Gaël Giraud
email: gael.giraud@parisschoolofeconomics.fr

On the Simultaneous Emergence of Money and the State

Keywords: Money, strategic market game, political economy, heterogenous beliefs. JEL Classification Numbers : D50, E40, E50, E58

We construct a infinite-horizon political game where the production of a public good is delegated to a politician. The politician is controlled by finitely many citizens who, on the other hand, trade commodities and pay taxes on a voluntary basis. We provide conditions in terms of heterogenous beliefs under which one single commodity is used both as a universal means of exchange and a means to pay taxes. These provide an analytical framework for the understanding of money as originating both from the private and the public sector simultaneously.

Introduction

There are at least two competing views about the origin of money. On the one hand, part of the literature claims that governments first issued money, which would place it in the civic realm and the world of politics. This argument stems partly from the early practices of paying obligations to religious or state authorities. As ? points out, the primitive notion of Wergeld (worth payment) referred to a compensation for injuries and damages in communal or tribal societies. Ingham draws the following conclusion:

All evidence points to the historical origins of money as a means of calculating obligations and debts in pre-market tribal and clan society. Early settled agricultural societies developed a more complex division of labour than the hunters and gatherers, generating a surplus that was distributed unequally. Measures for the assessment of differential social and political obligations were developed. These varied by the nature of the transgression and the status of the injured party, and formed the conceptual basis for money of account.1

According to this view, this first function of money was to pay debts to the state, and the establishment of the money of account was a means to uniformly measure the debt to be paid. this assignment of payment by the state might have easily provided a background for a second early practice: paying taxes. Only later did money function as a medium for the exchange of commodities. Furthermore, its capacity to serve as a medium of exchange was based on its credibility, which was maintained by the state. 2 This view differs from the goldsmith story, the traditional textbook explanation of the origin of paper money (see, e.g., ?). According to this story, once merchants had paper receipts instead of gold, the goldsmith "decided that they could get along by keeping only a fraction of their total deposits on reserve in their vaults and lending out the balance, they acquired the ability to create money" (p. 227). Fractional reserve banking, so goes the argument, means that money is credit and originates in the (private) banking system. Who should we therefore turn to: the government or the banks ? Conversely, we could ask whether a state did really exist before it started using some device, called money, in order to compute its liabilities.

According to ?, if money is indeed credit, it seems that the government story and the goldsmith story are actually telling the same narrative -the story of credit and debt. However, the traditional understanding of the goldsmith story is that the value of the receipts or paper money is backed by gold -a commodity. If money is viewed ultimately as a commodity (a substitute for gold or any physical asset), then the goldsmith story and the government view are not quite the same. This can be best viewed in the celebrated debate between Goldbugs and Greenbacks after the US Civil War. Farmers and laborers from the western and southern states (the Greenbacks) wanted the government to issue more greenbacks for the creation of wealth, and had a credit-view on money. The eastern-based bankers (known as Goldbugs) wanted, quite to the contrary, a return to a gold-backed currency. 3 Here, the commodity-view of money is clearly identified with banks playing the role of the foundational institution for the origin of money; similarly, the credit-view can be traced back to the government playing this role. We can therefore rephrase our first question: is money a provider, a means of provision or a commodity ?

This paper provides a political economy model where these two questions can be tackled. Our answer consists in providing analytical conditions under which money emerges both as a universal medium of exchange on markets and as a means to pay taxes. Therefore, the view sustained by our analysis is that credit-money issued by the state and commodity-money issued by banks cannot be disentangled: logically, they should appear simultaneously. In other words, money should be viewed both as a commodity and a promise or else money should not appear. This is not to say that, historically speaking, money indeed emerged chronologically both as a medium of trade and of taxes. However, the fact that money nowadays serves both purposes in virtually all countries should not be viewed as incidental according to the standpoint defended in this paper: it means that, eventually, the historical narrative of money has converged towards its logical potentialities.

More precisely, we deal with a market economy where, to begin with, all tradable commodities are treated symmetrically. In addition to commodities, investors can trade financial securities and may pay taxes to a politican. When a sufficiently high level of it is produced, a public good improves the welfare of all the citizens. The production and allocation of the public good is delegated to the politician. The political dilemma faced by the society is to ensure that the body to which the power of collecting taxes and producing the public good is delegated does not use it for its own interests. Here, we shall see that this "fundamental dilemma" (?) is partly resolved by the control of the politicians (say, through elections). As a consequence, we show that, along an equilibrium path, on the long run, the politician on power does indeed purchase inputs with the collected taxes in order to produce some positive amount of the public good. This can be interpreted as exhibiting the emergence of the State. It then turns out that money has a value and is used by all the traders as a universal medium of exchange. We therefore conclude that the emergence of the state and that of money are concomitant.

At variance with most of the literature devoted to optimal tax systems, here, taxes are paid on a voluntary basis. Indeed, it is well known that a State becomes legitimate only once it is able to raise taxes without having to exert any apparent violence on the citizens, i.e., whenever they voluntarily pay their due taxes. 4 Here, we do not take as granted the existence of such a legitimate State. Rather, we seek for the conditions of its emergence. Thus, we assume that politicians may be self-interested and that citizens can vote them out of office if dissatisfied with their performance (which conforms to the Political Economy literature, see ? or ?). But, in addition, we assume that the politician in power has no way to impose the tax level. What she decides on her own is the usage she makes from tax receipts. Either she uses them to purchase commodities for their own, private consumption ; or she purchases inputs for the production of the public good. In general, of course, the politician in power will do both. The peoples' willingness to pay taxes will then depend upon their satisfaction with the politician's policy.

Model

We first describe the basic trading mechanism involving private goods, beads and the public good. In subsection 2.2., this stage game is embedded into an infinite-horizon political game.

The trading mechanism

Consider a one-shot game at time t, where players act strategically, and prices form following a mechanism à la Amir-Sahi-Shubik-Yao (?).5

The economy is populated by H households. There are N commodities traded pairwise at 1 2 N (N -1) trading-posts. Each household h is characterized by an endowment

e h ∈ R N + . The action, a h , of household h consists of a N × N matrix B h = (b h,i j ) i,j=1,...,N such that (i) b h,i j ≥ 0 ∀i, j = 1, ..., N ; (ii) j b h,i j ≤ e h i
where b h,i j is the amount of commodity i that h sends for sale on the trading-post (i, j). The price matrix, P = (p i j ) i,j=1,...,N is given by:

p i j :=    h b h,i j h b h,j i if h b h,j i > 0; 0 otherwise.
The N th commodity is called "bead", and has an intrinsic value for consumption. We do not assume from the beginning that beads are used as a store of value of a universal medium of exchange. We will seek for conditions under which they can be endogenously chosen, along an equilibrium path, in order to play the role of a universal medium of exchange.

There are transaction costs. Let us denote by c i j ≥ 1 a measure of the transaction cost incurred by each trader when she purchases commodity i by means of commodity j. The final holding of player h is

x h i := e h i - j b h,i j + j c i j p i j b h,j i . (1)
For simplicity, for all i, j < N, c i j = c < 1 and c N i = c i N = 1 for every i. That is: trading with beads is costless while trading two commodities distinct from beads against each other implies some cost.

S h denotes the strategy set of player h, S := h S h is the set of strategy profiles. Non-trivial Nash equilibria exist in the one-shot game under standard conditions (see ?).

Public good and taxes

We now flesh out the previous game by adding a public good and taxes. At each time t, one of the players, called h t , receives the ability to produce a public good, G. This good is not marketed but gives utility to households. For simplicity there is a production function F : R N + → R + mapping inputs of private goods into a unique level of public good. Given a strategy profile, s ∈ S, and a level of public good, g, the utility of player h = 1, ..., H is u h (x h [s], g), where x h [s] is the final outcome of h induced by s ∈ S according to (??).

Player h t can buy inputs for the production of the public good. By doing so, h t acts as a latent Treasury. In order to finance her purchases, h t raises taxes. Payment of taxes, however, is made on a voluntary basis. No punishment is inflicted on players who refuse to pay taxes. For this purpose, h t sells tax receipts (good N +1) in exchange for beads. By institutional convention, no commodity i < N can be traded against commodity N + 1. The trading post (N, N + 1) operates at a zero transaction cost. Tax receipts do not enter the utility function of any player.

A strategy profile of player h = h t is now an N ×N matrix, as in the previous section, together with the supply, b h,N N +1 , of beads against tax receipts. The holding-in-advance constraint for beads now reads:

j=1,...,N +1 b h,N j ≤ e h N . (2)
For every h, we denote by

Σ h ⊂ S h × [0, e h N ]
the augmented set of strategies that fulfill (??).

Player h t strategically chooses a fraction, 0 ≤

y ht i [σ] ≤ x h i [σ], of her final holding, x ht i [σ],
in commodity i as an input for producing the public good. If y ht i [σ] = 0 for every i = 1, ..., N , then h t is entirely "selfish": she raises taxes solely in order to finance her own, private purchases, instead of using them to produce the public good. Let 5 Documents de Travail du Centre d'Economie de la Sorbonne -2012.94

τ ht i := (x ht i [σ] -y ht i [σ])/x ht i [σ].
We denote by Σ ht ⊂ S ht × [0, e ht N ] × [0, 1] N the strategy set of player h t . Given σ ∈ Σ := h=1,...,ht Σ h , the quantity of public good produced is

g[σ] := F (1 -τ ht i )x ht i [σ] i=1,...,N .
And the final payoff of player

h t is u ht (x ht [σ], g[σ]
).

The infinite-horizon game

Uncertainty and preferences

We embed the previous trading mechanism in an infinite-horizon economy in discrete time, populated by finitely many types of long-lived households, h = 1, ..., H, each of them being represented by a continuum of measure 1 of identical citizens.

In each period, t, the state of nature in the next period, t + 1, is chosen using a Markov transition matrix, ω, with a finite set of possible states of nature S = {1, ..., S}.

A node σ ∈ D can be interpreted as a date-event pair (s t-1 , s), where t ≥ 1 is the minimal length of a walk between σ and the root, σ 0 , of the event tree. The history

s t-1 ∈ t-1 t =1
S is the sequence of realizations of the state of nature up to t -1. 6 The N + 1 commodities and the public good are perishable.8 Each households' random endowment, e h σ ∈ R N +1

+

, verifies e h N +1,σ = 0 and e h σ > 0 for every σ.9 Individual preferences at time t = 0 are given by:

U h (x, g) = E h 0 ∞ t=0 β t u h (x h t , g t ), (3)
where

x ∈ ∞ + (R N ×S ) is a uniformly bounded stream of commodity bundles, g ∈ ∞ + (R S )
, a bounded sequence of public goods.

Assumption (C).

For every h, u h (•) : R N + → R is C 2 , differentiably strictly increasing and concave, and verifies the "ruin aversion" hypothesis: For some α h , g ∈ R × R + , 6 Time, uncertainty and the revelation of information are described by an event tree, i.e., a directed graph (D, A) consisting of a set D of nodes and a set A ⊂ D × D of (oriented) arcs. Let τ (σ) be the time at which node σ is reached, i.e. τ : D → N such that σ = (s t-1 , s) → t. Define a partial order ≥ on D by σ = (s t-1 , s) ≥ σ = (s t -1 , s ) if, and only if, there is a walk from σ to σ. Of course, if σ = σ and σ ≥ σ , then σ > σ . The unique predecessor of σ is denoted by σ -= (s t-2 , s ). 7 The set of immediate successors of σ, denoted by σ + , is the set of nodes that are adjacent from σ. For any node σ ∈ D, the set of all nodes with σ ≥ (>)σ is denoted by D(σ) (D(σ) + ) and is itself a tree with root σ.

lim x→∂R N + u h (x, 0) = -∞, and lim x→∂R N + u h (x, g) ≥ α h ∀g > g.
This "ruin-aversion" can be interpreted as follows: in the Middle-Age, random shocks may stand for (violent) aggressions or invasions, whose outcome was sometimes a complete loss of the households' ownerships. In this context, the public good, G, may stand for a security provision (army, etc.). In case of a "bad state", s (an invasion, say), somewhat could be saved from the peasants' culture provided the king could offer some security by protecting them. In modern times, a similar interpretation holds where the security provision stands for, say, Social Security (cf. ?).

Important, also, in (??) is the superscript, h, of the expectation operator, E h (•). It means that household h evaluates her expected discounted utility with respect to her own subjective probability measure. Equation (??) can thus be rewritten:

t,s t P h (s t )β t u h (x h t , g t ),
where P h (s t ) is the probability of the history, s t , according to h's beliefs.

Each citizen h can potentially become a politician. 10 The politician in power raises taxes in beads and decides the production of the public good.

The political game

At each time t, the timing is as follows. The economy starts with a politician in power, h t . Then, 1. Citizens trade according to the strategic market game described in the section ??. In particular, they decide the amount of beads they provide to h t .

2. The politician in power, h t , chooses τ ht := (τ ht i ) i=1,...,N ) (i.e., decides the amount of public good she produces out of her purchases).

3. Elections are held and citizens jointly decide whether to keep the politician or to replace her with a new one. We abstract from the details of the institutional arrangement driving the election process. For simplicity, let us assume that, if a proportion κ ∈ (0, H] of citizens are willing to replace h t , then h t becomes out of office (κ = H/2 corresponds to the simple majority rule). 11 In this case, another citizen h t+1 is chosen at random within T \{h t } with a uniform distribution. In a pre-democratic context, the replacement of a politician in power can be interpreted as the outcome of various processes, different from a voting procedure (such as a revolution, a putsch, or even the murder of the King...).

When money and the State emerge

At node σ = (s t , s), let

h t = (s t , (p τ ) τ <σ )
denote the public history of the game up to date t, and let H t be the set of all such histories. A subgame perfect equilibrium (SPE) is given by trading actions, (a * h ) h at time t, given history h t-1 , policy decision, y ht , by the politician in power given h t-1 , and electoral decisions by the citizens, given history h t-1 , that are best responses to each other for all histories. Since we allow households to have heterogenous beliefs, the ex ante maximization of one's expected utility need not coincide with the ex post maximization of her realized utility. Thus, we focus on SPE that are renegociationproof (cf. ?). A SPE is renegociation-proof if after any history, h t , there does not exist another SPE that can make all payers weakly better off and some strictly better off. 12 As already said, each household h has her own estimate, ω h , of the transition matrix. Following ?, we assume that each citizen's estimate is not too far from the truth, :

Assumption (P). For every h, (i) there exist at least two states s, s with ω h (s, s ) = ω(s, s ). s,s ) ω(s,s ) < ρ_h ∀s, s .13

(ii) ω(s, s ) = 0 ⇒ ω h (s, s ) = 0 ∀s, s (iii) ∃ρ h , r h > 0 such that r h < ω h (
For the next result we also make the following assumption, where g has been defined in Assumption (C) above:

Assumption (G) ∀h, ∃s | F (e h s ) < g. (4)
In words, no individual player can produce a level of public good higher than the threshold g in every state, only by using her own initial endowment.

Theorem 1 Under (C), (P) and (G), along any equilibrium path induced by a nonautarkic renegociation-proof SPE, there exists t such that no replacement of the politician in power, h t , occurs after t, and, at each subsequent date, t > t, h t produces g t ≥ g.

Proof.

As a benchmark, we shall consider the perfectly competitive equilibria under complete financial markets associated with the underlying infinite-horizon economy (no public good, and no political game). Consider the situation where, in each node σ, there are S financial securities. Financial security s delivers one unit of good N (beads) if state s happens at time t + 1 and zero units otherwise. Consumers can borrow and lend freely by buying and selling Arrow-Debreu state contingent securities, only subject to the no-Ponzi condition. A competitive equilibrium is then defined in the usual way.

On the other hand, we shall need to consider an auxiliary economy where transaction costs are incorporated into the utility functions of traders. For this purpose, let τ h ∈ R N be a net trade vector (with positive components representing purchases and negative components representing sales). Define, for every < N

τ h [c] := min{τ h , τ h c }.
One has: τ h (c) = τ h if τ h < 0 and τ h (c) = τ h /c otherwise. The economy E[c] with "cdiminished" trades is defined in entirely the same way as E, except that each household's utility is replaced by

14 ∀σ, u h σ,c (x) := u h (e h σ + (x h -e h σ )[c]).
Lemma 3.1 Every non-autarkic renegociation-proof SPE involves perfectly competitive trades in the auxiliary economy E[c].

Proof.

Since there is a continuum of each type of players, we know from ? and ?, that everything goes as if, along the equilibrium path, players would not condition their strategies over the actions of their opponents. Hence, we can focus on the conditionality over (random, past) states and public prices. Next, the transaction costs and the fact that each player is negligible imply that there is no wash sales along any equilibrium path. That is, for each player h and each pair of commodities (i, j), b h,i j b h,j i = 0. Indeed, suppose there is such a wash sale, then a player could obtain the same final outcome with no wash sale at a lower cost. Since she is negligible, the change of action does not affect prices, so that the equivalent action with no wash sale is indeed profitable.

Next, the "ruin aversion" property together with the no-wash-sale property imply that the hold-in-advance constraint is never binding: no player bids her entire endowment in any commodity, i.e., .

j b h,i j < e h i . (5)
Therefore, prices that form at each node, σ, are consistent, in the sense that, for any triple (i, j, k), one has: p i k = p i j p j k . Indeed, suppose, on the contrary, that there exists a triple (i, j, k) with, say, p i k < p i j p j k . Then, player h could take advantage of this arbitrage opportunity by an obvious infinitesimal change of her action. This change is possible thanks to (??) and will not affect prices, hence will not alter the inequality p i k < p i j p j k . 15 Moreover, transaction costs do not prevent the infinitesimal deviation from being profitable, which contradicts the equilibrium character of the original strategy profile.

Since each player is negligible, this implies that the outcome of a SPE is competitive. This follows from an adaptation of ?.

End of proof of the Theorem.

One can show (using the arguments of ?) that, along a perfectly competitive equilibrium (with no public good), for every player who has incorrect beliefs, almost surely, her consumption in some commodity i will go to zero as time goes to infinity. Indeed, since she makes mistakes in her expectations about future random shocks, she takes risky positions on the financial markets (despite the fact that they are complete). Sooner or later, she will bet on the incorrect state, and loose her wealth. (Cf. Proposition 1 in ?) More precisely, one shows that

lim t→∞ P h (s t ) P (s t ) = 0.
From this, using the first-order conditions of the maximization programme of a citizen (who takes prices as given) yields, for every h and every commodity i:

lim t→∞ ∂u h c (x h (s t )) ∂x = +∞
15 This would not be true if there was a finite number of player. ? provides a counter-example. This would also fail if there were wash sales at equilibrium since a player could bid her entire initial endowment in i and repurchase part of it through her supply of another commodity in exchange for i. Notice also that a consequence of this non-arbitrage property is that the bid-ask spread is 0 on each trading-post at equilibrium. which implies that x h (s t ) → ∂R N

+ . If, in addition, the quantity of public good produced after a finite time, t, does not exceed g, this cannot be a renegociation-proof SPE because of the "ruin aversion" property: the player whose consumption comes close to the boundary, ∂R N + , would rather not trade and keep her initial endowment. Every such player will therefore elect (in the next round) a politician who produces a quantity g > g of public good.

For this purpose, however, we have to make sure that, along a renegociation-proof SPE, players will indeed pay taxes. If no player pays any taxes when wealthy, then we know from (??) that, at best, an insufficient amount g < g of public good will be produced in each period. Moreover, after a sufficiently long time, almost surely, a single player will remain (the one who, so far, never made mistakes) and all the others will remain trapped at a consumption bundle arbitrarily close to the boundary, ∂R N

+ . This cannot be a renegociation-proof SPE for the losers. Therefore, they should have rather paid some taxes when they were still wealthy in order to have some chance to get the public good later (provided they succeed in electing a benevolent politician). 16 Thus, sooner or later, a majority of the players will pay taxes and remove every politician who does not produce more than g units of public good. Now, why should any politician accept to behave in a benevolent way ? Suppose that every politician on power simply consumes all her purchases, and never produces the public good. Then, we know from the preceding considerations that each such politician will loose power after a certain time. After having been removed, a politician becomes again an anonymous household (with incorrect beliefs). Sooner or later, she will make mistakes and end up with a consumption bundle arbitrarily close to 0 (in at least one commodity) with probability 1. At this time (say τ ), she would happily receive some public good, but, by assumption, the current politician on power at time τ will also refuse to produce a quantity g > g public good. Thus, our former politician should have rather accepted to produce this public good when she was on power, in order to keep being reelected and to ensure that the public good will be produced.

Finally, since after a certain time t * , a quantity g > g of public good is produced, this implies that, from t * on, a positive amount of taxes is paid by citizens. Hence, beads are used in each period in order to finance taxes. Our hypothesis on the transaction costs then implies that the transaction tree will be star-shaped from t * on.

That is to say : people are willing to pay taxes (hence to accept money as a universal medium of exchange) because they need a public good as a protection, not against uncertainty (markets are complete), but against their own misbeliefs. A household accepts to play the role of the government because it is safer to do it rather than incurring the risk that no public good is produced at all.

?, p. 105.

See also ?, who points out that during the Song dynasty in China, between the tenth and the thirteenth centuries, it was the state that created paper money.

See, e.g., ?. Similarly, the conflict between the Banking school and the Currency school in the UK at the beginning of the nineteenth century illustrates the same division of opinion. 2 Documents de Travail du Centre d'Economie de la Sorbonne -2012.94

Obviously, indeed, the police and tax administration needed to force people to pay taxes they are unwilling to settle implies a social cost. Contemporaneous Grece illustrates this issue.

Documents de Travail du Centre d'Economie de la Sorbonne -2012.94

This is one of the rare strategic market games of which we are aware and where all commodities are treated symmetrically. (Another example is ?, which can be viewed as an extension of ? to limit-orders).4Documents de Travail du Centre d'Economie de laSorbonne -2012.94

We could allow for durable beads without impairing our results, cf. Remark ?? infra.

Which means, e h i,σ ≥ 0 for every commodity i = 1, ..., N and e h σ = 0. 6 Documents de Travail du Centre d'Economie de la Sorbonne -2012.94

This contrasts with a large body of the literature devoted to Political Economy (e.g. ?) where politicians constitute a group distinct from the representative consumer. In our paper, households are heterogenous in endowments, preferences and beliefs, and all of them can become politicians.

Thus, at variance with ?), we allow for conflict of interest among citizens over the replacement decision.7Documents de Travail du Centre d'Economie de laSorbonne -2012.94

At variance with ?, however, we do not restrict ourselves to "best SPE".

With the convention 0/0 := 1.

Such an economy has been considered by ?. 9 Documents de Travail du Centre d'Economie de la Sorbonne -2012.94

Along this argument, we make use of the fact that we focus on renegociation-proof equilibria. Indeed, ex ante, it might be the case that no player anticipates her ruin.


Agnès Bénassy-Quéré

Dramane Coulibaly

Gunther Capelle-Blancard

Benjamin Carton

Jacques Melitz

The Impact of Market Regulations on Intra-European Real Exchange Rates *

Keywords: Real exchange rate, Balassa-Samuelson effect, Product market regulations, Employment protection JEL classification: F41, J50, L40

We study the contribution of market regulations in the dynamics of the real exchange rate within the European Union. Based on a model proposed by De Gregorio et al. (1994a), we show that both product market regulations in nontradable sectors and employment protection tend to inflate the real exchange rate. We then carry out an econometric estimation for European countries over 1985-2006 to quantify the contributions of the pure Balassa-Samuelson effect and those of market regulations in real exchange-rate variations. Based on this evidence and on a counter-factual experiment, we conclude that the relative evolution of product market regulations and employment protection across countries play a very significant role in real exchangerate variations within the European Union and especially within the Euro area, through theirs impacts on the relative price of nontradable goods.

Introduction

One key feature of the sovereign debt crisis that hit several countries of the Euro area in 2008 and following years was a sudden stop of private capital inflows, which had to be taken over by official financings (Member states, European Financial Stability Facility, International Monetary Fund), and by the intra-Euro area payment system (TARGET2). 1 Indeed, crisis countries generally displayed twin deficits, i.e. a fiscal deficit and a current account deficit. Unlike Japan, these countries were unable to rely on domestic private savings to refinance their government debt, making them vulnerable to a sudden stop in external financing. 2 The policy debate then pointed price divergence within the Euro area as one major cause of the crisis. As evidenced in Figure 1, from 1999 to 2008, the consumer price index increased by 17% in Germany against 36% in Greece and Ireland, 34% in Spain, 30% in Portugal and 25% in Italy. Such price divergence would not have been worrisome should it have corresponded to a catch-up process, consistent with the Balassa-Samuelson effect (BS effect, hereafter, see [START_REF] Balassa | The Purchasing Power Parity Doctrine: a Reappraisal[END_REF] and [START_REF] Samuelson | Theoretical Notes on Trade Problems Review of Economics and Statistics[END_REF]). 3 In 1999, however, Ireland had already caught up with Germany in terms of GDP per capita. In the other countries, although part of the price divergence observed during the decade may be explained by the BS effect, the extent of the drift calls for alternative explanations.

The consumer price index covers both tradable and nontradable goods. Excess price increase in tradable sectors impacts price competitiveness visà-vis foreign competitors, with a negative, demand-side effect on exports. In turn, excess price increase in nontradable sectors acts as an incentive to transfer resources from the tradable sectors to the nontradable ones, with a negative, supply-side effect on exports. This latter effect is often overcome by international trade analyses that tend to focus on the relative price of tradables across countries rather than their relative price compared to nontradables. Still, the bulk of price divergences observed between 1999 and 2006 within the Euro area seems to be attributable to nontradable sectors, as evidenced in Figure 2. This suggests that the supply-side effect may have been a significant driver of current account deficits over the period.

The question then is how to explain such divergences in nontradable prices beyond the BS effect. We argue that the relaxation of the assumption of per- fect competition in this sector -a key assumption of the BS model -can go a long way in explaining price divergences within the Euro area. Specifically, changes in product and labor market regulations are found able to magnify or offset the Balassa-Samuelson effect along the catching-up process. We construct a theoretical model that incorporates imperfect competition and employment protection in the classic BS framework. Our theoretical model predicts that market power in the nontradable sector and employment protection both affect the real exchange rate. Reduced competition in the nontradable sector or higher employment protection cause an appreciation of the real exchange rate. Based on econometric estimations for twelve European countries over 1985-2006, we finally quantify the contributions of the pure BS effect and those of product market regulations and employment protection in real exchange-rate variations. Through a counter-factual analysis, we find that, should product market regulations and employment protection have gradually converged to German levels over 1995-2006, the real exchange-rate appreciation observed in Mediterranean countries such as Greece, Portugal and Italy, would have been muted. The remainder of the paper is organized as follows. Section 2 briefly surveys the literature on the BS effect. In Section 3, we present the theoret- , 1999-2006 (1999=100) 1999 2001 2003 2005 1999 2001 2003 2005 1999 2001 2003 2005 1999 2001 2003 2005 1999 2001 2003 2005 1999 2001 2003 2005 1999 2001 2003 2005 1999 2001 2003 2005 1999 2001 2003 2005 1999 2001 2003 2005 1999 2001 2003 2005 1999 2001 2003 ical framework based on De Gregorio et al. (1994a). The data used in the estimations are described in Section 4. Section 5 presents the econometric strategy and reports the empirical estimation results. Section 6 presents a counter-factual exercise. Section 7 concludes.

A brief overview of the literature

The workhorse model for studying the evolution of nontradable prices in an open economy is the Balassa-Samuelson framework proposed by [START_REF] Balassa | The Purchasing Power Parity Doctrine: a Reappraisal[END_REF] and [START_REF] Samuelson | Theoretical Notes on Trade Problems Review of Economics and Statistics[END_REF]. The original model features a small open economy producing two goods: a tradable good whose price is set at the international level (law of one price), and a nontradable one whose price is set at the country level, under perfect competition. Labour is the only production factor. It is assumed to be perfectly mobile across sectors but immobile internationally. In this setting, a rise in labour productivity in the tradable sector triggers a rise in wages in both the tradable and the nontradable sector. The latter, which does not benefit from the productivity gain, experiences a rise in its unit labour cost, which is accommodated through a price increase. On the whole, a productivity increase in the tradable sector leads to a real exchange-rate appreciation through the increase of the relative price of the nontradable good. This is the Balassa-Samuelson effect. Several theoretical extensions of the BS setting have been proposed in the literature. 4 Asea and Corden (1994), [START_REF] Asea | The Balassa-Samuelson Model: A General-Equilibrium Appraisal[END_REF] and [START_REF] Turnovsky | Investment in a two-sector dependent economy[END_REF] study the BS effect within a model with two production factors: labour and capital. [START_REF] Asea | The Balassa-Samuelson Model: An Overview[END_REF] and [START_REF] Asea | The Balassa-Samuelson Model: A General-Equilibrium Appraisal[END_REF] examine the implications of incorporating a demand side in the BS framework. These theoretical extensions corroborate that productivity differentials are at the root of relative price variations between tradable and nontradable goods, hence also between home and foreign goods. [START_REF] Turnovsky | Investment in a two-sector dependent economy[END_REF] study the impact of demand shocks depending on relative sectoral capital intensities. Specifically, when the tradable sector is relatively intensive in nontradable capital, demand shocks cannot impact the real exchange rate; when the nontradable sector is relatively intensive in nontradable capital, demand shocks have only a transitory effect on the real exchange rate. In all cases, demand shocks appear unable to move the real exchange rate in the long run.

De Gregorio et al. (1994a) propose a two-sector, small open economy model in which nontradable goods are produced by monopolistically competitive firms and wages are determined by a centralized labor union. In this model, shocks to productivity, consumer tastes, government expenditures and the price of tradables affect labor demand, wages and consequently the relative price of nontradables goods. More recently, [START_REF] Sheng | Real exchange rate, productivity and labor market frictions[END_REF] extend the BS model to an environment with search unemployment. They show that matching efficiency influences the relationship between the relative price of nontradables and sectoral productivity: with limited labor market frictions, search unemployment is high and the BS hypothesis is violated. Both extentions of the BS model however assume market imperfections to be constant over time.

On the empirical side, there is a large literature that can be grouped into three strands. The first group consists of cross-sectional studies that generally show evidence of BS effect. The pioneer paper of [START_REF] Balassa | The Purchasing Power Parity Doctrine: a Reappraisal[END_REF] falls in this group. Using data from twelve OECD countries, [START_REF] Balassa | The Purchasing Power Parity Doctrine: a Reappraisal[END_REF] shows that countries with higher productivity in the tradable sector compared with the nontradable sector tend to diplay higher price levels. Subsequent papers such as [START_REF] Kravis | Toward and explanation of National price levels[END_REF], [START_REF] Clague | Determinants of national price level: Some empirical results[END_REF][START_REF] Clague | Purchasing power parities and exchange rates in Latin America[END_REF] and [START_REF] Rogoff | Traded goods consumption smoothing and the random walk behavior of the real exchange rate[END_REF] have confirmed this result, also based on cross-section data.

The second group of empirical studies relies on time-series data on a country-by-country basis. They generally support the BS effect (see [START_REF] Hsieh | The determination of the real exchange rate: The productivity approach[END_REF][START_REF] Bahmani-Oskooee | A time series approach to test the productivity bias hypothesis in purchasing power parity[END_REF][START_REF] Rogoff | Traded goods consumption smoothing and the random walk behavior of the real exchange rate[END_REF][START_REF] Strauss | Real exchange rates, PPP and the relative prices of nontraded goods[END_REF][START_REF] Strauss | The cointegration relationship between productivity, real exchange rates, and purchasing power parity[END_REF].

The last group uses panel data techniques and also finds empirical evidence in favor of the BS hypothesis (see, e.g. [START_REF] Asea | The Balassa-Samuelson Model: A General-Equilibrium Appraisal[END_REF], De Gregorio et al. (1994a,b), [START_REF] Strauss | Productivity differentials, the relative price of non tradables and real exchange rates[END_REF], [START_REF] Bahmani-Oskooee | Panel data and productivity bias hypothesis[END_REF] and [START_REF] Egert | The Balassa-Samuelson effect in Central and Eastern Europe: Myth or reality[END_REF]). The empirical study in [START_REF] Sheng | Real exchange rate, productivity and labor market frictions[END_REF] also falls in this last category. It provides empirical evidence of the relationship between sectoral productivity and the real exchange rate being influenced by labor market frictions.

Here we use the model of De Gregorio et al. (1994a), i.e. a BS model with monopolistic competition in the nontradable sector.5 Unlike De Gregorio et al. (1994a), however, we focus on variations in competition in the nontradable sector and changes in labor market friction as key drivers of the real exchange rate.

Theoretical framework

The economy is inhabited by a large number of identical households that live two periods. There are two goods in the economy: a tradable good denoted by T, and a nontradable one denoted by N. The tradable good is supplied on an international, perfectly competitive market. As for the nontradable good, it is supplied on the local, imperfectly competitive market. Namely, we assume regulations in the nontradable sector to maintain a markup over the marginal price in this sector. Labour is the only production factor. The wage rate is set by a centralized bargaining arrangement between employers of the two sectors and trade unions.

Household

The representative household is assumed to maximize the following expected utility function:

M ax {c T t ,c N t } t=1,2 log c T 1 γ c N 1 1-γ + βlog c T 2 γ c N 2 1-γ (1)
subject to the following budget constraint:

p T 1 c T 1 + p N 1 c N 1 + p T 2 1 + r c T 2 + p N 2 1 + r c N 2 = Y (2)
where c T t and c N t denote the consumption of the tradable and nontradable good, respectively, in period t (t = 1, 2), p T t , p N t their respective prices, γ ∈ [0, 1] the share of the tradable good in household's total expenditure at each period, β > 0 the subjective discount factor, r the interest rate and Y the intertemporal income. The budget constraint (2) implicitly assumes that there is no initial wealth (at the beginning of period 1) nor bequest (at the end of period 2). The intertemporal income is the discounted value of production in both sectors at both dates, y T t and y N t :

Y = p T 1 y T 1 + p N 1 y N 1 + p T 2 1 + r y T 2 + p N 2 1 + r y N 2 (3)
The tradable good is assumed non-differentiated. Its price is set at the international level. In contrast, the nontradable good consists of differentiated varieties j, each being produced by a different monopolistically-competitive local firm. There is a continuum of such firms of measure 1. Denoting by c N t (j) the consumption of the nontradable variety j in period t, the composite consumption of the nontradable good is

c N t = 1 0 c N t (j) θ-1 θ dj θ θ-1
, where θ > 1 is the elasticity of substitution between nontradable varieties. The solution of the household maximization program yields the following optimal intertemporal and intratemporal allocations:

c T 2 c T 1 = β(1 + r) p T 1 p T 2 (4) c T t c N t = γ 1 -γ p N t p T t for t = 1, 2 (5)
Equation ( 4) represents the Euler condition. It implies that spending on the tradable good (p T c T ) declines between period 1 and period 2 if β(1+r) < 1, increases in the opposite case and stays constant if β(1 + r) = 1. In turn, Equation ( 5) provides the optimal intratemporal allocation between tradable and nontradable goods. The distribution of the representative household's spending between the tradable and the nontradable good is constant over time, determined by the preference parameter γ. Equations ( 4) and ( 5) can finally be combined to recover the evolution of the consumption of the nontradable good between the two periods.

Combining equations ( 2) to ( 5), and remembering that by definition c N t = y N t for t = 1, 2, the intertemporal income can be rewritten in terms of tradable goods output as follows:

Y = 1 γ p T 1 y T 1 + 1 1 + r p T 2 y T 2 = Y T γ where Y T = p T 1 y T 1 + 1 1 + r p T 2 y T 2 (6)
Denoting by C t total spending (of both goods) in period t, the optimum spending in each period is:

C 1 = Y 1 + β = Y T γ(1 + β) (7) C 2 = β(1 + r)Y 1 + β = β(1 + r)Y T γ(1 + β) (8)
The consumption of tradables (resp. nontradables) represents a fraction γ (resp. (1 -γ)) of total consumption spending:

c T t = γ C t p T t and c N t = (1 -γ) C t p N t , t = 1, 2 (9)
Given the level of nontradable consumption, household's demand for each variety of nontradable good is:

6 c N (j) = p N (j) p N -θ c N = (1 -γ)C p N p N (j) p N -θ (10)
where

p N = 1 0 p N (j) 1-θ dj 1 1-θ (11)
Since there is no initial stock of external assets, the current-account balance in the first period is given by the excess supply of tradable goods:

ca 1 = y T 1 -c T 1 = β 1 + β y T 1 - p T 2 p T 1 1 (1 + r)β y T 2 (12)
Therefore, if the price of tradable goods (determined exogenously) is fixed over the two-periods, and if the utility discount rate equals the world interest rate, the first period current-account is given by the difference in the level of output of tradable goods in the two periods. Finally, the consumer price index is

p t = p T t γ p N t 1-γ so that C t = p t c t = p T t c T + p N t c N t where c t = γ -γ (1 -γ) -(1-γ) c T t γ c N t 1-γ being the aggregate consumption.

Firms

In both sectors, production uses labor as a single input. Labor is supplied inelastically by the representative household, but there is perfect labor mobility across the two sectors, ensuring a single wage is set, W .

Tradable sector

Production of the tradable good is subject to decreasing returns to scale:

y T = a T (l T ) α (13)
where a T is a technology, productivity-enhancing factor, l T denotes labor in the tradable sector, and 0 < α < 1. The price of the tradable good is set at international level. Profit maximization then yields:

αa T (l T ) α-1 = W p T (14)
Therefore, equilibrium output in the tradable sector is given by:

y T = (a T ) 1/(1-α) αp T W α/(1-α) (15

Nontradable sector

In the nontradable sector, there is a continuum of individual producers under monopolistic competition. We assume constant returns to scale for each producer. The production of each variety is thus given by:

y N (j) = a N l N (j) ( 16
)
where l N (j) denotes labor used to produce variety j, and a N represents mean and marginal productivity, which is constant.

Each firm j maximizes its profit accounting for its own demand function subject to its technological constraint. At equilibrium, the demand for each nontraded variety equals its production: y N (j) = c N (j). Hence, each producer j has the following maximization program:

M ax l N (j) p N (j)y N (j) -W l N (j) (17) subject to y N (j) = a N l N and y N (j) = p N (j) p N -θ c N . The solution of this program is: p N (j) = p N = θ θ -1 W a N = µ W a N (18)
where µ = θ/(θ -1) is the markup in the nontradable sector.

Given that p N (j) = p N , the equilibrium output of nontradable sector can easily be recovered:

y N = c N = (1 -γ)Y T γ(1 + β)p N = (1 -γ)a N Y T γµ(1 + β)W (19)

Labor union

Total labor demand is given by L d = l T + l N . From Equation ( 14), we get labour demand in the tradable sector:

l T = αa T p T W 1/(1-α) (20)
From equations ( 16) and ( 19) and since y N = (1/µ)a N l N , we get labour demand in the nontradable sector: So, total labour demand is given by:

l N = 1 0 l N (j)dj = µy N /a N = (1 -γ)Y T γ(1 + β)W (
L d = l T + l N = αa T p T W 1/(1-α) + (1 -γ)Y T γ(1 + β)W (22)
Denoting by w the consumption real wage (w = W/p), Equation ( 22) can be re-written as follows:

L d = l T + l N = αa T p T wp 1/(1-α) + (1 -γ)Y T γ(1 + β)wp (23)
Like De Gregorio et al. (1994a), we assume that the real wage w is determined by a centralized labor union. The objective of the union is to minimize a quadratic loss function of the deviations of employment (L) and the real wage (w) from their targets. This problem is:

M in w (L -L) 2 + λ(w -w) 2 (24) subject to L = L d (w) (25)
where L and w are the employment and real wage targets, respectively, and λ > 0 measures the relative weight given to wages (relative to employment) by the union. It is assumed that the union only sets the real wage of the current period, after observing current and anticipated values of productivities and markups.

From Equation ( 23), it can be seen that labor demand L d is nonlinear in w. Following De Gregorio et al. (1994a), we use a linear first-order Taylor approximation of L d : 7

L d = L 0 (a T + , a N + , p T + , µ - ) -ǫw (26)
where a T , a N , p T and µ affect L 0 with the same sign as they affect the labor demand and ǫ > 0. This formulation is similar to De Gregorio et al. (1994a), except for the markup µ that here is allowed to change.

The solution of union's program yields the following equilibrium real wage:

7 The first-order Taylor approximation of (23) around w 0 is given by L

d (w) = L d (w 0 ) + (w -w 0 )∂L d (w 0 )/∂w = L 0 + ǫw where ∂L d (w)/∂w = 1 (1-α)w αa T p T pw 1/(1-α) -(1-γ)Y T γ(1+β)pw 2 , L 0 = L d (w 0 ) -w 0 ∂L d (
w = λ λ + ǫ 2 w + ǫ λ + ǫ 2 (L 0 -L) (27)
If the values of a T , a N , p T , µ, w and λ are the same in period 1 as in period 2, then, at equilibrium, the real wage can be written as follows:

w = w(a T + , a N + , p T + , µ - , w + , λ + ) (28)
A permanent rise in productivity in the tradable or in the nontradable sector raises permanent income, hence labor demand and the real wage. A permanent fall in the markup in the nontradable sector sector has the same impact qualitatively as a rise in productivity. A rise in the price of the tradable amounts to positive shock on terms-of-trade, increasing the permanent income of households, hence the labor demand by the firms and the equilibrium real wage. Finally, labor market frictions have a positive, direct impact on the real wage set by the union. Note that both the target wage w and its weight λ in the unions' loss function (the relative power of insiders vis-à-vis outsiders and firms) interact in the determination of the real wage.

We now consider a change in the parameters determining the real wage over time. Specifically, Equation ( 29) shows how the parameters of both periods affect the real wage in period 1.

w 1 = w(a T 1 + , a T 2 + , a N 1 + , a N 2 + , P T 1 + , P T 2 + , µ 1 - , µ 2 - , w 1 + , λ 1 + ) ( 29
)
For instance, an expected fall in the markup µ in period 2 raises the real wage already in period 1. The reason is that a fall in µ 2 increases permanent income, hence labour demand in both periods. The rise in labor demand, hence in the real wage, is more limited in period 1, where it is driven by a demand effect, than on period 2, where firms in the nontradable sector do experiment the reduced markup. As for labor market frictions, we follow the literature in assuming that they do not affect wages through their impact on the permanent income. This assumption ensures that reduced labor market frictions have a negative impact on the real wage. Another implication is that only current labor market frictions affect the real wage.

The nominal wage can be recovered by noting that W = wp:

W 1 = w 1 p 1 = w 1/γ 1 p T 1 µ 1 a N 1 (1-γ)/γ = W (a T 1 + , a T 2 + , a N 1 - , a N 2 + , p T 1 + , p T 2 + , µ 1 + , µ 2 - , w 1 + , λ 1 + )
(30) A fall in µ (or a rise in a N ) has opposite effect on the nominal wage of period 1 depending on whether the shock occurs in period 1 or in period 2. In the latter case, the demand for nontradables increases in period 1, for a given supply. Hence the price of nontradables increases, and so does the nominal wage (which increases more than prices). In the former case, the rise in the demand for nontradables in period 1 is more limited than the rise in the supply. The price of nontradables falls, and so does the nominal wage (which falls by less than prices).

Balassa-Samuelson effect with a union and product market regulations

As shown in the previous subsection, a permanent decrease in µ, w or λ depresses the price of nontradables, hence triggers a real exchange rate depreciation. In turn, anticipating in period 1 a product market deregulation in period 2 leads to a rise in the nontradable price in period 1. The real exchange rate appreciates in period 1 and depreciates in period 2, when the supply of nontradables rises. This dynamic effect is absent in the case of an anticipated deregulation of the labor market.

Because it affects tradable output equally in the two periods, and since the tradable price is fixed, a permanent deregulation of the nontradable sector in period 1 has no impact on the current account (to the extent that the utility discount rate equals the world interest rate): ca = β/(1 + β). y T 1 -y T 2 ). However, an anticipated product market deregulation in period 2 has a negative impact on the current account in the first period and a positive one in the second one, when tradable output actually increases.

We are now interested in the long-term relationship between deregulation of product and labor markets and the real exchange rate. As argued above, a deregulation of the nontradable sector depreciates the real exchange rate, if not in the short run (when anounced), at least in the long run (when implemented). As for the deregulation of the labor market, it has no impact on the real exchange rate when anounced but depreciates the real exchange rate in the long run (when implemented). Denoting foreign variables by an F subscript, and assuming the same share of tradables γ for each country, under the law of price for the tradable sector, the bilateral real exchange rate between the home and the foreign country is given by:

RER = p p F = p T p T F γ p N p N F (1-γ) = p N p N F (1-γ) (31)
Assuming that the home and the foreign countries are identical except for productivity and market regulations, we get: regulations into quantitative indices. More specifically, the index measures the "knock-on" effects (i.e. the costs) of anti-competitive regulations in selected non-manufacturing sectors and in sectors of the economy that heavily rely on non-manufacturing inputs (see [START_REF] Conway | Product market regulation in the nonmanufacturing sectors of OECD countries: measurement and highlights[END_REF] for more details). In line with previous studies (De Gregorio et al., 1994b), we consider the following sectors as tradable: Agriculture, hunting, forestry and fishing; Mining and quarrying; Total manufacturing; Transport, storage and communication.

The following sectors are classified as nontradable: Electricity, gas and water supply; Construction; Wholesale and retail trade; Hotels and restaurants. Data on sectoral value-added are taken from EUKLEMS database.

The employment protection index (EP) is also collected from the OECD. It refers to all types of employment protection measures, whether grounded primarily in legislation, court rulings, collectively bargaining conditions of employment or customary practice (See Venn (2009)). Like the PMR index, the EP index scales quantitatively information that is mostly qualitative.

The real exchange rate and the real GDP per capita are recovered from the Penn World Table version 7.0 (PWT 7.0, [START_REF] Heston | Penn World Table Version 7.0[END_REF]. Following [START_REF] Frankel | The Balassa-Samuelson Relationship and the Renmibi[END_REF] and Rodrik ( 2008), we use the Penn World Table comparative prices as the real exchange rate. These comparative prices have the advantages of being internationally comparable in level. As in [START_REF] Frankel | The Balassa-Samuelson Relationship and the Renmibi[END_REF] and Rodrik ( 2008), we use GDP per capita at 2005 constant prices as a measure of productivity.

We need to select one country of the sample as "foreign". We pick up the largest country, namely Germany and relate all variables to the same variables in Germany.8 This choice also fits the debate on relative price divergences within the euro area since monetary unification. In the econometric estimation, the choice of a reference country is neutral since all estimations are performed in logarithms.

Figure 3 displays the dynamics of real exchange rates and real GDPs per capita. This figure highlights the standard BS effect, i.e., real exchange rate and real income are positively correlated, although the real exchange rate is more volatile especially before European Monetary Unification (EMU) and in the UK. 5 1985 1990 1995 2000 2005 1985 1990 1995 2000 2005 1985 1990 1995 2000 2005 1985 1990 1995 2000 2005 1985 1990 1995 2000 2005 1985 1990 1995 2000 2005 1985 1990 1995 2000 2005 1985 1990 1995 2000 2005 1985 1990 1995 2000 2005 1985 1990 1995 2000 2005 1985 1990 1995 2000 2005 1985 1990 1995 1985,1995,2006) Figure 6: Real exchange rates and market regulations, relative to Germany 0 .5 1 1.5 2 0 .5 1 1.5 2 0 .5 1 1.5 2 1985 1990 1995 2000 2005 1985 1990 1995 2000 2005 1985 1990 1995 2000 2005 1985 1995 2000 2005 1985 1990 1995 2000 2005 1985 1990 1995 2000 2005 1985 1990 1995 2000 2005 1985 1995 2000 2005 1985 1990 1995 2000 2005 1985 1990 1995 2000 2005 1985 1990 1995 2000 2005 1985 1995 4 and 5 report PMR and EP indices in 1985, 1995 and 2006, successively. 9 In all the countries of the sample the PMR tends to decline over time (Figure 4), albeit at different paces. The decline is relatively slow in Greece, and delayed in Italy and France. In 2006, all countries but Ireland display tighter regulations than Germany, and in most of them, the gap to Germany has increased since the mid-1990s.

Conversely, not all countries display a downward trend for EP: EP increases over time in France while it stays constant at a very low level in Ireland and the UK (Figure 5). In 2006, Germany appears in a median situation concerning EP.

Figure 6 compares the dynamics of the real exchange rate to those of PMR and EP indices (relative to Germany). In most countries, the real exchange rate seems positively correlated to both indices.

Econometric estimation

In this section, we intend to test our theoretical result that product market regulations in the nontradable sector, together with employment protection, impact the real exchange rate on the top of the traditional BS effect. More specifically, we intend to estimate the long-term relationship (33) through panel cointegration.

Panel unit root and cointegration tests

We first study the presence of unit roots in our series based on the panel unit root tests proposed by [START_REF] Im | Testing for Unit Roots in Heterogeneous Panels[END_REF] (IPS) and [START_REF] Pesaran | A simple panel unit root test in the presence of crosssection dependence[END_REF] Cross-sectionally Augmented Dickey-Fuller (CADF). The Pesaran CADF allows to take account of the cross-sectional dependence since it is based on Dickey-Fuller type regressions augmented with the cross-section averages of lagged levels and first differences of the individual series. The results of these tests are reported in Table 1. At conventional levels of significance, all series are found non-stationary in level, but stationary in first differences (see Table 1).

We then test for cointegration between the variables using the approach proposed by [START_REF] Westerlund | Testing for Error Correction in Panel Data[END_REF]. Specifically, we test whether there exists error correction for individual panel members or for the panel as a whole. This approach is flexible as it allows for heterogeneous specifications of both the long and short run parts of the error correction model, based on the data. Furthermore, the Westerlund panel cointegration test accounts for cross-section dependence since the robust critical values can be computed through bootstrapping. The case for cross-section dependence is especially compelling in our case where shocks to the German economy affect all individual observations simultaneously.

The null hypothesis of Westerlund's tests is the absence of cointegration. The G α and G τ statistics test whether there exits cointegration for at least one individual panel member. The P α and P τ statistics pool information over all the individual panel members to test whether there exits cointegration for the panel as a whole. As reported in Table 2, the four tests reject the null hypothesis of no cointegration at least at the 10 percent level. We conclude that there is evidence of cointegration.

Long-run relationship

Regarding the estimation of the long-run relationship, two approches have been proposed in the literature that both deal with serial correlation and the endogeneity of the regressors. The first one is the Fulled Modified Ordinary Least Squares (FMOLS) technique proposed by [START_REF] Phillips | Statistical inference in instrumental variables regressions with I(1) processes[END_REF] that provides optimal estimates of cointegrating regressions by modifying least squares. The second technique, the Dynamic Ordinary Least Squares (DOLS), provided by [START_REF] Saikkonen | Asymptotically efficient estimation of cointegration regressions[END_REF] and [START_REF] Stock | A simple estimator of cointegrating vectors in higher order integrated systems[END_REF] consists in using the leads and lags of the differenced endogenous variables as regressors. An extension to a panel framework was proposed by [START_REF] Pedroni | Fully modified OLS for heterogeneous cointegrated panels[END_REF] and [START_REF] Phillips | Linear regression limit theory for non stationary panel data[END_REF] for the FMOLS, and by [START_REF] Mark | Cointegration vector estimation by panel DOLS and long-run money demand[END_REF], for DOLS. In this paper, we use the panel DOLS proposed by [START_REF] Mark | Cointegration vector estimation by panel DOLS and long-run money demand[END_REF], since [START_REF] Kao | On the Estimation and Inference of a Cointegrated Regression in Panel Data[END_REF] show that DOLS outperforms both OLS and FMOLS estimators in estimating cointegrated panel regressions.

The empirical model corresponding to equation ( 33) is:

lnRER it = βln GDP GDP GER it + φ P M R ln P M R P M R GER it + φ EP ln EP EP GER it (34) +u i + λ it + θ t + ǫ it
where GER stands for Germany, u i is a country-specific effect, λ it is country-specific time trend, and θ t is a common-time effect that serves to account for cross-sectional dependence.

The PDOLS procedure consists in estimating Equation (34) by instrumental variables using leads and lags of differenced endogenous variables as instruments. By Monte Carlo experiments, [START_REF] Mark | Cointegration vector estimation by panel DOLS and long-run money demand[END_REF] show that the panel dynamic OLS provides much more precise estimates compared to the corresponding single-equation counterparts even for a small number of cross-sectional units. Table 3 reports the estimation of the BS effect with product market regulations and employment protection. For purpose of comparison to the standard BS effect, we also estimate the model without market regulations. For robustness, a first estimation is implemented with individual fixed effects and individual trends, while the second estimation adds a common trend with individual fixed effects and individual trends. The results in Table 3 show that all the explanatory variables (real GDP per capita, product market regulations index in the nontradable sector and employment protection index, all being relative to Germany) have the expected sign and are significant at the 1% level. In particular, the results highlight the standard BS effect, i.e., an increase in country differential GDP per capita leads to an appreciation of the real exchange rate relative to Germay. The impact of a one-percent growth differential ranges from a 0.34 to 0.86 percent relative exchange-rate appreciation, depending on the specification.10 Interestingly, introducing market regulations tends to depress the coefficient on the BS effect.

A rise in either the PMR or the EP index (relative to Germany) leads the real exchange rate to appreciate, the effect being stronger for PMR than for EP. Indeed, a one-percent increase in the PMR index (relative to Germany) triggers a 0.51 to 0.66 percent price increase relative to Germany. As evidenced in Figure 4, the German PMR index fell by 24% from 1995 to 2006 but only by 12% in Greece over the same period. Hence the Greek PMR increased by 12% relative to Germany which, according to our estimation, can explain a relative price increase of 6 to 8 percent.

In turn, a 1 percent increase in relative employment protection triggers a 0.18 to 0.23 percent relative price increase. Looking back to Figure 5, we see that between 1995 and 2006, the EP index fell by 31% in Germany and by 22% in Greece, hence the Greek EP index increased by 11% relative to Germany. According to our estimations, this can explain an additional 2 to 3 percent increase in the relative price of Greece. Adding up the effect of the PMR and that of the EP index, we get a 10-12 percent real exchange rate appreciation in Greece relative to Germany between 1995 and 2006, hence a large part of the observed 25 percent appreciation. We conclude that product and employment market regulations are far from anecdotal in explaining relative price variations within the Euro area. The next section proposes a counterfactual analysis to further measure the impact of these regulations.

To futher quantify the contributions of product and labor market regulations in real exchange-rate variations, we now conduct a counterfactual analysis. We consider a linear convergence of product and labor market regulations to their corresponding levels of Germany from 1995 to 2006.The results are displayed in Figure 7. For each country, the first bar reports the observed variation in the real exchange between 1995 and 2006. The second one shows the counterfactual variation in the real exchange rate under convergence of market regulations. The third and fourth bars report the contribution of PMR and EP, respectively, to the difference between the first two bars.

The charts in Figure 7 indicate that, under convergence of market regulations, real exchange appreciations observed in Greece, Italy and Spain would have been much reduced, while the real exchange rate would have even slightly depreciated (relative to Germany) in Austria, Belgium, Finland, France and Portugal. On the contrary, in Denmark, Ireland and the UK, the real exchange rate would have appreciated more under convergence. In most countries, the main contribution in these counterfactual results is the evolution of PMR. This is especially the case in Belgium, France, Greece, Italy and Portugal where the convergence of the PMR to the German level would have been enough to erase any real exchange-rate appreciation. The contribution of EP is smaller but still important for France, Greece and Portugal. In Ireland, convergence of both PMR and EP to German levels would have almost doubled the observed real exchange-rate appreciation over the period. This is because both indicators are much lower in this country than in Germany.

Conclusion

We have analyzed how product market regulations in nontradable sectors and employment protection influence the dynamics of the real exchange rate. The theoretical framework incorporates imperfect competition and employment protection in the classical Balassa-Samuelson model. Subsequently, we have conducted an econometric estimation for European countries over 1985-2006, confirming the prediction of the theoretical model that product market regulations in the nontradable sector and employment protection tend to inflate the real exchange rate. Finally, we have proposed a counter-factual exercise to quantify further the role of product market regulations and employment protection.

Our results confirm the role played by both types of market regulations in the evolution of intra-European real exchange rates. This effect is quantitatively large as it explains most of observed real exchange-rate appreciation vis-à-vis Germany between 1995 and 2006 for several countries of the Euro area. We conclude that structural reforms may be a powerful driver of relative price adjustment within the Euro area. Although they would not directly impact on external competitiveness (since their influence goes through the price of nontradables), they would raise output and labor demand in both sectors.

25 Documents de Travail du Centre d'Economie de la Sorbonne -2013.01

Figure 1 :

 1 Figure 1: Harmonized consumer price index in Euro area countries, 1999- 2011(1999=100)

Figure 2 :

 2 Figure 2: Consumer price index in Euro area countries, tradables versus nontradables, 1999-2006 (1999=100)

) 9

 9 Documents de Travail du Centre d'Economie de la Sorbonne -2013.01

  du Centre d'Economie de la Sorbonne -2013.01

  w 0 )/∂w and ǫ = -∂L d (w 0 )/∂w. Like De Gregorio et al. (1994a), we neglect here the effect of labor demand parameters on ǫ. 11 Documents de Travail du Centre d'Economie de la Sorbonne -2013.01

Figure 3 :

 3 Figure 3: Real exchange rate and real GDP per capita, relative to Germany

Figure 4 :

 4 Figure 4: Product market regulations(1985, 1995, 2006)

Figures

  Figures 4 and 5 report PMR and EP indices in 1985, 1995 and 2006, successively. 9 In all the countries of the sample the PMR tends to decline over time (Figure4), albeit at different paces. The decline is relatively slow in Greece, and delayed in Italy and France. In 2006, all countries but Ireland display tighter regulations than Germany, and in most of them, the gap to Germany has increased since the mid-1990s.Conversely, not all countries display a downward trend for EP: EP increases over time in France while it stays constant at a very low level in Ireland and the UK (Figure5). In 2006, Germany appears in a median situation concerning EP.Figure6compares the dynamics of the real exchange rate to those of PMR and EP indices (relative to Germany). In most countries, the real exchange rate seems positively correlated to both indices.

Figure

  Figure 7: Counterfactual analysis

Table 1 :

 1 Panel unit root testsNote: IPS denotes W t -bar of Im,[START_REF] Im | Testing for Unit Roots in Heterogeneous Panels[END_REF] panel unit root test and CADF is Cross-sectionally Augmented Dickey-Fuller test statistic of[START_REF] Pesaran | A simple panel unit root test in the presence of crosssection dependence[END_REF]. The two tests have the null hypothesis of a unit root. P-values are in parenthesis. Country-specific intercept and time trend were included in both tests. Source: Authors' calculations.

	Variable	Level	First difference
			IPS	CADF	IPS	CADF
	lnRER i	0.240	-2.193 -7.069 -3.089
			(0.595) (0.674) (0.000) (0.000)
	ln	GDP i GDP GER	-0.991 -2.356 -4.232 -2.626
			(0.161) (0.449) (0.000) (0.002)
	ln	P M R i P M R GER	1.218	-1.871 -9.865 -3.155
			(0.888) (0.945) (0.000) (0.000)
	ln	EP i EP GER	0.192	-1.542 -12.069 -2.323
			(0.576) (0.997) (0.000) (0.029)

Table 2 :

 2 Panel cointegration tests(Westerlund)

		Test Stat.	P-value
	G τ	-2.339**	0.030
	G α	-6.565**	0.040
	P τ	-6.668*	0.055
	P α	-5.735*	0.070
	Notes: Null hypothesis of no-cointegration.	P-
	values are obtained from 1000 bootstrap replications.
	*,**,*** denotes the significance at 10%, 5% and 1%
	level, respectively.
	Source: Authors' calculations.

Table 3 :

 3 Panel cointegration estimates of the Balassa-Samuelson effect with

	market regulations
			Dependent variable: lnRER
			No common trend	Common trend
	ln	GDP GDP GER	0.864*** 0.611*** 0.400*** 0.340***
			(0.207)	(0.115)	(0.193)	(0.118)
	ln	P M R P M R GER		0.510***	0.656***
				(0.161)	(0.191)
	ln	EP EP GER		0.233***	0.184***
				(0.061)	(0.071)
	Note: Standard errors, written in parenthesis, are based on
	Andrews and Monahan (1992) pre-whitening method. *** denotes
	the significance at 1% level.

Documents de Travail du Centre d'Economie de la Sorbonne -2013.01

See Bahmani-Oskooee and Nasir (2005) for a review.

We simplify the model by omitting government expenditures, the impact of which has been shown either neutral or ambiguous in the literature, see DeGregorio et al. (1994b).

Documents de Travail du Centre d'Economie de la Sorbonne -2013.01

Here we drop time subscripts for the sake of clarity. 8 Documents de Travail du Centre d'Economie de la Sorbonne -2013.01

Changing the reference country does not alter the main conclusion of our study, which emphasizes the role of PMR, although the impact of EP apppears more fragile. The results are available from the authors. 15 Documents de Travail du Centre d'Economie de la Sorbonne -2013.01

Intermediate years are available but skipped here to save space.

This range stays consistent with the basic BS framework with perfect competition, where the coefficient on the BS effect is equal to the share of nontradables in the economy.

Equation ( 32) encapsulates the traditional BS effect (first two terms). Here, however, market power in the nontradable sector (µ) and union demands in terms of real wages (λ, w) also affect the real exchange rate. Following [START_REF] Blanchard | Macroeconomic effects of regulation and deregulation in goods and labor markets[END_REF], we consider that anti-competition regulations (such as price controls or vertical integration, see [START_REF] Conway | Product market regulation in the nonmanufacturing sectors of OECD countries: measurement and highlights[END_REF]) tend to reduce the elasticity of substitution θ, hence to increase the markup µ. Our model does not explicitly account for firm entry, hence entry costs are not identified in the model. However, restrictions to entry can also be thought to increase the elasticity of substitution, hence to reduce the markup.

Assuming, as in the literature, that productivity grows faster in the tradable sector than in the nontradable one, the empirically testable model is given by:

GDP is the real GDP per capita. P M R stands for the product market regulation index (µ). Finally, EP represents an index of employment protection that refers to λ and w, where λ and w interact.

Data

We consider annual data for twelve European countries: Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Portugal, Spain and United Kingdom. These countries are selected based on data availability to get a balanced panel. We focus on EU countries for two reasons. First, the single market makes the law of one price more likely to apply in this region than in any other in the world. Second, we want to use our framework to shed some light in observed price divergences over the monetary-union period. Data cover the period 1985-2006.

The product market regulations (PMR) index in the nontradable sector is computed as a weighted average of product market regulations in individual sectors, weights being given by the shares in aggregate nontradable value-added. Data on sectoral regulations are collected from the OECD (OECD, 2011). The latter converts qualitative features such as laws and


D Le Quang

Y Babou

O Chazot

P André

INVESTIGATION OF SUPERSONIC AIR PLASMA JET PRODUCED IN THE VKI PLASMATRON FACILITY

Keywords:

Thermodynamic characterization of a supersonic air plasma jet produced in the VKI Plasmatron facility is presented. Plasma flow regimes corresponding to underexpanded and highly underexpanded situations are investigated by means of Optical Emission Spectroscopy (OES) technique. Several diagnostics are presented using both molecular and atomic radiative contributions. Electron density, excitational energy distribution and molecular spectra fitting are presented.

INTRODUCTION

During hypersonic atmospheric entries, the radiative heating experienced by a vehicle is a major issue for accurate prediction of thermal heat flux. Comparison of predictive computations with detailed description of kinetic processes experimentally investigated are mandatory to assess the reliability of nonequilibrium kinetic models. Due to the relatively large cost of missions and the difficulty of performing accurate measurements in flight, plasma source ground test facilities have been developed. The use of supersonic plasma jets to investigate non equilibrium processes is widely reported but most investigations deal with mono-atomic gases (Sember & al. Robin & al. [L.R94]). Supersonic plasma expansion are characterized by a rapid cooling and recombination which result in kinetic non equilibrium. Although Optical Emission Spectroscopy (OES) technique is convenient to investigate nonequilibrium plasma flows, characterization have to be carried out using cautious assumptions. Indeed, Sember & al. [V.S02] outlined that spectroscopic analysis might give questionable results due to non Boltzmann excited states distribution. Present investigation is carried out using the Inductively Coupled Plasma (ICP) Plasmatron facility operating with air mixture. The discussion is focused on the interpretation of spectroscopic measurements performed in the first expansion-compression structure of supersonic underexpanded plasma jets. Preliminary investigation of the plasma source performance was executed to insure high quality measurements. Comprehensive characterization of the flow by means of high speed imaging has been executed to identify suitable operating conditions in order to perform (OES). Operating the Plasmatron at constant power of 490 kW and 4.5 g/s mass flow rate, the pressure in the ignition region is maintained at 120 mbar. Expansion is performed through a sonic throat into a low pressure chamber. Two back pressure conditions ensuring low influence of power feeding oscillation on plasma emission, good signal to noise ratio and strong hydrodynamic gradients have been selected and correspond to 12 and 6 mbar chamber pressure. In section 2, experimental arrangement and spectra processing are presented. In section 3, spectroscopic diagnostics based on atomic and molecular contributions are detailed. Electron density, rotational temperature and excitational energy distribution are presented in section 4. Preliminary discussion are developed in 5.

EXPERIMENTAL ARRANGEMENT AND SPECTRA PROCESSING

Plasmatron facility and supersonic plasma jet generation

The VKI Plasmatron Inductively Coupled Plasma (ICP) source uses a high frequency, high power and high voltage generator (400 kHz, 1.2 MW, 11 kV), feeding a single-turn inductor [B. 97], [B. 00]. For the present experiments, the Plasmatron is operating at 490 kW power and 4.5 g/s mass flow rate. Supersonic plasma jet are obtained by expanding the plasma through a convergent nozzle (35 mm throat diameter) into a chamber maintained at low pressure. In the present study, the pressure in the chamber is maintained at 6 or 12 mbar corresponding respectively to a highly underexpanded (figure 1) and underexpanded figure (2) situation while the pressure in the reservoir is maintained at 120 mbar. A basic analysis of emission oscillation shows that typical fluctuations Figure 2. Supersonic air plasma jets -back pressure: 12 mbar.

sonic plasma flows encountered in this study evidence a pressure at the exit of the convergent being higher than in the chamber. In order to equilibrate the pressure difference at the exit of the convergent, expansion waves are created and directed towards the jet axis which are then reflected in the direction of the plasma jet boundaries. These expansion waves direct the flow towards the edge of the plasma jet, creating a radial expansion in addition to the axial expansion. The edges of the expansion zone are bright because of the reflection of the expanding flow by the cold dense surrounding gas, which gives rise to the so called barrel shocks. Reducing the chamber pressure, leads to the creation of a Mach disk downstream of the first expansion cell, leading to subsonic velocities downstream of this region with an increase of the local temperature and pressure. Abel inversion (figures 1 and 2) performed on raw images illustrates complex structures of compression and expansion zones in the jet caused by multiple reflections of expansion and shock waves. In particular, it evidences bright zones in the compression region mainly located on the edges. Through isentropic expansion calculations, we evaluate the Mach number in the expansion region before the shock using the expansion angle and assuming ideal air. The results are displayed figure 3.

Optical emission spectroscopy measurement

Optical Emission Spectroscopy (OES) allows to obtain information on excited states densities without disturbing the flow. Accurate measurements rely on stationary flow emission and low contamination of the jet. A conventional OES technique was set up and applied in a large spectral range on supersonic underexpanded air plasma jets in the first expansion zone (starting at 2.5 cm from the throat) and in the compression region. For clarity, figure 4 illustrates the location of axial measurements. Dashed lines correspond to 2. 5, 3.5, 4.5, 8.5, 10.5, 11.5, 12.5, 13.5, 15.5, 17.5 cm (resp.2.5, 3.5, 4.5, 6.5, 7.5, 8.5, 9.5, 10.5, 11.5, 12.5 cm) axial locations for 6 mbar (resp. 12 mbar) back pressure case. At each axial location, the line of sight plasma jet emission is collected through an aperture and then focused with a fused silica lens onto the entry of a Acton Series monochromator of 75 cm focal lengths. The spectrometer is combined with a ICCD PI-MAX camera with a frame of 1024 × 1024 pixels of 12.8 µm side. Emission issued from the jet is spatially resolved in the radial direction. A radial slice of about 19 cm height was optically conjugated using a 100 mm focal lens onto an image with a magnification factor of 0.07. It allows to capture the whole radial profile of the jet onto the CCD screen of the camera with a spatial resolution of about 180 microns. We focus our study on the visible spectral domain that includes mainly atomic contribution of oxygen and nitrogen atomic lines. The small contribution of N + 2 First negative system, H α and H β hydrogen lines have also been investigated. The radiation from oxygen and nitrogen atomic lines and the N + 2 First negative system were recorded using a 150 groves/mm grating as the hydrogen lines spectral resolution was improved by using a 1200 groves/mm grating in order to resolve the Stark broadening. The corresponding spectral resolutions were measured to be respectively 0.5 nm and 0.06 nm, setting the entrance slit of the monochromator to 3 microns. The recorded spectra were calibrated in absolute intensity combining a ribbon tungsten lamp and its documented absolute radiance and a deuterium source. Calibrated spectra at the plasma jet center line are shown in figure 5. At the conditions reported here, the air mixture is assumed to be optically thin and proper Abel inversion was applied on measured spectra allowing to rebuild the local spectral emission (W.m -3 .sr -1 .λ -1 ). On figures 6 and 7, mapping of the local emission integrated within [400-900] nm spectral range is displayed and show good agreement with pictures on figures 1 and 2.

SPECTROSCOPIC DIAGNOSTICS

Excited electronic states distribution

Measured emission ǫ ul of atomic transition allows a straight probing of the upper (emitting) level n u population density through the relation:

ǫ ul = n u A ul 4π hc λ ul (W.m -3 .sr -1 ), (1)
where A ul (s -1 ) is the Einstein coefficient associated to spontaneous emission from level u to level l respectively of energy E u and E l . λ ul designates the line position. Assuming Local Thermodynamic Equilibrium (LTE), the internal level population density of a level u of energy E u and degeneracy g u follows the Boltzmann distribution ruled by a single temperature T LT E given by:

n u (T LT E ) = N (T LT E ) g u exp -Eu kB TLT E Q int (T LT E ) (m -3 ),
(2) where species concentration N (m -3 ) and internal partition function Q int are calculated at equilibrium. The lack of information about the static pressure distribution within supersonic flows prevent from investigating absolute population. Relative population distribution of atomic excited states will be examined through the socalled Boltzmann diagram. In thermal plasmas, atomic state distribution function obeys Boltzmann equilibrium and the excitation temperature T exc is evaluated on the basis of the Boltzmann diagram method. This approach is convenient as no assumption is made concerning the species concentration. The upper level density being straightly related to emission through relation ( 1), it is expressed in terms of T exc combining equations ( 1) and

( 2) in the form:

ln n u g u = - 1 k b T exc E u + ln N Q int . (3)
Excitation temperature T exc is directly obtained from the slope of a straight line fitted on the set of experimental electronic excited states population logarithm values (left term of Equation 3). On figure 8, typical Boltzmann diagram using oxygen atomic lines is displayed. As the spectral window cover by the upper emitting levels of nitrogen lines is narrow, the study will focus only on oxygen lines. No obvious deviation from Boltzmann distribution has been detected. Althought a slight dispersion of measured population around the linear regression is observed, the excitation temperature will be derived from the set of thirteen oxygen lines displayed in the appendix.

Stark broadening of Hydrogen lines

The determination of the electron density is executed though the fitting of calculated hydrogen Stark broadened lines onto experimental data. electron density evaluated using CS model is plotted as a function of the Full Width at Half Maximum (FWHM) of H α and H β lines in the density range of interest. It shows that for the temperature range of interest, the influence of electron temperature on the FWHM is negligible. It has been also verify that the entire lineshape is not affected by the electron temperature. In CS database, line half-profiles are available in the form of tables where values of intensity are tabulated against wavelengths for certain values of electron temperature T e and density N e . In order to obtain a profile for any couple (T e ,N e ), a bilinear interpolation is performed from theoretical data. The theoretical line profile is convoluted with the instrumental broadening of the apparatus and Doppler broadening is assumed negligible. The program interpolates points from the theoretical line profile to match the grid of the experimental data set. Any background in the experimental data is zeroed so that the data is directly comparable to the theoretical profiles. Typical fittings obtained using this procedure are displayed in 10.

Rotational temperature

Plasma characterization using molecular spectra is done on the basis of common fitting approaches consisting of the minimization of the functional defined by the Root Mean Square Error (RMSE) between the experimental spectrum and the spectrum calculated under various equilibrium assumptions. The theoretical spectra required to determine the RMSE are calculated on the basis of an advanced tool developed and available at the EM2C laboratory and so-called High Temperature Gas Radiation (HTGR) code [M. 08]. Assuming thermal equilibrium, the temperature T thermal is obtained applying the fitting procedure on experimental spectra normalized to unity, which consist in the minimization of the functional expressed as:

RM SE (T thermal ) = 1 N N i=1 Sexp λi -Stheo λi (T thermal ) 2 (4)
where Sexp λi (resp. Stheo λi ) designates the normalized experimental spectrum (resp. calculated spectrum) and N is the number of experimental points in the considered spectral range. The HTGR code can support various assumption concerning the distribution of emitting levels or the number of species accounted. In this study, the fitting will be performed accounting for three molecular system belonging to N + 2 , N 2 and CN species assuming thermal equilibrium and chemical nonequilibrium. In this situation, the minimization is expressed as:

RM SE (T thermal , α 1 , α 2 ) = 1 N N i=1 Sexp λi -Stheo λi (T thermal,α1,α2 ) 2 (5)
where α 1 (resp. α 2 ) stands for the chemical non equi-

librium factor α 1 = N N + 2 NN 2 Qint(N2) Q int(N + 2 ) (resp. α 2 = N N + 2 NCN Qint(NCN ) Qint(N + 2 )
). Typical best fit obtained using multi- species spectra calculation is displayed in figure 11.

The fitting corresponds to measurement performed in the compression region (12 mbar case) at 9.5 cm from the nozzle exit. The robust method used for the fitting allows to fit three vibrational bands of N + 2 First Negative system despite several atomic lines overlapping. The good agreement between measured and calculated spectra evidences for thermal equilibrium.

RESULTS

In figure 12 (resp. 13), excitation temperature and electron density radial profiles are plotted for 6 mbar (resp. 12 mbar) back pressure case at two axial positions in the expansion region. Black (resp.red) lines correspond to 2.5 cm (resp. 3.5 cm) axial position. Electron density profiles determined using both H α and H β lines show good agreement. For clarity, only profiles determined from H β line are displayed. We assume that the main source of uncertainty on the electron density determination is due to the measured apparatus function. Therefore electron density profiles are displayed assuming +/ -5% error on the apparatus function. Strong recombining situation is clearly evidenced at the jet centerline in figure 12. Indeed, having similar excitation temperature for both axial locations, a significant disagreement is observed in electron density value. As an indication, for 15 mbar air plasma at LTE, equivalent drop in electron density should be accompanied by 12 % drop in temperature [B. 96]. This recombining state is no more occurring on the edge where temperature and density match for both axial locations. Oppositely, in figure 13 recombining situation Figure 13. Radial profiles -z = 2.5 cm (black), z = 3.5 cm (red). Excitation temperature (diamonds), electron density (circles). 12 mbar backpressure.

is much less significant at the jet centerline. Following the same argument, at 3.5 cm axial location, the outer part of the jet corresponding to the barrel shock (from 1.5 cm radial distance) evidences an ionizing situation.

Complex hydrodynamic structure lead to various thermodynamic non equilibrium situations and radial gradients have to be carefully accounted when analyzing axial profiles. In figure 14 (resp. 15), excitation temperature and electron density axial profiles are plotted for 6 mbar (resp. 12 mbar) back pressure. The radial position was chosen at 1.0 cm from the jet axis in order to get significant number of point on the profile. Indeed, electron density lower than 1.0 14 cm -3. cannot be determined using CS model and low atomic contribution at several locations prevent from a full radial profile determination. Both figures cannot be directly compared as radial gradients play an important role. Electron density and excitation temperature profiles shows coherent variations in the expansion zone.

Huge error bar at the end of the expansion region in the 6 mbar back pressure case denotes an important dispersion of atomic excited states around linear regression and the use multiple excitation temperatures might be relevant for further analysis. After the Mach disk, electron density is increasing faster in 12 mbar back pressure case.

In 6 mbar back pressure case, electron density and excitation temperature profiles in the compression region are decorrelated. Further analysis is possible by investigating the rotational temperature. Rotational temperature in the compression region for 12 mbar back pressure case is presented in figure 16 with the associated chemical non equilibrium factor for CN species (concentration of N 2 species being found negligible). Temperature profile is coherent with hydrodynamics structure of the jet. The slope of the chemical nonequilibrium factor of CN should be opposite to the slope of temperature which is the case on the edge of the jet because of plasma cooling. However in the shear layer, the concentration of CN species increases as the temperature increases which denotes for a nonequilibrium situation.

CONCLUSION

A qualitative description of supersonic jet structure was performed through Abel inverted raw images corresponding to underexpanded and highly unerexpanded cases. Various spectroscopic diagnostics have been used to characterize these plasma flows in the first expansioncompression zone. Preliminary results are encouraging and point out the main characteristics of supersonic plasma jets. Electron number density was determined by fitting experimental hydrogen lines onto theoretical lineshape. Atomic excited states distribution have been measured for oxygen atomic lines and evidences that Boltzmann assumption was valid in most regions of the jet. However, at the end of the expansion region, an important dispersion of atomic excited states around linear regression was evidenced and the use multiple excitation temperatures might be relevant for further analysis. At the jet centerline, the expansion of the plasma is accompanied by a rapid cooling and recombination which results in kinetic non equilibrium between electrons and heavy particles. Oppositely, shear layers are location of ionizing situation with presence of molecular radiation. The determination of rotational temperature has been performed where molecular spectra of N + 2 First Negative system are suitable for fitting procedure. Preliminary analysis on rotational temperature are in agreement with hydrodynamic structure of the jet and permits to determine the evolution of CN species concentration. Further comparison with excitation temperature will allow to identify nonequilibrium situations.

APPENDIX

O lines

De = 109837.02cm Table 2. Spectroscopic data of the considered O emission lines used for air plasma [NIS].

  [V.S02], Selezneva & al.[S.E01], Sanden & al. [M.C93], Drake & al. [D. 08] [D. 09] and

(

  Figure 1. Supersonic air plasma jets -back pressure: 6 mbar.

Figure 3 .

 3 Figure 3. Mach number estimation in the expansion region before the shock.

Figure 4 .

 4 Figure 4. Axial location of spectroscopic measurements. 6 mbar (top), 12 mbar (bottom) back pressure.

Figure 5 .

 5 Figure 5. Typical radiative signature of supersonic air plasma jet in the first expansion zone (r = 0 cm, z = 2.5 cm).

Figure 6 .

 6 Figure 6. Atomic contribution [400-900]nm -6 mbar back pressure.

Figure 7 .

 7 Figure 7. Atomic contribution [400-900]nm -12 mbar back pressure.

Figure 8 .

 8 Figure8. Boltzmann diagram at the center of the jet using oxygen atomic lines (r = 0 cm, z = 2.5 cm).

Figure 10 .

 10 Figure 10. Hydrogen lineshape fitting.

Figure 11 .

 11 Figure 11. Multi-species best fit (top) and detailed species contribution (bottom).

Figure 12 .

 12 Figure12. Radial profiles -z = 2.5 cm (black), z = 3.5 cm (red). Excitation temperature (diamonds), electron density (circles). 6 mbar back pressure.

Figure 14 .Figure 15 .

 1415 Figure 14. Axial profiles -r = 1.0 cm. Excitation temperature (diamonds), electron density (circles). 6 mbar back pressure.

Figure 16 .

 16 Figure 16. Radial profiles -z = 9.5 cm. Rotational temperature (black) and chemical non equilibrium factor for CN (red).

Table 1 .

 1 Calculation of the the Stark broadened line profiles have been reported in literature for the first three Balmer lines of hydrogen (H α , H β and H γ ). Well known databases are elaborated using different theoretical models named as quasi-static ion approximation model (VCS)[C. 73], Model Microfield Method (MMM)[B. 01] and Computer Simulation (CS)[M. 03].In this study, a favor is given to CS model as its up-to-date database allows to account for air mixture using reduced mass coefficient. The available parameters range belonging to this model are presented in table 1. In figure9, Plasma parameters validity range.

	Model Constraint on Ne (cm -3 ) Constraint on Te (K)
	CS	10 14 ≤ Ne ≤ 10 19	1042 ≤ Te ≤ 1.710 6