regions of the same country but trade more with other partners.

As underlined by [START_REF] Feenstra | Advanced International Trade: Theory and Evidence[END_REF] and [START_REF] Anderson | Gravity with Gravitas: a Solution to the Border Puzzle[END_REF], equation ( 7) Source: Penn World Table 6.2 can be properly estimated using country fixed effects that account for inward and outward multilateral resistance terms Π i and P j . We can therefore consistently estimate the effect of national independence on trade between two former members of the same country from (7). However, to assess the effect of country break-ups on trade with other partners, we need to compute the multilateral resistance terms from ( 8) and ( 9).

Assuming symmetric trade barriers, t ij = t ji , we have Π i = P i , and:

P 1-σ j = i P σ-1 i y i y w t 1-σ ij ∀j. ( 13
)
We assume the following trade cost function:

ln t ij = ln dist ij + h α h z h . ( 14
)
The vector of observable bilateral linkages affecting trade costs includes variables measuring geographical, cultural and historical proximity as well as trade policy variables:

Z ij = [Contig ij , Lang ij , Smctry ij , Colony ij , ComCol ij , Comcur ij , RT A ij W T O ij ] ( 15
)
where Contig ij , Lang ij and Comcur ij are dummies for countries sharing a common border, a common official language and a common currency respectively. RT A ij and W T O ij measure common membership of a regional trade agreement and the World Trade Organization, and Smctry ij , Colony ij and ComCol ij are dummies equal to 1 for, respectively, regions of the same country, countries ever in a colonial relationship and sharing a common colonizer since World War II.

So we have:

P 1-σ j = i P σ-1 i y i y w exp β 1 ln dist ij + h β h z h . ( 16
)
The β's coefficients in ( 16) may be consistently estimated from (7). We may then solve the vector of P 1-σ j using the system of N goods market equilibrium conditions ( 16), estimated coefficients from ( 5) and GDP shares. We are thus able to estimate the impact of the establishment of a political border on trade with former regions of the same country and with the rest of the world.

IV Empirics

Our empirical strategy consists of three steps. First, we need to estimate the impact of the components of the trade cost vector using a gravity equation with country fixed effects.

Second, we solve the vector of P 1-σ j using the system of N goods market equilibrium conditions (16). Indicators (WDI). The data on regional trade agreements originates from [START_REF] Vicard | On Trade Creation and Regional Trade Agreements: Does Depth Matter?[END_REF] and data on currency unions are an extended version of [START_REF] Glick | Does a currency union affect trade? The time-series evidence[END_REF] available at http://jdesousa.univ.free.fr/data.htm. Data on geographical distances and common official language come from the CEPII database 14 . The data on sovereign nations and colonial relationships are taken from the Correlates of War project 15 and completed by the CIA World Factbook. We consider countries that had a direct colonial link and countries that used to belong to the same country (Czech Republic and Slovakia) as a single category (Colony ij ). We define a second category for countries sharing a common colonizer (ComCol ij ). 16 2 Same country effect

In this section, we take advantage of the discrepancy between sovereign nations and entities in the DOTS to estimate the impact on bilateral trade of belonging to the same country.

In 2005, the DOTS database reports trade flows for 20 entities that are not sovereign states. 17

Substituting trade costs ( 14) into ( 7) and log-linearizing, we obtain the following econometric model:

ln x ij = β 1 ln dist ij + β 2 Contig ij + β 3 Lang ij + β 4 Smctry ij + β 5 Colony ij + β 6 ComCol ij +β 7 Comcur ij + β 8 RT A ij + γ 1 ln y i + γ 2 P i I i + γ 3 ln y j + γ 4 P j E i +ε ij (17)
where I i and E i are importer's and exporter's fixed effects and ε ij is the error term.

The estimation of ( 17) by OLS may indeed yield biased estimates: because of Jensen's inequality (E(lnε) = lnE(ε)). Santos [START_REF] Silva | The Log of Gravity[END_REF] show that estimating gravity equations in the standard log-linear form yields biased parameter estimates. They suggest using a Poisson quasi maximum likelihood (PQML) estimator, which yields consistent estimates in the presence of heteroscedasticity. The PQML technique also enables us to avoid dropping zero trade values, which represent 31% of observations in our dataset.

We thus estimate (17) in exponential form on a cross-section in 2005 using a PQML estimator.

Results are presented in column (1) of Table 5. The coefficients on standard gravity variables are in line with the literature. The coefficient on the common colonizer dummy is however not significant. Since we work on a cross-section in 2005, colonial business linkages may have vanished since independence [START_REF] Head | The erosion of colonial trade linkages after independence[END_REF]. However, when we include a dummy for countries sharing a common colonizer and still in an ongoing colonial 16 These definitions slightly differ from those adopted in [START_REF] Rose | One money, one market: the effect of common currencies on trade[END_REF] or [START_REF] Head | The erosion of colonial trade linkages after independence[END_REF]. For instance, Mali and Côte d'Ivoire were part of French West Africa before their independence. Each of them had a direct colonial link with France, but they were also part of the same territorial entity. Mali and Côte d'Ivoire are accordingly included in Colony ij instead of ComCol ij .

17 These entities are small and remote from the rest of the country they belong to. Our results should accordingly not be regarded as an estimation of the border effect put forward by [START_REF] Mccallum | National Borders Matter: Canada-U.S. Regional Trade Patterns[END_REF] and [START_REF] Anderson | Gravity with Gravitas: a Solution to the Border Puzzle[END_REF] using data on Canadian provinces and US States. They are however much more representative of the "border effect" between colonies and colonizer, since most colonies were also small and remote from their colonizer.

relationship, its coefficient is also insignificant, confirming the insignificance of common colonial history for trade relationships after independence. The inclusion of country fixed effects controlling for legal origin may however partially explain this result. Finally, the insignificant coefficient on the common currency dummy may reflect the fact that we consider the euro together with other common currencies without a long panel dataset [START_REF] Frankel | The Estimated Effects of the Euro on Trade: Why Are They Below Historical Effects of Monetary Unions Among Smaller Countries?[END_REF]. Countries that have ever been in a colonial relationship or part of the same country since 1945 trade 175% more than other country pairs, while regions currently in a colonial relationship trade on average e 1.01+0.96 -1 = 616% more. 18 Our estimates are conservative with respect to the literature exploring the impact of colonial history and country break-up on trade. [START_REF] Rose | One money, one market: the effect of common currencies on trade[END_REF] shows in his benchmark results for 1990 that the colonial relationship raises bilateral trade by a factor of 5.75, all other things being equal, while having had a common colonizer makes countries bilateral trade 80% larger. Papers dealing directly with the break-up of nations or colonial empires show that country break-up dra- 18 The colonial relationship dummy is also set to 1 for countries in an ongoing colonial relationship.

matically decreases bilateral trade. For instance, [START_REF] Fidrmuc | Disintegration and Trade[END_REF] find that, at the time of their independence, the Czech Republic and Slovakia were trading 43 times more together than with third countries. Five years later, this ratio had been reduced to 7. de Sousa and Lamotte (2007) nevertheless moderate this conclusion with a larger set of countries including Czechoslovakia, the Soviet Union and Yugoslavia. Examining the effect of independence on post-colonial trade, [START_REF] Head | The erosion of colonial trade linkages after independence[END_REF] conclude that independence gradually reduces colonial trade, by damaging business networks or institutions. On average, trade between a colony and its colonizer is reduced by two-thirds after 30 years of independence, from an initial level of trade on average 13.5 times larger than trade between other countries. This discrepancy may come from the fact that we use a PQML estimator to deal with the fact that the variance of the error term may be correlated with explaining variables in the log-linearized gravity equation, while other papers implement OLS. 19 Results using OLS confirm this explanation (column (3) of Table 5), since the effect of belonging to the same country is found to be five times larger.20

Multilateral resistance terms

In this section, we compute the multilateral resistance terms using the system of goods market-equilibrium conditions ( 16) and the trade costs estimated from equation ( 17).21

Multilateral resistance terms are critical for analyzing the effect of new political borders on trade with third countries. P i indeed measures the average trade barriers faced by country i. Since creating a political border between two regions i and j increases bilateral trade and therefore average trade costs of both countries, it is relatively easier for third countries to trade with countries i and j.

We have complete data for 181 countries, of which 448 pairs have been part of the same country or in a colonial relationship since 1945. For each country, computing (16) requires data on all trade partners, including the country itself. A difficulty here is to measure internal distance [START_REF] Head | Illusory Border Effects: Distance Mismeasurement Inflates Estimates of Home Bias in Trade[END_REF][START_REF] Redding | Economic geography and international inequality[END_REF]. We use 3 different measures of internal distance. First, we consider intra-national distance as the distance to the nearest neighbor divided by four [START_REF] Wei | Intra-National versus International Trade: How Stubborn are Nations in Global Integration?[END_REF][START_REF] Anderson | Gravity with Gravitas: a Solution to the Border Puzzle[END_REF]. Second, we compute distance as dist ii = 0.67 area/Π, which measures the average distance between producers and consumers in a country considered as a circle. Finally, we compute distances based on bilateral distances between the largest cities weighted by their population [START_REF] Head | Illusory Border Effects: Distance Mismeasurement Inflates Estimates of Home Bias in Trade[END_REF]. 22 The measurement of internal and international distances is consistent with this weighted measure of distance. The common border, common language, and the same country and colonial relationship dummies are also set to unity for intranational trade costs. We compute trade costs from ( 14) for the year 2005 and for our counterfactual world for each of the internal distance measures.23

The level of multilateral resistance P σ-1 is, as expected, lower for large countries such as the United States and Japan, and countries surrounded by other rich countries, such as EU countries (see appendix) or small and rich countries with large neighbors (Singapore, Hong-Kong). Conversely, small countries and remote islands face the largest multilateral resistances. The level of P σ-1 depends on the measure of internal distance used. Wei (1996)'s measure of internal distance places more weight on domestic GDP and reduces P σ-1 for rich countries and increases it for poor countries. The opposite is true for the measure of internal distance based on domestic area. Weighted distance increases P σ-1 for all countries with respect to [START_REF] Wei | Intra-National versus International Trade: How Stubborn are Nations in Global Integration?[END_REF]'s measure, but more for small and remote countries. The ranking of P σ-1 however changes only at the margin. Large countries, like the United States, have relatively larger internal distance with area based and weighted distance measures than with Wei (1996)'s measure, and have a relatively larger multilateral resistance compared to smaller countries like Japan.

The effect of our counterfactual exercise on multilateral resistance depends on the kind of countries considered (see appendix). Switching to 1945 borders decreases multilateral resistance in former colonies and former regions of a large country. The decrease is large for countries close to their former colonizer (Papua New Guinea, Namibia) or the former regions of the same country (former members of the USSR). Conversely, OECD countries exhibit no change in P σ-1 . France and the UK are exceptions since they experience a small decrease in their multilateral resistance, due to the removal of border barriers with their former colonies. Since former colonies are small and remote, removing border barriers with them has a limited impact on French and English average trade costs. Russia also exhibits an increase in its multilateral resistance. These results are basically similar for all three measures of internal distance.

Estimation of world trade

In this final section, we estimate trade flows for our sample of 181 countries in 2005 and for our counterfactual world. 24 More specifically, we compute:

ln xh ij = ln y i y j y w -0.79 ln dist ij + 0.54Contig ij + 0.17Lang ij + 0.96Smctry h ij + 1.01Colony h ij +0.27RT A ij + 0.36W T O ij + (σ -1) ln P h i + (σ -1) ln P h j , h = {a, c} (18)
where h = a stands for the actual world in 2005 and h = c for our counterfactual world.

xh ij is the predicted trade flow from i to j and Smctry h ij and Colony h ij are respectively regions of the same country and countries ever in a colonial relationship since World War II in each state of the world. P t i have been computed in the preceding section. Results using each of the three measures of internal distance are presented in table 6. The results are qualitatively similar for all three measures of internal distance. We thus focus our discussion on the simplest measure, the [START_REF] Wei | Intra-National versus International Trade: How Stubborn are Nations in Global Integration?[END_REF] measure of internal distance. Predicted trade flows in 2005 exhibit a fairly good fit; when compared to the 25675 observations for which we actually have trade data, the R-squared is 0.64. 25Changing political borders affects both the volume and the geography of trade flows.

Our results show that international trade, i.e. flows crossing a border, is 9% larger in 2005 than what it would have been with 1945 borders. The increase in the number of independent countries since WWII has led to a sizeable increase in measured international trade.

The picture is however different when we consider all trade flows, i.e. trade flows between the 181 countries for which data are available, irrespective of whether they cross a border or not. In 2005, all these countries are independent, so that all their trade flows are recorded as international trade. In our counterfactual world, 13% of trade takes place between regions of the same country or a colonizer and its colonies, and is not recorded as international trade. When all trade flows are considered, total trade in 2005 is 4% lower than what it would have been with 1945 borders. Increasing the number of independent countries therefore increases the measured international trade by increasing the number of flows recorded as international trade, but it reduces the volume of these flows by creating new border barriers.

As regards the geography of world trade, trade between former regions of the same country and between colonizers and their colonies in 2005 is half its value in our counterfac-tual world. The presence of new border barriers between these countries also affects their exchanges with the rest of the world because it increases their average trade barriers. In the aggregate, former regions of the same country and colonizers and their colonies trade 1.9% more with third countries. A country's break-up therefore affects third countries' trade.

Finally, trade between OECD countries is only marginally affected by new political borders. France and the UK are exceptions since their bilateral trade is estimated to have increased by 2% thanks to the decolonization process. In the aggregate, French and English trade with the rest of OECD countries is 1% larger in 2005 than in our counterfactual world. Notes: Computed from specification (1) in Table 5 for the Wei and area distance measures, and from specification (1) in Table 7 for the weighted distance measure. *Trade between colonizers and their colonies and regions of the same country.

V Conclusion

This paper investigates how the process of political break-up since World War II -the number of sovereign states has risen from 72 in 1948 to 192 today -, directly affects the volume and the geography of international trade. We first show that variation over time in the number of trade origins/partners recorded in international trade statistics create an accounting artefact in the measurement of world trade growth. Trade flows between regions of the same country in 1948 were indeed not recorded and, in the case of several colonies and countries, trade was simply not recorded in 1948. These discrepancies in the sample of countries included in the DOTS accounts for 17% of the growth in international trade between 1948 and 2007.

Second, we lay out an empirical strategy to investigate the impact of country breakups on world trade based on a structural estimation of a gravity model of trade à la [START_REF] Anderson | Gravity with Gravitas: a Solution to the Border Puzzle[END_REF]. We find that the rise in the number of independent countries since WWII has increased international trade by 9%, by raising the number of flows recorded as international trade, i.e. flows crossing a political border. It has however reduced total trade by 4%, i.e. including trade between former regions of the same country and former colonizers and their colonies, because new political borders create border barriers. Our results emphasize that the extensive margin of world trade related to the recognition of new sovereign states has a sizeable impact on the measurement of world trade growth since WWII. Our paper thus complements the results of [START_REF] Baier | The growth of world trade: tariffs, transport costs, and income similarity[END_REF] on the determinants of the intensive margin of the growth in world trade.

This paper shows that the distribution of world GDP across sovereign political entities and their number matter for the measurement of trade openness. It suggests to be cautious when measuring trade globalization only by the trend in the trade to GDP ratio, without taking into account the number of potential trading partners in the world.

Appendix A

Appendix B

Figure 1 :

 1 Figure 1: Number of independent countries in the world and global trade openness

Figure 2 :

 2 Figure 2: Sovereign states, trade origins and trade partners

Figure 3 :

 3 Figure 3: Number of trade flows from 1948 to 2007

Figure 4

 4 Figure 4 plots the evolution between 1950 and 2002 of the sum of the squared share of world GDP of independent countries and the US share of world GDP. It confirms that the size dispersion index has been declining since World War II, thanks in particular to the sharp decline of the US share of global GDP. The world with which the US were trading in 1950 was with an outside world slightly larger than itself but is now five times larger.

Figure 4

 4 Figure 4: Size distribution of countries

  Then we estimate bilateral trade flows in 2005 and for a counterfactual world in 2005 with 1945 borders. To be clear about our approach, our aim is not to compare world trade flows in 2005 to those in 1945 but world trade flows in 2005 to those that would have prevailed, all other things being equal, in 2005 should the political borders have remained the same as in 1945. 1 Data Trade flows are taken from the Direction of Trade Statistics (DOTS) database of the International Monetary Fund. GDP data are from the World Bank's World Development

Table 1 :

 1 Entities reporting to the DOTS in 1948 although they were not independent

	Algeria 1962 (FR)	Kenya 1963 (UK)	Sierra Leone 1961 (UK)
	Angola 1975 (PR)	Laos 1949 (FR)	Sudan 1956 (UK, Egypt)
	Cambodia 1953 (FR)	Madagascar 1960 (FR)	Suriname 1975 (Nth)
	Cameroon 1960 (FR-UN) Malaysia 1957 (UK)	Trinidad & Tobago 1962 (UK)
	Congo, D. R. 1960 (Bel)	Malta 1964 (UK)	Tunisia 1956 (FR)
	Cyprus 1960 (UK)	Mauritius 1968 (UK)	Uganda 1962 (UK)
	Ghana 1957 (UK)	Morocco 1956 (FR)	Vietnam 1953 (FR)
	Guyana 1966 (UK)	Mozambique 1975 (PR) Zambia 1964 (UK)
	Jamaica 1962 (UK)	Nigeria 1960 (UK)	Zimbabwe 1980 (UK)
	Notes: Colonizer in parenthesis. Date of independence are taken from
	Correlates of War Project. 2005. "State System Membership List,
	v2004.1"

Table 2 :

 2 Number and value of world trade flows by decade

		Nbr of positive flows	Value of trade flows
		Total	New	Former inter-	Total	New	Former inter-
				regional flows			regional flows
	1948	3003	0	0	55218.61	0	0
	1950	2900	116	0	50578.26	418.80	0
	1960	4692	435	0	112086.70	2807.52	0
	1970	8336	2072	0	293407.60	12778.69	0
	1980 10133	2907	2	1856672.00	146440.30	110.8
	1990 13402	4394	2	3345372.00	313067.50	108.2198
	2000 20130 10636	220	6205497.00	1228920.00	48701.5
	2007 21566 11783	226	13500000.00 3834935.00	161052.6
	Notes: Authors' calculations on the basis of DOTS.

Table 3 :

 3 Impact on French and world trade of the independence of FrenchWestern and Equatorial Africa (1959-1962)

		% of the value	% of French trade	% of the value	% of world trade
		of French trade 1962 increase (1959-1962) of world trade 1962 increase(1959-1962)
	Benin	0,16	0,49	0,03	0,12
	Burkina Faso	0,09	0,29	0,03	0,16
	Central African Rep..	0,08	0,25	0,00	0,00
	Chad	0,12	0,39	0,04	0,17
	Congo, rep. of	0,28	0,90	0,04	0,38
	Côte d'Ivoire	1,26	3,99	0,28	1,28
	Gabon	0,37	1,17	0,08	0,36
	Mali	0,10	0,30	0,01	0,04
	Mauritania	0,19	0,60	0,03	0,14
	Niger	0,14	0,43	0,03	0,15
	Senegal	1,46	4,59	0,22	1,02
	Total	4,25	13,39	0,83	3,81

Notes: Authors' calculations on the basis of DOTS.

Table 4 :

 4 Assessing the accounting artefact

		Value of trade flows	Artificial trade creation
		(millions of constant USD)	(share of total trade growth)
		total	artefact	cumulative	by decade
	1948	229123	0
	1959	334141	8334	7.9	7.9
	1960	378671	9459
	1969	690125	30266	6.6	3.2
	1970	756205	32844
	1979 2095359	162439	8.7	0.9
	1980 2253243	174605
	1989 2381311	235550	10.9	2.0
	1990 2559581	236689
	1999 3308888	335612	10.9	9.5
	2000 3603657	395374
	2007 6510982	1083380	17.2	0.3

Notes: Authors' calculations on the basis of DOTS. The last column reports the statistical artefact related to new trade origins/partners created during the decade only.

Table 5 :

 5 Gravity results

		(1)	(2)	(3)
	Dependent var.	M	M > 0 log(M)
	Estimator	Poisson QML	OLS
	Current colonial relationship dum.	0.96 c	0.89 c	1.53 a
		(0.51)	(0.49)	(0.41)
	Ever in a colonial relationship	1.01 a	0.98 a	2.16 a
	or part of the same country dum.	(0.10)	(0.10)	(0.10)
	Common colonizer dum.	-0.02	-0.03	0.75 a
		(0.16)	(0.16)	(0.07)
	Contiguity dum.	0.54 a	0.55 a	0.56 a
		(0.07)	(0.07)	(0.10)
	Log distance	-0.79 a	-0.79 a	-1.66 a
		(0.03)	(0.03)	(0.03)
	Common language dum.	0.17 a	0.17 a	0.66 a
		(0.06)	(0.06)	(0.05)
	Common currency dum.	0.04	0.04	-0.07
		(0.08)	(0.08)	(0.13)
	RTA dum.	0.27 a	0.27 a	0.25 a
		(0.06)	(0.06)	(0.05)
	WTO membership dum.	0.36 b	0.42 a	1.04 a
		(0.16)	(0.16)	(0.14)
	Observations	29721	20457	20457
	R-squared	0.92	0.92	0.73
	Notes: a, b, c denotes significance at the 1, 5 and 10% level.
	Heteroscedasticity-robust standard errors are in parenthesis.

Table 6 :

 6 Estimations of world trade in 2005 and in the counterfactual world

	Internal distance measure
	Wei	Area	Weighted

Table 7 :

 7 Gravity results: weighted distance

		(1)	(2)	(3)
		X	X > 0	log X
	Estimator	Poisson QML	OLS
	Current colonial relationship dum.	0.97 c	0.90 c	1.52 a
		(0.50) (0.49)	(0.41)
	Ever in a colonial relationship	1.02 a	0.99 a	2.16 a
	or part of the same country dum.	(0.09) (0.09)	(0.09)
	Common colonizer dum.	0.06	0.06	0.71 a
		(0.13) (0.14)	(0.07)
	Contiguity dum.	0.47 a	0.47 a	0.62 a
		(0.06) (0.06)	(0.10)
	Log distance	-0.89 a -0.89 a	-1.75 a
		(0.04) (0.04)	(0.03)
	Common language dum.	0.19 a	0.19 a	0.65 a
		(0.06) (0.06)	(0.05)
	Common currency dum.	-0.18 b	-0.18 b	-0.08
		(0.08) (0.08)	(0.13)
	RTA dum.	0.30 a	0.30 a	0.21 a
		(0.07) (0.07)	(0.05)
	WTO membership dum.	0.40 b	0.46 a	1.00 a
		(0.17) (0.17)	(0.14)
	Observations	29368	20289	20289
	R-squared	0.92	0.92	0.73
	Notes: a, b, c denotes significance at the 1, 5 and 10% level.
	Heteroscedasticity-robust standard errors are in parenthesis.

Table 8 :

 8 Multilateral resistance terms P σ-1 in 2005 and in the counterfactual world (CF)

	Internal Distance Country	CF	Wei 2005 2005/CF	CF	Area 2005 2005/CF	CF	Weighted 2005 2005/CF
	Belarus Tajikistan Kyrgyz Republic Moldova Georgia Latvia Namibia Ukraine Papua New Guinea Azerbaijan Marshall Islands Estonia Kazakhstan Turkmenistan Lithuania Micronesia. Fed. Sts. Palau Uzbekistan Armenia Eritrea Mauritania Central African Republic Niger Bosnia and Herzegovina Tunisia Mali Gambia. The Sierra Leone Chad Djibouti Algeria Morocco Guinea Vanuatu Sudan Togo Burkina Faso Libya Guyana Benin Dominica Comoros Senegal Madagascar Croatia Gabon Kiribati Zimbabwe Macedonia. FYR Solomon Islands Serbia Belize St. Kitts and Nevis Lesotho Malawi Malta Jordan Côte d'Ivoire Cameroon St. Vincent Ghana Zambia Grenada Antigua and Barbuda Slovenia	19.6 50.0 39.8 27.3 27.9 18.9 49.0 19.2 55.6 30.6 82.0 19.7 32.3 46.9 16.9 82.6 87.0 41.2 30.7 73.0 65.8 68.5 57.1 32.1 21.3 56.5 63.3 63.7 54.3 61.7 26.2 22.2 55.9 117.6 128.2 26.7 64.5 51.0 34.7 35.3 23.1 59.9 23.5 67.1 36.9 98.0 23.5 38.5 55.9 20.1 98.0 103.1 48.8 36.2 85.5 74.1 76.9 64.1 35.7 23.7 62.5 69.9 69.9 59.5 67.6 28.7 24.3 61.0 48.3 52.6 53.8 58.5 49.5 53.8 34.1 36.9 64.9 69.9 46.9 50.3 57.8 61.7 87.7 93.5 43.3 46.1 66.2 70.4 16.8 17.9 46.5 49.3 137.0 144.9 60.6 64.1 28.5 30.0 102.0 107.5 28.0 29.5 54.6 57.5 48.8 51.3 61.0 64.1 60.6 63.7 17.3 18.2 29.2 30.7 38.9 40.8 38.5 40.3 51.0 53.5 41.7 43.7 57.1 59.9 48.5 50.8 42.6 44.4 15.0 15.6	1.36 1.29 1.28 1.27 1.27 1.22 1.22 1.22 1.21 1.21 1.20 1.19 1.19 1.19 1.19 1.19 1.19 1.19 1.18 1.17 1.13 1.12 1.12 1.11 1.11 1.11 1.10 1.10 1.10 1.09 1.09 1.09 1.09 1.09 1.09 1.09 1.09 1.08 1.08 1.07 1.07 1.07 1.06 1.06 1.06 1.06 1.06 1.06 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.04 1.04	15.3 39.8 31.0 21.3 22.1 15.5 36.5 16.7 45.2 26.4 60.2 15.9 28.5 40.5 14.7 61.0 61.3 38.8 26.7 56.8 48.1 50.5 43.5 31.4 19.7 45.5 47.6 49.5 44.1 47.8 26.4 21.9 46.1 94.3 48.3 46.1 43.5 35.2 45.5 41.8 45.5 80.0 42.7 61.0 18.1 45.9 106.4 114.9 24.3 52.4 40.2 27.9 30.8 20.8 51.3 24.8 61.3 36.4 87.0 20.8 39.8 50.5 19.4 85.5 84.0 49.5 33.4 67.1 55.6 57.8 50.5 36.0 23.8 52.6 54.3 56.5 50.5 54.1 31.6 26.0 52.6 108.7 55.6 52.4 49.8 41.8 49.5 46.7 49.8 87.7 48.5 67.6 19.5 50.8 50.3 54.1 25.4 26.7 75.2 81.3 30.8 32.8 41.7 44.6 43.1 46.7 50.5 54.3 54.3 59.2 19.5 21.8 27.5 29.9 41.7 46.1 38.6 42.2 44.4 48.3 41.5 45.2 52.6 57.1 43.7 47.4 41.2 44.4 16.3 17.3	1.59 1.31 1.30 1.31 1.39 1.34 1.41 1.48 1.36 1.38 1.44 1.31 1.40 1.25 1.32 1.40 1.37 1.28 1.25 1.18 1.16 1.14 1.16 1.14 1.21 1.16 1.14 1.14 1.15 1.13 1.20 1.19 1.14 1.15 1.15 1.14 1.14 1.19 1.09 1.12 1.09 1.10 1.14 1.11 1.08 1.11 1.08 1.08 1.05 1.08 1.07 1.07 1.08 1.08 1.09 1.12 1.09 1.11 1.09 1.09 1.09 1.09 1.09 1.08 1.06	26.7 71.4 56.8 37.2 38.9 25.4 75.2 26.7 78.7 42.6 113.6 129.9 36.8 93.5 73.5 47.6 48.8 30.9 89.3 32.8 95.2 51.0 26.2 31.1 47.2 56.2 68.0 80.6 22.5 26.7 116.3 133.3 125.0 142.9 58.5 69.4 41.5 49.0 108.7 128.2 100.0 112.4 105.3 117.6 86.2 96.2 43.3 48.5 28.7 31.8 84.7 93.5 91.7 101.0 93.5 102.0 80.6 88.5 89.3 97.1 37.3 41.0 30.6 33.4 81.3 88.5 175.4 188.7 71.4 77.5 76.9 82.6 71.4 76.9 48.8 52.6 98.0 105.3 66.7 70.9 78.7 82.6 122.0 126.6 60.6 64.1 97.1 102.0 21.9 23.3 65.8 69.4 204.1 212.8 88.5 92.6 38.0 40.0 153.8 161.3 38.2 40.2 76.9 80.6 62.5 64.9 87.0 90.9 86.2 90.1 20.7 21.6 39.8 41.5 54.3 56.8 54.3 56.8 66.2 68.5 58.1 60.6 82.6 86.2 62.1 64.1 53.8 55.2 19.2 20.0 continued on next page 1.38 1.31 1.29 1.28 1.25 1.21 1.19 1.23 1.21 1.20 1.14 1.18 1.19 1.19 1.18 1.15 1.14 1.19 1.18 1.18 1.12 1.12 1.12 1.12 1.11 1.10 1.10 1.09 1.10 1.09 1.10 1.09 1.09 1.08 1.09 1.07 1.08 1.08 1.07 1.06 1.05 1.04 1.06 1.05 1.06 1.06 1.04 1.05 1.05 1.05 1.05 1.05 1.04 1.05 1.05 1.04 1.04 1.05 1.05 1.03 1.04 1.04 1.03 1.03 1.05

[START_REF] Hummels | The nature and growth of vertical specialization in world trade[END_REF] nevertheless show than small decreases in trade costs can lead to large increases in the volume of trade by fostering vertical specialization.

[START_REF] Alesina | Economic Integration and Political Disintegration[END_REF] argue that trade liberalization leads to political disintegration because being able to trade easily with the rest of the world decreases the advantage of having a large domestic market. They link political disintegration to the level of world trade freeness, while our paper links political disintegration to the observed volume of international trade for a given level of world trade freeness.

[START_REF] Jacks | Trade Booms, Trade Busts, and Trade Costs[END_REF] confirm the prevalence of decreasing trade costs during the first wave of globalization and of income growth during the second.

We exclude members that joined OECD after 1990.

[START_REF] Felbermayr | Exploring the Intensive and Extensive Margins of World Trade[END_REF] show that the share of positive trade flows in the total number of flows has remained fairly constant over time and distinguish the contribution of new flows between existing trade origin in 1948 and flows involving a new trade origin.

As mentioned previously trade origins in the DOTS are not necessarily independent states, and their definition has changed over time. Such changes are not neutral in term of measured international trade. For instance, from 1948 to 1996 Belgium and Luxembourg were considered as a single trade partner. In 1997, these two countries were for the first time considered as distinct trade partners, and their bilateral trade recorded in the DOTS.

The FrenchCustoms and Excise Department (1959) defines the French statistical territory as continental France (including the free zones of pays de Gex and Haute-Savoie), Corsica, Monaco and Sarre.

[START_REF] Gleditch | Expanded Trade and GDP Data[END_REF] argues that many zeros in the DOTS are problematic and should be treated as missing observations.

Note that the German reunification has had no effect on the accounting artefact since trade flows between the Federal Republic of Germany and the German Democratic Republic was null before reunification.

Note that the difference in the definition of the dummy for current and past colonial relationships does not drive this result.

The selection bias due to the exclusion of zero trade flows when using OLS is not significant (column (2) of Table5).

Computationally, we solve (16) for P1-σ i so that we do not need estimates of elasticity of substitution σ.

The general formula is dist ij = k∈i (pop k /pop i ) l∈j (pop l /pop j )dist kl where pop k is the population of agglomeration k belonging to country i and dist kl is the geodesic distance between agglomeration k and l.

When weighted distance is used to measure internal distance, we also re-estimate (17) using weighted international distance and use the estimated coefficients on trade costs. Results are presented in Table7in Appendix A.

German reunification is not taken into account here since Germany was divided into the Federal Republic of Germany and the German Democratic Republic in 1949.

We calculate R-squared as the squared correlation between the observed and the predicted bilateral exports.


Keywords: albuminuria, hyperglycemia, renal failure, diabetic complication, antidiuretic hormone

Purpose of review: The prevalence of diabetic kidney disease (DKD) is increasing worldwide. Despite major therapeutic advances in the last decades in DKD, the current standard of care let many people progress to severe stages an unmet need.

Vasopressin secretion is increased in diabetes, and its potential role in the onset and progression of DKD is being re-investigated.

Recent findings: Recently, observational studies evidenced an association between surrogates of vasopressin secretion (daily fluid intake or urine volume, and plasma copeptin concentration) and chronic kidney disease in the community, but also specifically in type 1 and in type 2 diabetes. Causality is strongly supported by a series of studies in rats conducted more than a decade ago, and by additional recent experimental data.

The mechanism underlying these adverse effects likely involves the hyperfiltration induced indirectly as a consequence of the tubular effects of the hormone mediated by the V2 receptor.

Summary: If chronic vasopressin action on the kidney is detrimental in diabetes as suggested so far, intervention studies should be designed. Available tools include V2 receptor blockade, as well as changes in daily water intake in vulnerable patients.

Safety and effectiveness should be tested, as it is currently done in patients with CKD (NCT01766687).

Introduction

Diabetic kidney disease (DKD) has become the most common cause of CKD (Chronic Kidney Disease) in the Western world, and the same trend is observed in developing countries. The human burden is huge because DKD may lead not only to ESRD, but also very often to cardiovascular events and premature death.

Hyperfiltration at the single-nephron level is usually considered as an important feature of DKD that predisposes to progressive nephron damage by increasing intraglomerular hydraulic pressure, albeit other mechanisms of damage have also been evidenced [1].

Circulating levels of vasopressin are increased in people with type 1 or type 2 diabetes, and in animal models with spontaneous or streptozotocin-induced diabetes (see review in [START_REF] Bankir | Vasopressin and diabetes mellitus[END_REF]). The causes of the increased level of vasopressin in diabetes are not fully elucidated, but it could result from a relative contraction of extracellular volume induced by glycosuria and/or from an increased sensitivity of hypothalamic osmoreceptor neurons to the plasma osmolarity [START_REF] Zerbe | Regulation of plasma vasopressin in insulin-dependent diabetes mellitus[END_REF]. From an adaptive perspective, high levels of vasopressin may be beneficial in the short term by limiting the water loss in urine induced by glycosuria [START_REF] Bankir | Vasopressin and diabetes mellitus[END_REF]. However, in the long term, persistently high levels of vasopressin might be deleterious to renal function [START_REF] Bankir | Vasopressin: a novel target for the prevention and retardation of kidney disease?[END_REF].

We will review the evidence available so far regarding plausible link between vasopressin and DKD. Most of the evidence in humans is related to surrogate markers of vasopressin secretion, like hydration markers and copeptin, and is very consistent in renal disease associated with diabetes or not. However, strong experimental data have been accumulated in the last decades supporting a direct causal role of vasopressin in the pathogenesis of CKD and DKD. This evidence is hypothesis-generating for potential preventive and therapeutic strategies in DKD.

Evidence supporting the beneficial effect of hydration in the prevention of CKD in the general population

Strippoli and coworkers observed an inverse linear relationship between fluid intake and prevalence of CKD (eGFR <60 ml/min/1.73 m 2 ) in two cohorts of over 5000 participants [START_REF] Strippoli | Fluid and nutrient intake and risk of chronic kidney disease[END_REF]. Those in the highest quintile of fluid intake (3.2 L/day) had a significantly lower risk of CKD. Sontrop and coworkers analyzed the 2005-2006 US National Health and Nutrition Examination Survey with consistent conclusions [START_REF] Sontrop | Association between water intake, chronic kidney disease, and cardiovascular disease: a cross-sectional analysis of NHANES data[END_REF].

Clark and coworkers used urine volume as a surrogate for the hydration status in a population-based Canadian prospective cohort [START_REF] Clark | Urine volume and change in estimated GFR in a community-based cohort study[END_REF]. After a follow-up of 6 years, the risk of rapid decline of renal function (defined as a eGFR loss exceeding 5% per year) was twofold lower in participants with a urine volume over 3 L/day at baseline, compared to the reference group (urine volume in between 1 and 1.9 L/day) (Figure 1).

Plasma copeptin as a biomarker of CKD risk in the general population

Copeptin, the COOH-terminal portion of the pre-provasopressin molecule, is much more stable than vasopressin in vitro, and as such is an easily measurable surrogate marker of vasopressin. Several studies have shown plasma copeptin and vasopressin concentrations to correlate strongly over a wide range of osmolalities [START_REF] Balanescu | Correlation of plasma copeptin and vasopressin concentrations in hypo-, iso-, and hyperosmolar States[END_REF][START_REF] Roussel | Comparison between copeptin and vasopressin in a population from the community and in people with chronic kidney disease[END_REF][START_REF] Szinnai | Changes in plasma copeptin, the c-terminal portion of arginine vasopressin during water deprivation and excess in healthy subjects[END_REF] Plasma copeptin has been shown to be positively associated with the prevalence of microalbuminuria in cross-sectional observational and long-term follow-up studies in the general population [START_REF] Meijer | Copeptin, a surrogate marker of vasopressin, is associated with microalbuminuria in a large population cohort[END_REF][START_REF] Enhorning | Copeptin, a marker of vasopressin, in abdominal obesity, diabetes and microalbuminuria: the prospective Malmo Diet and Cancer Study cardiovascular cohort[END_REF][START_REF] Ponte | Copeptin is associated with kidney length, renal function, and prevalence of simple cysts in a population-based study[END_REF]. In the large Dutch population-based PREVEND study, the prevalence of microalbuminuria (urinary albumin excretion ≥30 mg/24 hours) was twice higher in participants within the upper quintile of plasma copeptin distribution than in those in the lowest quintile, and the association was independent of confounding factors such as sex, age, blood pressure and eGFR (estimated Glomerular Filtration Rate) [START_REF] Meijer | Copeptin, a surrogate marker of vasopressin, is associated with microalbuminuria in a large population cohort[END_REF]. Enhörning and coworkers analysed data from 2064 participants from the Swedish prospective population-based Malmo Diet and Cancer Study -Cardiovascular Cohort [START_REF] Enhorning | Copeptin, a marker of vasopressin, in abdominal obesity, diabetes and microalbuminuria: the prospective Malmo Diet and Cancer Study cardiovascular cohort[END_REF]. They reported associations of baseline plasma copeptin with the incidence of microalbuminuria at re-examination after an average follow-up of 16 years. The association between copeptin and microalbuminuria was independent of incident diabetes and incident hypertension.

In a subset of 1234 participants from the DESIR study, a prospective cohort of the French general population, we assessed the association between plasma copeptin measured at baseline and the risk for progression towards CKD during a 9-year follow-up [14]. We considered two criteria of progression towards CKD. The first criterion was defined as eGFR below 60 ml/min/1.73m 2 (CKD stage 3 or worse) in at least one of the follow-up visits. The second criterion was a "Certain Drop in eGFR", as proposed by the Kidney Disease Improving Global Outcomes (KDIGO) group [START_REF] Group | KDIGO 2012 Clinical Practice Guideline for the Evaluation and Management of Chronic Kidney Disease[END_REF] . Baseline plasma copeptin was positively associated with both criteria of CKD progression, and the associations were independent of other classical risk factors for CKD, including age, sex, blood pressure and renal function at baseline.

Plasma copeptin and diabetic nephropathy

A few studies investigated the impact of high copeptin levels on renal function in people with diabetes [START_REF] Boertien | Copeptin, a surrogate marker for arginine vasopressin, is associated with declining glomerular filtration in patients with diabetes mellitus (ZODIAC-33)[END_REF][START_REF] Pikkemaat | Association between copeptin and declining glomerular filtration rate in people with newly diagnosed diabetes. The Skaraborg Diabetes Register[END_REF][START_REF] Velho | Plasma copeptin and renal outcomes in patients with type 2 diabetes and albuminuria[END_REF][19]. Boertien and co-workers analysed data from 1328 patients with type 2 diabetes of relatively recent onset (4 years of median duration of diabetes) from the Dutch ZODIAC prospective study [START_REF] Boertien | Copeptin, a surrogate marker for arginine vasopressin, is associated with declining glomerular filtration in patients with diabetes mellitus (ZODIAC-33)[END_REF]. They reported the higher quartile of baseline plasma copeptin to be associated with a faster decline in eGFR during a follow-up of 6.5 years. In a Swedish study of people with newly diagnosed type 2 diabetes from the Skaraborg Diabetes Register, plasma copeptin was positively associated with eGFR decline at re-examination after 12 years of follow-up [START_REF] Pikkemaat | Association between copeptin and declining glomerular filtration rate in people with newly diagnosed diabetes. The Skaraborg Diabetes Register[END_REF].

We studied the association of copeptin with the progression of diabetic nephropathy in 3101 French type 2 diabetic patients from the DIABHYCAR cohort, selected on the basis of persistent micro-or macroalbuminuria without renal failure at baseline [START_REF] Velho | Plasma copeptin and renal outcomes in patients with type 2 diabetes and albuminuria[END_REF].

The median duration of follow-up was 5 years and the main outcome was a renal event, defined as the doubling of the serum creatinine concentration, or the requirement of renal replacement therapy or renal transplantation during follow-up.

The higher tertile of baseline plasma copeptin was associated with a faster decline in renal function during follow-up, both in subjects with micro-or macroalbuminuria (Figure 2A), and with a ~300% increase in the incidence of renal events (Figure 2B). These associations were independent of relevant covariates such as age, duration of diabetes, blood pressure, and baseline levels of HbA1c, albuminuria and eGFR.

Analyses by ROC curves showed that plasma copeptin and albuminuria at baseline predicted similarly the incidence of renal outcomes (ROC area 0.73 and 0.77, respectively) and a 4% added effect was observed for the combined markers (ROC area 0.82) [START_REF] Velho | Plasma copeptin and renal outcomes in patients with type 2 diabetes and albuminuria[END_REF].

Recently, we assessed the association of plasma copeptin at baseline with the risk of subsequent kidney or coronary morbidity in ~1200 participants from 2 binational (Belgium and France) cohorts of people with long-standing type 1 diabetes [19] The main outcomes during follow-up were ESRD (requirement of haemodialysis or renal transplantation), a coronary event (myocardial infarction or coronary revascularisation) and all-cause mortality. High levels of plasma copeptin were associated with the prevalence of established and advanced diabetic nephropathy at baseline, and with increased risk during follow-up of ESRD, coronary events and allcause mortality. The association with the incidence of ESRD during follow-up remained significant following adjustment for relevant confounding factors (age, duration of diabetes, blood pressure, HbA1c, eGFR and albuminuria at baseline). On the other hand, the association of high plasma copeptin with increased risk of coronary events during follow-up could be accounted for by the higher blood pressure, eGFR and albuminuria observed in participants with higher plasma copeptin.

Experimental data supporting detrimental action of vasopressin on the kidney

The selective vasopressin V2 receptor agonist dDAVP (not inducing an increase in blood pressure) was shown to induce a marked increase in urinary albumin excretion both in rats and in healthy human subjects [20]. The involvement of the V2 receptor was confirmed by the fact that albuminuria also increased upon infusion of dDAVP in patients with nephrogenic diabetes insipidus (NDI) due to mutations of the AQP2 water channel, but failed to increase in patients with NDI due to mutations of the V2 receptor.

Involvement of vasopressin in experimental diabetic nephropathy

The previous experimental observation of vasopressin-induced hyperfiltration in normal rats [START_REF] Bouby | Vasopressin increases glomerular filtration rate in conscious rats through its antidiuretic action[END_REF], and the well-known increase in vasopressin secretion in diabetes (see review in [START_REF] Bankir | Vasopressin and diabetes mellitus[END_REF]) led us to hypothesize a role for vasopressin in DKD [14].

Brattleboro vasopressin-deficient rats were a relevant model to study the possible influence of vasopressin on glomerular hyperfiltration, albuminuria and kidney hypertrophy, characteristics of early diabetic nephropathy,. In these animals, a spontaneous single point mutation in the vasopressin gene prevents normal vasopressin synthesis, resulting in central diabetes insipidus (CDI) in rats homozygous for the mutation. Diabetes mellitus was induced by streptozotocin injection in CDI rats and in their Long Evans controls [START_REF] Bardoux | Vasopressin contributes to hyperfiltration, albuminuria, and renal hypertrophy in diabetes mellitus: study in vasopressin-deficient Brattleboro rats[END_REF]. After 4 weeks, glycemia was increased to the same extent in both groups. Creatinine clearance and albuminuria were increased in control rats but underwent no change in CDI Brattleboro rats, as shown in Figure 3. Kidney hypertrophy was much less intense in CDI rats lacking AVP. This shows that the well-known renal complications of diabetes require a normal vasopressin secretion. A mirror experiment was conducted in rats with normal vasopressin secretion in which diabetes mellitus was induced by streptozotocin [START_REF] Bardoux | Diabetes-induced albuminuria: role of antidiuretic hormone as revealed by chronic V2 receptor antagonism in rats[END_REF]. Half of the rats were treated for 3 months with the highly selective, orally active, non-peptide vasopressin V2 receptor antagonist, SR 121463A (Sanofi Aventis), mixed daily with their powdered food (diab-treated). The dose of antagonist was adjusted once a week so that urine osmolality was kept around 400 mosm/L, as compared to about 1000 mosm/L observed in control diabetic rats (diabcontrol). The purpose was to markedly reduce the urine concentrating activity of the kidney without inducing the formation of dilute urine (which might represent a confounding factor) [START_REF] Bankir | Vasopressin: a novel target for the prevention and retardation of kidney disease?[END_REF][START_REF] Bardoux | Diabetes-induced albuminuria: role of antidiuretic hormone as revealed by chronic V2 receptor antagonism in rats[END_REF] . The rise in glycemia and in glucose excretion rate was similar in both groups (Figure 4A) but the V2 antagonist treatment totally prevented the rise in albuminuria seen in diab-controls [START_REF] Bardoux | Diabetes-induced albuminuria: role of antidiuretic hormone as revealed by chronic V2 receptor antagonism in rats[END_REF]. At the end of the experiment, albuminuria was twice lower in diab-treated rats than in diab-controls (Figure 4A) although creatinine excretion was similar in both groups. Kidney weight per 100g body weight was 10% lower in diab-treated than in diab-control rats while liver or heart weights were identical in the two groups.

An interesting observation was made among the 13 diabetic rats of the control group that did not receive any treatment. They exhibited a marked inter-individual variability in GFR (as estimated by creatine clearance) and albuminuria. Three months after streptozotocin injection, significant correlations were observed between creatinine clearance or albuminuria and the solute-free water reabsorption T c H2O (the best reflect of vasopressin action on water reabsorption) (Figure 4B). The early signs of diabetic nephropathy were more visible in rats that showed a stronger urine concentrating activity, an activity that essentially depends on the action of vasopressin. These studies show that the antidiuretic effects of vasopressin play a significant role in the early manifestations of diabetic nephropathy in type 1 diabetes.

Further studies were designed to evaluate if vasopressin also contributes to diabetic nephropathy in type 2 diabetes [START_REF] El Boustany | Antagonism of vasopressin V2 receptor improves albuminuria at an early stage of diabetic nephropathy in a mouse model of type 2 diabetes[END_REF]. Experiments were conducted in an animal model, the obese db/db mouse. Obese db/db mice were treated for 8 weeks with the selective V2 receptor antagonist (30 mg /kg.d, mixed with the food, of SR 121463, Sanofi-Aventis, same as used above in rats) (= diab-treated) and compared to untreated obese db/db mice (diab-control). All mice were uninephrectomized 2 weeks before the start of the experiment to increase the susceptibility of the kidney to adverse events. As expected, the antagonist resulted in a significant increase in urine output, and decrease in urine osmolality. No difference was observed in body weight gain, glycaemia, hematocrit, and blood pressure between the two groups throughout the study but, after 4 and 8 weeks of treatment, the urinary albumin/creatinine ratio was significantly lower in diab-treated mice than in diab-control. Creatinine clearance (in ml/d) was significantly increased over time in diab-control mice, but remained stable in diab-treated mice (530 ± 86 vs 437 ± 51, NS) [START_REF] El Boustany | Antagonism of vasopressin V2 receptor improves albuminuria at an early stage of diabetic nephropathy in a mouse model of type 2 diabetes[END_REF].

Potential mechanism of vasopressin-associated renal damages

This mechanism is not fully understood. Of note, there is no reason to assume a role, in DKD, of the vasopressin-induced cyclic-AMP production in collecting duct cells, an effect involved directly in cyst enlargement in autosomic dominant polycystic kidney disease [START_REF] Devuyst | Osmoregulation, vasopressin, and cAMP signaling in autosomal dominant polycystic kidney disease[END_REF]. Vasopressin was shown to increase GFR in normal rats and humans [START_REF] Bankir | Vasopressin: a novel target for the prevention and retardation of kidney disease?[END_REF]14,[START_REF] Bouby | Vasopressin increases glomerular filtration rate in conscious rats through its antidiuretic action[END_REF]. It is well accepted that such "hyperfiltration" induces a vicious circle that leads to progressive renal damage, as proposed by Brenner and coworkers [START_REF] Hostetter | Hyperfiltration in remnant nephrons: a potentially adverse response to renal ablation[END_REF].

There are no V2 receptors in the glomerulus. The vasopressin-dependent hyperfiltration is likely due to a reduction in the tubulo-glomerular feedback control of GFR, secondary to a reduced sodium concentration at the macula densa. It has been proposed [14] that this reduction results from the complex vasopressin-dependent intrarenal handling of urea (secretion in the pars recta, reabsorption in the terminal collecting duct, recycling in the medullary circulation), leading to a greater flow and higher concentration of urea in the loops of Henle (Figure 5). Vasopressin-stimulated NaCl reabsorption in the thick ascending limb of Henle may also contribute to the lower sodium concentration at the macula densa [14,[START_REF] Hebert | Control of NaCl transport in the thick ascending limb[END_REF].

Discussion

Altogether, these studies suggest that the V2 receptor dependent antidiuretic effects of vasopressin are strongly associated with albuminuria in humans, and have a causal role in the early manifestations of nephropathy in animal models of both type 1 and type 2 diabetes.

The current recommendations of care to reduce the onset and progression of DKD are evidence-based and focused on the tight control of blood glucose and blood pressure. Particularly beneficial classes of drugs are identified, like renin-angiotensin system blockers, but also recently glucagon-like peptide 1 receptor agonists and sodium-glucose cotransporter type 2 inhibitors, two classes of antidiabetic agents.

Recently, stabilization of the incidence rates for DKD-related ESRD was observed in North America, but the number of patients with less severe stages of renal impairment is high and still increasing. Therefore, there is an important and unmet therapeutic need to limit the progression of the disease in this population. Many drugs and therapeutic strategies have been tested, but many failed, often because of intolerable side effects. Of note, lifestyle changes have been proposed for a long time in renal care (reduction of daily intake of salt, phosphate, potassium, or proteins).

The intake of water was more rarely addressed [28], except in advanced CKD with indication of reduced intake because of frequent hyperhydration. However, the KDIGO recommendations mention supplemental free water, but with a narrow scope, "for children with CKD and polyuria to avoid chronic intravascular depletion" [START_REF] Group | KDIGO 2012 Clinical Practice Guideline for the Evaluation and Management of Chronic Kidney Disease[END_REF]. Interestingly, the association mentioned above between fluid intake and prevalence of CKD was observed only for the intake of plain water, but not when considering other beverages such as energy drinks, sugar-or artificially-sweetened drinks, tea, coffee, alcoholic beverages, fruit and vegetable juice, and milk or other dairy drinks [START_REF] Sontrop | Association between water intake, chronic kidney disease, and cardiovascular disease: a cross-sectional analysis of NHANES data[END_REF]. Thus, it seems reasonable to include a claim for appropriate hydration by drinking plain water in future recommendations for the prevention of the onset of DKD, or against the progression of the disease in its early stages.

Conclusion

As described above, there is strong evidence from experimental studies in rodent models that vasopressin plays a significant role in albuminuria, CKD and DKD.

However, only observational data are available in humans. There is a tremendous need for interventional studies [29]. A randomized controlled trial with clinical outcomes is ongoing in a CKD population, not specifically in patients with diabetes [30]. Results are expected in the next future, but preliminary data already support the feasibility of an intervention based on increased water intake in this population, and the expected change in some parameters, including plasma copeptin concentrations. Next steps should include interventional studies in people with diabetes and early DKD, resistant to conventional care.

Key points

-The prevalence of diabetic kidney disease (DKD) is increasing sharply worldwide.

-Consistent clinical observational studies support an association between low fluid intake, other markers of vasopressin secretion, and chronic kidney disease in the community -Consistent evidence is available regarding DKD -Experimental data support causality in the association between vasopressin and chronic kidney damage -In the context of the unmet therapeutic need in DKD, interventions to attenuate chronic vasopressin action on the kidney in diabetes should be designed and tested

Conflicts of interest

Dr Roussel has been a consultant or on the speakers' bureau for AstraZeneca, Boehringer-Ingelheim, Janssen, Eli Lilly, Sanofi, Merck Sharp and Dohme, Physiogenex, and Novo-Nordisk, and has received research funding from Amgen, Sanofi, and Danone Research. Preliminary encouraging data on a first intervention randomized trial testing increased water intake in CKD

Dr

  Velho has no conflict to declare Dr Bankir is an occasional consultant for Danone Research, France Financial support: None Acknowledgements: None 28. Wang CJ, Grantham JJ, Wetmore JB: The medicinal use of water in renal disease. Kidney Int 2013, 84:45-53. 29. Clark WF, Sontrop JM, Huang SH, Gallo K, Moist L, House AA, Weir MA, Garg AX: The chronic kidney disease Water Intake Trial (WIT): results from the pilot randomised controlled trial. BMJ Open 2013, 3:e003666. °°30. Sontrop JM, Huang SH, Garg AX, Moist L, House AA, Gallo K, Clark WF: Effect of increased water intake on plasma copeptin in patients with chronic kidney disease: results from a pilot randomised controlled trial. BMJ Open 2015, 5:e008634.

Figure 1 .

 1 Figure1. Decline in kidney function over a 5.7 year follow-up period, as a function of categories of daily urine volume at baseline (n=2148); eGFR = estimated GFR. The decline was much smaller in people with large urine volumes (and thus probably higher fluid intakes). Modified after data shown by Clark et al[START_REF] Clark | Urine volume and change in estimated GFR in a community-based cohort study[END_REF]

Figure 3 .

 3 Figure3. Influence of urine concentration on the early manifestations of diabetic nephropathy. Diabetes mellitus was induced by an injection of streptozotocin in Brattleboro rats that cannot secrete vasopressin (no AVP) and in control Long Evans rats (normal AVP). Sham injected rats served as controls. Although glycemia rose to the same extent in the two strains of rats, the rise in creatinine clearance and urinary albumin excretion that were observed in control rats did not occur in the absence of AVP, and kidney hypertrophy was much less intense. Drawn after data shown in Bardoux et al[START_REF] Bardoux | Vasopressin contributes to hyperfiltration, albuminuria, and renal hypertrophy in diabetes mellitus: study in vasopressin-deficient Brattleboro rats[END_REF].

Figure 4 .

 4 Figure 4. A. Glycemia, urinary glucose excretion, and urinary albumin excretion in control rats (no DM) and in DM rats not treated (DM-Cont) or treated with a vasopressin V2 receptor antagonist (DM-SR). Open bars show results obtained in the basal period (before the anti-V2 treatment), and hatched bars show the results obtained after 9 weeks of treatment. Glycemia and glucose excretion were not affected by the treatment, but the rise in albuminuria seen in DM-Cont rats was totally prevented by the drug. B. Relationship between creatinine clearance (Ccreat) or urinary albumin excretion (UAE) and solute-free water reabsorption (TcH2O) during the last week of the study in control diabetic rats (receiving no treatment). Linear regressions and correlation coefficients are shown; (a) denotes two very high values excluded from the linear regression. Adapted from Bardoux et al. [23] with permission.

Figure 5 .

 5 Figure 5. Sequence of events initiated by increased vasopressin secretion in diabetes mellitus and accounting for its action on water conservation and for its possible involvement in diabetic nephropathy. Only a role for V2-receptor-mediated actions is presented here. An additional contribution of V1a-receptor-mediated events cannot be excluded, but should be less important because of a partial desensitization of V1a receptors in diabetes mellitus. The protection against progression of diabetic nephropathy afforded by the chronic blockade of the renin-angiotensin system could, at least in part, be explained by the fact that they interrupt one of the pathways by which vasopressin might influence renal function. Reproduced from[START_REF] Bankir | Vasopressin and diabetes mellitus[END_REF] with permission.

  Plasma glucose (mmol/L) Creatinine clear. (ml/min) Urinary albumin excr. (mmol/d) 2 Kidney weight (g/300 g)

. Figure 2 All subjects Macroalbuminuric subjects