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Stabilizations, crises and the “exit” problem – A theoretical model
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Journal of Macroeconomics 29 (2007) 876–890 www.elsevier.com/locate/jmacro
Stabilizations, crises and the ‘‘exit’’ problem – A theoretical model Michael Bleaney a, Marco Gundermann
b,*
a
b
University of Nottingham, School of Economics, United Kingdom University of Wales Institute Cardiff (UWIC), Business School, Colchester Avenue, Cardiff CF3 4TD, United Kingdom Received 22 July 2003; accepted 11 October 2005 Available online 9 May 2007
Abstract Exchange-rate-based stabilizations, even if successful, usually lack credibility initially. This is reflected in high (ex post) real interest rates and some degree of real exchange rate appreciation. Empirical observation suggests that wage inflation declines smoothly over time whilst interest rates are volatile. Our model captures these features and provides insights into: the eruption of exchange rate crises after a long period of apparently successful stabilization; the potential advantages of a heterodox approach; when to delay a stabilization attempt; and the optimal date for ‘‘exit’’ to a floating exchange rate. Ó 2007 Elsevier Inc. All rights reserved. JEL classification: E31; F41 Keywords: Credibility; Currency crisis; Exchange rate; Inflation
1. Introduction A feature of exchange-rate-based stabilizations is that, even if successful, success is not immediate. Agents in financial and labor markets are often skeptical initially, and this is reflected in real exchange rate appreciation and high nominal interest rates relative to the *
Corresponding author. Tel.: +44 292 0416368; fax: +44 292 0416940. E-mail address: [email protected] (M. Gundermann).
0164-0704/$ - see front matter Ó 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.jmacro.2005.10.021
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realized inflation rate (Dornbusch et al., 2001; Edwards, 1993; Kaminsky and Leiderman, 1998). Calvo and Ve´gh (1999) provide a useful survey. To judge by inflation differentials, most stabilization attempts that have not yet collapsed show evidence of increasing credibility over time. Nevertheless market-determined interest rate differentials tend to behave in a more volatile manner, suggesting a varying degree of speculative pressure. Traditionally, continuing wage inflation has been interpreted as a reflection of either backward-looking indexation or forward-looking expectations combined with doubts about the success of the stabilization. The key innovation in this paper is to build this feature into a theoretical model. The survival of the stabilization attempt is determined in a manner akin to ‘‘second-generation’’ models of currency crises (Masson, 1995; Obstfeld, 1996), but within this structure the fundamentals display persistence, reflecting the gradual adjustment of international competitiveness. In the model, this feature arises because domestic wage-setting is assumed to be based on a smoothly declining probability of an exchange rate crisis. These expectations fix the path of the fundamentals, and the paper explores the implications of this in the context of modern theories of currency crises in which financial markets form their expectations rationally. The path of the fundamentals has a crucial bearing on the likelihood of eventual success of the stabilization attempt. The paper characterizes the conditions under which a stabilization attempt is worthwhile, and also discusses the optimal date for a return to floating. 2. Background Calvo and Ve´gh (1999), in a detailed survey of exchange-rate-based stabilizations, find a consistent tendency to real appreciation and deterioration of trade and current account balances associated with slow convergence of the inflation rate to the rate of devaluation. The tendency for exchange-rate-based stabilizations to be accompanied by real exchange rate appreciation is illustrated in Tables 1 and 2. Table 1 gives data for Mexico, which pegged its exchange rate in 1988, but was forced to abandon the peg in the crisis of December 1994. Table 2 gives data for Argentina, which adopted a currency board in 1991 and has recently abandoned it. In Mexico the nominal exchange rate was never completely stabilized vis-a`-vis the United States dollar. Even by 1994, however, the crawling peg never quite compensated for the inflation differential and the cumulative real appreciation from 1988 to 1994 was over 29%. The same phenomenon occurred in the European Monetary Table 1 Mexico Year
Exchange rate (peso per 1 US-$)
Inflation rate
US inflation rate
Real exchange rate appreciation
1988 1989 1990 1991 1992 1993 % D 1988–93 1994
2.27 2.46 2.81 3.02 3.09 3.12 37.45 3.38
113.87 20.14 26.42 22.70 15.57 9.83 136.52 6.93
4.02 4.90 5.28 4.32 3.02 2.93 22.16 2.64
19.99 5.38 4.87 8.63 8.79 5.37 29.01 3.99
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Table 2 Argentina Year
Inflation rate
US inflation rate
Real exchange rate appreciation
1991 1992 1993 1994 1995 1996 % D 1991–96
168 25.37 10.71 4.30 3.09 0.00 49.25
4.32 3.02 2.93 2.64 2.77 2.9 15.10
61.08 17.83 7.03 1.60 0.31 2.90 22.88
System from 1979 to 1992: especially after the reforms of 1987, higher-inflation countries such as Italy experienced real exchange rate appreciation within the system. In Argentina, by contrast, the inflation differential was eliminated by 1994 and the cumulative real appreciation was smaller (23%). Interest rate differentials, on the other hand, tend to be much more volatile: for example, the interest rate differential between Argentina and the US rose from 2.1% in November 1994 to 8.1% in December and, after peaking at 13.3% in March 1995, was down to 1.3% by June. All this had no noticeable impact on wage behavior. Moreover the ultimate collapse of Argentina’s currency board highlights the issue of choosing the optimal exit date, given that inflation was effectively zero in Argentina from 1995 to 2001. The differences in the historical patterns of interest rate and inflation differentials are difficult to reconcile with the combination of (a) a lack-of-credibility explanation of continuing inflation differentials and (b) the assumption that all agents have identical expectations. If financial markets suddenly become worried about the collapse of a peg why is that not reflected in domestic wages and prices? If exchange-rate-based stabilizations fail, they normally end in a currency collapse and a rise in the inflation rate. It is natural, therefore, to consider such experiences within the framework of currency crisis theory. The theory of currency crises has evolved from the somewhat mechanical ‘‘first-generation’’ models of Krugman (1979) and Flood and Garber (1984) to ‘‘second-generation’’ models in which the authorities pursue monetary policies consistent with the peg until it becomes too painful to do so. The key to these models is that the pain of defending the peg is greater when output is low – as appeared to be the case in the European exchange rate crises of the early 1990s (Jeanne, 1997; Masson, 1995; Obstfeld, 1996). Formally, this arises because output depends in part on unanticipated inflation. Since inflation is lower if the peg is defended, and expectations of inflation are particularly high if agents believe that the peg will be abandoned, inflation will be considerably below its anticipated value in this combination of circumstances, depressing output. Output persistence can be simply incorporated into these models (Irwin, 2004). We pursue a slightly different route that reflects the evidence of inflation persistence and stickiness in goods prices (Dornbusch, 1976). As Fuhrer and Moore (1995) note, inflation persistence requires wage-setting to have a backward-looking component. In our model, wages are set one period in advance and incorporate expectations of the possible collapse of the peg, but the key point is that the probability of this event is assumed to evolve smoothly. By contrast financial market beliefs about this probability are not assumed to be tied down in the same way. Thus our approach is to assume different mechanisms of expectations formation in different markets. In terms of a currency crisis model, the effect is to introduce
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persistence into the fundamentals while maintaining the feature that adverse expectations in financial markets can precipitate a currency collapse. 3. The model Imagine a country with a history of inflation that decides to peg the exchange rate as part of a stabilization effort. As in the hyperinflations of the 1920s, fixing a highly visible price like the exchange rate is central to breaking the cycle of inflationary expectations and convincing private agents that the stabilization will succeed (Dornbusch and Fischer, 1986). Expectations are particularly important in the model because wages are assumed to be set one period in advance, so wage-setters have to assess the likelihood of the peg holding, and the size of the devaluation that might occur in the event that it does not. We also assume that domestic prices are tied down by purchasing power parity, so that any skepticism about the success of the stabilization attempt on the part of wage-setters is reflected in increasing real wages and real exchange rate appreciation (as measured by relative unit labor costs). This real exchange rate appreciation tends to depress output, and this is the main threat to the success of the stabilization attempt. If the authorities use the breathing space to reform monetary policy by, for example, increasing the independence of the central bank, that opens up an opportunity to exit from the peg without necessarily reigniting inflation (e.g. Brazil in 1999). We consider what factors influence the optimal exit date. The basic structure of the model is similar to that of ‘‘second-generation’’ currency crisis models such as those of Jeanne (1997), Masson (1995) and Obstfeld (1996). Output is boosted by unexpected depreciation, but the government also cares about price stability. Output is also influenced by international competitiveness, as in Bleaney and Fielding (2002). The government decides at time zero to peg the currency for an indefinite period in order to achieve price stability. The stabilization attempt may collapse in a devaluation at any date, if the current-period cost of sustaining the peg becomes too great. Essentially, a devaluation is triggered, if output falls to a low enough level under the peg. We treat this as a constraint – the peg becomes politically unsustainable at this point. This can happen because of a combination of real appreciation and high devaluation expectations. Thus the model has the familiar property that crises can be ‘‘self-fulfilling’’. Output depends on the fundamentals, whose path is determined by the evolution of the real wage, and on financial markets’ expectations of the exchange rate. The size of an expected devaluation, should one occur, is based on rational expectations, i.e. it is that which minimizes the authorities’ loss function. In the case of financial markets, we assume that the probability of a devaluation may take any value between zero and one in each time period. In the case of the labor market, we assume that this probability declines asymptotically towards zero with time. The currency peg can only be sustained so long as the output cost does not exceed the inflation cost of devaluation plus an additional term that reflects the ‘‘humiliation’’ costs of being forced off the peg. We assume that purchasing power parity holds, with foreign inflation of zero, so that inflation is equal to the rate of exchange rate depreciation. In each period output is defined by a Lucas surprise supply function, with the price surprise being measured relative to financial market expectations, augmented by a term in the real wage. Output is equal to its ‘‘natural’’ level, minus a real wage term, plus the expanding effect of the unexpected component of exchange rate depreciation:
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y t ¼ y 0 /aqt þ aðet eet Þ;
ð1Þ
where a > 0, yt is output in period t, et is the one-period change in the log of the exchange rate (domestic currency units per unit of foreign currency), eet = devaluation expectations in period t, y 0 = natural output level and qt is the (log) real wage (or equivalently the real exchange rate based on unit labor costs). The equilibrium value of qt is assumed to be zero. It is convenient to combine the term in the real wage and in equilibrium output. Defining yt, the effective or real-wage-adjusted natural rate of output at time t, as ‘y 0 /qt ’, (1) becomes: y t ¼ y t þ aðet eet Þ:
ð2Þ
The government is forced to abandon the peg in period t, if the following condition is met: peg 2 2 y t y > y devaluation y þ be2t þ C; ð3Þ t where yt is output in period t (with the superscript ‘‘peg’’ or ‘‘devaluation’’ according to whether the exchange rate peg is maintained or abandoned), y* is the output target value, b (>0) is a parameter that reflects the importance of the price stability objective relative to the output objective, and C (>0) is the humiliation cost of abandoning a pegged exchange rate without pre-announcement. Thus Eq. (3) says that a devaluation of the exchange rate occurs, if the one-period welfare losses from lower output under a pegged (fixed) exchange rate regime exceed the inflation and humiliation costs of devaluing. This equation may be 2 thought of as the outcome of minimizing a one-period loss function, L ¼ ðy t y Þ þ be2t þ jC; where j = 1 if the peg is abandoned and zero if not. Even if the future benefits of continuing to peg exceed the costs, the stabilization attempt collapses, if the above condition holds.1 In this model, the optimal rate of devaluation, should one occur, depends on market expectations. With rational expectations, if the devaluation probability is l, then the expected depreciation is la ½y y t : a2 ð1 lÞ þ b
ð4Þ
The game is structured as follows. At the beginning of period zero, there is an exchangerate-based stabilization. Then private sector agents set their expectations of the exchange rate, which they cannot revise until the next period. Finally, the government sets the exchange rate and output is determined. If the exchange rate peg has been maintained, the game is repeated in the next period. As mentioned above, expectations in the labor market and in the financial markets seem to be based on different processes. If wage increases reflect labor market expectations, then the experience of exchange-rate based stabilization suggests a pattern of a gradual increase in the credibility of the exchange rate peg over time. It seems plausible that expectations in a market where negotiations take place relatively infrequently and over agreements covering a longer time period are based on approximations of longer-term trends. One could model this process therefore as an adaptive mechanism.
1
What we have in mind is that the peg becomes politically unsustainable, if its current-period cost is too high.
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We turn now to the detailed specification of the model. We start by examining the problem from the point of view of labor market agents. These agents observe an exchange-ratebased stabilization in period zero. Let the labor market agents believe at the beginning of period zero that the exchange rate will be floated in that period with probability l and will remain pegged with probability (1 l). The parameter therefore measures initial skepticism or lack of credibility of the peg. We treat this parameter as exogenous. It is likely to reflect factors such as the consistency between fiscal and monetary policy, the level of foreign exchange reserves and the government’s political position. Wage-earners’ expectations of the depreciation rate in period zero are then exactly as stated in Eq. (4). If the peg is maintained in period 0, then in period 1 and all subsequent periods until the peg is abandoned, the peg is assumed to acquire credibility at a rate (1 k), where 0 < k < 1, and the game is repeated. More precisely, the perceived probability (by labor market agents) of a devaluation in period t is lkt. This is equivalent to the devaluation probability following a geometric progression towards the observed outcome, as in an adaptive expectations model. We conceive k as reflecting the gains in credibility simply from being able to sustain the peg over time. If k is low, credibility is gained quickly; if k is high, it only accrues slowly. As is shown below, this acquisition of credibility is favorable to the maintenance of the peg. On the other hand, as will become clear below, past lack of credibility drives equilibrium output further from the government’s target. This effect works in the opposite direction, because it increases the losses from the output element of Eq. (1). If the peg has lasted for t periods (0 to t 1), and is then abandoned, then the exchange rate is assumed by wage-earners to depreciate by ee;L t ¼
lkt a ½y y t : a2 ð1 lkt Þ þ b
ð5Þ
This straightforward adjustment of probabilities in each period can also be motivated by looking at the incentives agents face in the labor market. Analogously to the way Lux (1995) explains herd behavior in the financial markets, it can be argued that agents will maximize their expected future income, which is future real wage income times the probability of employment, by following the majority. If agents are more pessimistic than the majority about the sustainability of the fixed peg policy and consequently demand higher nominal wages, their probability of employment will fall significantly, with the increase in their demanded relative real wage. However, if agents are more optimistic, they will demand a lower relative real wage and have less income. Assuming that their last-period wage income, relative to its corresponding employment probability, was optimal,2 agents will maximize expected future income by demanding exactly the same proportionate increase in nominal wages as the majority of agents in the market. It pays therefore to act according to the market consensus. As the consensus becomes more optimistic over time, agents adapt accordingly. Labor market agents set wages one period in advance. Apart from the expected depreciation rate, they also take demand conditions in the domestic market into account, which 2 To be more precise, it also has to be assumed that this is an efficiency wage labor market. Offering lower wages does not significantly improve the individual employment probability, but demanding more than the efficiency wage will significantly lower the individual employment probability.
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depend negatively on the real wage.3 Therefore, wage inflation is assumed to be as follows: wt ¼ ee;L t1 dqt1 ;
ð6Þ
where 0 6 d 6 1. In contrast, indicators of financial market expectations, such as interest rates, point to almost continuous decision-making covering shorter time periods. We therefore assume a rational expectations process for financial markets. The crucial question is whether the exchange rate policy is sustainable in any given time period. Agents therefore take into account the policy condition of Eq. (3). They deduce the optimal devaluation rate (e*) from the government’s preferences over inflation and unemployment. Their expected devaluation rate will therefore be the optimal rate times the perceived devaluation probability (pt). The devaluation probability can have any value between 0 and 1. This reflects imperfect information about the actions of other speculators. The average beliefs of speculators as a group will be reflected in the expected devaluation rate, which in turn impacts on the policy condition for giving up the exchange rate policy. As is well known, this introduces the possibility of multiple equilibria into the model (i.e. the exchange rate decision may vary with pt). Finally, let us consider the dynamics of the real wage. So long as the peg holds, inflation is zero, so the current real wage is given by its last-period value plus the rate of nominal wage inflation: qt ¼ qt1 þ wt :
ð7Þ
From (6) we know that this is equivalent to qt ¼ ð1 dÞqt1 þ ee;L t1 :
ð8Þ
From (1) and (2) follows that y t ¼ y 0 /a½ð1 dÞqt1 þ ee;L t1 ;
ð9Þ
where / > 0. The inclusion of a in Eq. (9) simplifies the algebra. Eq. (9) says that, under a peg, the effective natural rate of output falls in proportion to wage-earners’ expected rate of depreciation in the previous period.4 The idea is that nonzero depreciation expectations reflect the lack of credibility of the peg as perceived by labor market participants. This lack of credibility is reflected in higher nominal wage settlements, putting pressure on international competitiveness. The strength of the effect is denoted by the parameter /. The parameter d measures the strength of the mean reversion5 element in the real wage. Over time, as credibility increases, the mean reversion element will eventually outweigh the ‘lack-of-credibility ð/ee;L t1 )’ element. The ‘lack-ofcredibility’ element decreases the effective natural rate of output over time and the mean reversion element has the opposite effect. However, assuming that d is small, the overall trend is likely to be one of an accumulating loss of competitiveness initially, until credibility has increased significantly or the exchange rate policy is abandoned.
3
This is plausible, as the efficiency wage also depends on demand conditions. It simplifies the model to use previous-period rather than current-period expectations here, without making any essential difference. 5 Mean reversion is a process, where a variable returns to its mean value over time. 4
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Eq. (10) says that, if the exchange rate is floated, the natural rate of output returns gradually to its initial level. This aspect will become relevant when we consider the exit problem. ðy t y 0 Þ ¼ wðy t1 y 0 Þ
ðfloatingÞ;
ð10Þ
where 0 6 w < 1. Eq. (9) can be re-stated as ðy t y 0 Þ ¼ /a½ð1 dÞqt1 þ ee;L y t1 y 0 Þ /ee;L t1 ¼ ð1 dÞð t1 : The evolution of the gap between the desired output level and the natural output level is determined as follows (whilst the peg is maintained), using (9) and (5): " # a2 /lkt1 ðy y t Þ ¼ ð1 dÞ þ ð11Þ ðy y t1 Þ: a2 ð1 lkt1 Þ þ b Effective natural output shrinks continuously, but at a rate that decreases with time, until the mean reversion effect outweighs the ‘lack-of-credibility’ effect and natural output increases again. The optimal devaluation rate in any period, if a devaluation occurs, is et ¼
a2 ð1
a ½y y t : pt Þ þ b
ð12Þ
The model works like this: At time zero yt is equal to y 0 and the government announces a peg of the exchange rate. The sets of agents in the private sector then set their expectations of the time zero exchange rate. To see whether the peg is abandoned or not, we compare the losses from continuing the peg (et = 0) with the losses from abandoning it (et ¼ et ). We are now in a position to analyze the various possible outcomes of the stabilization attempt. The losses from pegging at time t are Lfix t ¼
2 a2 þ b ð y y Þ : t a2 ð1 pt Þ þ b
ð13Þ
Losses if the policy is abandoned unannounced are Lflex ¼ t
b2 þ a2 b ða2 ð1
pt Þ þ bÞ
2
2
ðy t y Þ þ C:
ð14Þ
The policy condition for abandoning the exchange rate policy unannounced is a2 ða2 þ bÞ ða2 ð1 pt Þ þ bÞ
2
2
ðy t y Þ > C:
ð15Þ
The left-hand side of (15) is influenced by the difference between target output and effective natural output (which is solely determined by labor market expectations) and by financial market expectations (pt). Since financial market beliefs about the probability of devaluation can take any value between 0 and 1, there is a considerable degree of variance in the evolution of the loss functions.
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It should be noted that the effect of a given change in pt is smaller for the Lflex case than for the Lfix case. This follows from a comparison of the functions, where Lflex can be expressed relative to Lfix: Lflex ¼
b Lfix þ C: a2 þ b
The easiest way to look at the consequences of this is to consider the extreme cases of pt being equal to 0 or 1. If pt equals zero Eq. (15) becomes: a2 2 ðy t y Þ > C: a2 þ b
ð16Þ
This significantly reduces the left-hand side and therefore makes a crisis far less likely. The opposite happens if pt equals one, as can be seen in the corresponding equation: a2 ða2 þ bÞ ðy t y Þ2 > C: 2 b
ð17Þ
The time trend in Lflex and Lfix depends on the evolution of effective natural output. While the real wage is increasing, effective natural output falls, and the loss functions have an upward trend. However, from the point where the mean reversion effect dominates, real wages decline and the loss functions will fall again. In the tradition of models with significant resistance to reductions in the nominal wage, we assume d to be small. Consequently, the loss functions will decrease only after credibility has increased significantly. There are several possibilities, depicted in Figs. 1–3: The dashed lines represent Lflex. The possible realizations of both loss functions are illustrated by two lines each. The upper lines plot loss values against time, when p equals 1. The lower lines plot loss values against time, when p equals zero. So Lfix can at any time be on or between the solid lines and Lflex on or between the dashed lines. In the first case (shown in Fig. 1) a crisis is inevitable, but there is not one date at which the crisis definitely occurs. The inevitability of the crisis is shown by the fact that real wages reach a point where, whatever the value of p, the authorities prefer to devalue.
L L flex max L fix max L flex min L fix min t t1
t2
Fig. 1. Crisis occurs between t1 and t2. Notes: Lfix falls within the region between the two unbroken lines, and Lflex falls within the region between the two dashed lines, its exact position depending on the value of p. The lower line represents p = 0 and the upper line p = 1. A crisis is possible, if the upper unbroken line is above the upper dashed line, and inevitable, if the lower unbroken line is above the lower dashed line. In the region where a crisis is possible, there is a threshold value of p above which a crisis occurs.
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L
t Fig. 2. No crisis. Notes: Lfix falls within the region between the two unbroken lines, and Lflex falls within the region between the two dashed lines, its exact position depending on the value of p. The lower line represents p = 0 and the upper line p = 1. A crisis is possible, if the upper unbroken line is above the upper dashed line, and inevitable, if the lower unbroken line is above the lower dashed line. In the region where a crisis is possible, there is a threshold value of p above which a crisis occurs.
L
t t1
t2
Fig. 3. Possible crisis. Notes: Lfix falls within the region between the two unbroken lines, and Lflex falls within the region between the two dashed lines, its exact position depending on the value of p. The lower line represents p = 0 and the upper line p = 1. A crisis is possible, if the upper unbroken line is above the upper dashed line, and inevitable, if the lower unbroken line is above the lower dashed line. In the region where a crisis is possible, there is a threshold value of p above which a crisis occurs.
Although the crisis must occur by t2, when the lower unbroken line crosses the lower broken line, it can happen at any time from t1 onwards. At t1 a crisis can only occur, if pt is equal to one. At t2 a crisis will occur even if pt is equal to zero. Fig. 2 depicts a second case, where there is no crisis. Even if pt = 1, when speculators are completely convinced that a devaluation will occur, it never does. Finally, Fig. 3 represents an interesting intermediate case, where a crisis becomes possible from t1 onwards (pt has to equal one for a crisis to occur precisely at t1) until
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t2. Consequently, if expectations become sufficiently pessimistic at any time between t1 and t2, a crisis will occur. After t2, the peg is safe again. Which of these three cases applies may simply depend on the value of C, the fixed cost of abandoning the peg. For any given value of C, however, the rate of loss or gain of international competitiveness, as given by Eq. (11), is the critical factor. We can see from that equation that the higher are l (the initial level of labor market skepticism), k (its persistence) and / (the elasticity of output with respect to the real wage) and the lower is d (the rate of mean reversion in real wages), the greater the real appreciation under the peg and therefore the more likely it is that a crisis occurs. If / or l is low or d is high, then effective natural output does not shrink much below its initial value before starting to recover, whilst if k is low the shrinkage effect decays quickly to zero. These are the cases where a successful stabilization is most likely (as in Fig. 2). This model also provides a potential justification for heterodox policies, in which wage controls are implemented in the early stages of the stabilization. Such policies could prevent the loss of international competitiveness that exposes the stabilization attempt to a potential or inevitable currency crisis (as in Fig. 1 or Fig. 3) rather than keeping it in the secure region (as in Fig. 2). 4. Are all stabilization attempts worthwhile? Instead of considering a government that has already announced a stabilization attempt in period zero, and therefore incurs a cost from departing from the peg, we now turn to the case of a government, which has not yet made such an announcement. To keep things simple, in this section it is assumed that d equals zero. We also assume that the government initially has a crawling peg regime with devaluation at the rate a e ¼ ðy y 0 Þ; b which minimizes the government’s loss function given below. We show now that if the stabilization attempt has insufficient credibility, it is better to postpone it and to continue with the crawling peg. The issue is therefore whether to continue floating or to peg, assuming that the peg lasts for ever (i.e. the value of C is sufficiently large that it is never abandoned). Let the government’s discount factor be q (<1). The loss function for each individual time period is Lt ¼ ðy t y Þ2 þ be2t :
ð18Þ
If V is the present value of the government’s loss function L over all future periods, then with no stabilization attempt, where output stays at y 0 and et equals ba ðy y 0 Þ, we have: a2 2 V crawl ¼ ð1 þ q þ q2 þ Þ 1 þ ð19Þ ðy y 0 Þ : b If stabilization is attempted, from Eq. (13) we have: " # 2 2 a2 þ b a2 þ b fix V ¼ ðy y 0 Þ þ q 2 ðy y 1 Þ þ : a2 ð1 p0 Þ þ b a ð1 p1 Þ þ b
ð20Þ
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Note that Vfix depends on two factors: financial market expectations of a devaluation in each period (pt), and the evolution of the effective natural rate of output (yt) as given by Eq. (11). The stabilization attempt yields immediate gains in the form of reduced inflation, which may be more than offset by future losses from reduced output. If p0 < 1, the period 0 value of Lcrawl is higher than that of Lfix. In the most favorable case of l = 0 (100% labor market credibility and hence no loss of international competitiveness), yt stays at y 0 in future periods, which means that Vcrawl > Vfix. In the general case where l > 0, we can show that the values of the parameters may be such that Vcrawl < Vfix, implying that it may be preferable to postpone the stabilization attempt. Let us consider the simplest case where k = 0 (so that y is fixed at y1 after period 1) and pt = 0 for all periods. In that case Vfix > Vcrawl if q a2 a2 ðy y 1 Þ2 1 þ ðy y 0 Þ2 > ðy y 0 Þ2 : ð21Þ 1q b b The left-hand side of Eq. (21) represents the difference between Vfix and Vcrawl from period 1 onwards and the right-hand side equals Lcrawl Lfix in period 0. Substituting from Eq. (11) and rearranging, Eq. (21) becomes: q½ð1 þ ZÞ2 1 >
a2 ; b
Z¼
/a2 l : a2 ð1 lÞ þ b
ð22Þ
This condition can easily be met for high enough values of l.6 Thus, even in the case where the stabilization has 100% credibility amongst wage-earners in the second period (because k = 0), so that no further deterioration of the fundamentals occurs, the permanent loss of output from lack of credibility in the first period can be high enough to make the stabilization attempt unattractive. If k > 0, then Vfix is even greater for a given l. These results imply that stabilization attempts need to be well enough designed to bring l below some critical value to make the attempt worthwhile. If, for example, the government is too reliant on seigniorage revenue and cannot undertake the fiscal reforms necessary to reduce l below the critical level, it would do better to postpone the stabilization attempt. 5. The exit problem Suppose that, while the exchange rate is pegged, the authorities put in place institutional arrangements intended to keep inflation at zero with a view to exiting from the peg at a future date. At a certain date T, a return to floating is announced and implemented. Because the float was pre-announced, the cost C of an unannounced end to the peg is not incurred. After date T, natural output gradually reverts to y 0 as specified in Eq. (10). What happens to inflation? It seems reasonable to assume that, if the exit is successful, inflation stays at zero, but that if it is unsuccessful inflation returns to the pre-peg rate of ba ðy y 0 Þ. The problem is how to formulate the probability of the exit being successful. We want to include a factor that reflects the quality of post-exit institutional 6
For l = 1 it reduces to qu(2+((u2)/b)) > 1. Since / = 1 is a plausible value, q would have to be very low for this not to hold.
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arrangements, but the credibility of the peg is also likely to play a role. We could relate the success probability at date T to financial market expectations at that date (pt), but since we have no model of pt, it would be difficult to draw any useful conclusions. Instead, therefore, we relate the success probability to labor market expectations. Since labor market credibility increases over time, this means that the probability of a successful exit also increases with time – which does not seem unreasonable. We assume that post-float inflation stays at zero (i.e. the exit is successful) with probability 1 clkT, and with probability clkT inflation returns (i.e. the exit is unsuccessful). Thus the probability of failure is equal to labor market skepticism in period T (lkT), multiplied by a factor c (>1) that represents exit risk and is assumed to reflect the quality of the institutional reforms (the better the reforms, the closer c is to one). What determines the optimal exit date? Delaying exit by one period reduces the probability of failure by a factor k, but also keeps output low for one further period and causes the effective natural rate of output to move further from the target level. A further important consideration is that the peg might succumb to a crisis in period T, if exit is delayed. Assume for simplicity that w = 0 (i.e. that natural output returns instantaneously to y0 after exit). Then, with a discount factor of q, the expected multi-period losses from exit at time T are 2 1 T a V 1 ¼ ð1 qÞ 1 þ clk ð23Þ ðy y 0 Þ2 : b h i 2 2 This equation reflects the fact that the inflation losses ab ðy y 0 Þ are incurred with probability clkT. If exit is delayed for one period, either the peg collapses in period T (probability p) or it does not and exit occurs at time T + 1 (probability 1 p). Hence the expected losses are 1 a2 2 1þ V2 ¼p ðy y 0 Þ þ C 1q b 2 q 2 T þ1 a fix þ ð1 pÞ LT þ 1 þ clk ð24Þ ðy y 0 Þ ; 1q b where Lfix T is given by Eq. (13). We therefore continue to take the different expectations in the labor and the financial market into account. Let us consider first the case, where p = 0 (as in Fig. 2). In that case it pays to exit at time T rather than to delay further if 2 2 q 2 T a T a fix ð1 kÞclk LT > 1 þ clk ð25Þ ðy y 0 Þ þ ðy y 0 Þ2 : 1q b b This condition is more likely to be fulfilled if (a) q is smaller (the future is discounted more heavily), (b) c is smaller (post-exit anti-inflation strategy is better designed), (c) d is smaller and (d) / is larger (these last two factors increase real wages and their effect on output and therefore Lfix T through Eq. (11)). Moreover, in this case it can be assumed that pt = 0, since everyone can see that the peg is secure, and this keeps down the cost of continuing to peg (Eq. (13)). In the case of the labor market credibility parameters (l, k), matters are a bit more complicated, because both sides of Eq. (25) are increasing in l and k. Using Eqs. (13) and (11), however, we can see that Lfix T increases with T ðT 1Þ T T 2 , whereas the right-hand side of (25) is proportional to lk . Thus we can deduce l k
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that higher values of l and k favor an earlier exit, because of the cumulative impact on equilibrium output of continuing the peg. This necessarily implies, however, that the probability of a successful exit is reduced at the optimal exit date, since not only are l and k larger, but also T is smaller. Conversely, with greater credibility, it pays to wait until exit is safer. We may now consider the case where p > 0. Since the collapse of the peg produces the same result as an unsuccessful exit but with an additional humiliation cost of C, it is always better to exit, if p > clkT (i.e. if a crisis is more likely than an unsuccessful exit). In general, p > 0 implies an earlier exit then p = 0. Thus the examples shown in Figs. 1 and 3 suggest an earlier exit date (and therefore a riskier exit) than Fig. 2. In conjunction with those given earlier, these results imply that real exchange rate appreciation should lead governments to formulate plans for an early exit. Not only does real appreciation increase the risk of a currency crisis, but it also makes it optimal to exit at higher probabilities of failure to reduce output costs. In short, it is often better to jump than to risk being pushed. 6. Conclusions The purpose of the model presented here was to develop a formal bridge between the theory of currency crises and of exchange-rate-based stabilizations that is consistent with the stylized facts. One of these stylized facts is that interest rates are much more volatile than wage increases, which is not consistent with the assumption that all agents exhibit forward-looking behavior with identical expectations. The model captures this by assuming that wage-setters’ perceived probability of a collapse of the peg declines smoothly with time, whilst financial market agents’ perceptions of the same probability are not tied down in the same way. The model incorporates the assumption that, if the peg can last long enough, the stabilization attempt will succeed, because any initial real appreciation will eventually be reversed as wages fall back to their equilibrium level. In the intervening period of loss of international competitiveness, however, the peg may succumb to a currency crisis. If the authorities cannot succeed in making their overall macroeconomic policy consistent with price stability (for example if they are too reliant on seigniorage revenue), then initial skepticism about the success of any stabilization attempt is likely to be high, and this will be reflected in wage behavior. The output costs of the stabilization attempt will then be substantial, increasing the chance that it will end in a currency collapse. In general, weak stabilization attempts are better postponed until the authorities can put together a package with greater credibility. The model also sheds light on the ‘‘exit problem’’: when to abandon the peg with a good chance of retaining the price stability achieved by the stabilization. In general (assuming that output recovers more quickly under floating), it is optimal to exit before credibility reaches 100%, to reduce the output losses from overvaluation. More effective monetary reforms, such as greater central bank independence or inflation targeting, bring forward the optimal exit date. An early exit is particularly desirable in cases where, if the peg is maintained, there is a greater danger that it would collapse anyway under speculative pressure. Greater credibility gives policy-makers the luxury of postponing exit until the chances of success are higher.
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Acknowledgements We would like to thank former and present colleagues at the University of Nottingham, especially Atanu Ghoshray and Claudio Zoli, for insightful comments and discussions. We would also like to thank two anonymous referees for helpful comments on a previous version. References Bleaney, M.F., Fielding, D.J., 2002. Exchange rate regimes, inflation and output volatility in developing countries. Journal of Development Economics 68, 233–245. Calvo, G.A., Ve´gh, C.A., 1999. Inflation stabilization and BOP crises in developing countries. In: Taylor, J.B., Woodford, M. (Eds.), Handbook of Macroeconomics. Elsevier, Amsterdam (Chapter 4). Dornbusch, R., 1976. Expectations and exchange rate dynamics. Journal of Political Economy 84, 1161–1176. Dornbusch, R., Fischer, S., 1986. Stopping hyperinflations past and present. Weltwirtschaftliches Archiv 122, 1–46. Dornbusch, R., 2001. A primer on emerging market crises, Working paper no. 8326, National Bureau of Economic Research. Edwards, S., 1993. Exchange rates as nominal anchors. Weltwirtschaftliches Archiv 129, 1–32. Flood, R.P., Garber, P.M., 1984. Collapsing exchange rate regimes: Some linear examples. Journal of International Economics 17, 1–13. Fuhrer, J., Moore, G., 1995. Inflation persistence. Quarterly Journal of Economics 110, 127–160. Irwin, G., 2004. Currency boards and currency crises. Oxford Economic Papers 56, 64–87. Jeanne, O., 1997. Are currency crises self-fulfilling: A test. Journal of International Economics 43, 263–286. Kaminsky, G.L., Leiderman, L., 1998. High real interest rates in the aftermath of disinflation: Is it a lack of credibility? Journal of Development Economics 55, 198–214. Krugman, P.R., 1979. A model of balance-of-payments crises. Journal of Money, Credit and Banking 11, 311– 325. Lux, T., 1995. Herd behaviour, bubbles and crashes. Economic Journal 105, 881–896. Masson, P.R., 1995. Gaining and losing ERM credibility: The case of the United Kingdom. Economic Journal 105, 571–582. Obstfeld, M., 1996. Models of currency crises with self-fulfilling features. European Economic Review 40, 1037– 1047.
Journal of Macroeconomics 29 (2007) 876–890 www.elsevier.com/locate/jmacro
Stabilizations, crises and the ‘‘exit’’ problem – A theoretical model Michael Bleaney a, Marco Gundermann
b,*
a
b
University of Nottingham, School of Economics, United Kingdom University of Wales Institute Cardiff (UWIC), Business School, Colchester Avenue, Cardiff CF3 4TD, United Kingdom Received 22 July 2003; accepted 11 October 2005 Available online 9 May 2007
Abstract Exchange-rate-based stabilizations, even if successful, usually lack credibility initially. This is reflected in high (ex post) real interest rates and some degree of real exchange rate appreciation. Empirical observation suggests that wage inflation declines smoothly over time whilst interest rates are volatile. Our model captures these features and provides insights into: the eruption of exchange rate crises after a long period of apparently successful stabilization; the potential advantages of a heterodox approach; when to delay a stabilization attempt; and the optimal date for ‘‘exit’’ to a floating exchange rate. Ó 2007 Elsevier Inc. All rights reserved. JEL classification: E31; F41 Keywords: Credibility; Currency crisis; Exchange rate; Inflation
1. Introduction A feature of exchange-rate-based stabilizations is that, even if successful, success is not immediate. Agents in financial and labor markets are often skeptical initially, and this is reflected in real exchange rate appreciation and high nominal interest rates relative to the *
Corresponding author. Tel.: +44 292 0416368; fax: +44 292 0416940. E-mail address: [email protected] (M. Gundermann).
0164-0704/$ - see front matter Ó 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.jmacro.2005.10.021
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realized inflation rate (Dornbusch et al., 2001; Edwards, 1993; Kaminsky and Leiderman, 1998). Calvo and Ve´gh (1999) provide a useful survey. To judge by inflation differentials, most stabilization attempts that have not yet collapsed show evidence of increasing credibility over time. Nevertheless market-determined interest rate differentials tend to behave in a more volatile manner, suggesting a varying degree of speculative pressure. Traditionally, continuing wage inflation has been interpreted as a reflection of either backward-looking indexation or forward-looking expectations combined with doubts about the success of the stabilization. The key innovation in this paper is to build this feature into a theoretical model. The survival of the stabilization attempt is determined in a manner akin to ‘‘second-generation’’ models of currency crises (Masson, 1995; Obstfeld, 1996), but within this structure the fundamentals display persistence, reflecting the gradual adjustment of international competitiveness. In the model, this feature arises because domestic wage-setting is assumed to be based on a smoothly declining probability of an exchange rate crisis. These expectations fix the path of the fundamentals, and the paper explores the implications of this in the context of modern theories of currency crises in which financial markets form their expectations rationally. The path of the fundamentals has a crucial bearing on the likelihood of eventual success of the stabilization attempt. The paper characterizes the conditions under which a stabilization attempt is worthwhile, and also discusses the optimal date for a return to floating. 2. Background Calvo and Ve´gh (1999), in a detailed survey of exchange-rate-based stabilizations, find a consistent tendency to real appreciation and deterioration of trade and current account balances associated with slow convergence of the inflation rate to the rate of devaluation. The tendency for exchange-rate-based stabilizations to be accompanied by real exchange rate appreciation is illustrated in Tables 1 and 2. Table 1 gives data for Mexico, which pegged its exchange rate in 1988, but was forced to abandon the peg in the crisis of December 1994. Table 2 gives data for Argentina, which adopted a currency board in 1991 and has recently abandoned it. In Mexico the nominal exchange rate was never completely stabilized vis-a`-vis the United States dollar. Even by 1994, however, the crawling peg never quite compensated for the inflation differential and the cumulative real appreciation from 1988 to 1994 was over 29%. The same phenomenon occurred in the European Monetary Table 1 Mexico Year
Exchange rate (peso per 1 US-$)
Inflation rate
US inflation rate
Real exchange rate appreciation
1988 1989 1990 1991 1992 1993 % D 1988–93 1994
2.27 2.46 2.81 3.02 3.09 3.12 37.45 3.38
113.87 20.14 26.42 22.70 15.57 9.83 136.52 6.93
4.02 4.90 5.28 4.32 3.02 2.93 22.16 2.64
19.99 5.38 4.87 8.63 8.79 5.37 29.01 3.99
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Table 2 Argentina Year
Inflation rate
US inflation rate
Real exchange rate appreciation
1991 1992 1993 1994 1995 1996 % D 1991–96
168 25.37 10.71 4.30 3.09 0.00 49.25
4.32 3.02 2.93 2.64 2.77 2.9 15.10
61.08 17.83 7.03 1.60 0.31 2.90 22.88
System from 1979 to 1992: especially after the reforms of 1987, higher-inflation countries such as Italy experienced real exchange rate appreciation within the system. In Argentina, by contrast, the inflation differential was eliminated by 1994 and the cumulative real appreciation was smaller (23%). Interest rate differentials, on the other hand, tend to be much more volatile: for example, the interest rate differential between Argentina and the US rose from 2.1% in November 1994 to 8.1% in December and, after peaking at 13.3% in March 1995, was down to 1.3% by June. All this had no noticeable impact on wage behavior. Moreover the ultimate collapse of Argentina’s currency board highlights the issue of choosing the optimal exit date, given that inflation was effectively zero in Argentina from 1995 to 2001. The differences in the historical patterns of interest rate and inflation differentials are difficult to reconcile with the combination of (a) a lack-of-credibility explanation of continuing inflation differentials and (b) the assumption that all agents have identical expectations. If financial markets suddenly become worried about the collapse of a peg why is that not reflected in domestic wages and prices? If exchange-rate-based stabilizations fail, they normally end in a currency collapse and a rise in the inflation rate. It is natural, therefore, to consider such experiences within the framework of currency crisis theory. The theory of currency crises has evolved from the somewhat mechanical ‘‘first-generation’’ models of Krugman (1979) and Flood and Garber (1984) to ‘‘second-generation’’ models in which the authorities pursue monetary policies consistent with the peg until it becomes too painful to do so. The key to these models is that the pain of defending the peg is greater when output is low – as appeared to be the case in the European exchange rate crises of the early 1990s (Jeanne, 1997; Masson, 1995; Obstfeld, 1996). Formally, this arises because output depends in part on unanticipated inflation. Since inflation is lower if the peg is defended, and expectations of inflation are particularly high if agents believe that the peg will be abandoned, inflation will be considerably below its anticipated value in this combination of circumstances, depressing output. Output persistence can be simply incorporated into these models (Irwin, 2004). We pursue a slightly different route that reflects the evidence of inflation persistence and stickiness in goods prices (Dornbusch, 1976). As Fuhrer and Moore (1995) note, inflation persistence requires wage-setting to have a backward-looking component. In our model, wages are set one period in advance and incorporate expectations of the possible collapse of the peg, but the key point is that the probability of this event is assumed to evolve smoothly. By contrast financial market beliefs about this probability are not assumed to be tied down in the same way. Thus our approach is to assume different mechanisms of expectations formation in different markets. In terms of a currency crisis model, the effect is to introduce
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persistence into the fundamentals while maintaining the feature that adverse expectations in financial markets can precipitate a currency collapse. 3. The model Imagine a country with a history of inflation that decides to peg the exchange rate as part of a stabilization effort. As in the hyperinflations of the 1920s, fixing a highly visible price like the exchange rate is central to breaking the cycle of inflationary expectations and convincing private agents that the stabilization will succeed (Dornbusch and Fischer, 1986). Expectations are particularly important in the model because wages are assumed to be set one period in advance, so wage-setters have to assess the likelihood of the peg holding, and the size of the devaluation that might occur in the event that it does not. We also assume that domestic prices are tied down by purchasing power parity, so that any skepticism about the success of the stabilization attempt on the part of wage-setters is reflected in increasing real wages and real exchange rate appreciation (as measured by relative unit labor costs). This real exchange rate appreciation tends to depress output, and this is the main threat to the success of the stabilization attempt. If the authorities use the breathing space to reform monetary policy by, for example, increasing the independence of the central bank, that opens up an opportunity to exit from the peg without necessarily reigniting inflation (e.g. Brazil in 1999). We consider what factors influence the optimal exit date. The basic structure of the model is similar to that of ‘‘second-generation’’ currency crisis models such as those of Jeanne (1997), Masson (1995) and Obstfeld (1996). Output is boosted by unexpected depreciation, but the government also cares about price stability. Output is also influenced by international competitiveness, as in Bleaney and Fielding (2002). The government decides at time zero to peg the currency for an indefinite period in order to achieve price stability. The stabilization attempt may collapse in a devaluation at any date, if the current-period cost of sustaining the peg becomes too great. Essentially, a devaluation is triggered, if output falls to a low enough level under the peg. We treat this as a constraint – the peg becomes politically unsustainable at this point. This can happen because of a combination of real appreciation and high devaluation expectations. Thus the model has the familiar property that crises can be ‘‘self-fulfilling’’. Output depends on the fundamentals, whose path is determined by the evolution of the real wage, and on financial markets’ expectations of the exchange rate. The size of an expected devaluation, should one occur, is based on rational expectations, i.e. it is that which minimizes the authorities’ loss function. In the case of financial markets, we assume that the probability of a devaluation may take any value between zero and one in each time period. In the case of the labor market, we assume that this probability declines asymptotically towards zero with time. The currency peg can only be sustained so long as the output cost does not exceed the inflation cost of devaluation plus an additional term that reflects the ‘‘humiliation’’ costs of being forced off the peg. We assume that purchasing power parity holds, with foreign inflation of zero, so that inflation is equal to the rate of exchange rate depreciation. In each period output is defined by a Lucas surprise supply function, with the price surprise being measured relative to financial market expectations, augmented by a term in the real wage. Output is equal to its ‘‘natural’’ level, minus a real wage term, plus the expanding effect of the unexpected component of exchange rate depreciation:
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y t ¼ y 0 /aqt þ aðet eet Þ;
ð1Þ
where a > 0, yt is output in period t, et is the one-period change in the log of the exchange rate (domestic currency units per unit of foreign currency), eet = devaluation expectations in period t, y 0 = natural output level and qt is the (log) real wage (or equivalently the real exchange rate based on unit labor costs). The equilibrium value of qt is assumed to be zero. It is convenient to combine the term in the real wage and in equilibrium output. Defining yt, the effective or real-wage-adjusted natural rate of output at time t, as ‘y 0 /qt ’, (1) becomes: y t ¼ y t þ aðet eet Þ:
ð2Þ
The government is forced to abandon the peg in period t, if the following condition is met: peg 2 2 y t y > y devaluation y þ be2t þ C; ð3Þ t where yt is output in period t (with the superscript ‘‘peg’’ or ‘‘devaluation’’ according to whether the exchange rate peg is maintained or abandoned), y* is the output target value, b (>0) is a parameter that reflects the importance of the price stability objective relative to the output objective, and C (>0) is the humiliation cost of abandoning a pegged exchange rate without pre-announcement. Thus Eq. (3) says that a devaluation of the exchange rate occurs, if the one-period welfare losses from lower output under a pegged (fixed) exchange rate regime exceed the inflation and humiliation costs of devaluing. This equation may be 2 thought of as the outcome of minimizing a one-period loss function, L ¼ ðy t y Þ þ be2t þ jC; where j = 1 if the peg is abandoned and zero if not. Even if the future benefits of continuing to peg exceed the costs, the stabilization attempt collapses, if the above condition holds.1 In this model, the optimal rate of devaluation, should one occur, depends on market expectations. With rational expectations, if the devaluation probability is l, then the expected depreciation is la ½y y t : a2 ð1 lÞ þ b
ð4Þ
The game is structured as follows. At the beginning of period zero, there is an exchangerate-based stabilization. Then private sector agents set their expectations of the exchange rate, which they cannot revise until the next period. Finally, the government sets the exchange rate and output is determined. If the exchange rate peg has been maintained, the game is repeated in the next period. As mentioned above, expectations in the labor market and in the financial markets seem to be based on different processes. If wage increases reflect labor market expectations, then the experience of exchange-rate based stabilization suggests a pattern of a gradual increase in the credibility of the exchange rate peg over time. It seems plausible that expectations in a market where negotiations take place relatively infrequently and over agreements covering a longer time period are based on approximations of longer-term trends. One could model this process therefore as an adaptive mechanism.
1
What we have in mind is that the peg becomes politically unsustainable, if its current-period cost is too high.
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We turn now to the detailed specification of the model. We start by examining the problem from the point of view of labor market agents. These agents observe an exchange-ratebased stabilization in period zero. Let the labor market agents believe at the beginning of period zero that the exchange rate will be floated in that period with probability l and will remain pegged with probability (1 l). The parameter therefore measures initial skepticism or lack of credibility of the peg. We treat this parameter as exogenous. It is likely to reflect factors such as the consistency between fiscal and monetary policy, the level of foreign exchange reserves and the government’s political position. Wage-earners’ expectations of the depreciation rate in period zero are then exactly as stated in Eq. (4). If the peg is maintained in period 0, then in period 1 and all subsequent periods until the peg is abandoned, the peg is assumed to acquire credibility at a rate (1 k), where 0 < k < 1, and the game is repeated. More precisely, the perceived probability (by labor market agents) of a devaluation in period t is lkt. This is equivalent to the devaluation probability following a geometric progression towards the observed outcome, as in an adaptive expectations model. We conceive k as reflecting the gains in credibility simply from being able to sustain the peg over time. If k is low, credibility is gained quickly; if k is high, it only accrues slowly. As is shown below, this acquisition of credibility is favorable to the maintenance of the peg. On the other hand, as will become clear below, past lack of credibility drives equilibrium output further from the government’s target. This effect works in the opposite direction, because it increases the losses from the output element of Eq. (1). If the peg has lasted for t periods (0 to t 1), and is then abandoned, then the exchange rate is assumed by wage-earners to depreciate by ee;L t ¼
lkt a ½y y t : a2 ð1 lkt Þ þ b
ð5Þ
This straightforward adjustment of probabilities in each period can also be motivated by looking at the incentives agents face in the labor market. Analogously to the way Lux (1995) explains herd behavior in the financial markets, it can be argued that agents will maximize their expected future income, which is future real wage income times the probability of employment, by following the majority. If agents are more pessimistic than the majority about the sustainability of the fixed peg policy and consequently demand higher nominal wages, their probability of employment will fall significantly, with the increase in their demanded relative real wage. However, if agents are more optimistic, they will demand a lower relative real wage and have less income. Assuming that their last-period wage income, relative to its corresponding employment probability, was optimal,2 agents will maximize expected future income by demanding exactly the same proportionate increase in nominal wages as the majority of agents in the market. It pays therefore to act according to the market consensus. As the consensus becomes more optimistic over time, agents adapt accordingly. Labor market agents set wages one period in advance. Apart from the expected depreciation rate, they also take demand conditions in the domestic market into account, which 2 To be more precise, it also has to be assumed that this is an efficiency wage labor market. Offering lower wages does not significantly improve the individual employment probability, but demanding more than the efficiency wage will significantly lower the individual employment probability.
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depend negatively on the real wage.3 Therefore, wage inflation is assumed to be as follows: wt ¼ ee;L t1 dqt1 ;
ð6Þ
where 0 6 d 6 1. In contrast, indicators of financial market expectations, such as interest rates, point to almost continuous decision-making covering shorter time periods. We therefore assume a rational expectations process for financial markets. The crucial question is whether the exchange rate policy is sustainable in any given time period. Agents therefore take into account the policy condition of Eq. (3). They deduce the optimal devaluation rate (e*) from the government’s preferences over inflation and unemployment. Their expected devaluation rate will therefore be the optimal rate times the perceived devaluation probability (pt). The devaluation probability can have any value between 0 and 1. This reflects imperfect information about the actions of other speculators. The average beliefs of speculators as a group will be reflected in the expected devaluation rate, which in turn impacts on the policy condition for giving up the exchange rate policy. As is well known, this introduces the possibility of multiple equilibria into the model (i.e. the exchange rate decision may vary with pt). Finally, let us consider the dynamics of the real wage. So long as the peg holds, inflation is zero, so the current real wage is given by its last-period value plus the rate of nominal wage inflation: qt ¼ qt1 þ wt :
ð7Þ
From (6) we know that this is equivalent to qt ¼ ð1 dÞqt1 þ ee;L t1 :
ð8Þ
From (1) and (2) follows that y t ¼ y 0 /a½ð1 dÞqt1 þ ee;L t1 ;
ð9Þ
where / > 0. The inclusion of a in Eq. (9) simplifies the algebra. Eq. (9) says that, under a peg, the effective natural rate of output falls in proportion to wage-earners’ expected rate of depreciation in the previous period.4 The idea is that nonzero depreciation expectations reflect the lack of credibility of the peg as perceived by labor market participants. This lack of credibility is reflected in higher nominal wage settlements, putting pressure on international competitiveness. The strength of the effect is denoted by the parameter /. The parameter d measures the strength of the mean reversion5 element in the real wage. Over time, as credibility increases, the mean reversion element will eventually outweigh the ‘lack-of-credibility ð/ee;L t1 )’ element. The ‘lack-ofcredibility’ element decreases the effective natural rate of output over time and the mean reversion element has the opposite effect. However, assuming that d is small, the overall trend is likely to be one of an accumulating loss of competitiveness initially, until credibility has increased significantly or the exchange rate policy is abandoned.
3
This is plausible, as the efficiency wage also depends on demand conditions. It simplifies the model to use previous-period rather than current-period expectations here, without making any essential difference. 5 Mean reversion is a process, where a variable returns to its mean value over time. 4
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Eq. (10) says that, if the exchange rate is floated, the natural rate of output returns gradually to its initial level. This aspect will become relevant when we consider the exit problem. ðy t y 0 Þ ¼ wðy t1 y 0 Þ
ðfloatingÞ;
ð10Þ
where 0 6 w < 1. Eq. (9) can be re-stated as ðy t y 0 Þ ¼ /a½ð1 dÞqt1 þ ee;L y t1 y 0 Þ /ee;L t1 ¼ ð1 dÞð t1 : The evolution of the gap between the desired output level and the natural output level is determined as follows (whilst the peg is maintained), using (9) and (5): " # a2 /lkt1 ðy y t Þ ¼ ð1 dÞ þ ð11Þ ðy y t1 Þ: a2 ð1 lkt1 Þ þ b Effective natural output shrinks continuously, but at a rate that decreases with time, until the mean reversion effect outweighs the ‘lack-of-credibility’ effect and natural output increases again. The optimal devaluation rate in any period, if a devaluation occurs, is et ¼
a2 ð1
a ½y y t : pt Þ þ b
ð12Þ
The model works like this: At time zero yt is equal to y 0 and the government announces a peg of the exchange rate. The sets of agents in the private sector then set their expectations of the time zero exchange rate. To see whether the peg is abandoned or not, we compare the losses from continuing the peg (et = 0) with the losses from abandoning it (et ¼ et ). We are now in a position to analyze the various possible outcomes of the stabilization attempt. The losses from pegging at time t are Lfix t ¼
2 a2 þ b ð y y Þ : t a2 ð1 pt Þ þ b
ð13Þ
Losses if the policy is abandoned unannounced are Lflex ¼ t
b2 þ a2 b ða2 ð1
pt Þ þ bÞ
2
2
ðy t y Þ þ C:
ð14Þ
The policy condition for abandoning the exchange rate policy unannounced is a2 ða2 þ bÞ ða2 ð1 pt Þ þ bÞ
2
2
ðy t y Þ > C:
ð15Þ
The left-hand side of (15) is influenced by the difference between target output and effective natural output (which is solely determined by labor market expectations) and by financial market expectations (pt). Since financial market beliefs about the probability of devaluation can take any value between 0 and 1, there is a considerable degree of variance in the evolution of the loss functions.
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It should be noted that the effect of a given change in pt is smaller for the Lflex case than for the Lfix case. This follows from a comparison of the functions, where Lflex can be expressed relative to Lfix: Lflex ¼
b Lfix þ C: a2 þ b
The easiest way to look at the consequences of this is to consider the extreme cases of pt being equal to 0 or 1. If pt equals zero Eq. (15) becomes: a2 2 ðy t y Þ > C: a2 þ b
ð16Þ
This significantly reduces the left-hand side and therefore makes a crisis far less likely. The opposite happens if pt equals one, as can be seen in the corresponding equation: a2 ða2 þ bÞ ðy t y Þ2 > C: 2 b
ð17Þ
The time trend in Lflex and Lfix depends on the evolution of effective natural output. While the real wage is increasing, effective natural output falls, and the loss functions have an upward trend. However, from the point where the mean reversion effect dominates, real wages decline and the loss functions will fall again. In the tradition of models with significant resistance to reductions in the nominal wage, we assume d to be small. Consequently, the loss functions will decrease only after credibility has increased significantly. There are several possibilities, depicted in Figs. 1–3: The dashed lines represent Lflex. The possible realizations of both loss functions are illustrated by two lines each. The upper lines plot loss values against time, when p equals 1. The lower lines plot loss values against time, when p equals zero. So Lfix can at any time be on or between the solid lines and Lflex on or between the dashed lines. In the first case (shown in Fig. 1) a crisis is inevitable, but there is not one date at which the crisis definitely occurs. The inevitability of the crisis is shown by the fact that real wages reach a point where, whatever the value of p, the authorities prefer to devalue.
L L flex max L fix max L flex min L fix min t t1
t2
Fig. 1. Crisis occurs between t1 and t2. Notes: Lfix falls within the region between the two unbroken lines, and Lflex falls within the region between the two dashed lines, its exact position depending on the value of p. The lower line represents p = 0 and the upper line p = 1. A crisis is possible, if the upper unbroken line is above the upper dashed line, and inevitable, if the lower unbroken line is above the lower dashed line. In the region where a crisis is possible, there is a threshold value of p above which a crisis occurs.
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L
t Fig. 2. No crisis. Notes: Lfix falls within the region between the two unbroken lines, and Lflex falls within the region between the two dashed lines, its exact position depending on the value of p. The lower line represents p = 0 and the upper line p = 1. A crisis is possible, if the upper unbroken line is above the upper dashed line, and inevitable, if the lower unbroken line is above the lower dashed line. In the region where a crisis is possible, there is a threshold value of p above which a crisis occurs.
L
t t1
t2
Fig. 3. Possible crisis. Notes: Lfix falls within the region between the two unbroken lines, and Lflex falls within the region between the two dashed lines, its exact position depending on the value of p. The lower line represents p = 0 and the upper line p = 1. A crisis is possible, if the upper unbroken line is above the upper dashed line, and inevitable, if the lower unbroken line is above the lower dashed line. In the region where a crisis is possible, there is a threshold value of p above which a crisis occurs.
Although the crisis must occur by t2, when the lower unbroken line crosses the lower broken line, it can happen at any time from t1 onwards. At t1 a crisis can only occur, if pt is equal to one. At t2 a crisis will occur even if pt is equal to zero. Fig. 2 depicts a second case, where there is no crisis. Even if pt = 1, when speculators are completely convinced that a devaluation will occur, it never does. Finally, Fig. 3 represents an interesting intermediate case, where a crisis becomes possible from t1 onwards (pt has to equal one for a crisis to occur precisely at t1) until
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t2. Consequently, if expectations become sufficiently pessimistic at any time between t1 and t2, a crisis will occur. After t2, the peg is safe again. Which of these three cases applies may simply depend on the value of C, the fixed cost of abandoning the peg. For any given value of C, however, the rate of loss or gain of international competitiveness, as given by Eq. (11), is the critical factor. We can see from that equation that the higher are l (the initial level of labor market skepticism), k (its persistence) and / (the elasticity of output with respect to the real wage) and the lower is d (the rate of mean reversion in real wages), the greater the real appreciation under the peg and therefore the more likely it is that a crisis occurs. If / or l is low or d is high, then effective natural output does not shrink much below its initial value before starting to recover, whilst if k is low the shrinkage effect decays quickly to zero. These are the cases where a successful stabilization is most likely (as in Fig. 2). This model also provides a potential justification for heterodox policies, in which wage controls are implemented in the early stages of the stabilization. Such policies could prevent the loss of international competitiveness that exposes the stabilization attempt to a potential or inevitable currency crisis (as in Fig. 1 or Fig. 3) rather than keeping it in the secure region (as in Fig. 2). 4. Are all stabilization attempts worthwhile? Instead of considering a government that has already announced a stabilization attempt in period zero, and therefore incurs a cost from departing from the peg, we now turn to the case of a government, which has not yet made such an announcement. To keep things simple, in this section it is assumed that d equals zero. We also assume that the government initially has a crawling peg regime with devaluation at the rate a e ¼ ðy y 0 Þ; b which minimizes the government’s loss function given below. We show now that if the stabilization attempt has insufficient credibility, it is better to postpone it and to continue with the crawling peg. The issue is therefore whether to continue floating or to peg, assuming that the peg lasts for ever (i.e. the value of C is sufficiently large that it is never abandoned). Let the government’s discount factor be q (<1). The loss function for each individual time period is Lt ¼ ðy t y Þ2 þ be2t :
ð18Þ
If V is the present value of the government’s loss function L over all future periods, then with no stabilization attempt, where output stays at y 0 and et equals ba ðy y 0 Þ, we have: a2 2 V crawl ¼ ð1 þ q þ q2 þ Þ 1 þ ð19Þ ðy y 0 Þ : b If stabilization is attempted, from Eq. (13) we have: " # 2 2 a2 þ b a2 þ b fix V ¼ ðy y 0 Þ þ q 2 ðy y 1 Þ þ : a2 ð1 p0 Þ þ b a ð1 p1 Þ þ b
ð20Þ
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Note that Vfix depends on two factors: financial market expectations of a devaluation in each period (pt), and the evolution of the effective natural rate of output (yt) as given by Eq. (11). The stabilization attempt yields immediate gains in the form of reduced inflation, which may be more than offset by future losses from reduced output. If p0 < 1, the period 0 value of Lcrawl is higher than that of Lfix. In the most favorable case of l = 0 (100% labor market credibility and hence no loss of international competitiveness), yt stays at y 0 in future periods, which means that Vcrawl > Vfix. In the general case where l > 0, we can show that the values of the parameters may be such that Vcrawl < Vfix, implying that it may be preferable to postpone the stabilization attempt. Let us consider the simplest case where k = 0 (so that y is fixed at y1 after period 1) and pt = 0 for all periods. In that case Vfix > Vcrawl if q a2 a2 ðy y 1 Þ2 1 þ ðy y 0 Þ2 > ðy y 0 Þ2 : ð21Þ 1q b b The left-hand side of Eq. (21) represents the difference between Vfix and Vcrawl from period 1 onwards and the right-hand side equals Lcrawl Lfix in period 0. Substituting from Eq. (11) and rearranging, Eq. (21) becomes: q½ð1 þ ZÞ2 1 >
a2 ; b
Z¼
/a2 l : a2 ð1 lÞ þ b
ð22Þ
This condition can easily be met for high enough values of l.6 Thus, even in the case where the stabilization has 100% credibility amongst wage-earners in the second period (because k = 0), so that no further deterioration of the fundamentals occurs, the permanent loss of output from lack of credibility in the first period can be high enough to make the stabilization attempt unattractive. If k > 0, then Vfix is even greater for a given l. These results imply that stabilization attempts need to be well enough designed to bring l below some critical value to make the attempt worthwhile. If, for example, the government is too reliant on seigniorage revenue and cannot undertake the fiscal reforms necessary to reduce l below the critical level, it would do better to postpone the stabilization attempt. 5. The exit problem Suppose that, while the exchange rate is pegged, the authorities put in place institutional arrangements intended to keep inflation at zero with a view to exiting from the peg at a future date. At a certain date T, a return to floating is announced and implemented. Because the float was pre-announced, the cost C of an unannounced end to the peg is not incurred. After date T, natural output gradually reverts to y 0 as specified in Eq. (10). What happens to inflation? It seems reasonable to assume that, if the exit is successful, inflation stays at zero, but that if it is unsuccessful inflation returns to the pre-peg rate of ba ðy y 0 Þ. The problem is how to formulate the probability of the exit being successful. We want to include a factor that reflects the quality of post-exit institutional 6
For l = 1 it reduces to qu(2+((u2)/b)) > 1. Since / = 1 is a plausible value, q would have to be very low for this not to hold.
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arrangements, but the credibility of the peg is also likely to play a role. We could relate the success probability at date T to financial market expectations at that date (pt), but since we have no model of pt, it would be difficult to draw any useful conclusions. Instead, therefore, we relate the success probability to labor market expectations. Since labor market credibility increases over time, this means that the probability of a successful exit also increases with time – which does not seem unreasonable. We assume that post-float inflation stays at zero (i.e. the exit is successful) with probability 1 clkT, and with probability clkT inflation returns (i.e. the exit is unsuccessful). Thus the probability of failure is equal to labor market skepticism in period T (lkT), multiplied by a factor c (>1) that represents exit risk and is assumed to reflect the quality of the institutional reforms (the better the reforms, the closer c is to one). What determines the optimal exit date? Delaying exit by one period reduces the probability of failure by a factor k, but also keeps output low for one further period and causes the effective natural rate of output to move further from the target level. A further important consideration is that the peg might succumb to a crisis in period T, if exit is delayed. Assume for simplicity that w = 0 (i.e. that natural output returns instantaneously to y0 after exit). Then, with a discount factor of q, the expected multi-period losses from exit at time T are 2 1 T a V 1 ¼ ð1 qÞ 1 þ clk ð23Þ ðy y 0 Þ2 : b h i 2 2 This equation reflects the fact that the inflation losses ab ðy y 0 Þ are incurred with probability clkT. If exit is delayed for one period, either the peg collapses in period T (probability p) or it does not and exit occurs at time T + 1 (probability 1 p). Hence the expected losses are 1 a2 2 1þ V2 ¼p ðy y 0 Þ þ C 1q b 2 q 2 T þ1 a fix þ ð1 pÞ LT þ 1 þ clk ð24Þ ðy y 0 Þ ; 1q b where Lfix T is given by Eq. (13). We therefore continue to take the different expectations in the labor and the financial market into account. Let us consider first the case, where p = 0 (as in Fig. 2). In that case it pays to exit at time T rather than to delay further if 2 2 q 2 T a T a fix ð1 kÞclk LT > 1 þ clk ð25Þ ðy y 0 Þ þ ðy y 0 Þ2 : 1q b b This condition is more likely to be fulfilled if (a) q is smaller (the future is discounted more heavily), (b) c is smaller (post-exit anti-inflation strategy is better designed), (c) d is smaller and (d) / is larger (these last two factors increase real wages and their effect on output and therefore Lfix T through Eq. (11)). Moreover, in this case it can be assumed that pt = 0, since everyone can see that the peg is secure, and this keeps down the cost of continuing to peg (Eq. (13)). In the case of the labor market credibility parameters (l, k), matters are a bit more complicated, because both sides of Eq. (25) are increasing in l and k. Using Eqs. (13) and (11), however, we can see that Lfix T increases with T ðT 1Þ T T 2 , whereas the right-hand side of (25) is proportional to lk . Thus we can deduce l k
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that higher values of l and k favor an earlier exit, because of the cumulative impact on equilibrium output of continuing the peg. This necessarily implies, however, that the probability of a successful exit is reduced at the optimal exit date, since not only are l and k larger, but also T is smaller. Conversely, with greater credibility, it pays to wait until exit is safer. We may now consider the case where p > 0. Since the collapse of the peg produces the same result as an unsuccessful exit but with an additional humiliation cost of C, it is always better to exit, if p > clkT (i.e. if a crisis is more likely than an unsuccessful exit). In general, p > 0 implies an earlier exit then p = 0. Thus the examples shown in Figs. 1 and 3 suggest an earlier exit date (and therefore a riskier exit) than Fig. 2. In conjunction with those given earlier, these results imply that real exchange rate appreciation should lead governments to formulate plans for an early exit. Not only does real appreciation increase the risk of a currency crisis, but it also makes it optimal to exit at higher probabilities of failure to reduce output costs. In short, it is often better to jump than to risk being pushed. 6. Conclusions The purpose of the model presented here was to develop a formal bridge between the theory of currency crises and of exchange-rate-based stabilizations that is consistent with the stylized facts. One of these stylized facts is that interest rates are much more volatile than wage increases, which is not consistent with the assumption that all agents exhibit forward-looking behavior with identical expectations. The model captures this by assuming that wage-setters’ perceived probability of a collapse of the peg declines smoothly with time, whilst financial market agents’ perceptions of the same probability are not tied down in the same way. The model incorporates the assumption that, if the peg can last long enough, the stabilization attempt will succeed, because any initial real appreciation will eventually be reversed as wages fall back to their equilibrium level. In the intervening period of loss of international competitiveness, however, the peg may succumb to a currency crisis. If the authorities cannot succeed in making their overall macroeconomic policy consistent with price stability (for example if they are too reliant on seigniorage revenue), then initial skepticism about the success of any stabilization attempt is likely to be high, and this will be reflected in wage behavior. The output costs of the stabilization attempt will then be substantial, increasing the chance that it will end in a currency collapse. In general, weak stabilization attempts are better postponed until the authorities can put together a package with greater credibility. The model also sheds light on the ‘‘exit problem’’: when to abandon the peg with a good chance of retaining the price stability achieved by the stabilization. In general (assuming that output recovers more quickly under floating), it is optimal to exit before credibility reaches 100%, to reduce the output losses from overvaluation. More effective monetary reforms, such as greater central bank independence or inflation targeting, bring forward the optimal exit date. An early exit is particularly desirable in cases where, if the peg is maintained, there is a greater danger that it would collapse anyway under speculative pressure. Greater credibility gives policy-makers the luxury of postponing exit until the chances of success are higher.
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Acknowledgements We would like to thank former and present colleagues at the University of Nottingham, especially Atanu Ghoshray and Claudio Zoli, for insightful comments and discussions. We would also like to thank two anonymous referees for helpful comments on a previous version. References Bleaney, M.F., Fielding, D.J., 2002. Exchange rate regimes, inflation and output volatility in developing countries. Journal of Development Economics 68, 233–245. Calvo, G.A., Ve´gh, C.A., 1999. Inflation stabilization and BOP crises in developing countries. In: Taylor, J.B., Woodford, M. (Eds.), Handbook of Macroeconomics. Elsevier, Amsterdam (Chapter 4). Dornbusch, R., 1976. Expectations and exchange rate dynamics. Journal of Political Economy 84, 1161–1176. Dornbusch, R., Fischer, S., 1986. Stopping hyperinflations past and present. Weltwirtschaftliches Archiv 122, 1–46. Dornbusch, R., 2001. A primer on emerging market crises, Working paper no. 8326, National Bureau of Economic Research. Edwards, S., 1993. Exchange rates as nominal anchors. Weltwirtschaftliches Archiv 129, 1–32. Flood, R.P., Garber, P.M., 1984. Collapsing exchange rate regimes: Some linear examples. Journal of International Economics 17, 1–13. Fuhrer, J., Moore, G., 1995. Inflation persistence. Quarterly Journal of Economics 110, 127–160. Irwin, G., 2004. Currency boards and currency crises. Oxford Economic Papers 56, 64–87. Jeanne, O., 1997. Are currency crises self-fulfilling: A test. Journal of International Economics 43, 263–286. Kaminsky, G.L., Leiderman, L., 1998. High real interest rates in the aftermath of disinflation: Is it a lack of credibility? Journal of Development Economics 55, 198–214. Krugman, P.R., 1979. A model of balance-of-payments crises. Journal of Money, Credit and Banking 11, 311– 325. Lux, T., 1995. Herd behaviour, bubbles and crashes. Economic Journal 105, 881–896. Masson, P.R., 1995. Gaining and losing ERM credibility: The case of the United Kingdom. Economic Journal 105, 571–582. Obstfeld, M., 1996. Models of currency crises with self-fulfilling features. European Economic Review 40, 1037– 1047.