Vincent Bignon
email: vincent.bignon@banque-france.fr.

Régis Breton
email: ‡regis.breton@banque-france.fr

Mariana Rojas Breu
email: §mariana.rojas-breu@dauphine.fr.

Viral Acharya

Philippe Andrade

Luis Araujo

Aleksander Berentsen

Jean Cartelier

Laurent Clerc

Michael Bordo

Hubert Kempf

Antoine Martin

Julien Matheron

Raoul Minetti

Albrecht Ritschl

Guillaume Rocheteau

Eugene White

Currency Union with and without Banking Union *

Keywords: banques, union monétaire, crédit, défaut, engagement limité. codes J.E.L.: E42, E50, F3, G21 banks, currency union, credit, default, limited commitment J E42, E50, F3, G21

Cet article propose un modèle avec monnaie externe, banques et défaut endogène sur les emprunts afin d'analyser l'impact du degré d'imperfection du marché du crédit sur la désirabilité -pour les populations-des unions monétaires. Nous montrons que lorsque ces imperfections entraînent un coût plus élevé pour les banques d'octroyer un crédit sur l'étranger plutôt que dans leur juridiction, le bien-être peut être réduit en régime d'union monétaire. Nous montrons également que la mise en place d'une union bancaire qui supprimerait ces barrières à l'intégration des marchés du crédit restaure le résultat habituel d'optimalité des unions . Les implications empiriques de ces résultats pour l'organisation de l'union bancaire sont discutées.

Introduction

The conditions on the feasibility and optimality of a monetary union are key to the ongoing policy debate in the Euro zone, as policymakers and scholars discuss the features of a banking union to complement the European monetary union. Discussions focus mainly on the creation of a single supervisory mechanism and on the need for a federal fiscal backstop for banking resolution. 1In this paper we stress another dimension and point to the complementarity between the common currency -high powered money-and the degree of integration across the various bank intermediated credit markets of the zone. We notice that public authorities can easily unify currency conditions but have no direct command over the degree of credit market integration, since loan conditions depend heavily on the behavior of private banks. With the current Eurozone context in mind, we focus our analysis on the cost for banks of one region of the zone to grant credit to residents of another region of the zone. We show that if this cost is high enough, the welfare gains of a common currency and monetary policy may be wiped out.

The logic of this result runs as follows. Consider a situation in which imperfect credit market integration across regions of the zone entails high management costs for loans granted to non-residents, compared to management costs for loans granted to residents. In this environment, the increase in transactions associated with a common currency may worsen default incentives on bank loans. This effect is driven entirely by the distortions in consumption and funding pattern created by limited credit market integration. More specifically, banks charge a higher interest rate for crossborder vis-à-vis domestic purchases. For borrowers, this creates a wedge between the cost of foreign versus domestic consumption, which induces the consumption pattern of agents with no default record to be biased towards domestic goods compared to what would be simply dictated by their preferences. Instead, an agent that would default-something that does not arise on the equilibrium path-would lose access to credit and follow a consumption pattern more aligned with his preferences. Imposing conversion costs between currencies can thus make default less attractive, as this cost can affect more severely defaulters than non-defaulters, whereby relaxing borrowing constraints. By contrast, when cross-border credit does not entail additional costs, there is no home bias induced by differential access to bank credit, and a conversion cost cannot mitigate default incentives. Thus under perfect credit integration welfare is always higher with a common currency.

Before going further, it is important to be clear about what we mean by imperfect, or limited credit market integration. We define imperfect credit market integration as a situation in which non-residents of a country face more stringent credit conditions (e.g. higher costs) when financing purchases in the foreign country compared to borrowing for domestic consumption. This type of imperfection may come from technological or regulatory hurdles that banks face when granting credit to nonresidents. More importantly in the context of the current debate, those hurdles may originate in a lower ability to seize collateral or revenue across jurisdictions when no automatic procedure for judicial cooperation among jurisdiction is allowed. 2 They may reflect a higher cost for banks to access the credit history of non-residents compared to residents. 3 Impediments to cross-border credit could be exacerbated, or even created by local supervisors or resolution authorities to the extent that they exert 'moral suasion' on banks to favor domestic credit and collateral. 4 Consequently, one can have perfect integration with respect to the currency dimension -and hence no cost for agents to pay with currency-but imperfect integration of credit markets -and hence a higher cost for cross-border purchases-a configuration that fits the current situation in the Euro zone (see Section 2).

2 Insufficient harmonization of bankruptcy procedures can result in foreign lenders being more exposed to a borrower default than domestic lenders, if the legal procedure relies on implicit and non codified aspects, or if local judges differentiate among lenders on a domestic/foreign basis. 3 Jentzsch and San José Rientra (2003) reports more complex procedures for Euro-based banks from one country to access cross-border information on customers based in another Euro-area country than for U.S. banks to access cross-state information on a U.S. customer. [START_REF] Jentzsch | Do we need a European Directive for credit reporting?[END_REF] further argues that although the situation improved with the adoption of several European directives, "the Commission should ensure enforcement of the existing legislation and should conduct research as to whether there are discriminatory rules in laws at the national level. There are indications that such rules exist in several countries."Kalemli-Ozcan, Papaioannou, and Peydr (2010) report the uneven pace followed by the various member states to incorporate the provisions of the European directive into the national legislations. 4 Consistent with this view, [START_REF] Aglietta | The challenge of european integration for prudential policy[END_REF] emphasize the risks created by the disparate views of national prudential entities in a currency union and discuss the induced institutional dilemma. [START_REF] Manna | Home bias in interbank lending and banks' resolution regimes. Bank of Italy working papers[END_REF] shows that country-specific bank resolution procedures is an obstacle to credit market integration. [START_REF] Bertay | Is financial safety net a barrier to cross-border banking? European Bnaking Center Discussion Paper[END_REF] provide evidence suggesting that country-specific financial safety nets can act as a barrier to cross-border banking. [START_REF] Gros | The Single European Market in Banking in decline -ECB to the rescue?[END_REF] argues that local supervision encourages the fragmentation of the banking markets in the currency zone.

The result is shown in a symmetric two-country model of fiat money and banks in which the frictions that each help to overcome are explicitly modeled. Currency (fiat money) and bank credit are used in equilibrium by residents of a given country to purchase domestic or foreign goods. In each period, however, agents are subject to individual consumption and production shocks that cannot be efficiently insured by their cash holdings. As in [START_REF] Berentsen | Money, credit and banking[END_REF], banks provide insurance against those shocks: Agents with no current need for cash (producers) can deposit their currency holdings at their bank rather than keeping them as idle balances, while those with a current need for cash (consumers) can obtain credit from banks to finance additional consumption. By lending out cash received in deposits, banks effectively redistribute the money stock according to agents' current transaction needs. Banks can help finance home or foreign good consumption, albeit at different conditions for residents and non-residents. The various imperfections of credit market integration outlined above share the similarity of generating a cost differential for banks to provide credit for cross-border (foreign) consumption. Because agents cannot commit to repay their debt, banks resort to borrowing constraints and to the exclusion of defaulters from future access to their services to enforce debt repayment. As is standard, the debt enforcement constraint is either irrelevant or binding on equilibrium allocations, depending on the underlying parameters.

To evaluate the gains from a currency union in this environment, we compare two monetary arrangements: a common currency case, and a 'one country-one currency' case with positive conversion costs between the two currencies. The difference between the two cases lies in those conversion costs, and we ask whether the case with strictly positive conversion costs is dominated in terms of welfare by a currency union-which is equivalent to costless conversion. We first show that when the borrowing constraint is not active in equilibrium, a currency union unambiguously dominates the two currency scenario. We then show that this ranking can be reversed in a credit constrained equilibrium, but only if credit integration is limited.

This analysis provides a normative argument for why bank credit integration across regions of a currency zone may be required to (fully) reap the benefit of a currency union, or why a banking union-which should in principle foster credit integration-may be an important complement to a currency union. 5 The implica-tions in terms of design of a banking union are twofold. First, regulators and supervisors should avoid actions that create differences in the costs of managing credit among jurisdictions. Second national legislators must complete the unification of the gathering of information borrowers' creditworthiness; in addition, they should ensure an equal treatment of cross-border claims in national bankruptcy procedures.

The rest of the paper is organized as follows. Section 2 presents some facts on the level of credit market integration in the Euro zone. The environment is laid out in Section 3. The conditions and definition of (symmetric) equilibria are presented in Section 4. Section 5 presents the main results pertaining to the welfare effects of multiples monies and transaction costs. Section 6 discuss the relation of our paper with the literature. Section 7 concludes. Proofs are relegated to the appendix.

The Euro area: one currency, many credit markets

The currency of the Eurozone countries was unified when they created a unique institution -the European Central Bank (ECB)-to unify the rules governing the issuance of the currency, i.e. cash (banknotes/coins) and balances held on accounts at the ECB. The Maastricht treaty granted residents of those countries equal access to banknotes, independently of the country in which the Euro currency is withdrawn/issued. Hence the introduction of the Euro eliminates exchange rate risk, and it implies that the cost of a banknotes withdrawal is the same in any part of the zone and that credit institutions have an equal access to the Eurosystem operations.

This currency unification coexists with credit markets that are far from being perfectly integrated, despite initiatives aimed at creating a single European market for financial services. 6 In particular, retail banking markets remain largely unintegrated [START_REF] Kleimeier | Integrating Europe retail banking markets: Where do we stand?[END_REF]. While it is hard to measure the extent to which periodic localized banking crisis generated discussions on the redesign of the conditions of currency issuances [START_REF] Rockoff | Monetary Unions: Theory, History, Public choice, chapter How Long Did it Take the United States to Become an Optimal Currency Area[END_REF][START_REF] Rousseau | Politics on the road to the u.s. monetary union[END_REF]. Although those conditions stabilized somewhat with the National Banking Acts [START_REF] Weiman | The political economy of the u.s. monetary union: The civil war era as a watershed[END_REF], [START_REF] White | The political economy of banking regulation, 1864-1933[END_REF] argues that differences in regulatory frameworks caused unfulfilled demand for more banking services that "stimulated the public to press for currency and banking reform". It was not before the beginning of the 20th century that the national banking market integrated in terms of payment instruments [START_REF] James | From drafts to checks: The evolution of correspondent banking networks and the formation of the modern U.S. payments system, 1850-1914[END_REF] or national financial integration [START_REF] Davis | The investment market, 1870-1914: The evolution of a national market[END_REF][START_REF] Sylla | Federal policy, banking market structure and capital mobilization in the united states, 1863-1913[END_REF][START_REF] James | The evolution of the national money market, 1888-1911[END_REF][START_REF] Choi | Revisiting structural change and market integration in late 19th century american capital market[END_REF]. Since then it is commonplace to pay in New York with checks drawn on Chicago. residents of one jurisdiction experience differential access to credit in another jurisdiction or face restrictions in the pledgeability of cross-border collateral, anecdotal evidence abounds. We therefore review the metrics that have been used to provide indirect evidence of financial and credit markets integration in the Euro zone.

Financial market integration in the Euro area increased significantly during the 2000s as a consequence of the introduction of the Euro currency [START_REF] Hartmann | The euro area financial system: structure, integration and policy initiatives[END_REF]. Those improvements have been unevenly distributed across segments of the financial and banking markets during the last decade. A higher level of integration has been achieved mostly on the equity and bonds markets with a reduction in the home bias in equity and bond holdings [START_REF] Schoenmaker | Is the home bias in equities and bonds declining in europe?[END_REF]. [START_REF] Manna | Home bias in interbank lending and banks' resolution regimes. Bank of Italy working papers[END_REF] documents a deeper integration in money markets and wholesale banking with banks becoming increasingly interconnected before the subprime crisis, notably through interbank lending. Yet credit markets remain mostly local, with few foreign banks active in multiple jurisdictions, even from other countries of the Eurozone [START_REF] Sørensen | Euro area banking sector integration: using hierarchical cluster analysis techniques[END_REF]Gutirrez, 2006, Claessens and[START_REF] Claessens | Foreign banks: Trends, impact and financial stability[END_REF]. 7 As a matter of fact in many European countries -notably in core countries-foreign penetration is well below the level that prevails in the U.S.. 8

Given available evidence, this limited integration of retail banking markets appears to be a robust feature in the Eurozone. The 2007 ECB report on Financial Integration in Europe writes that "while interbank and capital market-related activities show signs of increasing integration, retail banking markets continue to be less integrated, which is also reflected in the fragmented underlying financial infrastructure" ECB (2007, p.6). This assessment is maintained in subsequent releases of this report: "Financial integration was remarkably fast in money and financial Union financial directives into the state legislation to show that "cross-border banking activities increased significantly among European countries that quickly adopted the financial services directives of the FSAP", suggesting the endogeneity in the adoption of the legal framework to the preference for cross border integration. 8 As of 2009, the percentage of foreign bank assets among total bank assets was 6 for France, 12

for Germany, 6 for Italy, and 2 for Spain, compared to 18 for the U.S. The respective figures for the percentage of foreign banks was 6, 14, 10, and 7, compared to 32 for the U.S. [START_REF] Claessens | Foreign banks: Trends, impact and financial stability[END_REF], tables 1-2). This fact is consistent with the view that retail banking in the U.S. is much more integrated than in the Eurozone. [START_REF] Gropp | A new metric for banking integration in Europe[END_REF] present additional evidence in support of this difference in integration levels, using a measure for retail banking integration based on convergence in banks' profitability.

markets; but it was slower and, in fact, never completed in other segments, as described extensively in previous issues of this report. [. . . ]. This judgment has not changed in subsequent years. Cross-border banking through branches or subsidiaries has remained limited, in stark contrast to other forms of banking integration, like interbank deposits or securities holdings, partly as a result of informational asymmetries stemming from supervisory fragmentation" (ECB, 2012, p.90-91).

The Eurozone crisis partly wiped out the gains in the market segments where financial and banking integration was most advanced, notably because of the impairments of the functioning of interbank markets. The de-leveraging of banks balance sheets has been mostly asymmetric, with increase in home bias in several dimensions. [START_REF] Jochem | Portfolio holdings in the euro area -home bias and the role of international, domestic and sector-specific factors[END_REF] find that in each country of the Eurozone "banks have substantially reduced their investment abroad". [START_REF] Acharya | The greatest carry trade ever? understanding eurozone bank risks[END_REF] use data released by the European Banking Authority to document a marked increased in banks' asset holding home bias. [START_REF] Manna | Home bias in interbank lending and banks' resolution regimes. Bank of Italy working papers[END_REF] uses BIS data on the flow of funds between banking systems of both Eurozone and non-Eurozone countries and computes a quarterly index of interbank market integration. The Eurozone number is computed as the average over 10 countries of a measure of home-bias in domestic bank funding vis-à-vis other countries that belong or not to the Eurozone. As shown on graph 1 reproduced from [START_REF] Manna | Home bias in interbank lending and banks' resolution regimes. Bank of Italy working papers[END_REF], the Eurozone evolution of home bias in bank funding is U-shaped with a maximum integration in 2007. But in countries of the control group -US, UK, Sweden, Denmark, Switzerland-interbank relationships were not durably impacted by the crisis. This illustrates how the funding of each banking system of the Euro area was re-nationalize during the crisis, which may be related to the variety of resolution mechanisms for distressed banks.

Overall, the evidence points to less than perfect credit integration across countries of the Euro zone, consistent with our emphasis on the distinction between integration in the currency and credit dimensions.

Environment

Our model is based on [START_REF] Rocheteau | Money in search in competitive equilibriu, and in competitive search equilibrium[END_REF] and [START_REF] Berentsen | Money, credit and banking[END_REF].

Time is discrete and continues forever. There are two identical countries, the home country and the foreign country, each populated by a continuum of infinitely-lived agents of unit mass. There are two perfectly divisible and non-storable goods: a home good, denoted as q h , and a foreign good, denoted as q f . Agents discount Before the first market opens, agents receive an idiosyncratic shock that determines whether they are producers/sellers for the current period and get no utility from consumption (with probability (1b)), or consumers/buyers in which case they want to consume but cannot produce (with probability b). In the second market, all agents can produce and consume a good denoted as x, and utility from consumption (or disutility of working) is linear in the quantity of good.

Buyers' preferences in the first subperiod are

max [u (q f ) + ηq f , u (q h )] ( 1
)
where η is a preference shock which can take values η = 0, η 1 or η 2 with probabilities π 0 , π 1 and π 2 , and 0 < η 1 < η 2 . The function u satisfies the usual Inada conditions.

Preferences in (1) are such that in equilibrium buyers will consume the home good in periods in which their idiosyncratic shock η is low and consume the foreign good in periods in which η is high. In addition, we assume that

β < [1 + b (π 1 η 1 + π 2 η 2 )] -1 .
For sellers, producing a quantity q i (with i = (h, f )) in the first subperiod represents a disutility equal to c (q i ) = q i .

There are two storable, perfectly divisible and intrinsically useless currencies, the home currency and the foreign currency. For simplicity, the quantity of each currency at the beginning of period t is denoted as M . The money supply in each country grows at the gross rate γ = M +1 /M where the subscript +1 indicates the following period. Agents receive monetary lump-sum transfers from the central bank equal to T = (γ -1) M -1 during the second market in period t. Consistently with the current Eurozone situation, we assume that the central bank has no power to tax agents so γ ≥ 1. 9 Currencies can be exchanged before the first market opens.

Exchanging currencies represents a disutility cost ε proportional to the real amount of money exchanged. Given that the money growth rate is assumed to be the same for the two countries, the case in which the cost ε is zero is equivalent to a currency union. 10

In order to motivate a role for a medium of exchange, traders are assumed to be anonymous so that sellers require compensation at the same time as they produce.

This assumption rules out bilateral credit but not banking credit. Agents can deposit money in banks and borrow to them to finance their purchase. Banking activities take place before the first market opens and after agents have traveled to the foreign country or stayed in their home country. Banks are competitive. Deposits are taken by banks and paid back during the second subperiod with the corresponding interest.

A loan is a bilateral contract between an agent and a individual bank. The loan and the interest payment are paid back -if the borrower has an interest to do soduring the period of opening of the second market.

Banks have no enforcement power but can store information on agents. More precisely they possess a technology to keep track of financial histories of agents: i.e., they can recognize agents who have defaulted in the past. However, the cost for a bank of identifying a home agent is lower than the cost that the bank incurs to identify a non-resident. For simplicity, we assume that banks incur zero cost in order 9 This restriction implies that the Friedman rule is not a feasible policy, so that it is optimal for agents to insure against idiosyncratic shocks using both (costly) cash holdings and banks. This assumption could be relaxed, for instance by assuming that government can use lump-sum taxes but that agents can evade taxation by not participating in the market -see [START_REF] Hu | Coalition-proof trade and the Friedman rule in the Lagos-Wright model[END_REF] and [START_REF] Andolfatto | Essential interest-bearing money[END_REF]. 10 We focus on the case in which agents only hold the currency of their country of residence.

This is for simplicity and could be justified by assuming that agents face an extra cost (e.g. an accounting cost) when holding a mixed portfolio. The mechanism of the paper does not hinge on this assumption

to recognize residents and they may incur a positive cost in order to recognize a nonresident as described below. Since defaulters are recognized by banks, they can be punished by being excluded from the banking system for the rest of their lifetime; i.e., after defaulting, agents are prevented from borrowing and depositing. The threat of exclusion allows bank credit to be supported in equilibrium. We assume that defaulters are further excluded from monetary transfers.

In addition, agents who stay in the home country can only contact a bank located in the home country (they cannot contact a bank located in the foreign country).

Similarly, agents who travel can only contact a bank located in the foreign country.

A bank located in the home (foreign) country incurs a cost c per real unit of money lent in order to identify a foreign (home) agent. Since banks are competitive and make zero profit in equilibrium, this cost is transferred to borrowers. For simplicity, c is modeled as a disutility cost incurred by agents at the same time as they take out a loan. When c = 0, borrowing from a home bank is equivalent to borrowing from a foreign bank, and so banking integration is perfect. If c > 0, borrowing from a foreign bank is more costly and so there is limited banking integration.11

Symmetric equilibrium

We focus on stationary equilibria in which end-of-period real money balances are constant, so that

γ = M/M -1 = φ -1 /φ (2)
where φ is the price of money in real terms during the second market. Let V (m) denote the value function of an agent who holds an amount m of money at the beginning of a period. W (m, ) is the expected value from entering the second market with m units of money balances and an amount of loans (a negative amount denotes deposits). Since countries are perfectly symmetric, in what follows we only present the optimal choices by agents of the home country. The program for an agent in the second market is max

| | t t -1 t + 1 V (m) seller buyer 1 -b b 1st market 2nd market 0 η 1 η 2 βV (m + ) Banks V (m) seller buyer 1 -b b 1st market 2nd market 0 η 1 η 2 βV (m + ) Banks
x,m +1 W (m, ) = x + βV (m +1 ) s.t. x + φm +1 -φm + φ (1 + i) -φT = 0
where φ is the price of money in terms of goods in the second market and T = (γ -1) M -1 are lump-sum transfers from the central bank.

Inserting the budget constraint in the objective function, the above program

simplifies to max m +1 [-φm +1 + φm -φ (1 + i) + φT + βV (m +1 )]
The first-order condition on m +1 is

βV (m +1 ) = φ (3)
The envelope conditions are

W m = φ W = -φ (1 + i) (4)

The first market

Sellers

The program for a seller in the first market is max

qs, s [-q s + W (m -1 + s + pq s , s )] s.t. -s ≤ m -1
wheres are deposits by the seller, p is the price of first-market goods and q s is the quantity sold by the seller. The first-order condition on q s is

W m p = 1 Using (4), it becomes φp = 1 (5)
The first-order condition on s can be written as

φi = µ s (6)
where µ s is the multiplier associated with the deposit constraint.

Buyers

Buyers set a threshold η * : If η ≤ η * , they consume the home good; if η > η * , they consume the foreign good. Denote as q h and q η f the consumption quantity of home goods and the consumption quantity of foreign goods, respectively. Denote as h the loan taken by a buyer who consumes the home good. Similarly, let η f the loan taken by a buyer with preference shock η = 0, η 1 , η 2 who consumes the foreign good (notice that, given preferences, q h and hence h do not depend on η). Since banks can distinguish domestic transactions from foreign transactions, they can potentially set different borrowing limits. Let ¯ f indicate the borrowing limit for the agent who travels and ¯ h indicate the borrowing limit for an agent who consumes in the home country.

The program for a buyer with η > η * is max

q η f , η f u q η f + (η -ε) q η f -c η f /p + W m -1 + η f -pq η f , η f s.t. q η f ≤ m -1 + η f /p, η f ≤ ¯ f
This buyer maximizes the utility from consuming q η f , net from the conversion cost on his good purchases εq η f and the banking cost c proportional to the real amount of loans taken for consumption of foreign goods. The first constraint is the cash constraint by which the buyer cannot spend more than his initial money holdings plus his borrowing. The second constraint is the borrowing constraint set by banks (to be determined below).

Using ( 4) and ( 5), the first-order condition on q η f is

u q η f + η = 1 + ε + µ η f /φ (7)
where µ η f is the multiplier associated with the cash constraint for a buyer with η > η * . The first-order condition on η f can be written as

u q η f + η -ε -c = 1 + i + λ η f /φ (8)
where λ η f is the multiplier associated with the borrowing constraint by the buyer with η > η * .

The program for a buyer with η ≤ η * is max

q h , h u (q h ) + W (m -1 + h -pq h , h ) s.t. q h ≤ (m -1 + h ) /p, h ≤ ¯ h
The first-order condition on q h is

u (q h ) = 1 + µ h /φ (9)
where µ h is the multiplier associated with the cash constraint by the buyer with

η ≤ η * .
The first-order condition on h for this buyer can be written as

u (q h ) = 1 + i + λ h /φ (10)
where λ h is the multiplier associated with the borrowing constraint by the buyer with η ≤ η * .

Market clearing

Market clearing in the loan market yields

(1 -b) s + b η≤η * π η h + b η>η * π η η f = 0 (11)
In addition, for sellers it is optimal to deposit their entire money holdings for γ ≥ 1, so m -1 =s . Using (11), this equality becomes

m -1 = b 1 -b η≤η * π η h + b 1 -b η>η * π η η f (12)
Since countries are symmetric, market clearing in the first market for goods yields

b η≤η * π η q h + b η>η * π η q η f = (1 -b) q s (13)

Marginal value of money

The expected utility for an agent who starts a period with m units of money is:

V (m) = b η≤η * π η [u (q h ) + W (m + h -q h , h )] + b η>η * π η u q η f + (η -ε) q η f -φ η f c + W m + η f -q η f , η f + (1 -b) [-q s + W (m + s + q s , s )]
Given assumptions on preferences, buyers are cash-constrained for all realizations of η if γ ≥ 1. Thus,

φ (m -1 + h ) = q h φ m -1 + η f = q η f (14)
Using ( 4), ( 6) and ( 9), the marginal value of money is:

∂V /∂m = bφ η≤η * π η u (q h ) + bφ η>η * π η u q η f + η -ε + (1 -b) φ (1 + i)
Using ( 2) and (3), this condition becomes:

γ/β = b η≤η * π η u (q h ) + b η>η * π η u q η f + η -ε + (1 -b) (1 + i) (15)
The left-hand side of this equation represents the marginal cost of acquiring an additional unit of money while the right-hand side represents its marginal benefit:

With probability b the agent consumes the home good (for η ≤ η * ) or the foreign good (for η > η * ), and with probability (1b) the agent is a seller and earns interests on his deposits.

Borrowing constraint

Banks do not have enforcement power. Therefore, banks must set a borrowing constraint which ensures voluntary debt repayment: They choose the amount of loans h and η f such that the pay-off to an agent who repays his debt is at least equal to the pay-off to a defaulter.

Denote as η * the threshold value of the preference shock η for an agent who has defaulted in the past. In periods in which η ≤ η * the defaulter consumes the home good, whereas in periods in which η > η * the defaulter consumes the foreign good.

Let V (m) indicate the expected utility for a defaulter who starts a period with m units of money. V (m) is

V (m) = b η≤η * π η [u (q h ) + xh ] + b η>η * u qη f + (η -ε) qη f + xη + (1 -b) (-q s + xs )
where xh , xη and xs are net consumption in the second market by the defaulter if he is buyer with η ≤ η * , if he is a buyer with η > η * , and if he is a seller, respectively.

Defaulters do not have access to the banking system. In addition, like nondefaulters, defaulters are cash-constrained for all realizations of η for γ ≥ 1. Thus, we can set qη h = qη f = q for all η. The amount of money balances that a defaulter holds at the end of each period is then determined by the following optimal condition:

γ/β = bu (q) + b η>η * π η (η -ε) + 1 -b (16)
Lemma 1 Borrowing limits set by banks satisfy ¯ h = ¯ η f for all η. The borrowing constraint set for agents who consume the home good can be written as

-φ [ h (1 + i) + m -1 ] + βb 1 -β    η≤η * π η [u (q h ) -q h ] + η>η * π η u q η f + (η -1 -ε) q η f -φ η f c    (17) ≥ βb 1 -β   u (q) -q + η>η * π η (η -ε) q  - (γ -β) q 1 -β
The left-hand side of the borrowing constraint in Lemma 1 represents the pay-off to an agent who does not default. In period t, this agent works to pay his loan with the corresponding interest and to recover his money holdings. From t + 1 on, his expected utility is determined by the net utility of consuming the foreign good (minus conversion costs and the banking cost associated with loans for foreign-goods consumption) each time he turns out to be a buyer with η > η * or the home good each time he turns out to be a buyer with η ≤ η * .

The right-hand side of the borrowing constraint represents the pay-off to a defaulter. If an agent defaults, he does not work to repay the loan taken at the beginning of t nor the interest on it. His expected lifetime utility is given by the net utility of consuming q as a buyer from t + 1 on, minus the cost of adjusting money holdings from t on, equal to (γβ) q/ (1β).

Travel decision

The non-defaulter sets the threshold η * such that the utility from staying in the home country (consuming the home good) is equal to the utility from traveling to the foreign country (consuming the foreign good). Thus, η * is determined by the following condition:

u (q h ) -φ h (1 + i) = u q η * f + q η * f (η * -ε) -φ η * f (1 + i + c) (18)
given that m -1 + hpq h = m -1 + η fpq η f = 0 for all η. The defaulter sets the threshold η * as follows u (q) = u (q) + (η *ε) q

given that m-1pq = 0 for all η. Hence,

η * = ε (19)
Definition 2 An equilibrium is a vector of consumption quantities, threshold values of the preference shock, interest rate, price of money, money holdings and loans

q h , q η f , q, η * , η * , i, φ, m -1 , h , η f for η ∈ {0, η 1 , η 2 } which satisfy m -1 = M -1 , (8),
and ( 12) -( 19). An equilibrium is unconstrained if the borrowing constraint ( 17)

is slack for all values of η. An equilibrium is fully constrained if the borrowing constraint ( 17) binds for all values of η.

Proposition 3 Assume that β > 1b. Then there is γ such that if γ ≥ γ, a unique unconstrained equilibrium exists.

According to Proposition 3, if the monetary growth rate is sufficiently high, then there is a unique equilibrium and this equilibrium is unconstrained: for all realizations of η, agents are able to borrow as much as they desire for the prevailing interest rate. This proposition states the usual result in monetary models with limited commitment12 . Since inflation punishes relatively more defaulters than nondefaulters, there is a level of inflation above which agents who choose to reimburse their loans are able to borrow their desired amount given equilibrium interest rates.

Proposition 4 There is γ1 , γ2 with γ1 < γ2 < γ such that if γ ∈ γ1 , γ2 a fully

constrained equilibrium exists. γ1 = 1 if c = 0 and γ1 > 1 if c > 0.
Conversely, if inflation is low enough a constrained equilibrium exists as stated in Proposition 4. In a constrained equilibrium, at the equilibrium interest rate buyers would like to borrow more than banks allow them to. According to Proposition 4, the interval of values of γ for which a constrained equilibrium exists depends on c.

If c = 0, then γ1 = 1. However, if c > 0 no equilibrium with credit exists at γ = 1, so γ1 > 1. The reason is that if c > 0 and γ = 1 financing good purchases through the banking system is too costly relatively to doing it by only holding outside money across periods. Since exclusion from the banking system imposes a mild punishment, incentives to default are too high and credit cannot be sustained in equilibrium.

The welfare effect of conversion costs

In this section, we analyze the effect of making currency exchange costly. As a benchmark, we first assess the effect of implementing conversion costs between the two currencies when agents are not borrowing constrained.

Proposition 5 In an unconstrained equilibrium, imposing positive conversion costs worsens welfare.

Proposition 5 states that imposing positive conversion costs is unambiguously detrimental to welfare if agents are not borrowing constrained. Thus, this proposition replicates a well-known result in monetary theory: Imposing a transaction cost on currency exchange makes agents less willing to trade. Since a conversion cost increases the marginal cost of purchasing goods, buyers choose to increase their marginal utility from consumption and hence consumption decreases.

The following proposition refers to the case in which agents are borrowingconstrained and financial integration among countries is perfect; i.e., c = 0.

Proposition 6 Let c = 0. Then in a fully constrained equilibrium imposing positive conversion costs is welfare worsening.

According to Proposition 6, imposing positive conversion costs is welfare worsening when financial markets of the two countries are perfectly integrated so that there are no borrowing cost associated with foreign-goods consumption. The intuition for this result is that non-defaulters who are consumers choose to travel if their preference shock η is equal or higher than the conversion cost ε; η * = ε. As a result, η * = η * ; i.e., non-defaulters consume the foreign good as often as defaulters. Thus, non-defaulters get punished by conversion costs as much as defaulters do. As when agents are unconstrained, the increase in conversion costs makes agents reduce their consumption and so it is unambigously detrimental to welfare.

Proposition 7 Assume π 1 > (1/β -1) π 2 . If c > η 1 / (1 -b)
, then there is γ2 with γ1 < γ2 ≤ γ2 such that for γ ∈ γ1 , γ2 in a fully constrained equilibrium imposing positive conversion costs improves welfare.

Proposition 7 states that imposing positive conversion costs is welfare improving if agents are credit-constrained and the banking cost associated with loans for foreign consumption is sufficiently high. If c is high enough, buyers' decision on how often to consume the foreign good relatively to consuming the home good is distorted.

If c > η 1 / (1b), buyers choose to consume the home good instead of the foreign good for η = η 1 in order to avoid the cost c. By contrast, defaulters do not have access to the banking system, so their decisions are not affected by this cost. Thus, defaulters choose to consume the foreign good whenever it provides them higher utility than the home good; i.e., for η = η 1 and η = η 2 . Since defaulters consume the foreign good more often than non-defaulters, an increase in conversion costs punishes them relatively more than non-defaulters. As a result, conversion costs make default less attractive. In equilibrium a higher provision of credit can be sustained thereby allowing higher consumption. However, since conversion costs still increase the marginal cost of purchasing goods from the buyers' point of view, it must be that π 1 > (1/β -1) π 2 so that this negative effect on trade is more than compensated by the effect of conversion costs on incentives to default. Intuitively, this condition states that the probability that all agents incur the conversion costs, π 2 , must be relatively low compared to the probability that only defaulters incur the conversion costs, π 1 . 13

Conversion costs and optimal inflation

Proposition 7 shows that under appropriate conditions strictly positive conversion costs -and thus multiple currencies-can relax borrowing constraints and improve welfare compared to the benchmark case of a uniform currency. One important insight of the analysis is that less-than-perfect credit integration is a necessary precondition for this welfare increasing effect.

It should be mentioned that these results are obtained taking as given the exogenous inflation rate (γ). However, previous studies of economies with credit and limited commitment have shown that inflation can be used to curb default incentives [START_REF] Aiyagari | Money and dynamic credit arrangements with private information[END_REF]Williamson, 2000, Corbae and[START_REF] Corbae | Decentralized credit and monetary exchange witwith public record keeping[END_REF]). The mechanism is that a positive inflation rate can hurt more defaulters that non-defaulters since the former are forced to rely on cash transactions to carry their future consumption plans while the latter are partially insulated from inflation through credit arrangements. 14

Given this, it is natural to ask whether strictly positive conversion costs are likely to be part of an optimal policy when society can use both instruments ( and γ) to mitigate the impact of the debt repayment constraint.

The simulation reported in figure 3 shows that there exist configurations for which positive conversion costs allow higher welfare than what can be attained by a policy of optimal inflation with no conversion costs. 15 The dotted line corresponds to welfare as a function of the inflation rate when there are no conversion costs.

13 If c > η2/ (1 -b) non-defaulters choose to consume the home good for all realizations of η and so this condition is no longer required.

14 In other words, in this type of environment default is a cash-intensive activity. A positive inflation rate thus acts as a tax that helps to discourage default. In the setup we consider, default is a conversion-intensive activity. 15 The figure is drawn with the specification u(q) = (q α )/α and parameters β = 0.7, b = 0.3, c = 0.25, η1 = 0.05, η2 = 0.2, π1 = 0.2, π2 = 0.01. It has been checked -using Mathematica-that the conditions required for the existence of the fully constrained equilibrium are satisfied for the range of inflation rates that is reported on the horizontal axis. Welfare is maximized at an optimal inflation rate γ * > 1. The solid line corresponds to welfare attained with small, but strictly positive conversion costs. Hence in this example, conversion costs and multiple currencies are optimal, even when choosing inflation optimally. 16

Relation to the literature

Our symmetric framework serves to underscore our contribution to the literature on currency and monetary unions. In particular, we abstract from any source of heterogeneity or asymmetric shocks, so that the type of tradeoffs emphasized in the literature on optimal currency areas do not arise in our setup [START_REF] Mundell | A theory of optimum currency areas[END_REF][START_REF] Grauwe | Economics of Monetary Union[END_REF]. Our work also differs from studies analyzing public authorities commitment issues, since we consider monetary authorities that are fully committed to a given exogenous inflation rate, and importantly implement the same policy in both countries. 17 For instance, it as been argued that countries that lack internal discipline can commit to monetary stability by joining a currency union with a 16 Of course, even though it is not straightforward from figure 3, the optimal inflation rate also depends on conversion costs. 17 However, our results do not hinge on exogenous inflation, and the effect of conversion costs that we identify does not disappear when inflation is chosen optimally (see section 5.1).

low-inflation anchor country [START_REF] Alesina | Currency unions[END_REF]. 18 On the other hand, some studies have shown that countries may fail to realize the mutual gains to a currency union since by deviating they can use inflation to tax the holding of the foreign holders of domestic currency [START_REF] Cooper | Commitment and the adoption of a common currency[END_REF]. 19 Another theme emphasized in the vast majority of studies on monetary unions relates to the interaction between monetary and fiscal policies, and how sustainability considerations dictate the type of objectives or constraints that must be imposed on decentralized fiscal authorities.

This surge of empirical and theoretical work was aimed at clarifying the terms of the debate on the Maastricht treaty and then on the fiscal and growth pact enacted by the EU. In particular, some argued that sustainability creates a free-rider problem as governments may be tempted to run fiscal deficits financed with others' members resources. Others argued that when default on public debt is not an option, a currency union may be unsustainable because it forbids over-indebted governments to devalue their own currency. 20

Our work is also related to a few papers analyzing the potential benefits of multiple monies when there is a commitment issue on the side of private agents rather than public authorities. Building on [START_REF] Ravikumar | A benefit of uniform currency? manuscript[END_REF], [START_REF] Kiyotaki | A cost of unified currency[END_REF] build a model to show that multiple currencies may be preferred to a common currency when it allows agents to enjoy the benefits of a greater degree of specialization in the production of goods. [START_REF] Kocherlakota | A signaling model of multiple monies[END_REF] provide a setup where multiple monies can be optimal because they allow agents to credibly signal private information concerning the type of goods (home vs. foreign) they prefer. We emphasize a distinct tradeoff, making the point that with imperfect credit integration a common currency can increase the outside option associated with default, and exacerbate agents' incentive to default on their bank loans.

18 See [START_REF] Clerc | To be or not to be in a monetary union: A synthesis[END_REF] for a synthesis combining stabilization and credibility considerations. 19 In a related vein, Liu and Shi ( 2010) build a search model of money with local congestion on the goods' markets to show that a currency area may not be implemented because with independent monetary policy a country can manipulate its exchange rate to change terms of trades in its favor. 20 See inter alia [START_REF] Buiter | Excessive deficits: Sense and nonsense in the Treaty of Maastrich[END_REF]Frankel (1993), Von Hagen and[START_REF] Hagen | Federalism, fiscal restraints, and European Monetary Union[END_REF], [START_REF] Cooper | Overturning mundell: fiscal policy in a monetary union[END_REF], [START_REF] Chari | On the need for fiscal constraints in a monetary union[END_REF]Kehoe (2007), Cooper, Kempf, and[START_REF] Cooper | Is it is or is it ain't my obligation? Regional debt in a fiscal federation[END_REF], Sargent (2012)

Conclusion

We have presented a two-country model with money and banks to analyze the conditions for the sustainability of a currency union. We stress the role played by limited credit market integration, that we capture by a difference between domestic and foreign loan management costs. In the model this wedge in management cost triggers a 'bank-induced' home-bias that distorts local consumption towards domestic products and settle the stage for our main result. Because defaulters are excluded from the consumption of banking services, their consumption is more balanced between regions of the zone. This explains why residents of one region may contemplate breaking the currency union by implementing conversion costs. In a situation of banking fragmentation an in conversion costs decreases the incentive to default by reducing the value of opportunities of foreign consumption. A banking union that unifies credit conditions across jurisdictions of the zone annihilates this effect.

Two main conclusions are noteworthy. Imperfect banking integration can feedback on the organization of the currency union and even threaten its integrity. This result is new in the theoretical literature analyzing the optimality ,or lack thereof, of currency unions. It may go a long way to explain the lesson taught by students of 19th century U.S. history that localized banking crisis threatened the organization of currency issuance [START_REF] Rockoff | Monetary Unions: Theory, History, Public choice, chapter How Long Did it Take the United States to Become an Optimal Currency Area[END_REF][START_REF] Rousseau | Politics on the road to the u.s. monetary union[END_REF]. [START_REF] White | The political economy of banking regulation, 1864-1933[END_REF] argues that during the 1890s differential regulatory treatment between types of banks by public authorities rationed the supply of banking services and stimulated lobbying in favor of a currency and banking reform. The existence of this feedback loop is also coherent with 19th century European evidence on the existence of a correlation between currency integration and banking market integration [START_REF] Cohen | The Geography of Money[END_REF][START_REF] Helleiner | The Making of National Money: Territorial Currencies in Historical Perspective[END_REF].

Another appealing feature of the analysis is that it suggests a novel connection between the degree of credit integration, the extent of local home-bias and the desirability (or, sustainability) of a currency union. This has two broad implications.

First -when applicable-moving towards deeper credit integration by reducing the underlying impediments to cross-border credit may be a necessary condition to fully reap the economic gains from a currency union. In that context the main goal to assign to a banking union consists in unifying the credit conditions among regions, in suppressing any regulatory-or politically-induced barriers to integration of lo-cal credit markets. Second, if credit integration remains insufficient, integration of the currency itself rather than fostering credit deepening may turn into a source of increased credit rationing on some borrowers, as banks behavior adapt to their borrowers' incentives to default. This potential issue may be more acute in times of crisis. if impediments to cross-border credit increase in times of crisis, credit constraints may react more strongly in a currency union.

Appendix

Proof of Lemma 1. When the settlement stages arrives, the pay-off to a buyer with preference given by η ≤ η * who repays his debt is:

x h + βb 1 -β    η≤η * π η [u (q h ) + x h ] + η>η * π η u q η f + (η -ε) q η f -φ η f c + x η    - β (1 -b) 1 -β (q s -x s )
where x h , x η and x s are net consumption by the buyer with η ≤ η * , the buyer with η > η * , and the seller, respectively. The pay-off to a defaulter with η ≤ η * is

xh + βb 1 -β    u (q) + η≤η * π η xh + η>η * π η (η -ε) qη f + xη    - β (1 -b) 1 -β (q s -xs )
where xh is net consumption by the defaulter with η ≤ η * in the period in which he defaults and xh , xη and xs are net consumption by the defaulter in subsequent periods in case he is a buyer with preference shock η ≤ η * , a buyer with preference shock η > η * , or a seller. In a symmetric equilibrium, m -1 = M -1 . Thus, net consumption quantities x h , x η and x s are

x h = -φ h (1 + i) -φm +1 + φT = -φ h (1 + i) -φm -1 x η = -φ η (1 + i) -φm +1 + φT = -φ η f (1 + i) -φm -1 x s = -φ s (1 + i) + φpq s -φm +1 + φT = -φ s i + q s (20)
Using ( 11), ( 12), ( 13) and ( 14

with φ m+1 = γφ m-1 = γ q. Using ( 20) and ( 21), the borrowing constraint for agents consume the home good can be rewritten as in ( 17). Analogously, the borrowing constraint for agents who consume the foreign good is 17) and ( 22), it follows that ¯ h = ¯ η f for all η.

-φ η f (1 + i) + m -1 (22) + βb 1 -β    η≤η * π η [u (q h ) -q h ] + η>η * π η u q η f + (η -1 -ε) q η f -φ η f c    ≥ βb 1 -β   u (q) -q + η>η * π η (η -ε) q  - (γ -β) q 1 -β From (
Proof of Proposition 3. Conjecture an unconstrained equilibrium by setting λ h = 0 and λ η f = 0 for all η > η * . From (15), it follows

γ/β -b η>η * π η c = 1 + i (23)
Thus, from ( 8) and (10) q h and q η f are immediatetly pinned down for a given value of γ. In addition, from (11), ( 12) and ( 14),

φ h = (1 -b) q h -b η>η * π η q η f -q h ( 24
)
and q h -φ h = q η f -φ η f for all η. By the mean value theorem, u (q h )-u (q)-q

h + q > [u (q h ) -1] (q h -q). Similarly, u q η f + (η -ε -1) q η f -u (q) -(η -ε -1) q > u q η f + η -ε -1 q η f -q .
Hence, a sufficient condition for the borrowing con-straint ( 17) to be non-binding is

-φ h i -q h - βb 1 -β η>η * π η φ η f c + βb 1 -β    η≤η * π η u (q h ) -1 (q h -q) + η>η * π u q η f + η -ε -1 q η f -q    ≥ - (γ -β) q 1 -β Since u (q h ) = u q η f + η -ε -c = 1 + i and q h -φ h = q η f -φ η f , this condition can be rewritten as -φ h i -q h + βbc 1 -β η>η * π η (q h -φ h ) + βbi 1 -β   η≤η * π η q h + η>η * π η q η f   ≥ - (γ -β) q 1 -β + βb -β   i + η>η * π η c   q
Using (23) and ( 24), it becomes

-(1 -b) q h i + b η>η * π η q η f -q h i -q h + βbc 1 -β η>η * bπ η   q h + η>η * π η q η f -q h   + βbi 1 -β   η≤η * π η q h + η>η * π η q η f   ≥ -βi 1 -b 1 -β q
Since the right-hand side in the above inequality is negative and q h < q η f , a sufficient condition for this inequality to hold is

-(1 -b) q h i -q h + βbc 1 -β η>η * bπ η q h + βbi 1 -β q h ≥ 0 Simplifying, βbc η>η * bπ η + (β + b -1) i ≥ 1 -β
Given (23), it follows that this inequality always holds if β > 1b and

γ ≥ βb β + b -1   1 -(1 -b) (1 -β) c η>η * π η  
If the borrowing constraint does not bind for any agent, (23) pins down i and hence q h and q η f for all η so the equilibrium is unique.

Proof of Proposition 4.

Case ε + (1 -b) c < η 1 .
Consider the borrowing constraint in and conjecture a fully constrained equilibrium. Since in this equilibrium all buyers are credit-constrained, let q denote q = q h = q 1 f = q 2 f . From ( 18), the threshold η * is determined by

η * = ε + (1 -b) c
Since η * < η 1 , ( 15) and ( 16) can be rewritten as follows:

γ/β -1 = b u (q) + π 1 (η 1 -ε) + π 2 (η 2 -ε) -1 + (1 -b) i (25)
whereas ( 16) is

γ/β -1 = b u (q) + π 1 (η 1 -ε) + π 2 (η 2 -ε) -1 (26)
In addition, rewrite (17) as follows:

i (1b) qq (27)

+ βb 1 -β {u (q) -q + π 1 (η 1 -ε) q + π 2 (η 2 -ε) q -(π 1 + π 2 ) (1 -b) cq} = βb 1 -β {u (q) + [-1 + π 1 (η 1 -ε) + π 2 (η 2 -ε)] q} - (γ -β) q 1 -β Differentiate (27) with respect to γ to get - ∂i ∂γ (1 -b) q -[i (1 -b) + 1] ∂q ∂γ + βb 1 -β u (q) -1 + π 1 (η 1 -ε) + π 2 (η 2 -ε) -(π 1 + π 2 ) (1 -b) c ∂q ∂γ = βb 1 -β u (q) -1 + π 1 (η 1 -ε) + π 2 (η 2 -ε) ∂ q ∂γ - γ -β 1 -β ∂ q ∂γ - q 1 -β
Since 1/β = bu (q) (∂q/∂γ) + (1b) (∂i/∂γ), we use ( 25) and ( 26) to get

∂q ∂γ = (1 -β) q/β - q (1 -β) bu (q) q + γ -1 -i (1 -b) -βb (π 1 + π 2 ) (1 -b) c and β (1 -b) ∂i ∂γ = γ -1 -i (1 -b) -βb (π 1 + π 2 ) (1 -b) c + βbu (q) q γ -1 -i (1 -b) -βb (π 1 + π 2 ) (1 -b) c + (1 -β) bu (q) q (28)
For a constrained equilibrium to exist, it must be that i ≥ 0, which implies q ≥ q given (25) and ( 26). Denote as γ1 the value of γ such that q = q in a fully constrained equilibrium. From ( 25) and ( 26), i = 0 at γ = γ1 . Thus, (27) γ1

satisfies γ1 = 1 + βb (π 1 + π 2 ) (1 -b) c.
From ( 27), we get

-i (1 -b) -1 = βb 1 -β u (q) + [-1 + π 1 (η 1 -ε) + π 2 (η 2 -ε)] q q - (γ -β) q/q 1 -β - βb 1 -β u (q) -q + π 1 (η 1 -ε) q + π 2 (η 2 -ε) q -(π 1 + π 2 ) (1 -b) cq q Therefore, γ -i (1 -b) -1 -βb (π 1 + π 2 ) (1 -b) c (29) = γ -βb (π 1 + π 2 ) (1 -b) c + βb 1 -β u (q) + [-1 + π 1 (η 1 -ε) + π 2 (η 2 -ε)] q q - (γ -β) q/q 1 -β - βb 1 -β u (q) -q + π 1 (η 1 -ε) q + π 2 (η 2 -ε) q -(π 1 + π 2 ) (1 -b) cq q
By the mean value theorem, u (q)u (q)q + q > [u (q) -1] (qq) for q > q.

Therefore, for q > q (or i > 0) we verify from (29) that

γ -i (1 -b) -1 -βb (π 1 + π 2 ) (1 -b) c < -β (1 -b) i q q so γ -i (1 -b) -1 -βb (π 1 + π 2 ) (1 -b) c is unambiguously negative for i > 0 and
given γ1 it is equal to zero for i = 0. Therefore, from (28) it follows that ∂i/∂γ > 0 for i > 0 provided that the borrowing constraint binds. At γ = γ1 , i = 0 by definition of γ1 . Therefore, from (28) ∂i/∂γ > 0 at γ = γ1 and so i > 0 at γ slightly higher than γ1 . In turn, this implies that

γ -i (1 -b) -1 -βb (π 1 + π 2 ) (1 -b) c is
negative for γ slightly higher than γ1 and hence it follows from (28) that ∂i/∂γ > 0 at γ slightly higher than γ1 . Therefore, i > 0 for γ even higher. Hence there is an interval γ1 , γ2 such that if γ ∈ γ1 , γ2 then i ≥ 0 and so a constrained equilibrium exists.

Case

η 1 -ε < (1 -b) c < η 2 -ε.
Consider the borrowing constraint in ( 17) and conjecture a fully constrained equilibrium. Since in this equilibrium all buyers are credit-constrained, let q denote q = q h = q 1 f = q 2 f . From ( 18), the threshold η * is determined by

η * = ε + (1 -b) c
Since η 1 < η * < η 2 , (15) can be rewritten as:

γ/β = bu (q) + bπ 2 (η 2 -+ (1 -b) (1 + i) (30)
Money holdings by defaulters are determined by

γ/β -1 = b u (q) + π 1 (η 1 -ε) + π 2 (η 2 -ε) -1 (31)
In addition, rewrite (17) as follows:

-

i (1 -b) q -q + βb 1 -β {u (q) -q + π 2 [η 2 -ε -(1 -b) c] q} (32) = βb 1 -β {u (q) + [-1 + π 1 (η 1 -ε) + π 2 (η 2 -ε)] q} - (γ -β) q 1 -β Differentiate (32) with respect to γ to get - ∂i ∂γ (1 -b) q -[i (1 -b) + 1] ∂q ∂γ + βb 1 -β u (q) -1 + π 2 [η 2 -ε -(1 -b) c] ∂q ∂γ = βb 1 -β u (q) -1 + π 1 (η 1 -ε) + π 2 (η 2 -ε) ∂ q ∂γ - γ -β 1 -β ∂ q ∂γ - q 1 -β
Since 1/β = bu (q) (∂q/∂γ) + (1b) (∂i/∂γ), use ( 30) and (31) to get

∂q ∂γ = (1 -β) q/β - q (1 -β) bqu (q) + γ -1 -(1 -b) i -βbπ 2 (1 -b) c and (1 -b) β ∂i ∂γ = βbu (q) q + γ -1 -(1 -b) i -βbπ 2 (1 -b) c (1 -β) bu (q) q + γ -1 -(1 -b) i -βbπ 2 (1 -b) c (33)
For a constrained equilibrium to exist, it must be that i ≥ 0. As in the case ε + (1b) c < η 1 , let γ1 denote the value of γ such that q = q in a fully constrained equilibrium. From ( 30) and ( 31)

, at γ = γ1 (1 -b) i = bπ 1 (η 1 -ε) so that i > 0.
Thus, from (32), in this case γ1 satisfies γ1 = 1

+ βbπ 2 (1 -b) c + bπ 1 (η 1 -ε).
From (32), we get

-i (1 -b) -1 = βb 1 -β u (q) + [-1 + π 1 (η 1 -ε) + π 2 (η 2 -ε)] q q - (γ -β) q/q 1 -β - βb 1 -β u (q) -q + π 2 [η 2 -ε -(1 -b) c] q q Therefore, γ -i (1 -b) -1 -βbπ 2 (1 -b) c (34) = γ -βbπ 2 (1 -b) c + βb 1 -β u (q) + [-1 + π 1 (η 1 -ε) + π 2 (η 2 -ε)] q q - (γ -β) q/q 1 -β - βb 1 -β u (q) -q + π [η 2 -ε -(1 -b) c] q q
By the mean value theorem, u (q)u (q)q + q > [u (q) -1] (qq) for q > q.

Therefore, for q > q (or i > bπ 2 (η 2ε) / (1b)) we verify from (34) that

γ -i (1 -b) -1 -βbπ 2 (1 -b) c < β [bπ 1 (η 1 -ε) -(1 -b) i] q/q (35)
The right-hand side in ( 35) is negative for q > q (or bπ

1 (η 1 -ε) < (1 -b) i) and
it is equal to zero at γ = γ1 ; i.e., for q = q (or (1

-b) i = bπ 1 (η 1 -ε)).Therefore γ -i (1 -b) -1 -βbπ 2 (1 -b) c
is unambiguously negative for q > q and it is equal to zero at γ = γ1 . Hence from (33) ∂i/∂γ > 0 at γ = γ1 so i > bπ 1 (η 1ε) / (1b) > 0 at γ slightly higher than γ1 . In turn, this implies that γ-i (1b)-1-βbπ 2 (1b) c is negative for γ slightly higher than γ1 and hence it follows from (33) that ∂i/∂γ > 0 at γ slightly higher than γ1 . Therefore, i > bπ 1 (η 1ε) / (1b) > 0 for γ even higher. Hence there is an interval γ1 , γ2 such that if γ ∈ γ1 , γ2 then i ≥ 0 and so a constrained equilibrium exists. Notice from (32) that given assumptions on c at γ = 1 there is no equilibrium with credit.

Case η 2 -ε < (1 -b) c.
Consider the borrowing constraint in (17) and conjecture a fully constrained equilibrium. Since in this equilibrium all buyers are credit-constrained, let q denote q = q h = q 1 f = q 2 f . From (18), the threshold η * is determined by

η * = ε + (1 -b) c
Since η * > η 2 , (15) can be rewritten as:

γ/β = bu (q) + (1 -b) (1 + i) (36)
Money holdings by defaulters are determined by

γ/β -1 = b u (q) + π 1 (η 1 -ε) + π 2 (η 2 -ε) -1 (37)
In addition, rewrite (17) as follows:

- 36) and (37) to get

i (1 -b) q -q + βb 1 -β [u (q) -q] (38) = βb 1 -β {u (q) + [-1 + π 1 (η 1 -ε) + π 2 (η 2 -ε)] q} - (γ -β) q 1 -β Differentiate (38) with respect to γ to get ∂i ∂γ (1 -b) q -[i (1 -b) + 1] ∂q ∂γ + βb 1 -β u (q) -1 ∂q ∂γ = βb 1 -β u (q) -1 + π 1 (η 1 -ε) + π 2 (η 2 -ε) ∂ q ∂γ - γ -β 1 -β ∂ q ∂γ - q 1 -β Since 1/β = bu (q) (∂q/∂γ) + (1 -b) (∂i/∂γ), use (
∂q ∂γ = (1 -β) q/β - q (1 -β) bqu (q) + γ -1 -(1 -b) i and (1 -b) β ∂i ∂γ = βbu (q) q + γ -1 -(1 -b) i (1 -β) bu (q) q + γ -1 -(1 -b) i (39)
For a constrained equilibrium to exist, it must be that i ≥ 0. As in previous cases, let γ1 denote the value of γ such that q = q in a fully constrained equilibrium.

From ( 36) and (37), at γ = γ1 (1b) i = bπ 1 (η 1ε) + bπ 2 (η 2ε) so that i > 0.

From (38), in this case γ1 satisfies γ1 = 1 + bπ 2 (η 2ε) + bπ 1 (η 1ε).

From (38), we get

-i (1 -b) -1 = βb 1 -β u (q) + [-1 + π 1 (η 1 -ε) + π 2 (η 2 -ε)] q q - (γ -β) q/q 1 -β - βb 1 -β u (q) -q q Therefore, γ -i (1 -b) -1 (40) = γ + βb 1 -β u (q) + [-1 + π 1 (η 1 -ε) + π 2 (η 2 -ε)] q q - (γ -β) q/q 1 -β - βb 1 -β u (q) -q q
By the mean value theorem, u (q)u (q)q + q > [u (q) -1] (qq) for q > q.

Therefore, for q > q (or i

> b [π 1 (η 1 -ε) + π 2 (η 2 -ε)] / (1 -b)) we verify from (40) that γ -1 -(1 -b) i < β [-(1 -b) i + 1 (η 1 -ε) + bπ 2 (η 2 -ε)] q q (41)
The right-hand side in (41) is negative for q > q (or bπ 1 (η

1 -ε) + bπ 2 (η 2 -ε) < (1 -b) i
) and it is equal to zero at γ = γ1 ; i.e., for q = q (or (1

-b) i = bπ 1 (η 1 -ε) + bπ 2 (η 2 -ε)).Therefore γ -1 -i (1 -b) is unambiguously negative for q > q and
it is equal to zero at γ = γ1 . Hence from (39) ∂i/∂γ > 0 at γ = γ1 so i

> b [π 1 (η 1 -ε) + π 2 (η 2 -ε)] / (1 -b
) > 0 at γ slightly higher than γ1 . In turn, this implies that γ -1i (1b) is negative for γ slightly higher than γ1 and hence it follows from (39) that ∂i/∂γ > 0 at γ slightly higher than γ1 . Therefore, i >

b [π 1 (η 1 -ε) + π 2 (η 2 -ε)] / (1 -
b) > 0 for γ even higher. Hence there is an interval γ1 , γ2 such that if γ ∈ γ1 , γ2 then i ≥ 0 and so a constrained equilibrium exists.

Notice from (38) that given assumptions on c at γ = 1 there is no equilibrium with credit.

Proof of Proposition 5. In an unconstrained equilibrium all agents borrow as much as they desire. Since λ h = λ η f = 0, (8) and (10) become

u (q h ) = 1 + i u q η f + η -ε -c = 1 + i (42) Therefore (15) becomes γ/β = u q η f + η -ε -   b η≤η * π η + 1 -b   c Hence ∂q η f /∂ε = 1/u q η f ( 43
)
so that q η f is decreasing in ε. From ( 42) and ( 43), ∂q h /∂ε = 0. Therefore, an increase in ε decreases agents' expected lifetime utility.

Proof of Proposition 6. Let c = 0 and consider a fully constrained equilibrium in which λ h , λ η f > 0 and the borrowing constraint (17) holds with equality. Thus, we can set φ h = φ η f = φ and q h = q η f = q for all η. From ( 11), ( 12) and ( 14) φ = (1b) q and φm -1 = bq. From (18), η * = ε if c = 0. Rewrite the borrowing constraint ( 17) by setting c = 0 and η 2 > η 1 > ε:

-

[1 + (1 -b) i] q + βb 1 -β {u (q) -q + [π 1 (η 1 -ε) + π 2 (η 2 -ε)] q} (44) = βb 1 β {u (q) -q + [π 1 (η 1 -ε) + π 2 (η 2 -ε)] q} - (γ -β) q 1 -β Differentiate with respect to ε to get -[1 + (1 -b) i] ∂q ∂ε -(1 -b) ∂i ∂ε q - βb (π 1 + π 2 ) 1 -β q (45) + βb 1 -β u (q) -1 + π 1 (η 1 -ε) + π 2 (η 2 -ε) ∂q ∂ε = βb 1 -β u (q) -1 + π 1 (η 1 -ε) + π 2 (η 2 -ε) ∂ q ∂ε - βb (π 1 + π 2 ) 1 -β q - γ -β 1 -β ∂ q ∂ε
Rewrite ( 15) and ( 16) as follows

γ/β = bu (q) -b + b [π 1 (η 1 -ε) + π 2 (η 2 -ε)] + 1 + (1 -b) i (46) γ/β = bu (q) -b + b [π 1 (η 1 -ε) + π 2 (η 2 -ε)] + 1 (47)
Differentiating ( 46) with respect to ε yields (1b) (∂i/∂ε) = -bu (q) (∂q/∂ε) + b (π 1 + π 2 ). Rewrite (45) using ( 46) and (47) to get

∂q ∂ε = b (π 1 + π 2 ) [(1 -β) q + β (q -q)] γ -1 -(1 -b) i + (1 -β) bqu (q) (48)
From ( 46) and ( 47), q = q when i = 0 and q > q when i > 0. From Proposition 4, when c = 0 the value of γ such that i = 0 and q = q, γ1 , is γ1 = 1 and q ≥ q for γ ∈ γ1 , γ2 . Therefore, the numerator at the right-hand side in (48) is positive for γ ∈ 1, γ2 . A sufficient condition for the denominator to be negative is that 44), when the borrowing constraint binds γ -1 -

γ -1 -(1 -b) i ≤ 0. From (
(1 -b) i is γ -1 -(1 -b) i = -β (1 -b) i
+ βb [u (q)u (q)] -{γβ + βb [π 1 (η 1ε) + π 2 (η 2ε) -1]} (qq)

Since q ≥ q and i ≥ 0 for γ ∈ 1, γ2 , it follows that γ -1i (1b) ≤ 0 for γ ∈ 1, γ2 . Thus, the denominator at right-hand side in (48) is negative. It follows that in a fully constrained equilibrium ∂q/∂ε < 0 for γ ∈ 1, γ2 .

Proof of Proposition 7. Consider a fully constrained equilibrium in which λ h , λ η f > 0 and the borrowing constraint (17) holds with equality. It follows that q h = q η f = q and φ h = φ η f = φ for all η. Thus, from ( 11), ( 12) and ( 14) φ = (1b) q and φm -1 = bq. From (18), η * = ε + (1b) c.

Case ε < η 1 < ε + (1 -b) c < η 2 .
Rewrite the borrowing constraint (17) as follows:

-[(1 -b) i + 1] q + βb 1 -β {u (q) -q + π 2 [η 2 -ε -(1 -b) c] q} (49)
= βb 1β {u (q)q + [π 1 (η 1ε) + π 2 (η 2ε)] q} -(γβ) q 1β where (19) has been used. Differentiate with respect to ε to get

-(1 -b) ∂i ∂ε q - βb 1 -β [π 2 q -(π 1 + π 2 ) q] (50) -[1 + (1 -b) i] ∂q ∂ε + βb 1 -β u (q) -1 + π 2 [η 2 -ε -(1 -b) c] ∂q ∂ε = βb 1 -β u (q) -1 + [π 1 (η 1 -ε) + π 2 (η 2 -ε)] ∂ q ∂ε - γ -β 1 -β ∂ q ∂ε
Rewrite (15) and ( 16) as follows γ/β = b u (q) -1 + π 2 (η 2ε) + 1 + (1b) i (51)

γ/β = b u (q) -1 + π 1 (η 1ε) + π 2 (η 2ε) + 1 (52) Differentiating (51) with respect to ε yields (1b) (∂i/∂ε) = -bu (q) (∂q/∂ε) + bπ 2 . Using (51) and ( 52), (50) becomes

∂q ∂ε = bπ 2 q + βb [π 2 q -(π 1 + π 2 ) q] / (1 -β) bu (q) q + [γ -1 -(1 -b) i -βb (1 -b) π 2 c] / (1 -β) (53)
A sufficient condition for the denominator in (53) to be negative is that γ - 49), when the borrowing constraint binds

1 -(1 -b) i -βb (1 -b) π 2 c ≤ 0. From (
γ -1 -(1 -b) i -βb (1 -b) π 2 c is γ -1 -(1 -b) i -βb (1 -b) π 2 c (54)
= -β (1b) i + βb [u (q)u (q)] -{γβ + βb [π 2 (η 2ε) -1]} (qq) q + βbπ 1 (η 1ε) q/q From Proof of Proposition 4, when η 1 < ε + (1b) c the value of γ such that q = q, γ1 , is γ1 = 1 + βbπ 2 (1b) c + bπ 1 (η 1ε). In addition, q ≥ q and i ≥ bπ 2 (η 2ε) / (1b) for γ ∈ γ1 , γ2 . Therefore, given (54) γ -1 -(1b) iβb (1b) π 2 c ≤ 0 for γ ∈ γ1 , γ2 . Thus, the denominator at the right-hand side of (53) is negative.

For γ = γ1 , q = q and so the numerator at the right-hand side of ( 53) is negative since π 2βπ 1 / (1β) < 0. Therefore, ∂q/∂ε > 0 at γ = γ1 . However, since q is increasing in ε as long as the numerator at the right-hand side of ( 53) is positive and q is decreasing in ε given (52), the numerator at the right-hand side of ( 53) is increasing in ε. Define γ2 the value of γ such that for {q, q, i} which satisfy ( 49), ( 51) and ( 52) the numerator at the right-hand side of ( 53) is zero. In addition, let γ2 = min γ2 , γ2 . Then ∂q/∂ε > 0 for γ ∈ γ1 , γ2 and so in a fully constrained equilibrium conversion costs increase agents' lifetime utility.

Case ε < η 1 < η 2 < ε + (1 -b) c. Assume that η 2 ≤ η with bη = u (q) -u (bq) q -(1 -b) u (q) (55)
(55) obtains from (18) if it is assumed that agents do not resort to banks for foreigngood consumption in a fully constrained equilibrium.Therefore, assuming η 2 ≤ η allows to dismiss the case in which agents would choose to consume the foreign good without resorting to banks in a fully constrained equilibrium. Rewrite the borrowing constraint (17) as follows:

-

[(1 -b) i + 1] q + βb 1 -β [u (q) -q] (56) = βb 1 -β {u (q) -q + [π 1 (η 1 -ε) + π 2 (η 2 -ε)] q} - (γ -β) q 1 -β
where (19) has been used. Differentiate with respect to ε to get

-(1 -b) ∂i ∂ε q + βb 1 -β (π 1 + π 2 ) q (57) -[1 + (1 -b) i] ∂q ∂ε + βb 1 -β u (q) -1 ∂q ∂ε = βb 1 -β u (q) -1 + [π 1 (η 1 -ε) + π 2 (η 2 -ε)] ∂ q ∂ε - γ -β 1 -β ∂ q ∂ε
Rewrite (15) as follows γ/β = b u (q) -1 + 1 + (1b) i (58) whereas money holdings by defaulters are determined by

γ/β = bu (q) -b + b [π 1 (η 1 -ε) + π 2 (η 2 -ε)] + 1 (59)
Differentiating ( 38) with respect to ε yields (1b) (∂i/∂ε) = -bu (q) (∂q/∂ε). Using ( 58) and ( 59) and, (57) becomes

∂q ∂ε = -βb (π 1 + π 2 ) q/ (1 -β) bu (q) q + [γ -1 -i (1 -b)] / (1 -β) (60)
A sufficient condition for the denominator at the right-hand side of (60) to be negative is that γ -1 -(1b) i ≤ 0. From (56), when the borrowing constraint binds

γ -1 -(1 -b) i is γ -1 -(1 -b) i (61) = -β (1 -b) i + βb [π 1 (η 1 -ε) + π 2 (η 2 -ε)] q/q + βb [u (q) -u (q)] -(γ -β + βb) (q -q) q
From Proof of Proposition 4, when ε + (1b) c < η 2 the value of γ such that q = q, γ1 , is γ1 = 1 + bπ 1 (η 2ε) + bπ 2 (η 2ε). In addition, q ≥ q and i ≥ b [π 1 (η 1ε) + π 2 (η 2ε)] / (1b) for γ ∈ γ1 , γ2 . Therefore, given (61) γ -1 -(1b) i ≤ 0 for γ ∈ γ1 , γ2 . Thus, the denominator at the right-hand side of (60) is negative. Since the numerator at the right-hand side of (60) is always negative, it follows that ∂q/∂ε > 0 for γ ∈ γ1 , γ2 and so in a fully constrained equilibrium conversion costs increase agents' lifetime utility.

7

  [START_REF] Kalemli-Ozcan | What lies beneath the euro's effect on financial integration? currency risk, legal harmonization, or trade?[END_REF] exploit differences in the timing of the transposition of European

Figure 1 :

 1 Figure1: Home bias in banking system, Euro area countries versus control countries (U.S., U.K., Sweden, Denmark, Switzerland). Source:Manna (2011, p. 11)

Figure 2 :

 2 Figure 2: Sequence within a period

Figure 3 :

 3 Figure 3: Welfare as a function of inflation with and without conversion costs. (dotted line: = 0; solid line; = 0.01)

  ), we verify the market clearing condition in the second market b η≤η * π η x h + b η>η * π η x η + (1b) x s = 0 Net consumption quantities by the defaulter xh , xh , xη and xs are xh = xh = xη = -φ m+1 xs = xη + φ m-1 + q s

See for instance[START_REF] Beck | Banking Union for Europe: Risks and Challenges[END_REF],[START_REF] Nieto | Will bank supervision in Ohio and Austria be similar? a transatlantic view of the Single Supervisory Mechanism[END_REF].

The U.S. experience during the 19th century exemplifies the distinction between a currency union and a full-fledged monetary union. The dollar currency was created after independence but

Alternatively, the cost c could be rationalized by a different set of assumptions. Assume that banks can only identify residents (the cost to identify a non-resident is infinite) and that agents can contact a bank located at their country regardless of their location. Then the cost c will be the cost that a home agent who travels incurs in order to contact a home bank from abroad. A third possibility is to assume that banks are able to keep track of the location at which agents purchase goods, which happens if agents pay their purchases using a debit card, as in[START_REF] He | Money, banking & monetary policy[END_REF]. This would allow banks to transfer a cost c to customers whenever they consume abroad.

See Aiyagari and Williamson (2000),[START_REF] Corbae | Decentralized credit and monetary exchange witwith public record keeping[END_REF],[START_REF] Berentsen | Money, credit and banking[END_REF],[START_REF] Gomis-Porqueras | Optimal monetary policy in a model of money and credit[END_REF].


Malika Leneuve-Dorilas

Anne Favre

Gabriel Carles

Alphonse Louis

Mathieu Nacher

RISK FACTORS FOR PREMATURE BIRTH IN FRENCH GUIANA: The importance of reducing health inequalities

French Guiana has the highest birth rate in South America. This French territory also has the highest premature birth rate and perinatal mortality rate of all French territories.

The objective was to determine the premature birth rate and to identify the prevalence of risk factors of premature birth in French Guiana.

A retrospective study of all births in French Guiana was conducted between January 2013 to December 2014 using the computerized registry compiling all live births over 22 weeks of gestation on the territory.

During this period 12 983 live births were reported on the territory. 13.5% of newborns were born before 37 WG (1 755/12 983). The study of the registry revealed that common sociodemographic risk factors of prematurity were present. In addition, past obstetrical history was also important : a scarred uterus increased the risk of prematurity adjusted odds ratio=1.4. 95%CI [1.2-1.6]). Similarly, obstetrical surveillance, the absence of preparation for birth or of prenatal interview increased the risk of prematurity by 2.4 and 2.3, the excess fraction in the population was 69% and 72.2%, respectively.

Known classical risk factors are important. The present study allowed to calculate excess fractions in order to prioritize interventions to reduce the prematurity rate.

In most industrialized countries. prematurity has increased during the past 3 decades. [START_REF] Lacroze | Prématurité : définitions, épidémiologie, étiopathogénie, organisation des soins[END_REF] In these countries. 5 to 11 % of children are born before term (<37 weeks of amenorrhea (WA)). with an increasing rate since the early 1980's. [START_REF] Wen | Epidemiology of preterm birth and neonatal outcome. Seminars in Fetal and Neonatal Medicine[END_REF] The frequency of premature labor is estimated between 12 and 13 % in the USA and between 5 and 7 % in Europe. [START_REF] Ancel | Une fréquence en augmentation: Épidémiologie de la prématurité[END_REF] Premature births are important contributors to neonatal morbidity and mortality. and are the cause of nearly 50 % of perinatal handicaps which. in France. represents 3 500 children each year. [START_REF] Ancel | Une fréquence en augmentation: Épidémiologie de la prématurité[END_REF] Whether prematurity is spontaneous or induced. it is presently admitted that its causes are heterogeneous. Certain studies have listed several risk factors such as maternal age <18 years. addictions. low educational level. low socio-economic level. single parenthood. black populations. low body mass index. parodontal disease. a low intergenesic interval. prior prematurity. and multiple pregnancies. Certain obstetrical complications are strongly associated with prematurity such as hypertension and pre-eclampsia, diabetes. general or loco-regional infection.(1) (4) (5) (6) [START_REF] Macdorman | Race and Ethnic Disparities in Fetal Mortality, Preterm Birth, and Infant Mortality in the United States: An Overview[END_REF] There are marked disparities between mainland France and French overseas territories French Guiana. Guadeloupe and Reunion island. According to the national perinatal survey in 2010. these disparities are particularly marked for prematurity with a twofold increase in French overseas territories relative to mainland France : 7.4% in mainland France versus 15.4% in the overseas territories (out of 514 births in the overseas territories for this study). [START_REF]La situation périnatale en France en 2010 -Premiers résultats de l'enquête nationale périnatale -Etude et résultats[END_REF] Situated on the North Eastern part of the South American continent 7 100 km from Paris, French Guiana has an ethnically and socioeconomically diverse population of 250 000 persons living on a 83 846 km² territory (the size of Portugal) [START_REF] Montabo | Le grand livre de l'histoire de la Guyane: Des origines à 1848[END_REF] . On average, there are 6 500 births per year (26 per 1000 and 88% of births out of wedlock) which makes it the French territory with the second highest birth rate after Mayotte and the highest birth rate in South America. In French Guiana there is one level III obstetrics ward, and 2 level II wards. Given the marked isolation of certain towns that can only be accessed by air or by boat, there are 23 mother and child care centers and 21 health centers that are administered by Cayenne hospital.

In these structures, midwives are not present full time and deliveries cannot guaranty the safety of the mother and newborn child. Thus, since 1994 itinerant obstetrical consultations have been organized and in utero transfers to the nearest hospital have become policy. Women are transferred at a term of 37 weeks in order to deliver in a hospital, and if there is any obstetrical pathology women are transferred to the sole level III obstetrical ward of French Guiana, located in Cayenne.

The pregnancy outcome registry was created in 1992 and allowed to quantify premature births on the territory of French Guiana. Since its creation the registry has shown a stable proportion of premature births in French Guiana around 13.5% which is nearly double the 7% reported in mainland France [START_REF] Cardoso | Périnatalité en Guyane française: Evolution de 1992 à 1999[END_REF] .

Apart from known risk factors, French Guiana also has specificities that may explain this higher prematurity rate : unemployment (a quarter of the active population has no employment), insufficient pregnancy surveillance, the frequency of teen pregnancies (7% of all births), the frequency of anemia with 70% of pregnant women concerned in Western French Guiana, and dengue epidemics. [START_REF] Basurko | Maternal and foetal consequences of dengue fever during pregnancy[END_REF] The relative impact of the above factors results from a combination of their frequency and the strength of their link with prematurity. The relative ranking of these factors is not known in French Guiana. Given the numerous particularities of the territory, and given the absence of reduction of the prematurity rate, the present study aimed to determine the risk factors of prematurity in French Guiana and to obtain excess fractions in order to help identify priorities in order to reduce the high prematurity rate.

METHODS

Study site. This retrospective study took place in all health structures in French Guiana. Data collection. The exhaustive data from the delivery registry (RIGI (Registre d'Issue de Grossesses Informatisé managed by the Reseau Perinat, a network of health professionnals around perinatality)) was studied for a period of 2 years from January first 2013 to December 31 st 2014. Premature births occurring after the 22 WA fetal viability threshold were tallied. The data was entered in the delivery wards by the midwives who deliver the babies. The data management was performed by the mother and child care (PMI) center and the health regional agency.

Recommendations for pregnancy follow up in French Guiana

In France, seven prenatal visits are recommended, one of which should be in the first trimester, then followed by one visit every month after the third trimester. Three obstetrical ultrasonographies are recommended during the follow up, one at each trimester. A prenatal interview is systematically proposed either individually or as a couple during the first trimester of pregnancy. This prenatal interview is recommended by the Health authorities since 2005. This interview is not a medical obstetrical consultation. The objective of this interview is to identify vulnerability situations and to orient women towards specialized support, to give information on risk factors, risk behaviours, and nearby resources. [START_REF] Ehrenthal | A population study of the contribution of medical comorbidity to the risk of prematurity in blacks[END_REF] Preparation for birth was historically focused on relieving pain. However, it is now oriented towards global accompaniment of women and couples. In France, 8 prenatal sessions are reimbursed by health insurance. The preparation for birth has the objective of letting women express their needs, to evaluate parental knowledge, to explain the course of pregnancy, delivery and post partum. It contributes to the identification of early symptoms and warning signs that should motivate an urgent consultation. ( 12) Data analysis A descriptive analysis was first performed looking at each variable individually (distribution. summary statistics) then cross tabulating pertinent variables. Births were classified as premature or not. The distribution of medical or socioeconomic variables was studied across the groups defined by the main outcome. Qualitative variables were compared using a Chi square test or Fischer's exact test where appropriate. Quantitative variables were compared using Student's t-test or non parametric tests when variables where non Gaussian or if variances were heteroscedastic. Crude odds ratios and adjusted odds ratios were computed using prematurity as the outcome variable and different predictors as independent variables. Although attributable fractions are often used for causal biological exposures, they may also be computed for retrospective studies that cannot prove causation. [START_REF] Taylor | Simple Estimation of Population Attributable Risk from Case-Control Studies[END_REF] In this context where causation cannot be firmly established, it has been suggested that excess fraction should be used instead of attributable fraction. ( 14) Thus, excess fractions in the exposed and in the population were computed in order to determine the most important variables. Multivariate analysis was performed to adjust for potential confounding. The variables selected in the model were those known to be associated with prematurity in the medical literature and those significantly linked in the bivariate analysis. The statistical significance threshold was p<0.05. The data was analyzed with R and Stata. Regulatory and ethical aspects. The data base has been approved since 1992 by the Commission Nationale Informatique et Libertés, the French Structure that overseas medical research data and projects.

RESULTS

Socio-demographic data

From January 2013 to December 2014, 12 983 births > 22 WA were notified in French Guiana. The mean age of the study population was 27.5 years (median 27 years, range 12 -52 years). Minors (< 18 years) represented 6.2% of the study population (803 /12 983) and women over 40 years. 4.5% (588/12 983). The natives of French Guiana were the most represented population, 40.6% (5 266/12 983). followed by Surinamese 22.2% (2 888/12 983) and Haitian nationals 12.9% (1 679/12 983). Brazilian natives represented 8% of the study population (1 038/12 983).

The surface of French Guiana being covered by 90% of equatorial forest, populations living in the interior face relative isolation from health and social structures. Figure 1 shows the map of the administrative origin of women in the Study:

-Central Coastal in green (6 communes)

Risk factors for prematurity

Table 1 shows the prematurity risk factors. Being under 18 years was associated with preterm delivery in the bivariate analysis but not in the multivariate. However, when looking at younger age groups (<16 years) a young age was associated with an increased risk of prematurity AOR=1.5 [95%CI=1.02-2.12], p = 0.04.

On the study sample, age was associated with preterm birth. Although 16.1% of those< 18 years delivered prematurely, this was not significantly associated with prematurity in the multivariate model. Having an age 40 and above was significantly associated with preterm birth. The mother's birth place was significantly associated with preterm birth in the bivariate analysis, with women born in Suriname at greater risk of preterm delivery OR =1.5, 95%CI= [1. [START_REF] Lacroze | Prématurité : définitions, épidémiologie, étiopathogénie, organisation des soins[END_REF][START_REF] Wen | Epidemiology of preterm birth and neonatal outcome. Seminars in Fetal and Neonatal Medicine[END_REF]. The place of residence was also a significant risk factor for preterm birth (p<0.0001), after adjusting for age, birth place, family situation, profession and health insurance situation. The generation of an interaction term between Suriname and Saint Laurent du Maroni (where most Surinamese women are seen) was not significantly associated with the outcome in the multivariate model and was thus removed from the final model. Table 2 shows the medical and obstetrical risk factors for premature delivery.

Grand multigravida and grand multipara were significantly linked to preterm birth in the bivariate analysis OR= 1.2 [95%CI=1.1-1.3] and 1.3 [95%CI=1.2-1.5].

An early pregnancy follow up with a first prenatal visit during the first trimester was associated with a lower risk of preterm delivery in the bivariate analysis. Similarly, having benefitted from preparation for birth programme, and a prenatal interview were associated with a lower risk of premature birth.

Table 3 shows the prevalence of various pathologies among the studied women and their associated risk factors for premature delivery, with preeclampsia the pathology with the highest crude and associated odds ratios. Table 4 shows the crude excess fractions in the exposed and in the population. The absence of prenatal interview and the absence of preparation for birth had by far the highest excess fractions among the explored risk factors.

DISCUSSION

The present study identified a number of predictors of premature delivery in French Guiana. Most of these predictors are known risk factors for premature delivery. Here, in the special context of French Guiana we used excess fractions to rank the factors in terms of their potential impact, and their changeability. Thus the main message from this analysis would be that most of the progress against premature delivery could be achieved by proper follow up of pregnancy, a message that is both encouraging and challenging given the social and geographical complexity of French Guiana.

Socio-demographic factors

French Guiana has a cosmopolitan population. Apart from common risk factors for prematurity, there have been reports of a higher risk of prematurity among the population of African ancestry. (6) [START_REF] Macdorman | Race and Ethnic Disparities in Fetal Mortality, Preterm Birth, and Infant Mortality in the United States: An Overview[END_REF]. A study in the USA showed that the risk of premature delivery was 3 times higher in the African-American population than in the Caucasian population. The study showed that socioeconomic factors were important but could not completely explain the excess prematurity in the black population. ( 6) Here mothers born in French Guiana (mostly creole) had a higher risk of premature delivery than mothers born in mainland France (mostly Caucasian). This may have reflected more frequent preterm deliveries linked to African ancestry however, despite the plausibility of this explanation, ancestry was not available. Moreover, despite adjustments for potential confounders, there may have been residual confounding explaining these differences In addition, the overseas French territories are the areas were teen pregnancies are most frequent in France. In the Réunion Island, teen pregnancies represent 3.8% of births, in the French Antilles it represents 2.8% versus 6.2% in French Guiana. [START_REF] Guiot | Grossesses évolutives chez les mineures en Guadeloupe : nouvel état des lieux[END_REF] [START_REF]ANTIANE ECO : La revue économique et sociale des Antilles-Guyane[END_REF] In Mainland France this rate has been < 1% for over 10 years, fluctuating around 0.8%. [START_REF] Alouini | Facteurs de risques de la grossesse, de l'accouchement et du post-partum des adolescentes dans le département du Loiret[END_REF] Overall 6.2% of the population was minor. Women < 18 years had increased premature delivery 1.2 fold but after adjustments this was no longer significant. However, after adjustment for potential confounders, there was a significant link between preterm birth and age<16 years AOR=1.5 (95%CI [1.02-2.12], p = 0.04. Another study conducted in western French Guiana has however shown a significant association between pregnancies <15 years of age and preterm delivery after adjustment for potential confounders. [START_REF] Soula | Grossesses et accouchement chez les adolescentes de moins de 15 ans: Étude de 181 cas en Guyane française[END_REF] Social and behavioural elements such as pregnancy denial or concealment from one's family and late consultation may have confounded the link with being under 18 years of age. [START_REF] Guiot | Grossesses évolutives chez les mineures en Guadeloupe : nouvel état des lieux[END_REF] Other studies in Sudan, Saudi Arabia and Nigeria have also found conflicting results regarding the influence of teen pregnancies on premature delivery. [START_REF] Adam | Maternal and perinatal outcome in teenage pregnancies in Sudan[END_REF] In addition to teen pregnancy, social determinants of health are particularly important in French Guiana.

In 2014, the unemployment rate was 22.3% in French Guiana versus 9.9% in mainland France. (ref INSEE Institut national de la statistique et des études économiques).

Here 68.5% of the population was without profession (88 99/12 983). The employment rate in French Guiana for 2014 was 46.2% which was much lower than the 64.3% in mainland France (ref INSEE).

In addition to unemployment, precariousness is linked to income, family ties, housing… In 2011, poverty affected an estimated 87 000 persons in French Guiana, which represents a poverty rate of 44.3 %. This rate is much higher than in other French territories, such as Guadeloupe (19.4 %), Martinique (21.1 %), or mainland France (14.3 %). [START_REF] Soula | Grossesses et accouchement chez les adolescentes de moins de 15 ans: Étude de 181 cas en Guyane française[END_REF] The proportion of households living on welfare reaches 23.4% versus 5.1% in Mainland France. These social conditions are known risk factors for poor pregnancy follow up and increased obstetrical complications, notably preterm births. (20) (21) [START_REF] Gayral-Taminh | Caractéristiques socio-démographiques et risques périnatals des mères en situation de précarité[END_REF] In 2008, a study on 1444 women revealed that for 1057 women for whom the number of consultations was available, 24.6% had a late first consultation (2 nd or 3 rd trimester) and 43.9% had less than 7 prenatal consultations versus 8.5% in mainland France. A study of 1 057 women conducted in French Guiana showed that 46.5% of pregnant women had a late first obstetrical consultation (between the second and the third trimester of pregnancy) and that 32.4% of them had had less than the 7 recommended prenatal consultations versus 8.5% in mainland France. [START_REF]Frequence, Determinants Et Consequences Du Mauvais Suivi Des Grossesses En Guyane Francaise[END_REF] In the present study, after adjusting for health insurance, family situation, age, and pregnancy follow up patients without a job were significantly more likely to have preterm delivery. When looking at excess fractions, 24.2% of premature delivery in unemployed women could be linked to unemployment. Among these women prenatal follow up was generally insufficient. In the general population of pregnant women 17.8% of preterm deliveries were attributable to the absence of professional activity. Access to rights thus seems to be a crucial element to reduce preterm deliveries. [START_REF] Giami | Chapitre 80 -Précarité et périnatalité[END_REF] Health insurance for those in a precarious situation (Universal coverage, state medical aid) was associated with a reduction in the risk of preterm birth and conversely absence of health insurance was independently associated with preterm birth. [START_REF] Ehrenthal | A population study of the contribution of medical comorbidity to the risk of prematurity in blacks[END_REF] Apart from these common sociodemographic criteria, the place of residence was associated with preterm delivery. Women living in western French Guiana had a significantly increased odds of preterm birth. An ongoing study in Western French Guiana showed that 24.1% of 529 pregnant women had increased lead concentration (>50 µg/dl). Although professional and environmental exposures have been considerably reduced, adverse obstetrical consequences have also been observed for lead blood concentrations deemed «acceptable» (≤ 10 µg/dl). ( 25) [START_REF] Kapoor | Effects of heavy metal poisoning during pregnancy[END_REF] In addition, in Western French Guiana, apart from women with sickle cell anemia, the prevalence of anemia in pregnant women is 70% [START_REF] Louison-Ferte | Lutte contre l'anémie de la femme enceinte dans l'Ouest Guyanais : diagnostic et mise en oeuvre d'actions par le Réseau Périnat Guyane autour d'une évaluation des pratiques professionnelles[END_REF], which can also contribute to the increase of preterm delivery. [START_REF] Beucher | Anémie par carence martiale et grossesse. Prévention et traitement[END_REF] [START_REF] Levy | Maternal anemia during pregnancy is an independent risk factor for low birthweight and preterm delivery[END_REF] The Maroon population, living mostly in French Guiana, may also have an increased risk of preterm delivery for ethnic or geographical reasons. Further investigations measuring the concentration of lead, mercury (linked to gold mining in the region) and other environmental toxics may be useful to better disentangle the determinants of this increase of preterm births in Western French Guiana.( 26)

Medical obstetrical factors

As described by others [START_REF] Weaver | The increasing trend in preterm birth in public hospitals in northern Argentina[END_REF]. primiparous women had a higher risk of preterm delivery after adjustment for potential confounders. [START_REF] Goldenberg | Epidemiology and causes of preterm birth[END_REF] After adjustment for potential confounders, multiparity was not associated with preterm delivery. Thus, more than the actual number of pregnancies, it was the specific obstetrical events, which are more frequent in those with multiple pregnancies, that were associated with preterm delivery. A scarred uterus, notably caesarian section during the second phase of labor subsequently increased the risk of preterm delivery. [START_REF] Levine | Does stage of labor at time of cesarean delivery affect risk of subsequent preterm birth?[END_REF] Finally, as emphasized by the excess fractions, pregnancy follow up has a major importance to prevent preterm delivery with among women giving premature births would explain 59% of prematurity and 7.5% in the total population of pregnant women. Excess fractions should not be viewed here as biological constants but as reflecting the studied population and the specific distribution of other covariables influencing the outcome in French Guiana. [START_REF] Greenland | Conceptual problems in the definition and interpretation of attributable fractions[END_REF] In the context of French Guiana, the absence of preparation for birth and prenatal interview were thus identified as major risk factors with excess fractions in the population of 69 and 72.2% respectively, which is far greater than any other risk factor. Thus if the health system aims to reduce preterm birth, the study of excess fractions points towards a very pragmatic intervention: improving the follow up of pregnant women, notably those who are most socially vulnerable.(32) More generally, beyond the context of French Guiana, studies on predictors of preterm delivery could also use excess fractions to better rank risk factors within each population in order to identify intervention priorities. As emphasized by the World Health Organization in 2012, midwives have a major role in prevention, screening for complications and follow up of pregnant women, in developed and in developing countries. Their role spans the course of pregnancy but also may concern minors before pregnancy or women well after 28 days post partum. A 2014 review compiled over 50 outcomes that could be improved by midwives among which preterm birth, with a more efficient use of resources when provided by properly trained midwives, thus supporting a system-level shift from care focused on identification and treatment of pathology for a minority of women to skilled care for all women. In the context of the low medical density the high frequency of obstetrical complications, and perinatal deaths in French Guiana there is definitely an important place for more midwives, notably for prevention in the remote areas with the aim of reducing preterm birth in the most vulnerable women.

CONCLUSION

Given the slow reduction of perinatal mortality and French Guiana [START_REF] Cardoso | Périnatalité en Guyane française: Evolution de 1992 à 1999[END_REF] and the high burden of prematurity (comparable to some African countries [START_REF] Howson | Save the Children. WHO. Born Too Soon: The Global Action Report on Preterm Birth[END_REF] ) and its relative stagnation, it is crucial to devise targeted interventions with maximum impact. The present study has shown the predictive factors of prematurity in French Guiana and has allowed to rank them in terms of expected impact. Although there is no magic bullet, the present results point for a very obvious intervention: improving the follow up of the poorest pregnant women. Given the saturation of the obstetrical professionals, this may require further outreach mechanisms and specific funding to change health-seeking behavior, improve access to care to reduce social inequalities of health.

Table 2

 2 During the study period, premature births represented 13.5% (1 755/12 983) of all births. Of these, spontaneous prematurity represented 51.3% (901/ 1 755) of premature births versus 48.7% (854/ 1 755) induced prematurity (labor induction or elective cesarean section). describes the obstetrical profile of patients and elements relative to pregnancy follow up and events having occurred during pregnancy. The first column lists the studied variables.

	represents 43.6% of the study population

DECLARATION OF INTERESTS

The authors declare no conflict of interest regarding this study.