The Dynamics of Unemployment in a Fixed-Exchange Rate System: Theory and Application to the "Franc Fort" Policy

Olivier Jeanne

Center for German and European Studies, University of California at Berkeley

February, 1997

Abstract

This paper studies the dynamics of unemployment in a fixed-exchange rate system with an escape clause. The interesting aspects of these dynamics come from the interaction between unemployment and the devaluation expectations. While an increase in the unemployment rate raises the devaluation expectations, reciprocally the latter influence the unemployment rate through the level of interest rates. We present a model in which this interaction tends to increase the level and the persistence of unemployment, and can even generate some instability in the unemployment dynamics that is associated with currency crises. The estimation of the model in the case of the French franc sheds new light on the franc crisis of 1992-3, as well as the "franc fort" policy and the convergence criteria of the Maastricht Treaty.

Olivier Jeanne, Dept. of Economics, University of California, Berkeley

1 Introduction

One of the main lessons of the 1992-3 crisis of the European Monetary System (EMS) is the importance of the business cycle for the stability of fixed exchange rate systems (Eichengreen and Wyplosz 1993, Svensson 1994, De Grauwe 1994). While the speculation against EMS currencies was motivated by a number of factors, like the real overvaluation of some currencies or the political uncertainty surrounding the ratification of the Maatricht treaty, it also came at a time at which most european countries were entering a recession, raising doubts about their willingness to bear the cost of high German interest rates much longer. Indeed a high and rising unemployment rate is the only economic factor that may explain the speculation against a currency like the French franc, that was slightly undervalued respective to the German mark in 1992 according to most measures (see, e.g., Eichengreen and Wyplosz 1993, Svensson 1994) and moreover supported by an inflation rate lower in France than in Germany and a positive trade balance. It may seem surprising, in this perspective, that european central banks usually do not aknowledge unemployment as one of the economic fundamentals determining the stability of a fixed exchange rate peg arrangement and at any rate reject the idea that it should be monitored by them as such. European central banker's most conspicuous creation, the Maastricht treaty, not only does not include unemployment in its convergence criteria but also does not explicitly make the interpretation of its criteria contingent on the business cycle. ₁ While this apparent lack of concern for unemployment may be justified in theory by the desire to build a reputation of conservativeness, central bankers often justify it in practice by the view that the european unemployment problem is not a monetary policy issue but a structural problem that should be treated by reforms tending to make labor markets more flexible.

The purpose of this paper is to construct a theory of the relationship between unemployment and the credibility of a fixed exchange rate peg. We base this theory on two building blocks that try to capture the original and salient features of the recent history of the EMS. First, we assume that the evolution of unemployment is influenced by two factors, some structural rigidity that fetters the adjustment of the labor market toward full employment, and the level of real interest rates. Second, the credibility of the exchange rate peg is determined by the beliefs of rational speculators about the decision of an optimizing policymaker to opt out or not. By incorporating these two assumptions into a formal model, we show that they generate a relationship between the credibility of the fixed peg and the dynamics of the unemployment rate that goes both ways and may deeply alter the latter. While on the one hand a rising unemployment rate fosters devaluation expectations by increasing the temptation to devalue for the policymaker, conversely high devaluation expectations tend to increase the unemployment rate by raising the real interest rate. We show that as a result of this circularity the fixed exchange rate peg increases the average level of the unemployment rate (i.e., the apparent natural unemployment rate) because of a peso effect, as well as the persistence of unemployment shocks. It follows that the apparent persistence of unemployment in the fixed exchange rate peg regime is the sum of two components, that due to the structural rigidity in the labor market and that due to the exchange rate regime itself. We also show that when the unemployment rate increases above a critical level the defense of the fixed peg may get stuck into a vicious circle, in which interest rates and unemployment snowball until the policymaker eventually "chooses" to devalue.

Our model also constitutes a good framework to study the delegation of exchange rate policy to a conservative central banker as well as the costs and benefits of a monetary union. We show that delegating monetary policy to a central banker who is ready to endure higher unemployment than the government reduces both the average level and persistence of unemployment, at the cost of maintaining the fixed peg when unemployment is high and a devaluation would be optimal. This analysis applies to a monetary union managed by the foreign country, to the extent that the latter may be viewed as the delegation of monetary policy to an infinitely conservative domestic central banker, i.e., a central banker that never exerts the escape clause so that the fixed peg is irreversible and perfectly credible.

We then apply our theory to a case in which the interplay between unemployment and currency credibility seems to be especially important: the "franc fort" policy. As we mentioned earlier, while other currencies may have been weakened by a number of economic fundamentals, unemployment is the only good candidate for the French franc. Conversely, the French unemployment problem has been indicted by some to the high real interest rate levels imposed by the "franc fort" policy. We estimate a generalized version of our model in the case of the French franc, which leads us to a rather balanced position in this debate. On the one hand, we find that the high persistence of unemployment in France cannot be attributed to the exchange rate regime (i.e., one cannot reject that the non-stationarity of unemployment is entirely structural) and that a rise in the short-term interest rate has a very small (though statistically significant) impact on unemployment. On the other hand, we also find that the German monetary unification shock and the interest premium paid by France in 1992-3 have had a non-negligible impact on French unemployment (1.4 % and 0.9 % by the end of 1993 respectively). We argue that the latter findings, far from constituting a puzzle, are a logical implication of the former ones. This is precisely because unemployment is structurally so persistent that small interest rate shocks going always in the same direction can have large cumulative effects.

This paper lies at the intersection of several related branches of literature analysing the working of fixed exchange rate systems and monetary unions. First, it belongs to the "escape clause" approach to fixed exchange rate arrangements and currency crises that was initiated by Obstfeld (1991) and developed considerably following the 1992-3 EMS crisis (Obstfeld 1994 1996, Buiter Corsetti and Pesenti 1995, Isard 1995 chapter 9, Jeanne 1995 1996, Masson 1995, Bensaid and Jeanne 1997, Velasco 1996). While the traditional monetary monetary theory of currency crises studies speculative attacks that are due to an exogenous monetary creation (Krugman 1979, Flood and Garber 1984), the interesting results from the escape clause approach rather come from the interaction between the policymaker's incentives and the market's beliefs. This interaction may give rise to multiple equilibria and self-fulfilling speculation (Obstfeld 1991, 1994, 1996; Jeanne, 1996; Jeanne and Masson, 1996; Velasco, 1996) but this is not the kind of property we study here. Our model is more closely related to the contributions by Drazen and Masson (1994) and Masson (1995), who also scrutinize the link between unemployment and the credibility of the commitment to a fixed peg by an optimizing policymaker. These authors have stressed that defending a fixed peg at the cost of rising unemployment may improve the reputation of the policymaker without reinforcing the credibility of his commitment to the fixed peg. We do not model such reputational effects in the present paper, and study instead the dynamics of unemployment and how they are influenced by the form of the exchange rate arrangement.

The empirical part of the paper is also related to the empirical literature studying the determining factors of the stability of fixed exchange rate systems (Caramazza, 1993; Chen and Giovannini, 1994; Rose and Svensson, 1994; Eichengreen, Rose and Wyplosz, 1995; etc). The estimation of the model leads us to study the correlation between the devaluation expectations of the French franc and macroeconomic fundamentals like the unemployment rate or the real exchange rate. Our results are broadly consistent with those obtained by previous authors as well as the theoretical predictions. The only originality of the present paper, in this respect, lies in the methodology: we estimate a non-linear model rather than regressing linearly the devaluation expectations on the fundamentals.

We also contribute to some extent to the literature studying the costs and benefits of a monetary union. While under the impulsion of Mundell's seminal article of 1961 the literature on optimal currency areas has focused on the comparison between a monetary union and a flexible exchange rate system, the present paper compares the monetary union to a fixed exchange system. The only difference between the two latter monetary arrangements lies in the existence or not of an opting out clause, the consequences of which is precisely the topic of this paper

Finally, the paper is obviously related to the small literature on the "franc fort" policy. It is closer in spirit to the papers stressing the level of the real interest rates (Atkinson et al, 1993a) than those emphasizing the competitive disinflation aspects of the "franc fort" policy (Blanchard et Muet, 1993).

The paper is structured as follows. Sections 2 and 3 present the assumptions and properties of a simple model of a fixed exchange rate peg, with a special emphasis on the dynamics of unemployment. Section 4 then scrutinizes the experience of the French franc with the help of a generalized version of our model. Section 5 concludes.

2 The model

We consider an open economy in discrete time t = 1,2,.... The domestic country belongs to a fixed exchange rate system that requires to maintain the (log of the) exchange rate of the domestic currency with respect to a foreign currency to a level ‾e. The commitment to the fixed exchange rate system is not irreversible: the domestic policymaker can exert an escape clause at any time t, and devalue the domestic currency by an amount d. Thus, the domestic policymaker is confronted with the following alternative at each time t: either maintain the parity (e_t = ‾e) or devalue (e_t = ‾e + d). We assume that the domestic policymaker takes his decision so as to minimize the loss function:

where δ _t is a dummy variable characterizing the policymaker's decision, equal to 1 if he devalues and to zero if not, u_t is the (log of the) the unemployment rate, ‾u the (log of the) natural unemployment rate, and C_t is the opting out cost. It is noteworthy that in contrast with the literature about rules versus discretion, the policymaker does not try to reduce the unemployment rate below the natural level.

This type of loss function, which is used in similar contexts by Obstfeld (1994,1996), Vélasco (1996), Buiter et al (1995), Ozkan and Sutherland (1995), Jeanne (1995), provides a convenient way to model the trade-off between the domestic employment objective and the foreign exchange objective with which policymakers are typically faced in fixed exchange rate arrangements. The variable C is intended to represent the various costs that the domestic policymaker would bear if he chose to quit the fixed exchange rate system. These costs may find their source in the negative impact of exchange rate volatility on international trade and investment, ₂ the loss of anti-inflationary credibility, ₃ the automatic coordination of monetary policies, ₄ or may be political costs. Most of these costs presumably fluctuate with time. For the sake of simplicity, we assume at this stage that the opting out cost is equal to a constant plus a shock:

where η is an i.i.d. stochastic variable of mean zero. We assume that η is unbounded, with a probability density function that is symmetric, increasing in ] - ∞, 0[ and decreasing in ]0, +∞[. These assumptions are satisfied for a wide class of probability density functions, including the normal distribution that we shall use in the empirical part of the paper.

The exchange rate is assumed to satisfy at each period instantaneous purchasing power parity:

where the (log of the) foreign price level p ^* is assumed to be constant. ₅ We assume that international investors have access to foreign bonds yielding a riskless nominal (and real) return r ^*. One can interpret r ^* as the "natural" real interest rate, that would be equal to the investors' psychological discount rate in an explicit intertemporal optimization framework. Because they are risk neutral, investors ask the same expected real return on domestic and foreign bonds. It follows that i_t , the domestic nominal interest rate between t and t + 1, must satisfy the interest parity condition i_t = r ^* + E_t (p _p+1 - p_t ), which may also be written in terms of the exchange rate:

We assume that the unemployment rate is determined by:

where r _t-1 is the ex post real interest rate observed at date t, given by:

The first term of equation (4) is intended to reflect a phenomenon of persistence in the dynamics of unemployment. It is a well-known empirical fact that unemployment exhibits very significant persistence in developed economies, and in particular european ones. The theoretical literature provides us with a number of explanations for this phenomenon, including insider/outsider relationships (Blanchard et Summers, 1986; Lindbeck et Snower, 1988), adjustment costs (Nickell, 1986; Saint-Paul, 1995), or the depreciation of the human capital of unemployed workers (Pissarides, 1992). Broadly speaking, these explanations attribute the persistence of unemployment to structural inflexibilities of the labor market, so that we can interpret ρ as an index reflecting the structural persistence of unemployment. ₆ If ρ is equal to 1, the unemployment rate exhibits no tendency to converge towards a natural level, a situation that is often called hysteresis. We assume in what follows that ρ ∈]0, 1[, the limit case ρ = 1 corresponding to "structural hysteresis".

The unemployment rate also depends on the ex post real interest rate. Equation (4) aims to express the fact that, while the interest and unemployment rates should both stay close to their natural levels in the long run, a temporary increase in the ex post real interest rate raises unemployment. The unemployment rate can depend on the ex post real interest rate through the balance sheet channel of monetary policy, the microfoundations of which have been studied in particular by Bernanke and Gertler (1989, 1995). ₇ These authors show how a rise in the ex post real interest rate, by reducing the cash flow of debtors (firms or households), can reduce their ability to draw external funds and finance new expenses. It is important to note that the monetary transmission channel at work in equation (4) is different from the most standard one, which is based on the ex ante real interest rate i_t + E_t (p _t+1 - p_t ). While it would not be difficult to include the ex ante interest rate in equation (4) in addition to the ex post one, this would not change the model since it directly follows from the purchasing power and interest parity assumptions that the ex ante real interest rate is constant and equal to r ^*.

Equation (4) may seem very different from the Phillips curve that is usually assumed in the literature, but it is not difficult to see that it yields the same reduced form determination of unemployment, so that all the results of the theoretical section could also be derived from a traditional Phillips curve. It easily follows from the purchasing power and interest parity conditions that the deviation of the ex post real interest rate from its natural level is given by:

so that the equation governing the dynamics of the unemployment rate may also be written:

which may be viewed as an expectations augmented Phillips curve with some persistence in unemployment. This type of equation was used in a similar context by Drazen and Masson (1994), Masson (1995), Jeanne (1996). The reason why we use equation (4) is that it does not give the same reduced form for unemployment as a Phillips curve when the foreign interest rate is not constant. According to equation (4), an increase in the foreign real interest rate raises domestic unemployment, an effect that would not obtain in a Phillips curve model. Thus the formulation we have adopted seems more adapted to study the EMS crisis, in which the high level of the German interest rates seems to have been important.

3 The dynamics of unemployment in the fixed exchange rate system

This section is dedicated to the characterization of the equilibria. We first show, in section 3.1, that the credibility of the policymaker's commitment is a well-defined function of the domestic unemployment rate. We then analyse the dynamics of unemployment, and show that some of them are associated with currency crises (section 3.2).

3.1 The devaluation expectations

The credibility of the fixed parity is not perfect, since the policymaker enjoys an escape clause that he may exert at any period. We denote by π _t the probability at t that the policymaker will devalue the following period.

Let us consider the decision of the policymaker at date t + 1. Given the preceding period nominal interest rate:

the policymaker can maintain the fixed parity, at the cost of setting the ex post real interest rate at r^F _t = r^* + π_td and the unemployment rate at:

or devalue, in order to obtain the ex post real interest rate r^D _t = r^F _t - d and the unemployment rate:

Thus, devaluing allows the policymaker to lower the unemployment rate by an amount:

The policymaker devalues if this lowers his loss function (1), i.e., (u^F _t+1 - ‾u)² > (u^D _t+1 - ‾u)² + C_t+1, or:

The policymaker's optimal decision is to devalue if the unemployment rate implied by the fixed exchange rate system goes beyond a critical level that depends on the opting out cost. It follows that π _t may be written:

or, denoting by F(⋅) the cumulative distribution function of η/2v (and by f(⋅) = F'(⋅) the corresponding probability density function):

This equation implies that the devaluation probability is determined by the unemployment rate as stated in the following proposition (the proof of which may be found in the Appendix).

Proposition 1 . If vf(0) < 1, the devaluation probability is uniquely determined by the unemployment rate, and may be written at t:

where function Π(⋅) is strictly positive, increasing and satisfies lim_-∞ Π(⋅) = 0, lim_+∞ Π(⋅) = 1.

The devaluation probability is an increasing function of unemployment. Because of the structural persistence in unemployment, a rise in current unemployment increases the probability that the unemployment rate will be larger than the critical level the following period and the policymaker devalues. Moreover, the devaluation probability is different from zero whatever the level of the unemployment rate, which means that the life expectancy of the fixed exchange rate system remains finite. ₈

Proposition 1 also states a condition, vf(0) < 1, for the devaluation probability to be uniquely defined. If this condition is not satisfied, the presence of π _t on both sides of equation (8) can generate multiple equilibria. This possibility is interesting insofar as it makes possible to study how speculation can become self-fulfilling during currency crises (see, e.g., Jeanne, 1996). In this paper, however, we study the properties of the model leaving aside the multiplicity of equilibria, and assume that the condition vf(0) < 1 is satisfied.

3.2 The dynamics of unemployment

Plugging equation (9) into equation (6) yields a first order equation characterizing the dynamics of unemployment in the fixed exchange rate system:

(where the upper index F has been dropped for the sake of convenience).

Differentiating the unemployment rate at t + 1 with respect to the previous period unemployment rate gives us the unemployment persistence that is observed in the fixed exchange rate system:

The apparent persistence is the sum of two terms. The first term, ρ, summarizes the persistence mechanisms that are assumed to come from the structural rigidities of the labor market. The second term is due to the exchange rate regime: an increase in the unemployment rate at a given period raises the interest rate premium and the unemployment rate in the following periods if the policymaker does not devalue.

Let us scrutinize how the exchange rate regime influences the dynamics of unemployment, considering first the case when unemployment does not exhibit structural hysteresis (ρ < 1). Figures 1 and 2 shows us two possible representations of equation (10) in this case. ₉ In both figures, the unemployment rate converges towards a level ‾u which is strictly larger than the natural level. The difference between figures 1 and 2 lies in the stationarity of the unemployment dynamics. While in figure 1, the unemployment rate converges towards a level that does not depend on the initial conditions, in the case of figure 2 the dynamics of unemployment are non-stationary. The unemployment rate converges to ‾u^F ₁ if it is intially lower than ‾u^F ₂, and towards ‾u^F ₃ if not. One might characterize the latter situation by saying that the exchange rate regime generates some hysteresis in the unemployment dynamics, but it is important to note that this hysteresis is apparent only as long as the policymaker stays in the fixed exchange rate system. It is not effective in the long term, since the fixed exchange rate system has a finite life expectancy. The following proposition summarizes our findings, and states the conditions under which apparent hysteresis can arise.

Proposition 2 . Assume that there is no structural hysteresis in unemployment (ρ < 1). Then as long as the policymaker stays in the fixed exchange rate system, the unemployment rate converges towards a level ‾u^F that is strictly larger than the natural level ‾u. Moreover, if vf (0) > 1 - ρ and the opting out cost C lies in an interval]\??\C, ‾C[, the fixed exchange rate system can generate apparent hysteresis in the dynamics of unemployment, i.e., the unemployment rate converges towards a low level ‾u^F ₁ or a high level ‾u^F ₃ depending on whether it is initially lower or higher than a threshold ‾u^F ₂. When the unemployment rate is close to ‾u^F ₃, the life expectancy of the fixed exchange rate peg is shorter than two periods.

The proof of this proposition, as well as explicit formula for \??\C and ‾C, may be found in the Appendix. The phenomenon behind proposition 2 is essentially a "peso effect". Persistent devaluation expectations constrain the policymaker to raise the nominal interest rate, which translates into high ex post real interest rate and unemployment rate as long as the policymaker does not devalue. The stationary level of the unemployment rate that is compatible with the fixed peg crucially depends on the opting out cost. If the opting out cost is above the higher bound ‾C, the economy converges towards a state in which both the unemployment rate and the devaluation expectations may be low. If the opting out cost is under the lower bound \??\C, the unemployment rate converges towards a high level ‾u^F ₃. If C takes intermediate values between \??\C and ‾C, the unemployment rate may also converge towards ‾u^F ₃, but only if it is initially higher than a critical threshold ‾u^F ₂.

As the last part of proposition 2 shows, the policymaker becomes very likely to devalue when the unemployment rate converges towards ‾u^F ₃, and the economy exhibits the symptoms of a currency crisis, i.e., a sharp increase in devaluation expectations and deteriorating domestic economic conditions. The logic of these currency crises relies on a vicious circle, in which high unemployment gives rise to devaluation expectations that constrain the policymaker to increase interest rates and unemployment even further.

In the case where unemployment exhibits structural hysteresis (ρ = 1), equation (10) reduces to:

from which it directly follows that the unemployment rate is increasing.

Proposition 3 . If unemployment exhibits structural hysteresis (ρ = 1), the unemployment rate grows as long as the policymaker stays in the fixed exchange rate system.

The exchange rate regime introduces a positive drift in the unemployment dynamics when the latter are non-stationary. Of course the fixed exchange rate system is intrinsically unstable in such a situation. As unemployment increases, the policymaker is more and more likely to devalue and the economy enters a currency crisis sooner or later. From this point of view, the equilibrium that arises when ρ = 1 is observationnally not very different from the one where unemployment exhibits no structural hysteresis but the opting out cost is too small to stabilize the unemployment rate at a low level (C < \??\C).

The level of the opting out cost is crucial for the stability of the fixed exchange rate system. In practice, the level of the opting out cost is partly determined by the fundamental economic conditions. For example, one may expect the real overvaluation of the currency to decrease the benefit that the domestic country derives from belonging to the fixed exchange system, or equivalently to reduce the opting out cost. The opting out cost may also be determined by the institutional form of monetary policy. In the spirit of Rogoff (1985), delegating the defense of the fixed exchange rate peg to a central banker chosen for his high opting out cost may constitute a means to mitigate the peso effect. If unemployment exhibits no structural hysteresis, this delegation increases the critical unemployment threshold above which the currency crisis is triggered, and can even remove the possibility of currency crisis altogether. Delegating is not without cost, however, when the unemployment rate is high and the central banker sticks to the fixed peg. A central banker with opting out cost \??\C > C will devalue only if the unemployment rate imposed by the system goes beyond ‾u + (\??\C/v> + v)/2, which is higher than the policymaker's critical threshold ‾u + (C/v + v)/2. When the unemployment rate lies between the policymaker's threshold and that of the central banker, delegation increases the policymaker's loss.

Another -extreme- way to increase the institutional component of the opting out cost is to remove the escape clause altogether, i.e., establish a monetary union with the foreign country. This can be interpreted in our model as the limit case C = +∞. In the absence of structural hysteresis, the unemployment rate will converge towards its natural level at a speed that depends on the structural persistence index ρ. From this point of view, the benefit of monetary union is to remove the interest rate premium and the associated unemployment, while its cost is to remove an opting out clause that may be valuable when unemployment is high.

4 Application to the "franc fort" policy

The purpose of this section is to confront our model to the history of the "franc fort" policy between 1987 and 1993. We first briefly review the recent history of the French franc, focusing in particular on the relationship between the French unemployment rate and the credibility of the franc/mark parity (section 4.1). We then present a generalization of our model more proper to the estimation than the stylised model presented in the previous section (section 4.2). The last section is dedicated to the presentation and interpretation of our results.

4.1 Stylised facts

The French monetary authorities have been developing a consistent effort to maintain the parity of the franc with respect to the German mark for the last ten years-what came to be called the "franc fort" policy. Initially motivated by the desire to emulate the German inflationary performance, the franc fort policy was later justified by French policymakers as a condition for France to keep a leading role in EMU. While the origin of this policy can be traced back as early as 1983 when the French socialist government converted to economic orthodoxy for the sake of the european construction (Sachs and Wyplosz, 1987), it became really effective only from 1987, since when the central ERM parity of 3.35 FF/DM has never been realigned. The EMS crisis of 1992-3 and the subsequent widening of the ERM margins constitute a break in the continuity of the franc fort policy, but only a relative one since the Bank of France, that was made independent in 1993, adopted a policy of maintaining the franc in the old narrow margins. We shall restrict our discussion and empirical investigation to the period 1987-1993, however, in order to deal with a time period that is unambiguously without change of regime.

A short glance at the data readily brings out two distinct periods in the history of the franc fort policy. The first period, that extends from 1987 to mid-1992, is dominated by a logic of convergence between the franc and the mark. The gradual improvement in the franc credibility shows up in the evolution of the franc/mark one-month interest rate differential, that decreased from around 4% in 1987 to almost zero in 1991 (see Chart 1a). The strengthening of the franc was overall associated with a favorable evolution of the economic fundamentals. First, the real competitiveness of the franc improved slightly between 1987 and 1992, an evolution that must be attributed essentially to a relative appreciation of the dollar during the period (Chart 1c). ₁₀ The unemployment rate also steadily decreased until 1990, when the trend reversed (Chart 1d). However, the better credibility of the franc did not translate into a decrease of the French nominal and real interest rates because of the concomitant rise in the German interest rate, that was due in 1988 and 1989 to the concerns of the Bundesbank about the resurgence of inflation in a booming economy and, from 1990 onwards, to the German monetary unification shock (Charts 1a-b).

The second period, from September 1992 to July 1993, was dominated by speculation, and the reappearance of a large and volatile interest rate premium. Following Moutot (1994), one can distinguish three successive episodes of acute speculation, that clearly show up in the interest rate differential (Chart 1a). The first episode was associated with the french referendum on the Maastricht treaty in September 1992, and the EMS-wide wave of speculation that forced the lira and the sterling out of the ERM. The second episode of speculation was more proctrated than the first one without being less intense, since it constrained the french monetary authorities to raise the interest rate to higher levels than in September for several months in a row, from December 1992 to March 1993. This episode came at a time when it was becoming increasingly clear that the french economy was entering a full-fledged recession and that unemployment was increasing at a very quick pace. In this context, market participants began to doubt the willingness of the french monetary authorities to raise the interest rate to defend the parity of the franc. The speculation against the franc intensified in the runup to the parliamentary elections of March 1993, but abated after Edouard Balladur formed a strongly pro-european government on the 29th of March. The respite was short-lived, however. In July, the issue of very bad unemployment statistics, together with the rumor of a disagreement between the French and German finance ministers triggered a new wave of speculation against the franc, which that time turned out to be successful. While the unemployment rate was approaching the record high level of 12%, the french monetary authorities aknowledged the unsustainability of defending the franc by raising the interest rate and let the franc stuck at its ERM ceiling on the 30th of July, leaving the burden of defending the franc to the Bundesbank. On the 2nd of August, the european finance ministeres and central bank governors decided in an emergency meeting to widen the ERM margins from 2.25% to 15%.

Interestingly the fight between central banks and speculators over the franc also took the form of a debate about what constituted the relevant fundamentals of the franc credibility. On the one hand, the Bank of France and the Bundesbank repeatedly asserted that the fundamentals were sound, by which they meant that the franc was not overvalued, that French inflation was low (in particular, lower than in Germany) and the French trade balance was in surplus. Some French policymakers even stretched the argument to the point of saying that the franc was ready to replace the mark as the anchor of the EMS (The Economist, June 26, 1993, p.101). On the other hand, as the following quote of the economists of Goldman Sachs makes clear, market participatns were scrutinizing quite another type of fundamental, namely the contradiction between the rise in the unemployment rate and the level of interest rates required by the maintenance of the franc parity:

"in many respects the "fundamentals"-trade flows, inflation, PPP, etc.- are strongly supportive of the franc. However, it should be equally obvious that current ERM pressures are not wholly linked to such "fundamentals", but have more to do with other fundamentals, such as the need to reduce real interest rates in countries where recession is biting". (The International Economics Analyst vol.7 (11), dec.92/jan.93, p.3.08).

The data represented in Chart 1 confirm that unemployment was the only macroeconomic variable susceptible to explain the speculation against the franc from 1992 onwards. While the franc appreciated in real terms in 1992 because of the fall in the dollar and the devaluation of other EMS currencies, this evolution was transitory and too small in amplitude to influence the trade balance, that remained positive at the end of the sample period. It is true that the fiscal deficit (not shown) increased sharply in 1993, but this evolution was largely unanticipated at the beginning of the crisis and cannot explain per se the speculation against the franc. ₁₁ While the episodes of speculation were often associated with political events, the essence of the political uncertainty was really whether the increasing popular reluctance to bear the perceived unemployment cost of the franc fort policy would find a political representation or not.

Not only unemployment was the essential fundamental, but there is also informal evidence that the interrelationship between the unemployment rate and devaluation expectations that we have modeled in the preceding section was important in the franc crisis. In particular, the strategy of raising the interest rate to defend the franc that was consistently followed by the French monetary authorities was perceived as largely counterproductive by the market to the extent that it contributed to aggravate the economic slump that was at the root of the franc weakness. For example, when the Bank of France raised its interest rate at the end of 1992, as it had done with success a few months earlier, this move was received by the market with much more scepticism than in September. The Financial Times noted: "...another interest rate rise would undoubtedly affect corporate confidence and set back the government's hope of a recovery in industrial investment. Such a scenario would further lock the economy in a vicious circle." (FT, January 6 1993, "French change tack in fight for franc"). The logic of the vicious circle that market participants apparently had in mind is the one that we have modeled in the previous section.

4.2 Estimation

While the stylised model of section 3 was a good framework to present the logic of our results, it is much too simplistic to lend itself to econometric estimation. We present in this section a generalized version of our model including more shocks and lagged variables, before we review the data and the estimation method.

Like in section 2, we consider a policymaker that can stay in a fixed exchange rate system or devalue the domestic currency by an amount d, and takes his decision so as to minimize loss function (1). Opting out allows him to reduce the unemployment rate by v but entails cost C _t at date t. We assume that equations (2), (3) and (4) become:

The first equation generalizes (2) by assuming that the expected component of the opting out cost can depend on time and the real exchange rate. As we argued before, one may expect a real overvaluation of the currency to affect negatively the benefit of maintaining the fixed peg, i.e., to reduce the opting out cost. The trend can result from a reputational effect. As time goes by, the anti-inflationary reputation of the policymaker improves, so that the opting out cost in terms of reputation increases. The shock η is assumed to be i.i.d. and distributed according to a normal law of variance σ² _η.

The second equation generalizes (3) by allowing the foreign nominal interest rate to change with time. Variable n corresponds to the number of periods in one year (that we must take into account in the interest parity condition to the extent that the interest rate are expressed in annual terms). Equation (12) may also be written in terms of the devaluation probability: ₁₂

The third equation generalizes (4) by adding a shock and lagged explanatory variables. We assume that ε is i.i.d. and follows a normal law of variance σ² _ε.

Proceeding as in section 3, we find that the policymaker devalues at t + 1 if and only if:

which allows us to endogenize the devaluation probability as:

where F _σ(⋅) is the cumulative distribution function of the normal law of variance σ² = (σ_η/2v)² = σ² _ε, and Λ_t is the adjusted opting out cost at time t, given by:

Let us denote by r^* _t = i^* _t - (p_t+1 - p_t) the imported ex post real interest rate, i.e. the ex post real interest rate that would prevail in the domestic country in the absence of devaluation expectations. Then adding an i.i.d. normal model prediction error ν to equation (14) gives us the dynamic stochastic system:

Equations (15) and (16) constitute a reduced form model of the determination of the unemployment rate and the devaluation probability, in which the exogenous explanatory variables are the imported real interest rate r^* _t and the adjusted opting out cost Λ_t. The simple theoretical model of sections 2-3 can be viewed as a particular case of this model, corresponding to θ_u = θ_r = 1, ε_t = ν _t = 0 and γ₂ = γ₃ = 0.

It is noteworthy that we have not used the assumption of instantaneous purchasing power parity to derive equations (15) and (16), but only the assumption that devaluing reduces the unemployment rate by an amount v. The assumption of instantaneous PPP is notoriously rejected by the data, and would be anyway difficult to reconcile with our hypothesis that the real exchange rate matters for the opting out cost. On the other hand, the assumption that devaluing reduces the unemployment rate is much weaker, and may be justified by other monetary transmission channels (but more complicated to model) than the one we have used in section 2. Accordingly, we do not take into account the restriction v = α₁ nd that would be implied by instantaneous PPP in the estimation.

The estimation consists in finding the structural parameters cu, (αk)θr k=1, (ρk)θu k=1, σ and (γk)3 k=1 that allow the model to give the best account of the observed series (ut)T 1, (πt)T 1, (r* t)T 1 and (rert)T 1, which we do using the Maximum Likelihood Method.

We estimate the model using monthly data (n = 12) between February 1987 and July 1993 (included), which is the longest period without change in regime for the franc in the ERM (78 months). Interest rates are the monthly average of the daily one-month eurorates as they are collected each day by the Bank of France at 11:30 a.m. (Chart 1a). The other data come from the IMF's International Financial Statistics. Variable Δp is the moving average over six months of the monthly change in the CPI index (line 64 in the International Financial Statistics). We took the logarithms of the unemployment rate and real exchange rate in the estimation. Moreover, we assumed that the expected amount of the devaluation is d = 5%, and θ_u = 6, θ_r = 3.

4.3 Results

Table 1 gives the results of the estimation by the maximum likelihood method. The first column indicates the values of the parameters for the unrestricted model, while in the second column unemployment is assumed to exhibit structural hysteresis (Σ⁶ ₁ρk = 1) and two of the α coefficients were set to zero (α₁ = α₃ = 0). We have indicated in parenthesis the P-values of the coefficients, i.e., the significance levels at which they are different from zero. ₁₃ These values were estimated by applying the likelihood ratio test to the null hypothesis for each coefficient.

The estimation gives an empirical content to the equation of unemployment (15) and the equation giving the devaluation probability (12). We shall comment each equation in turn, before we come to the synthetic picture of the franc history that they give us together.

In the unemployment equation (15), one observes that the sum of the ρ coefficients is very close to 1 (it is equal to 0.9846). In fact, it is not possible to reject the hypothesis of structural hysteresis Σ⁶ _k=1ρk = 1 at the 10% level in the unrestricted model. ₁₄ Moreover the likelihood ratio test shows that it is not possible to reject the restricted model of column 2 (table 1) when it is compared to the unrestricted one. Therefore, the estimation does not attribute the apparent hysteresis in unemployment to the exchange rate regime rather than to structural rigidities of the labor market.

Another important aspect of the estimation is to know whether coefficients α are positive and significantly different from zero, because these are the coefficients that generate the relationship between unemployment and the devaluation expectations that is at the root of the interesting properties of the model. As one can see it in Table 1, these coefficients are not significantly different from zero when considered individually, but a test of the hypothesis α₁ = α₂ = α₃ = 0 using the likelihood ratio test allows us to reject it at a level close to 1%. ₁₅ Moreover, their sum is positive in column 1 and α₂ is positive and strictly different from zero in column 2. This means that the impact of a rise in the real interest rate on unemployment is statistically significant, but the data do not indicate precisely whether this impact comes about with a lag of 1, 2 or 3 months.

Chart 2 shows the response of the unemployment rate to a transitory shock of 1% in the real interest rate, starting from a stationary steady state in which the unemployment rate is equal to 8%. In the case of the restricted model, this response is very small and slow since the unemployment rate increases by less than 0.03% after two years, before it converges back to the natural level following small oscillations. In the restricted model, unemployment reacts in a similar way in the first two years, but does not converge back to the initial level in the long term since it is non-stationary.

Chart 3 allows us to assess the success of the model in predicting devaluation expectations by comparing the actual level of the devaluation probability with the fitted one. One observes that the model explains the essential movements of the devaluation probability, except for the episodes of intense speculation. In the estimated model the devaluation probability is determined by several exogenous fundamental variables: the unemployment rate, the real exchange rate and time. The last two variables appear in the adjusted opting out cost Λ, the variations of which are represented in Chart 4. As expected, the opting out cost is increasing with time (γ₂ > 0), which may be interpreted as a reputational effect, and decreasing with the real exchange rate (γ₃ < 0), both effects being highly statistically significant. The opting out cost exhibit a clear upward trend during the sample period: about two thirds of this increase can be attributed to time, while the real exchange rate explains the remaining part. The stabilizing effect of the increase in the opting out cost was offset from 1991 onwards by the rise in the unemployment rate. It is not difficult to see from the values given in Table 1 that a 1% increase of the unemployment has the same effect on the devaluation probability as a real appreciation of the franc by 1%. ₁₆

Thus, the competitiveness of the franc does not seem to have been less important than unemployment for the franc credibility. The importance of the real exchange rate in the fundamental may seem surprising in view of the analyses that argue that the French franc was not overvalued in 1992-3 (Eichengreen and Wyplosz, 1993; Svensson, 1994). It should be noted, however, that while these analyses focus on the real competitivity of the franc with respect to the mark, this is the exchange rate relatively to non-EMS currencies-especially the dollar- that seems to matter here. There are several channels through which the fluctuations of the dollar can influence the stability of the EMS, the most convincing ones being related less to real competitiveness than to the portfolio allocation of international investors. As Giavazzi and Giovannini (1986) have documented, when the dollar is weak investors reallocate their portfolio toward German mark denominated assets, which tends to generate tensions in the EMS. Our analysis suggest that this effect may have been more important in the French franc crisis than is usually aknowledged.

We then study the behavior of the model economy by running two counterfactual experiments. The first counterfactual experiment consists in estimating the evolution of unemployment in France if EMU had been implemented during the sample period, so that the French interest rate would have been strictly equal to the German level (Chart 5). ₁₇ We find that as France would not have had to bear the interest rate premium, the unemployment rate would have been 0.4% (0.7%) lower if EMU had been implemented in June 1992 (July 1990). Thus, the large interest rate premium that was imposed upon France during the 1992-3 crisis does not seem to have had a negligible impact on the unemployment rate. ₁₈

The second counterfactual experiment assesses the evolution of French unemployment in the absence of the German monetary shock. For this purpose, we have to make assumptions about what would have been German monetary policy without German monetary unification. For the sake of simplicity, we have assumed that after German monetary unification, i.e. from July 1990 onwards, the interest rate would have been equal to the minimum of its realized level and the average over July 89-June 90. As Chart 6 shows, we find that the unemployment rate would have been 1.4% lower at the end of the sample period in the absence of German shock.

The large response of unemployment that is produced by our counterfactual experiments may seem surprising in view of the very small sensitivity of the unemployment rate to the real interest rate (Chart 2). The two findings may be reconciled by combining the peso effect with the high structural persistence of unemployment. By virtue of the peso effect the interest rate shocks always go in the same (restrictive) direction as long as the monetary authorities defend the fixed exchaneg rate peg. And because of the persistence of unemployment these repeated shocks end by building a non-negligible cumulative stock of unemployment. Interestingly this point may be related to the larger debate over whether monetary policy matters to the business cycle. Some economists argue that monetary policy is not an important source of business fluctuations because in VAR regressions money shocks explain only a small fraction of the variance of output. This statement is certainly consistent with the impulse response function given in Chart 2, which is not likely to associate interest rate shocks of the order of magnitude that we observe with large fluctuations of unemployment. This does not mean, however, that monetary policy has no effect on unemployment, if the interest rate shocks are subject to a peso effect and their impact is reinforced by a high structural persistence in real variables.

Taken together, the different pieces of the franc story resulting from the estimation are broadly consistent with most analyses of the crisis. Between 1987 and 1990, the improving French competitiveness and the fall in the unemployment rate both reinforced the credibility of the franc/mark parity, which made possible a progressive reduction of the interest rate differential to almost zero in 1991. The increase in the French unemployment rate from 1990 onwards, which must be attributed partly to the German monetary shock, fragilized the credibility of the franc after 1992. This evolution was reinforced by the deterioration of the franc competiveness between mid-92 and mid-93, that was due to the appreciation of the franc vis-a-vis the dollar.

5 Concluding comments

We conclude this paper by discussing first some extensions and paths for further research and then summarizing its contributions to the debates over the "franc fort" policy and EMU.

5.1 Extensions

A government that wants to reduce unemployment without devaluing the currency can resort to fiscal stimulus. While the Maastricht treaty restricts considerably the room for fiscal expansion, it remains interesting, at least from a theoretical level, to study the dynamics of unemployment in an escape clause fixed exchange rate system when this type of policy is permitted. While traditional theory predicts that public deficits should foster devaluation expectations because of the expectation that the public debt will be monetized, our analysis suggests otherwise. Sustainable deficits might stabilize a fixed exchange rate peg to the extent that they prevent unemployment to reach levels at which maintaining the peg becomes too costly to be credible.

Moreover, whether given levels of public deficits or public debts are sustainable or not might be analysed along the same lines as in the present paper. The dynamics of public debt are governed by an equation that is not without analogy with (4), since the real stock of public debt at a given date depends on its level at the preceding period, the current deficit and the level of real interest rates. Assuming that the objective function of the government is decreasing with the real stock of public debt (because of tax distorsion, say), the dynamics of public debt for a given level of public deficit could be determined as that of unemployment in the present model. One may conjecture that in a model combining unemployment and public debt, the long-term viability of the fixed exchange rate peg would depend on the initial levels of unemployment and debts.

Another natural extension of the model would be to endogenize the domestic price level. The simple model of sections 2 and 3 was developed under the assumption of Instantaneous Purchasing Power Parity, which is not an assumption that we could defend in the estimated model, where the domestic price level had to be taken as exogenous. It would be interesting to make the domestic price level depend on interest rates as unemployment. (But this might also be difficult since it would require a much more structural model than the one we have developed).

5.2 Franc fort and EMU

The French monetary authorities' answer to the charge that the "franc fort" policy is responsible for the high level of the French unemployment rate critic is that (i) the increases in the short-term interest rate that may be required by the defense of the franc have a negligible effect on unemployment, which depends more on long-term interest rates and (ii) structural rigidity in the labor market is the real culprit. In fact, our empirical findings are consistent with this claim: we find that a transitory shock in the short-term interest rate has a negligible (though statistically significant) impact on the unemployment rate, and that the persistence of the unemployment rate should be attributed essentially to structural factors rather than the exchange rate regime. On the other hand, we also find that the high level of the real interest rates imposed by the franc fort policy explain a non-negligible part of the French unemployment problem. As we have argued, this finding is a logical implication of the premises of the argument of French monetary authorities. This is precisely because unemployment is structurally persistent that the accumulated effect of small short-term interest shocks can produce important effects in the long term. Thus, the rigidity of the labor market, far from relieving monetary policy from its responsibility, exacerbates its effects. From this point of view, the debate over the "franc fort" policy might be compared to a discussion between two plumbers about whether a bath overflows because it is clogged or the tap leaks. De-clogging the bath may be the best long-term solution but as long as it is not implemented, the leak also contributes to the problem and makes it more difficult to solve.

The contribution of this paper to the analysis of monetary union is limited since it concerns only one benefit of the union, which is the disappearance of the interest rate premium. Our empirical findings suggest that this benefit is not negligible, which reinforces the case for EMU (at least for France). On the other hand, our analysis would lead us to be rather critical of the way the transition towards EMU is planned in the Maastricht treaty, that requires the respect of many nominal criteria, in particular the stability of the exchange rate, and leaves aside real fundamentals like unemployment. According to the analysis developed here, the essential benefit of a monetary union is to stabilize the dynamics of the devaluation expectations and unemployment in conditions under which they would be unstable in the corresponding fixed exchange rate system. From this point of view, requiring the stability of the fixed exchange rate system as a condition for monetary Union is a bit like conditioning a medical treatment on the patient's good health.

APPENDIX

Proof of Proposition 1.

Figure 3 represents equation (8). The devaluation probability corresponds to the intersection between the curve representing the r.h.s. with the 45° line. The question is whether this curve intersects the 45° line in one or several points. Under the condition given in the Proposition, the maximal value of the curve's slope is v max F' = vf(0) < 1. The curve has a slope everywhere strictly smaller than 1, whence the uniqueness of its intersection with the 45° line. Hence π may be written as a well-defined function of u _t. This function, denoted by Π(⋅) in the Proposition, is stricly increasing, since increasing u _t translates the curve leftwards, which increases π. In the limit, when u _t goes to plus (minus) infinity, π converges towards 1(0).Q.E.D.

Proof of Proposition 2.

A stationary equilibrium ‾u ^F , ‾π ^F necessarily satisfies:

Eliminating ‾π ^F gives:

A stationary unemployment rate therefore corresponds, on Figure 4, to an intersection between the curve representing the r.h.s. of equation (17) and the ray of slope 1- ρ. Two conditions are necessary for multiplicity. First, the curve must have a slope larger than 1- ρ in some points. As the maximal value of this slope is vf(0), we find the first condition given in the Proposition. Second, the inflexion point of the curve must not be too far from the ray, which occurs iff C ∈]\??\C, ‾C[, where \??\C and ‾C are characterized by the tangency conditions:

and:

In order to find ‾C, we first note that the first tangency condition and ‾u^F ₃ - ‾u - (‾C/v + v)/2 > 0 imply:

Plugging this expression into the second condition then gives:

Eliminating ‾u^F ₃ from the preceding two equations then yields an expression for ‾C:

In order to find an expression for ‾C, one proceeds in the same way, noting however that given ‾u^F ₁ - ‾u < (‾C/v + v)/2, the first tangency condition must be inverted as:

from which it follows that:

In order to prove the last part of the Proposition, we note that ‾u^F ₃ - ‾u > v/2(1 - ρ) implies ‾π^F ₃ > 1/2. Hence when the unemployment rate is close to ‾u^F ₃, the life expectancy of the system is shorter than 1/2 + 1/2² + ... = 2 periods. Q.E.D.

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Note 1: Thus, the Reports on Convergence of the European Monetary Institute do not refer to unemployment, except as a variable influencing indirectly the real exchange rate through wage pressure. Back.

Note 2: While this cost is the often deemed as the most important by economic agents, empirical studies usually do not estimate them to be large (see, e.g., Frankel and Wei, 1993, in the case of the EMS). Back.

Note 3: The anti-inflationary credibility effect of fixed pegs have been emphasized especially in the case of the EMS, to the point of being presented as the foundation of this system (Giavazzi and Giovannini, 1989). Back.

Note 4: Begg and Wyplosz (1987) model the benefit of the EMS in this way, while Oudiz (1985) attempts to estimate its size. Back.

Note 5: Like in many models of exchange rate determination, the assumption of instantaneous PPP is adopted for convenience in spite of its notorious empirical rejection by the data. We show in the empirical part of the paper that it is possible, under some condition, to dispense with it. Back.

Note 6: An equation with the same type of unemployment persistence as in (4) is derived from a model of bargaining between unions and employers by Lockwood and Philippopoulos (1994). Back.

Note 7: See Mishkin (1995) for a recent review of the main transmission channels of monetary policy. Back.

Note 8: This property comes from the assumption that η is unbounded. If η were always larger than -(C/v+v)/2 (i.e., F[-(C/v+v)/2] = 0), one could have equilibria where the devaluation probability is equal to zero. Back.

Note 9: The asymptotes represented as dotted lines in figures 1 and 2 result from the fact that function Π(⋅) converges towards 1 in +∞ and towards 0 in -∞ (see Proposition 1). Back.

Note 10: Chart 1c shows the real exchange rate of the French franc as it is computed by the International Monetary Fund (line reu of the International Financial Statistics). An increase in this index corresponds to a real appreciation of the franc. The inflation differential between France and Germany, that was the primary target of the "competitive desinflation" strategy underlying the franc fort policy never contributed significantly to the fluctuations of the real exchange rate, that rather reflect the fluctuations of the franc vis-a-vis the dollar and other currencies. Back.

Note 11: In August 1992, the economists of Goldman Sachs selected France and Luxembourg as the only european countries satisfying the Maastricht convergence criteria, including those related to public debts and deficits (The International Economics Analyst 7(7/8), 1992, p.2.05). Back.

Note 12: Unlike Svensson (1993), we do not correct this equation to take into account the fluctuations of the exchange rate inside the band. We found that taking this effect into account does change our empirical results in any essential way, and significantly decreases the estimated likelihood of the model. Back.

Note 13: Except for σ, which cannot be set to zero in the estimation. Back.

Note 14: The likelihood ratio corresponding to this hypothesis is LR = 1.840, under the 10% critical level of 2.705. Back.

Note 15: The likelihood ratio is LR = 6.536, virtually equal the 1% critical level of 6.635. Back.

Note 16: In the model the impact of the fundamentals on the devaluation probability is represented by variable E _t(u _t+1-C _t+1). An increase in the unemployment rate from 10% to 11% raises E _t(u _t+1-C _t+1) by ρ₁/10. A 1% real exchange rate increase raises E _t(u _t+1 - C _t+1) by -γ₃/100, which is approximately equal to ρ₁/10. Back.

Note 17: The simulation presented in Chart 5 was run with the unrestricted model. The results of the restricted model are not very different. Back.

Note 18: These results may be compared with those of Bini-Smaghi and Tristani (1995) who estimate at 1/4% of French GNP the cost of the interest rate premium between mid-92 and mid-93 using a macroeconometric model. Back.