Éric Langlais
email: eric.langlais@u-paris10.fr.z

Marie Obidzinski
email: marie.obidzinski@univ-fcomte.fr.

Andreea Cosnita

Nuno Garoupa

Elected vs appointed public law enforcers

Keywords: law enforcement, deterrence, monetary sanctions, punishment, electoral competition, democracy, rent seeking, dictature. JEL classi…cation codes : D72, D73, H1, K14, K23, K4

This paper revisits the issue of law enforcement and the design of monetary sanctions when the public law enforcer's incentives depart from those of a benevolent authority, which is the most frequent assumption made in the literature on crime deterrence. We …rst consider the case of an elected enforcer. We …nd that when the harm generated by o¤enses is quite small relative to the average private bene…ts, equilibrium with weak enforcement/low sanction prevails. Instead, when the harm generated by o¤enses is high relative to the average private bene…ts, it is the equilibrium with strong enforcement/high sanctions that prevails. Therefore, we provide an explanation for the empirical puzzle highlighted by Lin(2007): elected enforcers punish major (minor) crimes more (less) severely than the benevolent social planer. The case of an appointed enforcer prone to rent seeking is also considered. The monetary sanction under rent seeking is closer to the utilitarian level, as compared with the one under election.

Introduction

As compared with autocratic or dictatorial regimes, the speci…city of the design and enforcement of criminal law1 in democratic countries relies on the fact that they both come out from the decision process of an elected enforcer. The public enforcer (the State -the Government, the Parliament -sometimes the Town Council) determines the level of sanction (with a margin of discretion left to judges) and the means devoted to the o¤enders' detection, apprehension and conviction. Therefore, a realistic view of the law enforcer is to consider that her/his decisions regarding the level of sanction and the means given to the police might be in ‡uenced by the citizens'preferences. The implicit assumption behind this statement is that the elected law enforcer has proposed and enforced a platform which has won the support of the majority of the voters. In other words, the candidate has incentives to propose a policy which enables her/him to win the election. This issue has not received much attention in the law & economic literature, which is quite surprising since the debate regarding the way in which citizens'individual preferences may be revealed has long ago expanded beyond social choice theory. Moreover, regarding the debate about the roles and objectives of the penal code, both the proponents of the utilitarian approach [START_REF] Becker | Crime and Punishment: an Economic Approach[END_REF]; including the precursors [START_REF] Beccaria | Traité des Délits et des Peines[END_REF][START_REF] Bentham | An Introduction to the Principles of Morals and Legislations[END_REF] or its critics [START_REF] Dau-Schmidt | An Economic Analysis of the Criminal Law as a Preference-Shaping Policy[END_REF][START_REF] Lewin | The Social Value of Crime?[END_REF][START_REF] Stigler | The Optimal Enforcement of Laws[END_REF] have insisted on the role played by social norms and social preferences, thus linking the design of the sanctions to ethical and moral considerations that, at a given moment, are shared and must be consolidated in the social group.

On a priori grounds, it is not so easy to predict in which way social preferences and the election process may in ‡uence the design of the penal codebeyond the basic distinction between what is seen as legal and illegal behaviors. Very few attempts have been made in order to verify empirically whether di¤erences arise in criminal law enforcement policies according to the level and quality of democracy. [START_REF] Lin | Does Democracy Increase Crime ? The Evidence from International Data[END_REF] uses an index of political liberty from the comparative freedom survey to distinguish "low democracies" from "high democracies"; he shows that countries characterized by a higher level of democracy tend to punish major crimes more severely as compared to countries with a low level of democracy, the reverse being true for minor crimes. More precisely, the deterrence of homicides is quite strong 2 and the homicide rate lower in high democracy by comparison with low democracy. On the contrary, it seems that democracy has a negative impact on less serious crimes such as burglary, robbery, car theft. However, no explanation of such an empirical result has been yet provided. This paper addresses this issue, in a framework where both the lawmaking process and the control of undesirable behaviors are endogenous. Here, the lawmaking process is limited to setting the monetary sanction. The paper focuses on two kinds of public institutions, widely spread in democratic countries, which may have some power in the setting of appropriate sanctions: they result either from the electoral process, in the case of political competition, or from the decisions of an appointed bureaucrat, in the regulatory case.

The issue on whether/how political market and electoral competition impact policy choices has been largely investigated regarding judicial decision making, both theoretically [START_REF] Epstein | The Independence of Judges: The Uses and Limitations of Public Choice Theory[END_REF][START_REF] Hanssen | The E¤ect of Judicial Institutions on Uncertainty and the Rate of Litigation: the Election Versus Appointment of Judges[END_REF][START_REF] Klerman | The Value of Judicial Independence: Evidence from Eighteenth Century England[END_REF][START_REF] Porta | Judicial Checks and Balances[END_REF] and empirically (Blanes i Vidal and Leaver 2011, [START_REF] Hanssen | Is There a Politically Optimal Level of Judicial Independence?[END_REF][START_REF] Schneider | Judicial Career Incentives and Court Performance: An Empirical Study of the German Labour Courts of Appeal[END_REF]. Interestingly enough, Matsuaka (2010) has provided empirical evidence that congruence is higher when judges must stand for reelection. The empirical literature has also documented the in ‡uence of the electoral cycle on the orientation of public policies against criminality. [START_REF] Levitt | Using Electoral Cycles in Police Hiring to Estimate the E¤ect of Police on Crime[END_REF] uses the increase in policemen recruitments before the elections as an instrument to evaluate the relevance of Becker's deterrence theory. [START_REF] Dyke | Electoral Cycles in the Administration of Criminal Justice[END_REF] shows that the district attorneys are less likely to dismiss cases in the election year. [START_REF] Berdejó | Crime, Punishment, and Politics: an Analysis of Political Cycles in Criminal Sentencing[END_REF] present evidence that elected judges (in the State of Washington) tend to respond to political pressure by increasing the severity of their judgment: sentences are around 10% longer at the end of a judge's political cycle than at the beginning. In the case of Argentina, [START_REF] Meloni | Is There an Electoral Motivated Crime Rate Cycle? Evidence from Argentina[END_REF] showed that incumbent governors dedicate additional e¤orts in election years in order to get short-run improvements in crime indicators. Public choice literature has also recognized the importance of taking into account the incentives of the bureaucrats and politicians in charge of public policy [START_REF] Alesina | Bureaucrats or Politicians? Part I: A Single Policy Task[END_REF] as well as the principal agent literature [START_REF] Maskin | The Politician and the Judge: Accountability in Government[END_REF]. More speci…cally, [START_REF] Alesina | Bureaucrats or Politicians? Part I: A Single Policy Task[END_REF] investigate the choice between giving a policy task to bureaucrats (guided by career concerns) or to politicians (guided by reelection concerns), focusing on the ability to perform a task and therefore explaining the delegation of highly technical tasks to agencies.

In contrast, the law enforcement economic literature stemming from [START_REF] Becker | Crime and Punishment: an Economic Approach[END_REF] seminal article has largely ignored the incentives of enforcers, with the exception of corruption. The public enforcer is indeed generally considered as either benevolent or corrupted3 , with the exception of [START_REF] Becker | Law Enforcement, Malfeasance, and Compensation of Enforcers[END_REF]. Between these two extremes lies a range of situations where the enforcer is merely (as any other agent) self interested, as argued4 by [START_REF] Friedman | Why Not Hang Them All: The Virtues of Ine¢ cient Punishment[END_REF]. Building on this statement, [START_REF] Garoupa | Optimal Law Enforcement with a Rent-Seeking Government[END_REF] developed a model of a rent seeking government5 , that is a government which seeks to maximize the revenues minus the harm to the government and the cost of law enforcement. 6Rent seeking seems indeed clearly relevant to consider the case of dictatorship, or the case of an independent agency.

Our paper deals also with the issue highlighted by [START_REF] Friedman | Why Not Hang Them All: The Virtues of Ine¢ cient Punishment[END_REF] regarding law enforcers' incentives. The literature about law enforcement considers criminals as highly sophisticated and rational individuals, while the State is usually considered as a simple « proxy » (benevolent automat) or7 « a wise, benevolent and wholly altruistic organization » . However, as Friedman emphasized, societies do not generally choose the most e¢ cient way to enforce law in practice. One explanation lies with the incentives of the law enforcers; they wish to maximize their own rents rather than the social welfare, thus departing from the socially optimal solution of the literature. Our general point in the paper is in the same spirit as Friedman's, in the sense that we analyze situations where the law enforcer's incentives may re ‡ect the general institutional context where the enforcer operates; thus these incentives may be shaped by speci…c institutions such as the existence of statutes (when the enforcer is a regulatory agency) or through the in ‡uence of political/social pressures (when the enforcer is the State).

Finally, our paper is a contribution to the analysis of cases where public authorities' preferences might diverge from benevolence, and to analyze the consequences for the design of the penal code and the level of deterrence. We analyze the e¤ects of the political market on the design of public policies in the area of crime deterrence, introducing a basic model of electoral competition. We focus on electoral strategies based on a policy against criminality, and which allow candidates to maximize their chances to win the elections. Our aim is to discuss in a simple framework whether/how democracy and political competition may promote the toughness of the sanctions in the various domains of the penal law. Then we compare the case of a utilitarian public authority with the case of a rent seeking enforcer. [START_REF] Garoupa | Optimal Law Enforcement with a Rent-Seeking Government[END_REF] and Dittman ( 2004) also analyze law enforcement and the choice by a rent seeking authority, but assume that sanctions are exogenously set. This framework can represent an independent agency regulating a sector as the enforcer does not fear not to be reelected. To some extent, this framework represents also the case of dictatorship. Therefore, our paper provides a detailed analysis of deterrence with an elected versus an appointed law enforcer.

The paper is organized as follows. Section 2 sets the general framework. and recall the results obtained in the standard beckerian approach relying on a benevolent planer in order to de…ne our benchmark. Section 3 analyzes the case where the public enforcer is elected with a simple model of Downsian electoral competition. Section 4 develops the case of rent seeking government. Section 5 compares the di¤erent cases and section 6 concludes.

The general framework

We introduce here our basic framework, which elaborates on the model of law enforcement à la Becker8 . Let us consider the case where the illegal activity allows the (risk neutral) criminal to bene…t from b which will be called the type of the criminal. Public authorities do not observe the type b, but only know that it is distributed according to the uniform law on [0; B]. The (external) loss/harm to the rest of the society in case of crime is h, whatever the private bene…t for the criminal9 , with the following assumption:

Assumption 1. B > h Monitoring the criminal activity entails a cost for public authorities, equal to m(p), where for the sake of simplicity p is the probability of control (encompassing apprehension, conviction and punishment for an illegal behavior). As usually in the literature, we assume that this cost is …nanced through a lump sum tax t plus the expected …ne levied on the fraction of the population which is seen as criminal (either for whom the harmful activity entails the harm, or is not deterred from committing the crime).

We focus here on punishment, i.e. the choice of a monetary sanction (penalty or …ne) f > 0. We assume that the management costs (associated with the monetary penalty) are negligible. We also assume that the maximal …ne is the legal wealth of the population w, i.e. f 2 [0; w]: we consider that w is large enough in order for (almost) all equilibria to be de…ned as interior solutions. However, we assume that expenditures in the monitoring of criminals'behavior are exogenously set throughout in the paper. Given that p is the probability of control (0 < p < 1), it re ‡ects both the action of police (…rst investigations and apprehension) and justice (complementary investigations, conviction and punishment). p is supposed to be set exogenously in order to focus on the level of sanction 10 f .

As a benchmark, we …rst focus on the enforcement strategy of the authority when it is assumed to behave according to a perfectly benevolent planner. In this case, the game (or sequence of moves) between the public authority and the citizens is the usual one: after Nature moves (choosing the type of citizens, not observable for public authorities) at stage 0, the authority makes at stage 1 its announcement regarding the level of …ne applied; at stage 2, citizens decide whether or not they abide the law; at stage 3, the law is enforced.

Criminals and honest people

We assume that the cost of a crime hurts citizens through a pure externality term a¤ecting individuals'utility level, with a very simple formulation: E = qh, where is q 2]0; 1[ the probability of crime. As usual in the literature on crime enforcement, we will show that q =

u c = w + b t pf E = w + b t pf 1 b B h
while for an honest individual, we have:

u h = w t E = w t 1 b B h
Hence as usual, b is de…ned by u c = u h ; a potential criminal decides to undertake the activity if the bene…t he receives from doing it is higher than the expected punishment, i.e. if b pf = b.

Benevolent public enforcers

The public budget constraint writes as:

m(p) = t + 1 b B pf (1)
This means that we consider here only balanced-budget policies.

Assume that the policy maker acts as a benevolent planner, and uses a pure utilitarian criterion 11 : the social welfare function is the weighted sum of u h and u c given the structure of the population, i.e. the weights are de…ned by the shares respectively of the honest and criminal populations. This results in the following social function of a benevolent planner:

S = 1 B Z b 0 u h db + 1 B Z B b u c db = w t + 1 B Z B b (b pf h)db (2)
and substituting with (1) yields:

1 1 Since [START_REF] Stigler | The Optimal Enforcement of Laws[END_REF], the introduction of illegal gains in the social value function is a controversial issue. Both the signi…cance and the objective of the penal code are still in debate among scholars; see [START_REF] Dau-Schmidt | An Economic Analysis of the Criminal Law as a Preference-Shaping Policy[END_REF] and [START_REF] Lewin | The Social Value of Crime?[END_REF]; and also more recently Dari-Mattiacci and Garoupa (2007), Fleurbaey, Tungodden andChang (2003) and [START_REF] Kaplow | Any Non-welfarist Method of Policy Assessment Violates the Pareto Principle[END_REF].

S = w + 1 B Z B pf (b h)db m(p) (3)
which is the standard formulation considered in the literature. The …rst (integral) term of S correspond to the expected private bene…t associated with the illegal activity. The last one is the cost of monitoring for public authorities. In the case of an act-based sanction, the …ne paid by the criminal when arrested is a mere transfer (the perceived probability of paying the …ne, is equal to the perceived probability of collecting it).

Lemma 1 The social-welfare maximizing sanction is f u = h p . Proof. The derivative of S with respect to f is given by:

@S @f = ( b h)p = (h pf )p implying that @S @f jf =0
> 0, and thus f > 0. Hence, assuming that @S @f jf =w < 0 , h pw < 0 , h < h 1 pw, and solving the F.O.C. for the optimal sanction f u yields:

f u = h p
which leads to the …rst best level of deterrence h. The associated cumulative probability of crime is q = 1 pfu B = 1 h B .

3 Punishment when the public enforcer is elected

In this section, we depart from the usual assumption that the enforcer is benevolent. We introduce a simple model of electoral competition in the vein of the framework known as Downsian model (see Downs, 1957, Persson and[START_REF] Persson | Political Economics. Explaining Economic Policy[END_REF]. Assume there exist two candidates i = 1; 2 representative of two political parties, competing for national (presidential or legislative) or local (municipal) elections. Competing for elections here is alike a rent seeking contest, where V , the exogenous rent obtained in case of victory is attached to holding o¢ ces, ministries and so on. Thus, we do not consider the case of opportunistic politicians, responding to lobbies pressures or adopting Leviathan behavior (following strategies of capture).

An electoral campaign or platform f consists in setting the monetary sanction. The objective of politician i is to maximize the expected value of the rent simply votes for the candidate whose platform allows him to reach the highest utility level, and if he is indi¤erent, he tosses a coin to decide for whom he votes.

Let us denote as n(f 1 ) = n 1 2 [0; 1] the proportion of the population voting for candidate 1. Then the probability that candidate 1 wins the elections can take three values:

l = 8 < : 0 if n 1 < 1 n 1 1 2 if n 1 = 1 n 1 1 if n 1 > 1 n 1
The electoral competition game between the candidates and the citizens/voters is as follows: after Nature moves at stage 0 (choosing the type of citizens, not observable for politicians), the electoral competition begins at stage 1, which is a simultaneous move (non cooperative) game between the candidates, where they both choose and announce their platforms (f 1 ), (f 2 ), both satisfying the balanced budget constraint (1); at stage 2, elections take place, and citizens simultaneously choose between the two candidates 12 ; at stage 3, the elected candidate implements his policy 13 -it becomes a law; at stage 4, citizens choose to abide or not the law; at stage 5, law is enforced.

In the appendix, we prove the next result, where f h (f c ) sets for the choice of sanction by the honest (respectively, criminal) population:

Proposition 1 Under electoral competition, three cases must be distinguished:

i) The "strong enforcement" equilibrium: If h > B 2 , then the unique equilibrium is such that both candidates announce the monetary sanction f = f h

1 2 h h p + B p i
, and each candidate wins the elections with probability 1 2 . The probability of crime is q = 1 2 1 h B < 1 4 . ii) The "weak enforcement" equilibrium: If h < B 2 , then the unique equilibrium is such that both candidates announce the monetary sanction f = f c 1 2 h p , and each candidate wins the elections with probability 1 2 . The probability of crime is q = 1 1 2 h B > 3 4 . iii) The multiple equilibria: If h = B 2 , there exist four equilibria 14 , either symmetric or asymmetric; i.e. the next four pro…les of strategies are equilibria of the electoral game: candidate l announces f h , and candidate r announces f c ; candidate l announces f c , and candidate r announces f h ; both candidate l and candidate r announce f h ; both candidate l and candidate r announce f c . In all of these equilibria, each candidate wins the elections with probability 1 2 . When f h is implemented, the probability of crime is q = 1 4 ; but when f c is implemented, the probability of crime is q = 3 4 .

1 2 Every citizen votes, anticipating their future behavior, i.e. whether they will behave as honest people or criminals.

1 3 i.e., we assume that candidates commit to their own electoral platform -without specifying the reasons explaining neither why those platforms are credible announcements, nor how they become a law. These (obviously important) issues are beyond the scope of the paper.

1 4 Note that we focus only on pure strategies equilibria.

It is easy to check that the monetary sanction is higher in the "strong enforcement" equilibrium and the proportion of criminals lower in the "weak enforcement" equilibrium.

The prevailing equilibrium depends crucially on the level of the harm relative to the maximal private bene…t of crime. In the case where the harm done to society h is higher than the average private bene…t B 2 15 , the "strong enforcement/low level of crime" equilibrium prevails. At this point, the honest people represent the majority of the voters. Therefore, both candidates have incentive to propose the same platform, which maximizes the bene…ts of those citizens. On the contrary, when the harm h is weaker than the average private bene…ts B 2 , the "weak enforcement/high level of crime" equilibrium emerges.

Punishment when the public enforcer is rent seeker

Let us consider now the case where the public enforcer is rent seeker, such as in a non democratic government (as suggested in [START_REF] Garoupa | Optimal Law Enforcement with a Rent-Seeking Government[END_REF], or an independent agency which is able to keep the …nes it sets. 16 This situation can be characterized as the case of "appointed law enforcer". In order to discuss this point in a very simple framework, let us assume now that an appointed public enforcer sets the level of sanctions, in order to maximize the rent (i.e. pure capture):

R = 1 B Z B pf (pf h)db m(p) = 1 pf B (pf h) m(p) (4)
with R > 0, and where 2]0; 1] represents the share of the harm that may hurt directly the appointed law enforcer, that is the agency [START_REF] Garoupa | Optimal Law Enforcement with a Rent-Seeking Government[END_REF]. The next proposition highlights the main implications:

Proposition 2 Sanctions with rent seeking. The rent maximizing sanction is

f r = 1 2 h p + B
p , and is associated with a probability of crime equal to q r = 1 2 1 B h . In practice, the enforcement of many public regulations is delegated to (public, private or mixed) agencies, whose agents are not elected by citizens. These agents may be civil servants or employed under private contracts, but they are endowed with the power to monitor the activity of citizens and to set the penalties in case where infractions are detected (the …ne is legally capped).

Proof. The derivative of R relative to f is:

@R @f = 1 + B h 2 p B f implying that @R @f jf =0 > 0, hence f > 0. Assuming that @R @f jf =w < 0 , h < h 2 2 p w B
, and solving the FOC for the optimal sanction f r yields:

f r = 1 2 h p + B p
Assessing the level of deterrence, we obtain that the probability of crime is

q r = 1 pfr B = 1 2 1 B h .
Note that the optimal sanction with a rent seeker law enforcer depends crucially on the share of the harm that may hurt him/her directly. The lower this share, the lower the optimal sanction f r ; and the higher the probability of crime.

Comparison and discussion

Let us compare in this section the level of sanction with the di¤erent enforcer's types: utilitarian, elected and rent seeker.

Proposition 3 Utilitarian versus elected public enforcer:

f h > f u > f c Proof. i) if h > B
2 , then political competition yields a sanction which is larger than the social welfare maximizing one since :

f h f u = 1 2 h p + B p h p = 1 2 B p h p
and thus under assumption 1,

f h > f u . ii) if h < B 2
, then political competition yields a sanction which is smaller than the social welfare maximizing one since:

f c f u = 1 2 h p h p
and thus f c < f u .

In the "strong enforcement" equilibrium, the policy announced and implemented is more severe than that of the benevolent law enforcer. Elections reveal the preferences of the majority (which is composed by the people not committing the o¤enses in this case). To put it di¤erently, under the "strong enforcement" equilibrium (where the proportion of criminals is lower than one fourth of the population), the preferences re ‡ected in the policy chosen by the elected enforcer are those of the honest people who are prone to accept for higher sanctions. The reverse holds under the "weak enforcement" equilibrium.

This result has to be understood hand in hand with the level of harm. The fact that the majority is composed by honest people depends on the level of harm h generated by the crime (relative to the maximum private bene…ts B). Recall that the honest equilibrium prevail if h > B 2 (the harm caused by the o¤ense is large compared to its private bene…ts).

In each case, it is worth stressing that the decisions of an elected enforcer involve an ine¢ cient level of deterrence, since the sanctions f h and f c di¤er from the social welfare maximizing sanction f u . The strong enforcement equilibrium is associated with a level of deterrence which is higher than the one associated with a benevolent planer, and thus this equilibrium induces overdeterrence (pf h > h under assumption 1). In contrast, the weak enforcement equilibrium entails a level of deterrence smaller than the one associated with a benevolent planer, that is underdeterrence (pf c < h under assumption 1).

Proposition 4 Utilitarian versus rent seeker enforcer.

i

) If = 1, then f u < f r . ii) If < 1, the sign of f u f r is ambiguous; in particular, there exists = 2 B h such that < ) f u > f r , while > ) f u < f r .
Proof. We have:

f u f r = 1 2p [(2 ) h B]
i) If = 1, then f r = f h and thus f u < f r (under assumption 1). ii) However, if < 1 (the public enforcer partially bears the harm done by the o¤ender) the sign of f u f r is given by the sign of (2 ) h B. Hence the result.

When the rent seeking enforcer incurs a large share of the social harm, the society reaches an equilibrium associated with overdeterrence; as this share decreases, the level of the sanction decreases, and so does the level of deterrence. Above the threshold , rent seeking is associated with overdeterrence; under the threshold , it induces underdeterrence. Finally, the following result holds:

Proposition 5 Rent seeker versus elected enforcer:

f h f r > f c . Proof. Straightforward since 2 [0; 1].
Note that if the public enforcer entirely incurs the harm generated by the o¤ense ( = 1), the …ne equals the one set by an elected enforcer under the honest equilibrium case f r = f h : Indeed, the rent seeker enforcer does not take into account the criminal bene…ts and fully bears the harm done by the o¤ense. In such a case, there is no di¤erence between an appointed law enforcer (an independent agency or a dictatorship) and an elected enforcer.

When it is not the case ( < 1), the rent seeking sanction is lower than the electoral sanction under the "strong enforcement equilibrium f r < f h , but higher than the electoral sanction under the "weak enforcement" equilibrium. From the restrictive point of view of …ne setting, the appointed law enforcer fares better here than the elected one, in the sense that the rent seeking sanction f r is closer to the utilitarian sanction f u than the sanctions under election. If < 1, we have f h > f r ; f u > f c . The sign of f u f r is ambiguous and depends on the level of , the share of the social harm incurred by the enforcer.

Concluding remarks

The central issue of our paper is the relationships between law enforcers'incentives, the revelation of social preferences, and the public enforcement of law. Since [START_REF] Becker | Crime and Punishment: an Economic Approach[END_REF], the debate about the roles and objectives of the penal code has made clear that ethical and moral considerations are not enough to explain the content and structure of the penal law. At a given moment, citizens adhere to beliefs and social norms that the penal law consolidates in order for individual decisions to adhere to these norms. Those norms are revealed thanks to the electoral competition and the political process in democracies. As a result, depending on whether an act is considered as entailing either a large or a small external cost to society (as compared to its private bene…t), the level of the punishment will be set accordingly at a high or low level. When the harm perception of an act evolves, the content of the penal code also changes accordingly.

The main contribution of the paper is to show that elected enforcers punish major crimes more severely than the benevolent social planer (the reverse being true for less serious crimes). This paper provides a theoretical justi…cation for the empirical result of [START_REF] Lin | Does Democracy Increase Crime ? The Evidence from International Data[END_REF], who shows that democratic governments punish major (minor) crime more (less) severely than non democratic ones. When the harm generated by an o¤ense is small relative to the maximal private bene…t, a "weak (strong) enforcement" equilibrium should emerged, provided that the o¤enders (respectively, honest citizens) represent the majority.

The implications in terms of social welfare are obvious: democracy does not maximize social welfare (the social welfare is lower under democracy than in the implausible utilitarian social planer). However, our results do not suggest leaving the design of law enforcement to bureaucrats, as rent seeking behavior might also lead to suboptimal results. The comparison between deterrence with an elected and with a rent seeker law enforcer is more tricky and leads to ambiguous results. If the rent seeker public enforcer entirely bears the harm generated by the o¤ense, he will behave as an honest individual in case of an election. The monetary sanction is as high as in the "strong equilibrium case". In the opposite case, the sanction designed by an appointed law enforcer prone to rent seeking is closer to the utilitarian sanction than the one designed by an elected enforcer. Therefore, a signi…cant result of our paper is that the public enforcer is doing worse in the election framework than when looking for increasing her/his rent, as in the appointment case. This result sheds a new light on institutional constraints and their consequences for o¤enses deterrence.

Our paper also contributes to the debate concerning the ‡aws of the beckerian approach, and mainly the early criticisms that focused on the inclusion of crime bene…ts in the social welfare function [START_REF] Lewin | The Social Value of Crime?[END_REF], the preference shaping function of law and so on [START_REF] Dau-Schmidt | An Economic Analysis of the Criminal Law as a Preference-Shaping Policy[END_REF]. According to [START_REF] Lewin | The Social Value of Crime?[END_REF], including criminal bene…ts in the social welfare function lowers the deterrence threshold. Dau-Schmidt (1990) also argues that it is morally shocking to include criminal bene…ts in the social welfare function. Taking as a starting point that social preferences are revealed through the political process, our model assumes that o¤enders are part of the society and vote for their preferred law enforcement policy. As a result, when the "strong enforcement" equilibrium emerges, the preferences of criminals (and thus, crime bene…ts) are no longer taken into account to design the monetary sanctionsin a sense, in this case criminals' preferences are not representative of social preferences, since these correspond to the majority of citizens. But, it cannot be ignored that a "weak enforcement" equilibrium emerges, in which the criminals' preferences become representative of social preferences.

Our paper also provides an explanation for the paradox of crime deterrence: on the one hand, the issue of criminality became a main concern in electoral campaigns for more than a decade in most European countries; on the other hand, there is an ongoing debate about the non criminalization/legalization of some o¤enses, such as drug consumption (except in relation with international tra¢ cs and criminal networks) or illegal downloading. In the …rst case, the growing place of crime deterrence in electoral campaigns can be seen as a consequence of the election strategies of the politicians, anticipating the "strong enforcement" equilibrium for major crimes. In the second case, some o¤enses such as drug consumption or burglary might be considered as minor relatively to their private bene…ts (the evaluation of those depending on cultures or countries).

A limitation of our paper is the quite strong assumption on the commitment of elected law enforcers to enforce their electoral platform. Here, we deal with pre-election politics, and assume that electoral promises are binding and enforceable. A signi…cant extension would be to study the case where politicians could decide not to implement the announced policy despite reelection concerns. Furthermore, we also abstract from the existence of lobbying activities that yield other kinds of imperfections on the political market. We leave for future research the analysis of public enforcement when industry pressures exist, which will allow to study the e¤ects of di¤erent assumptions departing from the one of a benevolent enforcer.

platform f l 6 = f r cannot be an equilibrium, since either the distribution of voters satis…es n l > n r and thus candidate r would change his platform, otherwise he looses the elections for sure; or on the contrary, the associated distribution satis…es n l < n r , and now candidate l has an incentive to make a di¤erent announcement. Thus, any subgame perfect equilibrium must be such that both candidates choose and announce the same programme: f l = f r = f and both have a 50% chances to win the elections.

Given that f h = 1

B

  db = 1 b B , with b the deterrence threshold. Let us denote the utility level of a risk neutral criminal as:

1 5

 5 Recall than the distribution of the private bene…ts is uniform over [0; B], and therefore

  unique subgame perfect equilibrium is associated with the announcement by both candidates of the monetary sanction f h , such that b h B According to the same argument, any subgame perfect equilibrium must be such that both candidates choose and announce the same programme: f l = f r = f , and both have a 50% chances to win the elections. Given that f a c unique subgame perfect equilibrium is associated with the announcement by both candidates of the monetary sanction f c , such that b h B Whatever the annoucement, f h or f c , the associated probability of voters is 1 there exist four kinds of equibria:(f h ; f c ) ; (f h ; f h ) ; (f c ; f h ) ; (f c ; f c ).

Note that we have a broad de…nition of what the penal code is, encompassing both criminal and administrative laws. We are aware of existing criticisms against this approach (Dau-Schmidt, 1990;[START_REF] Lewin | The Social Value of Crime?[END_REF]. Note also that the sentencing guidelines in the United States were determined in 1984 by a commission(Reinganum,

2000); the United States Sentencing Commission. This commission is an independent agency in the judicial branch of the government.2 According to multiple criteria: average prison length, average clearance rates.

See the survey on corruption by[START_REF] Bowles | Corruption[END_REF], and on the economics of crime byEide et al. (2006).

See also the empirical analysis of[START_REF] Glaeser | What Do Prosecutors Maximizes? An Analysis of the Federalization of Drug Crimes[END_REF].

See also[START_REF] Gradstein | Rent Seeking and the Provision of Public Goods[END_REF], for an analysis of the impact of a rent seeking government for the provision of public goods.

This issue of self interest has been raised for judges'decision making notably by[START_REF] Epstein | The Independence of Judges: The Uses and Limitations of Public Choice Theory[END_REF].

Cf Friedman, 1999, p. 262.

See the surveys by[START_REF] Garoupa | The Theory of Optimal Law Enforcement[END_REF] and[START_REF] Polinsky | The Economic Theory of Public Enforcement of Law[END_REF].

Thus, as usually in the literature, the …rst best level of deterrence corresponds to the illegal bene…t b = h (assuming it can be obtained at a small enforcement cost). Given that the type of the criminals is not observable, it is generally never attainable.1 0 See Dharmapala andGaroupa (2004).

i V , where i is the probability that he wins the elections. To this end, candidate i proposes to electors an electoral platform f i . We consider the (simple) majority rule for voting. All citizens are electors and do participate: each voter

Appendix

Using the analysis of paragraph 2.1, it is straightforward that the deterrence threshold at equilibrium is b = pf , and the probability that citizens be honest is b B = pf B . Moreover, it is straightforward that honest people, thereafter characterized with the subscript h, prefer a monetary sanction which is set at a higher level than the citizens who commit a crime/o¤ense (criminals) henceforth denoted with the subscript c, since according to the de…nition of their respective satisfaction levels, we have for an honest individual u h = w t 1 b B h and thus:

while for a criminal, we have

under assumption 1. These two populations due to their di¤erent attitudes regarding the law, also have di¤erent preferences regarding the strategy of vote at the electoral competition stage. For an honest individual, we de…ne now the preferred sanction as: f h = arg max f fu h g under the public budget constraint de…ned by (1) [and f lower than w]. Substituting (1) in u h leads now to:

, the …rst order condition is given by: @u h @f = 0 or:

hence solving for f h :

Furthermore, the proportion of honest people is larger than the proportion of criminals when

For a criminal, let us denote: f c = arg max f fu c under (1)g. Substituting (1) in u c yields:

Assuming that @u h @f jw < 0, the …rst order condition @uc @f = 0 writes:

which yields:

Furthermore, under assumption 1, the proportion of honest people under f c is lower than the proportion of honest people under f h :

This result is used to establish the: Proof of proposition 1 Note …rst that the fraction of voters for f h is b h B > 1 2 , while the fractions voting for f c is 1 bc B > 1 2 . Then, it is easy to verify that:

and thus, (recall that

At the electoral competition stage, note …rst that both candidates anticipate that, once the elections are held (i.e. considering any subgame beginning once a platform f is implemented), the enforced law f will split the population in two sub-groups: citizens who abide the law, and citizens who commit a crime/o¤ense. Secondly, a situation where the candidates announce a di¤erent


Blaise Gnimassoun

Valérie Mignon
email: valerie.mignon@u-paris10.fr.

Current-account adjustments and exchange-rate misalignments 

Keywords: JEL classification: F32, F31, C33 current-account imbalances, current-account persistence, exchange-rate misalignments, panel smooth transition regression models

This paper aims at studying current-account imbalances by paying a particular attention to exchange-rate misalignments. We rely on a nonlinear model linking the persistence of currentaccount imbalances to the deviation of the exchange rate to its equilibrium value. Estimating a panel smooth transition regression model on a sample of 22 industrialized countries, we show that persistence of current-account imbalances strongly depends on currency misalignments. More specifically, while there is no persistence in cases of currency undervaluation or weak overvaluation, persistence tends to augment for overvaluations higher than 11%. In addition, whereas disequilibria are persistent even for very low overvaluations in the euro area, persistence is observed only for overvaluations higher than 14% for non-eurozone members.

Introduction

The magnitude of current-account imbalances and, especially, their persistence in several industrialized countries have become a key issue. While the U.S. current deficit represented on average only 1.6% and 1.7% of GDP during the 1990 and 1980 decades, the United States has surpassed the $ 600 billion current deficit over the 2004-2008 period, reaching almost 6% of U.S. GDP. This pattern is also observed for some euro area countries such as Spain, Portugal and Greece which have reached respectively current-account deficits of 8%, 10% and 11% of GDP. At the same time, other countries such as Germany, the Netherlands, Norway and Switzerland recorded current-account surpluses, exceeding 10% of GDP for Norway and Switzerland.

Within this context of global imbalances, several theoretical and empirical contributions have been devoted to the study of current-account imbalances' sustainability and the adjustment mechanisms towards equilibrium. 1 Most of the empirical studies on current-account adjustment indicate that such process takes place through major correction in the exchange rate, without having however established upstream an empirical link between currency misalignments and current-account imbalances [START_REF] Freund | Current account adjustment in industrial countries[END_REF][START_REF] Debelle | Current Account Adjustment and Capital Flows[END_REF][START_REF] Obstfeld | The Unsustainable US Current Account Position Revisited[END_REF]. 2 If the current account -real exchange rate nexus is well established from a theoretical viewpoint [START_REF] Mundell | A theory of optimum currency areas[END_REF][START_REF] Dornbusch | Exchange rates and the current account[END_REF][START_REF] Rodriguez | The role of trade flows in exchange rate determination: A rational expectations approach[END_REF][START_REF] Branson | Macroeconomic Determinants of Real Exchange Rates[END_REF], very few empirical studies have investigated this relationship (see [START_REF] Arghyrou | Current Account Imbalances and Real Exchange Rates in the Euro Area[END_REF]. More surprisingly, to our best knowledge, no empirical contribution has focused on the relationship between exchange-rate misalignments-i.e., the difference between the observed exchange rate and its equilibrium value-and persistence of current-account imbalances. In addition, the literature that attempts to address this issue is confined to the link between the current account and the real exchange rate, without actually paying attention to exchange-rate misalignments or current-account gaps (see for example [START_REF] Belke | Current account imbalances in the euro area: Catching up or competitiveness?[END_REF]. [START_REF] Arghyrou | Current Account Imbalances and Real Exchange Rates in the Euro Area[END_REF] were the first to investigate the link between real effective exchange rates and current-account adjustment for euro area countries. They show that the real exchange rate and the current account exhibit a significant relationship which is subject to nonlinearity. They mention that these findings should however be interpreted with caution since both the current account and the real exchange rate are endogenous variables that notably depend on productivity shocks. Consequently, a thorough examination of the current account -real exchange rate nexus requires to control ex ante each of the two variables by its fundamentals, such as productivity shocks. This highlights the interest and the relevance of investigating the relationship between exchange-rate misalignments and the gap between the observed current account and its equilibrium level calculated from its traditional determinants. Such investigation constitutes the core of our contribution.

Examining the link between exchange-rate misalignments and current-account imbalances is of crucial importance for two main reasons. First, if current-account imbalances receive a lot of attention in the perspective of global imbalances reduction, current-account surpluses or deficits become truly problematic only when the current account diverges from its fundamental level. Indeed, as long as the evolution of the current account reflects that of its economic fundamentals, current-account surpluses or deficits are natural phenomena that do not require a particular adjustment-or, at least, the correction is done naturally without important economic costs. However, when the gap between the current account and its equilibrium level becomes persistent, reversion to equilibrium often requires important costs from an economic viewpoint. This is particularly acute when countries form a monetary union, since adjustment by (nominal) exchange rates is not operational. Consequently, by arguing that correction of current-account imbalances requires a realignment of exchange rates, previous literature [START_REF] Mussa | Sustaining global growth while reducing external imbalances[END_REF][START_REF] Freund | Current Account Deficits in Industrial Countries: The Bigger They Are, The Harder They Fall?[END_REF][START_REF] Edwards | On current account surpluses and the correction of global imbalances[END_REF][START_REF] Méjean | Current Account Rebalancing and Real Exchange Rate Adjustment between the US and Emerging Asia[END_REF] implicitly assumes that exchange-rate misalignments are the main cause of current disequilibria. Second, there is no consensus in the literature regarding whether current-account imbalances mainly result from currency misalignments. Indeed, as [START_REF] Blanchard | Current account deficits in the euro area: the end of the Feldstein-Horioka puzzle?[END_REF], [START_REF] Stevens | Les déséquilibres mondiaux vus au travers du prisme de l'épargne et de l'investissement[END_REF] argues that the causes of current-account imbalances should rather be sought in the disequilibrium between savings and 2 [START_REF] Edwards | Is the US current account deficit sustainable? And if not, how costly is adjustment likely to be?[END_REF] provides a review of empirical studies dealing with the "required" dollar adjustment to correct the U.S. current account imbalance.

investment, instead of focusing on exchange-rate misalignments. On the contrary, the study by [START_REF] Arghyrou | Current Account Imbalances and Real Exchange Rates in the Euro Area[END_REF] highlights the relevance of exchange rates in explaining currentaccount imbalances.

Contributing to this strand of the literature and within this context of global imbalances, our aim in this paper is to study the persistence of current-account disequilibria, as well as the adjustment mechanism towards equilibrium by paying a particular attention to the impact of exchange-rate misalignments. More specifically, we investigate whether the persistence of the gap between the observed current-account position and its equilibrium value depends on the deviation of the exchange rate to its equilibrium. To this end, we consider a panel of 22 industrialized countries over the period ranging from 1980 to 2011. Our contribution in this paper is threefold. First, we specifically account for the structural determinants of the current-account position by estimating a relationship linking the current account to its key fundamentals. This allows us to derive more reliable current-account equilibrium (or fundamental) values than those based on usual Hodrick-Prescott filtered series. Second, while many other contributions consider only the reversal phases of the current account and rely on probit specifications (see Section 2), we specifically model the adjustment process of the current account through a panel nonlinear specification. We consider panel smooth transition regression models that allow us to investigate whether the size and the sign of the exchange-rate deviation to its equilibrium value impacts the degree of persistence of current-account imbalances. Third, we analyze whether the relationship between current-account imbalances and currency misalignments differs depending on whether countries belong or not to a monetary union by considering two sub-samples of countries-distinguishing between eurozone members and the other economies.

Our main findings are the following. First, persistence of current-account imbalances strongly depends on currency misalignments. More specifically, while there is no persistence in cases of currency undervaluation or weak overvaluation, persistence tends to augment for overvaluations higher than 11%. Second, belonging or not to a monetary union impacts the conclusions. Indeed, whereas disequilibria tend to be persistent even for very low exchange-rate overvaluations in the euro area, this is not the case for non eurozone members. For the latter, persistence is observed for overvaluations higher than 14%.

The rest of the paper is organized as follows. Section 2 briefly reviews the literature. Section 3 details our methodology. Data and estimation of equilibrium values are presented in Section 4. Section 5 displays our estimation results and Section 6 concludes.

A brief review of the literature

Several theoretical and empirical contributions have focused on current-account imbalances' sustainability and the adjustment mechanisms towards equilibrium. 3 Most of those studies find that the adjustment of the current account is associated with a slowdown in economic growth and a real depreciation of the exchange rate. Indeed, using a dataset including 25 adjustment episodes from 1980 to 1997, [START_REF] Freund | Current account adjustment in industrial countries[END_REF] shows that there is a threshold level of current-account deficit that is consistent with its sustainability: current-account reversals typically start when the currentaccount deficit reaches 5% of GDP, leading to a significant decline in output growth and a real depreciation of the currency around 10 to 20%. Examining episodes of current-account adjustment in developed countries, [START_REF] Debelle | Current Account Adjustment and Capital Flows[END_REF] also find that current-account reversals are associated with a notable slowdown in domestic growth and large exchange rate depreciation. Accounting for the influence of financial variables, [START_REF] Croke | Financial market developments and economic activity during current account adjustments in industrial economies[END_REF] show that some phases of current-account adjustments lead to a substantial decline in economic growth without necessarily being associated with a sharp depreciation of the exchange rate. By contrast, the episodes of current-account adjustments that have not leaded to a decline in GDP growth have often resulted in a significant depreciation of the exchange rate. Focusing on the U.S. deficit using a general equilibrium model, Obstfeld andRogoff (2005, 2007) show that a reversal of the U.S. current account would result in a significant depreciation of the U.S. real effective exchange rate, leading to severe consequences for economic growth. Some studies also pay a particular attention to the speed of the adjustment process of the current account towards equilibrium. 4 Freund and Warnock (2007) show that large deficits take more time to adjust than small ones, and are associated with a significant slowdown in GDP growth with a greater impact in countries where exchange-rate movements are limited. Besides, they find that deficits resulting from investment growth are less painful in terms of exchange-rate adjustment than deficits driven by consumption. Relying on threshold autoregressive models for the G7 countries, [START_REF] Clarida | Are there thresholds of current account adjustment in the G7?[END_REF] highlight that the adjustment speed of the current account is slow, especially when some threshold levels of deficit are reached. They also underline that exchange rates tend to depreciate in phases of current-account deficits, and appreciate during current-account surplus episodes. [START_REF] Edwards | On current account surpluses and the correction of global imbalances[END_REF] provides a scenario for the correction of global imbalances through a realignment of global economic growth, with Japan and the eurozone growing faster and the U.S. moderating its growth. He finds that such adjustment could only make a modest contribution towards the resolution of global imbalances, putting forward that significant exchange-rate movements are needed. Focusing on eurozone countries, [START_REF] Arghyrou | Current Account Imbalances and Real Exchange Rates in the Euro Area[END_REF] rely on logistic smooth threshold error correction specifications and show that the relationship between real exchange rates and current accounts is substantial in size and subject to important nonlinear effects. Using a probit specification to model the probability of reversals versus non-reversals, De [START_REF] De Haan | What Do Current Account Reversals in OECD Countries Tell Us About the US Case?[END_REF] show that a deeper current-account deficit, absence of spare capacity in the economy, and a beginning real depreciation significantly increase the predictive power of an upcoming reversal of the current account. In addition, the exchange-rate regime matters since the reversal of a large current-account deficit is less probable under a peg or moving band regime than under crawling peg. They also find that current-account adjustments lead to recessions and severe currency devaluations in half of the reversal cases. Using a similar approach, Pancaro (2013) highlights as well the importance of the exchange-rate regime on the current-account adjustment. Real exchange rate depreciation is a significant trigger only under flexible regimes, and the adjustments of current-account imbalances are not per se harmful to economic activity, neither in the whole sample of 22 industrialized countries, nor in the sub-sample containing economies with fixed exchange-rate regimes.5

Methodology

To investigate whether the persistence of current-account imbalances nonlinearly depends on the deviation of the exchange rate from its equilibrium value, we rely on the panel smooth transition regression (PSTR) methodology introduced by [START_REF] González | Panel Smooth Transition Regression Models[END_REF]. According to this specification, the observations are divided in-say-two regimes, with estimated coefficients that vary depending on the considered regime. The change in the estimated value of coefficients is smooth and gradual, since PSTR models are regime-switching processes in which the transition from one state to the other is smooth rather than discrete. Let CA , is our dependent variable, namely the gap between the observed current account and its equilibrium value-the latter being derived from the estimation of a model including current account's key determinants (see Section 4). Mis i,t denotes the misalignment series, given by the deviation of the observed real effective exchange rate to its equilibrium value-the latter being derived from the Behavioral Equilibrium Exchange Rate (BEER) methodology (see Section 4). Mis i,t acts as the transition variable in our PSTR specification, which is given by:

  t i t i gap t i gap t i i gap t i c Mis F CA CA CA , , 1 , 1 1 , 0 , , ;             (1)
where  i denotes the country-fixed effects and  i,t is an independent and identically distributed (i.i.d.) error term. This specification hence allows us to investigate whether the persistence of current-account imbalances varies according to the sign and size of exchange-rate misalignments. The transition function F is normalized and bounded between 0 and 1, and is given by [START_REF] González | Panel Smooth Transition Regression Models[END_REF]:

    1 1 , , exp 1 , ;                        m j j t i t i c Mis c Mis F   (2)    0  
stands for the slope parameter, and c j , j = 1, …, m, are the threshold parameters

satisfying m c c c    ... 2 1
. The two most common cases in practice correspond to m = 1 (logistic) and m = 2 (logistic quadratic). In the case of a logistic function, the dynamics is asymmetric and the two regimes are associated with small and large values of exchange-rate misalignments relative to the threshold. In the case of a logistic quadratic function, the dynamics is symmetric across the two regimes, but the intermediate regime follows a different pattern compared to that in the extremes.

We follow the three-step methodology proposed by [START_REF] González | Panel Smooth Transition Regression Models[END_REF] to apply PSTR models. 6 The aim of the first, identification step is twofold: (1) testing for homogeneity against the PSTR alternative; and (2) selecting (i) between the logistic and logistic quadratic specification for the transition function, and (ii) the transition variable. In the second, estimation step, nonlinear least squares are used to obtain the parameter estimates, once the data have been demeaned [START_REF] Hansen | Threshold effects in non-dynamic panels: Estimation, testing, and inference[END_REF][START_REF] González | Panel Smooth Transition Regression Models[END_REF]. In the third, evaluation step, various misspecification tests are implemented to check the validity of the estimated PSTR model and determine the number of regimes.

Data and equilibrium values

We rely on a panel of 22 countries 7 , including: (i) 11 eurozone members, namely Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, the Netherlands, Portugal and Spain; and (ii) 11 non-eurozone countries: Australia, Canada, Denmark, Iceland, Japan, New Zealand, Norway, Sweden, Switzerland, United Kingdom, and the United States. Data are annual, spanning the period from 1980 to 2011.

Medium-term current-account estimation

Our dependent variable, denoted as

gap t i
CA , , is defined as follows:

t i t i gap t i A C CA CA , , ,   (3) 6
For details regarding the methodology, the reader is referred to the original contributions by [START_REF] Hansen | Threshold effects in non-dynamic panels: Estimation, testing, and inference[END_REF] and [START_REF] González | Panel Smooth Transition Regression Models[END_REF]. 7 We have initially considered the 31 high-income OECD countries (according to the World Bank) and selected the 22 countries for which data were available over the whole period under study. Thus, our 22 countries are among the most developed economies, allowing us (i) to deal with a relative homogenous sample, and (ii) to distinguish between countries belonging to a monetary union and the others.

where t i CA , stands for the observed current account (in percentage of GDP) and

t i A C ,
ˆ denotes its estimated equilibrium value. The latter is given by the estimation of the following specification:

     n j t i j t i j i t i Z b a CA 1 , , ,  (4)
with n denoting the number of explanatory variables Z i,t ,  i,t being an i.i.d. error term, and a i standing for country-fixed effects. Following the literature on current-account medium-term determinants [START_REF] Lane | External adjustment and the global crisis[END_REF], we consider various explanatory variables of the current account: (i) the relative fiscal balance (rdef) expressed as a ratio to GDP, (ii) the lagged net foreign asset position (nfa) expressed as percentage of GDP, (iii) the relative level of PPPadjusted GDP per capita (prod), (iv) the relative GDP growth rate (rgrw), (v) the aging rate (raging) defined as the expected change in the old-age dependency ratio in the future (constructed as the difference between the age dependency ratio in year t+20 and the same ratio in year t, the t+20 estimate being based on United Nations' population projections), (vi) the oldage dependency ratio (rold) defined as the ratio of the population aged 65 and older to the working-age population, (vii) the population growth rate (popg), (viii) a proxy of financial deepening (m2) given by the M2 to GDP ratio, (ix) the degree of openness (open) given by the ratio of exports plus imports of goods and services to GDP, (x) terms of trade (tot), and (xi) the oil balance (oilb) expressed as percentage of GDP. Data sources for each series are presented in Table A1 in Appendix.

All variables but nfa, m2, open, tot and oilb are expressed in relative terms, since only idiosyncratic shifts in fundamentals should affect the current account (see [START_REF] Lane | External adjustment and the global crisis[END_REF]. To this end, they are measured relative to a weighted average of country i's trading partners. The weights are the same as those used by the Bank for International Settlements (BIS) for the calculation of real effective exchange rates considered in the present study. This allows us to have consistency in the way of calculating the variables expressed in relative terms, including the real effective exchange rate.

Tables A2 andA3 in Appendix report the estimation results of Equation (4). In Table A2, all series are considered as 4-year averages to smooth business-cycle fluctuations.8 Given that this reduces automatically the number of observations, we also estimate Equation ( 4) without averaging the data as a robustness check. The corresponding results are displayed in Table A3.

The different specifications explain nearly 70% of current-account variance-an explanatory power which is significantly higher than what is usually obtained in previous panel data empirical studies reviewed in Section 2. Figure A1 in Appendix illustrates the accuracy of our estimations by scattering the observed current account against its estimated, equilibrium value. Although slight differences can be highlighted, the two types of regressions-based on averaged data and on annual data-give very similar results. In addition, our estimates are robust to the retained specification. Indeed, as shown in Table A4 in Appendix, correlations between current-account gaps calculated from different specifications are larger than 96% for both types of regressions, illustrating the robustness of our estimations.

Several interesting findings can be highlighted from our results. Fiscal policy, the net foreign asset position, demographic factors such as population growth and aging rate, trade openness and oil balance exert robust significant effects on the current-account dynamics in our advanced countries. The terms of trade and financial deepening also significantly affect the current account, but to a lesser extent. In addition, the positive link established between the fiscal balance and current account simply means that an improvement in the former tends to ameliorate the latter in the same way that deterioration in the fiscal balance would be detrimental for the current account. This finding is consistent with the predictions of several theoretical specifications including among others [START_REF] Blanchard | Debt, deficits and finite horizons[END_REF]'s finite-horizon model and overlapping generation models [START_REF] Obstfeld | Foundations of international macroeconomics[END_REF], stating that deteriorations in the fiscal balance tend to have the same effect on the current account to the extent that they involve a redistribution of income from future to present generations.

The positive net foreign assets' (NFA) effect on the current account was also expected given that an improvement in the net foreign asset position leads to an increase in net investment income, which is a direct component of the current account. Regarding demographic factors, two opposite effects are at play in our panel of advanced countries. The aging rate positively affects the current account because it is associated with a higher level of savings [START_REF] Lane | External adjustment and the global crisis[END_REF], while population growth contributes to the deterioration of the current account due in particular to the lack of savings among the very young population. The oil balance-that captures countries' dependence to the evolution of oil prices-is also positively correlated with the current account, indicating that the more countries deficient in oil are, the more the deficit in the current account. Finally, the positive link between current account and openness is justified to the extent that it could reflect the choice of countries' tariff policy with regard to international trade. Indeed, the ability of the most open economies to generate foreign exchange earnings through exports could signal a greater ability to service external debt [START_REF] Chinn | Medium-term determinants of current accounts in industrial and developing countries: an empirical exploration[END_REF].

Regarding previous empirical studies, our findings are close to those of [START_REF] Lane | External adjustment and the global crisis[END_REF]. Indeed, relying on a similar panel of developed countries, they find that the fiscal balance significantly explains the current account with a positive estimated coefficient of 0.27. This is also the case for the aging rate, lagged NFA and oil balance, with respective estimated coefficients of 0.22, 0.05 and 0.26. Our estimated coefficients-ranging from 0.24 to 0.33 for the fiscal balance, 0.23 to 0.32 for the aging rate, 0.05 to 0.06 for the lagged NFA position, and 0.30 to 0.36 for the oil balance-are thus quite close to those obtained by [START_REF] Lane | External adjustment and the global crisis[END_REF]. Using similar estimation techniques, [START_REF] Chinn | Medium-term determinants of current accounts in industrial and developing countries: an empirical exploration[END_REF] also show that the NFA to GDP ratio positively influences the medium-term current-account dynamics with an estimated coefficient of 0.07 (close to ours) but fail to establish other significant links. However, when they rely on cross-section estimation techniques, other variables such as fiscal balance, relative income, terms-of-trade volatility and average GDP growth significantly impact the current account-the fiscal balance coefficient is estimated at 0.34, close to ours. Using panel estimation techniques on annual data over the 1975-2007 period for 11 euro area countries, Decrassin and Stavrev (2009) find that the current account is essentially determined by population growth, oil balance, NFA, old dependency ratio, fiscal balance and relative per capita income-the respective estimated coefficients being -2.79, 0.54, 0.04, -0.17, 0.18 and 0.06. In a simplified current-account model, Gagnon (2011) also shows that the latter is mainly affected by the fiscal balance and net foreign asset position in industrial countries, with respective estimated coefficients of 0.30 and 0.07. On the whole, our findings are thus in line with previous empirical studies. 9

Equilibrium exchange rates and misalignments

To derive currency misalignments, we estimate equilibrium exchange-rate values relying on the BEER approach [START_REF] Macdonald | What determines the real exchange rate? The long and the short of it[END_REF][START_REF] Clark | Exchange Rates and Economic Fundamentals: A Methodological Comparison of BEERs and FEERs[END_REF]. Following [START_REF] Alberola | Global equilibrium exchange rates: Euro, Dollar, 'ins', 'outs' and other major currencies in a panel cointegration framework[END_REF] and [START_REF] Bénassy-Quéré | Robust estimations of equilibrium exchange rates within the G20: A panel BEER approach[END_REF], 2011) among others, we consider a simple stock-flow model and express the real effective exchange rate (reer, in logarithms) as a function of the net foreign asset position (in percentage of GDP) and a proxy for relative productivity given by the variable prod:

t i t i it i t i u nfa prod reer , , , ,       
(5) u i,t being and i.i.d. error term, and i  accounting for country-fixed effects. The estimation of the long-term, cointegrating relationship (5) gives the equilibrium value of the real effective exchange rate. OLS estimates being biased and dependent on nuisance parameters, we rely on the Dynamic OLS (DOLS) method introduced by [START_REF] Kao | On the estimation and inference of a cointegrated regression in panel data[END_REF] and [START_REF] Mark | Cointegration vector estimation by panel Dynamic OLS and long-run money demand[END_REF] in the context of panel cointegration. 10 Roughly speaking, the DOLS procedure consists in augmenting the cointegrating relationship with lead and lagged differences of the regressors to control for the endogenous feedback effect. Using this procedure, we get the following results 11 :

t i t i i est t i nfa prod reer , ) 03 . 0 ( , ) 150 . 0 ( , 069 . 0 400 . 0 ˆ    (6)
where standard errors of the estimated coefficients are given in parentheses. As expected, a rise in 9

Note that other empirical studies (for example [START_REF] Bussière | Current account dynamics in OECD and EU acceding countries-an intertemporal approach[END_REF][START_REF] Gruber | Explaining the global pattern of current account imbalances[END_REF][START_REF] Cheung | China's current account and exchange rate[END_REF]Ca'Zorzi et al., 2012) have not been discussed here mainly because they are based on non-comparable country samples or estimation procedures. 10 As a robustness check, we have also used the PMG approach introduced by [START_REF] Pesaran | Pooled mean group estimation of dynamic heterogeneous panels[END_REF] which allows the short-run coefficients to differ freely across countries while the long-run coefficients are restricted to be the same for all individuals. Results (available upon request) are similar to those obtained with the DOLS procedure.

11 Second generation panel unit root and cointegration tests-accounting for cross-section dependences-have been applied, showing that our three series can be considered as unit root processes and are cointegrated (see Tables A5 andA6 in Appendix). Note also that cross-section dependences have been accounted for in the DOLS estimation of the long-term, cointegrating relationship.

the relative productivity as well as in the NFA position leads to an exchange-rate appreciation. In addition, both those explanatory variables are significant at conventional levels.

The corresponding currency misalignments are then given by:

est t i t i t i reer reer Mis , , ,

 

where a positive (resp. negative) sign refers to an overvaluation (resp. undervaluation).

PSTR estimation results

We start by testing the null hypothesis of linearity in Equation ( 1) against the PSTR alternative using the first-lagged misalignment series as the transition variable. In other words, we test whether the persistence of current-account imbalances differs according to the deviation of the exchange rate from its equilibrium value. Results are reported in Table 1 and show that the null of linearity is rejected in favor of the alternative of logistic PSTR specification. This finding indicates that currency misalignments impact the current-account gap differently, depending on the sign and size of the exchange-rate deviation to its equilibrium value. We thus now proceed to the estimation of the PSTR model to investigate this property more deeply. As shown in Table 2, the effect of currency misalignments on persistence of current-account imbalances is clearly nonlinear. Indeed, for undervaluations and overvaluations up to 11%, the autoregressive coefficient is equal to 0.58, meaning that around half of disequilibrium is corrected. For overvaluations larger than 11%, persistence strongly increases, reaching the unit value in the extreme case (i.e., when F = 1).

These findings globally confirm the predictions of a number of simulation models according to which exchange-rate misalignments (overvaluation and undervaluation) lead to current-account imbalances (excessive surplus or deficit).12 Some international institutions like the International Monetary Fund support this view and believe that a readjustment of the exchange rate constitutes one of the privileged tracks to correct global imbalances. Our results also partly explain the lack of consensus in the empirical literature regarding the current account -real exchange rate nexus and, hence, the relevance of our nonlinear, threshold specification. Indeed, small variations in the exchange rate that do not conduct to under-or overvaluation of the currency may not lead to current-account imbalances. However, beyond a certain threshold (11% in our case) of misalignment (an overvaluation here), current-account deficits are widening, thereby involving costly adjustment (or reversal). Furthermore, our results are also consistent with the stylized facts highlighted by several empirical studies according to which the reversal of current-account deficits is usually done through strong depreciation of the currency (see, among others, [START_REF] Freund | Current account adjustment in industrial countries[END_REF]Obstfeld and[START_REF] Obstfeld | The Unsustainable U.S. Current Account Position Revisited[END_REF].

Given that our panel of countries includes eurozone members and non-members, we now investigate whether belonging to a monetary union has an influence on our previous findings. To this end, we split our panel in two sub-samples: a panel including 11 euro area members, and a panel encompassing the other countries. While, as shown in Table 3, the null of linearity is also rejected for both sub-samples at the 5% significance level, interesting differences can be highlighted from the results displayed in Table 4. The estimated threshold for the euro area is close to 0. This means that undervaluations and overvaluations impact differently the persistence of current-account imbalances. More specifically, while disequilibria tend to be corrected in cases of undervaluations, persistence increases in cases of overvaluations, but the estimated autoregressive coefficient remains lower than 1 even in the extreme case (the autoregressive coefficient is equal to 0.89 when F = 1). The situation is quite different for the other countries, with current-account imbalances that tend to accelerate in cases of overvaluations larger than 14%. In other words, while corrections of disequilibria are at play in the euro area even if they are persistent when the euro is overvalued, this is not the case in non-eurozone economies for which imbalances are enhanced when facing strong overvaluations.

These results are in line with the predictions of the optimum currency area theory [START_REF] Mundell | A theory of optimum currency areas[END_REF] and [START_REF] Friedman | The case for flexible exchange rates[END_REF], according to which countries with flexible exchange-rate regimes are more likely to adjust their current-account imbalances. Indeed, the main cost of monetary union membership is the loss of autonomy in the conduct of monetary policy and, therefore, an inability to adjust the exchange rate against the economic environment. Consequently, an exchange-rate misalignment (in particular an overvaluation) will result in a systematic deterioration of the current account, especially when internal adjustment measures (such as wage compression) are not set up to correct the loss of competitiveness. Euro area countries have very little leeway on their price competitiveness and, hence, weak overvaluations can lead to highly persistent currentaccount deficits. This is particularly true for countries such as Greece and Portugal which have experienced very deep current-account deficits in recent years. Figures A2 in Appendix illustrate these findings, with the clear link between the Greek and Portuguese overvaluations and persistent huge current-account deficits since the mid-1990s. Countries outside the euro area having more leeway in their price competitiveness, they can afford to have larger misalignments to suit their trade policy (or exchange-rate policy). However, our findings show that this autonomous management of exchange-rate policy is limited as beyond a certain level of overvaluation (14% in our case), the current-account deterioration can be much deeper. This is notably the case for Canada (Figures A2) for which the persistent current-account deficit is in line with the important overvaluation of the Canadian dollar at the end of the period under study.

Conclusion

Within the current context of global imbalances, the aim of this paper is to study persistence of current-account disequilibria, as well as the adjustment mechanism towards equilibrium by paying a particular attention to the impact of exchange-rate misalignments. We investigate whether the persistence of the gap between the observed current-account position and its equilibrium value depends on the deviation of the exchange rate to its equilibrium. To this end, we estimate a nonlinear panel smooth transition regression model on a sample of 22 industrialized countries over the period ranging from 1980 to 2011.

Our findings show that persistence of current-account imbalances is strongly dependent on currency misalignments. More specifically, there exists a misalignment threshold beyond which current-account imbalances are widening and tend to persist. Indeed, while there is no persistence in cases of currency undervaluation or weak overvaluation, persistence tends to augment for overvaluations higher than 11%. Decomposing our panel between members and non-members of the euro area, we show that belonging or not to a monetary union affects the current accountmisalignments nexus. Indeed, while disequilibria tend to be persistent even for very low exchange-rate overvaluations in the euro area, this is not the case for non eurozone members. For the latter, persistence is observed for overvaluations higher than 14%. Our findings show that, due to the impossibility of exchange-rate adjustment in the euro area, a currency overvaluation will result in systematic current-account deterioration.

Our results have important policy implications, and suggest that exchange-rate misalignments should be followed with great attention. This is especially crucial for countries belonging to a monetary union, in order to avoid abrupt and significant economic costs linked to the adjustment of unsustainable current-account imbalances-such adjustment being impossible through the nominal exchange rate. Exchange-rate misalignments constituting a leading indicator of potential currency crises [START_REF] Holtemöller | Exchange rate regime, real misalignment and currency crises[END_REF], they should, as the output gap, be a key instrument in the conduct of economic policy. By systematically monitoring exchange-rate misalignments and early alerting governments when the (effective) real exchange rate follows any adverse trend, monetary authorities should play a preventive role. This involves accurately estimating exchange-rate misalignments, using methods for which the member countries of the monetary union agreed. A restrictive fiscal policy would be more appropriate in cases of overvaluation to limit the loss of competitiveness and the deterioration of the current account.

Conversely, in times of undervaluation, a more expansionary policy should be conducted. Such reactions are particularly desirable in a monetary union because important competitiveness divergences are harmful to the union. In a long-term perspective, countries with persistent current-account deficits should undertake structural changes (including more fiscal discipline, labor market reform, strengthening of private savings) to achieve a comparable level of productivity and competitiveness with their main trading partners.

Finally, if exchange-rate misalignments obviously impact current-account imbalances, other factors such as overheating of economic activity are likely to contribute to the deterioration of the current account (see [START_REF] Blanchard | The U.S. Current Account and the Dollar[END_REF]. Consequently, a promising extension of our paper would be to investigate the interactions between these macroeconomic discrepancies (output gap, misalignment, current-account gap), as well as their causal links to provide an in-depth analysis of the various necessary measures to reduce global imbalances.

  Figure A1. Estimation accuracy: observed current account and estimated current account (from the specification (6) of TableA3)

Table 1 . Results of linearity tests (p-values), whole sample

 1

	r = 0	r = 1

Note: LM and F denote Lagrange Multiplier and F tests for linearity. r =0 refers to the null hypothesis of linearity against the alternative of a PSTR model with two regimes. r =1 refers to the null hypothesis of PSTR model with two regimes against the alternative of a PSTR model with three regimes.

Table 2 . Results of the PSTR estimation, whole sample

 2

	Variable	Coefficient	t-statistic
	gap t i CA 1 , 	0.5806***	8.51
	gap t i CA 1 ,   F	0.4968*	1.70
	Threshold c ˆ	0.1124
	Slope coefficient ˆ	17.2894

Note: *** (resp. **, *): significant at the 1% (resp. 5%, 10%) level.

Table 3 . Results of linearity tests (p-values), sub-samples

 3 LM and F denote Lagrange Multiplier and F tests for linearity. r =0 refers to the null hypothesis of linearity against the alternative of a PSTR model with two regimes. r =1 refers to the null hypothesis of PSTR model with two regimes against the alternative of a PSTR model with three regimes.

		Euro members	Others
	Variable	r = 0	r = 1	r = 0	r = 1
	LM	0.018	0.338	0.021	0.190
	F	0.019	0.348	0.023	0.200

Note:

Table 4 . Results of the PSTR estimation, sub-samples

 4

		Euro members	Others
	Variable	Coefficient	t-statistic	Coefficient	t-statistic
	gap t i CA 1 , 	0.6055***	8.28	0.5162***	7.52
	gap t i CA 1 ,   F	0.2892***	2.99	1.28***	4.49
	Threshold c ˆ	-0.0073		0.1406
	Slope coefficient ˆ	880.7212		1279.3
	Note: *** (resp. **, *): significant at the 1% (resp. 5%, 10%) level.

Table A2 .Current-account estimation (Panel OLS with 4-year averaged data)

 A2

		(1)	(2)	(3)	(4)	(5)	(6)
	Variables	CA	CA	CA	CA	CA	CA
	rdef	0.239***	0.247***	0.257***	0.257***	0.327***	0.327***
		(0.0844)	(0.0847)	(0.0887)	(0.0887)	(0.0813)	(0.0813)
	nfa	0.0534***	0.0576***	0.0528***	0.0528***	0.0612***	0.0612***
		(0.00876)	(0.00839)	(0.00917)	(0.00917)	(0.00649)	(0.00649)
	prod	0.0425	-0.0917	0.0360	0.0360
		(0.109)	(0.0697)	(0.111)	(0.111)
	prods	-0.000492	0.0608	0.00365	0.00365
		(0.0542)	(0.0386)	(0.0555)	(0.0555)
	rgrw	0.0973	0.0808	0.0463	0.0463
		(0.190)	(0.190)	(0.201)	(0.201)
	raging	0.305***	0.321***	0.307***	0.307***	0.229***	0.229***
		(0.0857)	(0.0856)	(0.0893)	(0.0893)	(0.0659)	(0.0659)
	rold	0.0203	0.00582	0.0200	0.0200
		(0.0253)	(0.0238)	(0.0257)	(0.0257)
	popg	-2.714***	-2.829***	-2.720***	-2.720***	-2.718***	-2.718***
		(0.872)	(0.873)	(0.887)	(0.887)	(0.659)	(0.659)
	m2	-0.0127**	-0.0135**	-0.0129	-0.0129
		(0.00627)	(0.00628)	(0.00822)	(0.00822)
	open	0.0471***	0.0467***	0.0470***	0.0470***	0.0438***	0.0438***
		(0.00825)	(0.00830)	(0.00844)	(0.00844)	(0.00774)	(0.00774)
	tot	0.0298	0.0161	0.0265	0.0265
		(0.0214)	(0.0197)	(0.0225)	(0.0225)
	oilb	0.341***	0.296**	0.303**	0.303**	0.357***	0.357***
		(0.123)	(0.121)	(0.133)	(0.133)	(0.105)	(0.105)
	Constant	-9.984		-9.675		-2.203***
		(6.224)		(6.357)		(0.788)
	Observations	154	154	154	154	154	154
	R-squared	0.683	0.677	0.688	0.688	0.669	0.669
	Note: Robust standard errors are in parentheses; *** (resp. **, *): significant at the 1% (resp. 5%, 10%) level; (1): Model including all explanatory
	variables and constant; (2): Model including all explanatory variables without constant; (3): Model including all explanatory variables + constant + time
	dummy; (4): Model including all explanatory variables without constant + time dummy; (5): Model including only significant explanatory variables +
	constant + time dummy; (6): Model including only significant explanatory variables -constant + time dummy.

Table A3 . Current-account estimation (Panel OLS with annual data)

 A3 Robust standard errors are in parentheses; *** (resp. **, *): significant at the 1% (resp. 5%, 10%) level; (1): Model including all explanatory variables and constant; (2): Model including all explanatory variables without constant; (3): Model including all explanatory variables + constant + time dummy; (4): Model including all explanatory variables without constant + time dummy; (5): Model including only significant explanatory variables + constant + time dummy; (6): Model including only significant explanatory variables -constant + time dummy.

		(1)	(2)	(3)	(4)	(5)	(6)
	Variables	CA	CA	CA	CA	CA	CA
	rdef	0.197***	0.193***	0.206***	0.206***	0.210***	0.210***
		(0.0359)	(0.0362)	(0.0368)	(0.0368)	(0.0359)	(0.0359)
	nfa	0.0550***	0.0584***	0.0556***	0.0556***	0.0610***	0.0610***
		(0.00367)	(0.00355)	(0.00375)	(0.00375)	(0.00298)	(0.00298)
	prod	0.0725	-0.0564*	0.0676	0.0676
		(0.0502)	(0.0309)	(0.0501)	(0.0501)
	prods	-0.0223	0.0363**	-0.0189	-0.0189
		(0.0248)	(0.0171)	(0.0248)	(0.0248)
	rgrw	-0.0466	-0.0530	-0.0639	-0.0639
		(0.0658)	(0.0662)	(0.0673)	(0.0673)
	raging	0.215***	0.215***	0.226***	0.226***	0.204***	0.204***
		(0.0399)	(0.0402)	(0.0414)	(0.0414)	(0.0365)	(0.0365)
	rold	-0.00425	-0.0183*	-0.00400	-0.00400
		(0.0115)	(0.0107)	(0.0115)	(0.0115)
	popg	-2.830***	-2.958***	-2.829***	-2.829***	-2.570***	-2.570***
		(0.357)	(0.357)	(0.357)	(0.357)	(0.285)	(0.285)
	m2	-0.00793***	-0.00805***	-0.00987**	-0.00987**	-0.00910**	-0.00910**
		(0.00290)	(0.00292)	(0.00383)	(0.00383)	(0.00382)	(0.00382)
	open	0.0399***	0.0392***	0.0398***	0.0398***	0.0400***	0.0400***
		(0.00398)	(0.00400)	(0.00402)	(0.00402)	(0.00380)	(0.00380)
	tot	0.0359***	0.0300***	0.0321***	0.0321***	0.0335***	0.0335***
		(0.00838)	(0.00823)	(0.00892)	(0.00892)	(0.00891)	(0.00891)
	oilb	0.398***	0.388***	0.356***	0.356***	0.414***	0.414***
		(0.0473)	(0.0476)	(0.0532)	(0.0532)	(0.0491)	(0.0491)
	Constant	-8.876***		-9.638***		-5.254***
		(2.738)		(2.777)		(1.047)
	Observations	682	682	682	682	682	682
	R-squared	0.665	0.661	0.684	0.685	0.678	0.679
	Note:

Table A4 . Correlation between the estimated current-account gaps

 A4 Note: The correlation matrix above the diagonal relates to the different estimates of the currentaccount gap with 4-year averaged data, while the correlation matrix below the diagonal (in bold) refers to the different estimations of the current-account gap from annual data.

				CA	1 gap	CA	gap	2	CA	gap	3	CA	gap	4	CA	gap	5	CA	gap	6
	CA	1 gap	1	0.9910	0.9921	0.9921	0.9628	0.9628
	CA	gap	2	0.9923	1		0.9832	0.9832	0.9684	0.9684
	CA	gap	3	0.9703	0.9628	1		1.0000	0.9703	0.9703
	CA	gap	4	0.9703	0.9628	1.0000	1		0.9703	0.9703
	CA	gap	5	0.9614	0.9617	0.9892	0.9892	1		1.0000
	CA	gap	6	0.9614	0.9617	0.9892	0.9892	1.0000	1

Table A6 . Westerlund (2007) panel cointegration tests

 A6 Note: P-values are robust critical values obtained through bootstrapping with 1000 replications.The Bartlett kernel window width is set according to

			With constant		With constant and trend
	Statistics
		Value	Z-Value	P-Value	Value	Z-Value	P-Value
	t G	-2.338	-1.546	0.189	-3.077	-3.063	0.197
	a G	-4.930	3.137	0.249	-5.382	5.279	0.071
	t P	-9.271	-1.196	0.005	-12.542	-2.008	0.003
	a P	-6.912	-0.878	0.006	-9.044	1.002	0.004

In this section, we mainly focus on developed countries. Regarding developing countries, the reader can refer to[START_REF] Milesi-Ferretti | Current Account Reversals and Currency Crises: Empirical Regularities[END_REF] or[START_REF] Edwards | Thirty Years of Current Account Imbalances, Current Account Reversals and Sudden Stops[END_REF].

For a recent study regarding the adjustment of large current-account imbalances that preceded the global financial crisis, see the very interesting contribution by[START_REF] Lane | External adjustment and the global crisis[END_REF].

Considering 170 countries over the1971-2005 period, Chinn and Wei (2008) do not find clear empirical evidence to support Friedman (1953)'s hypothesis according to which a flexible exchange-rate regime would facilitate the current-account adjustment. According to[START_REF] Ghosh | Is the exchange rate regime really irrelevant for external adjustment?[END_REF], these results are due to the inability of existing regime classifications to capture exchange-rate flexibility relevant to external adjustment. Using a trade-weighted bilateral exchange-rate volatility measure, they obtain results that are consistent with Friedman's hypothesis.

In using averaged data, we follow the existing literature on the medium-term current account (see references in Section 2). Note however that this seems to be more relevant for developing or emerging countries for which measurement errors are also at play, in addition to short-run fluctuations.

See for example[START_REF] Mussa | Sustaining global growth while reducing external imbalances[END_REF],[START_REF] Goldstein | China's exchange rate policy dilemma[END_REF], andObstfeld and Rogoff (2005, 2007).

Appendix