Stressing the inßuence of expected devaluation on currency crises, this paper shows that, in a
Þxed exchange-rate system with an escape clause, partial delegation of exchange-rate policy to an
inßation-averse central banker reduces the probability of crisis

Boinet, V

English

Brunel University Research Archive

Partial Delegation in a Model of Currency CrisisVirginie Boinet∗AbstractStressing the inßuence of expected devaluation on currency crises, this paper shows that, in aÞxed exchange-rate system with an escape clause, partial delegation of exchange-rate policy to aninßation-averse central banker reduces the probability of crisis.Keywords: Currency crisis; Multiple equilibria; Credibility; Monetary delegationJEL classiÞcation: E52; F411 IntroductionA well-known result in the literature on currency crisis is that the cost of defending a Þxedrate increases when private agents expect a devaluation (Krugman, 1998). In this context,this paper considers partial delegation of exchange-rate policy to a central banker who ismore inßation averse than the government: the decision as to whether to maintain the pegis left to the government, but the magnitude of any realignment is delegated to the centralbanker. Looking at the inßuence of expected devaluation, it shows that, in a Þxed exchange-rate system with an escape clause, this partial delegation reduces the probability of crisis.In particular, it underlines the fact that it is more eﬀective to devolve exchange-rate policywhen private agents expect a future realignment, as the reduction of the probability of crisis∗Department of Economics and Finance, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK. Tel:++44-1895-203386, fax: ++441895-203384. E-mail address: Virginie.Boinet@brunel.ac.uk.I would like to thank John Bennett, Eric Girardin, Christos Ioannidis and Chris Martin for very helpfulcomments.1is greater. These results are strengthened if the central bankers degree of inßation aversionis greater, for the probability of self-fulÞlling crisis is reduced and the stability of the Þxedexchange-rate system increased.2 Partial delegation2.1 The modelThe framework is based on a model of currency crisis à la Obtsfeld (1994). In a small openeconomy, the log of employment n can be expressed byn = n∗ + ρ (Π− Πe) n∗ = 0, ρ > 0 (1)where Π and Πe denote actual and expected inßation. The natural employment rate n∗ isassumed to be zero. Inßation expectations are formed at the beginning of the period asprivate agents sign nominal contracts. Then Þrms determine the demand for labor and thepolicy maker decides whether to maintain the peg.Purchasing Power Parity (PPP) holds. Foreign prices are exogenous and normalized to 1.Control of exchange-rate variations ∆e and of the inßation rate Π are therefore equivalent.The aim of exchange-rate or monetary policy is to minimize deviations of inßation andemployment from their target levels. The loss functions of the government and the centralbanker are respectivelyLG =12£Π2 + (n− en)2¤+ ΩC (2)LCB =12£(1+ ε)Π2+(n− en)2¤ (3)The target level of employment en is above the natural rate, and so can be interpreted as aninßationary bias. The inßation target is zero. C represents the realignment cost incurredby the policy maker (in terms of credibility for instance) after the abandonment of the peg.Consequently, Ω is a binary variable equal to 0 when the policy maker maintains the pegand equal to 1 when he devalues. We assume partial delegation of exchange-rate policy to acentral banker who has the same targets as the policy maker but who places greater weight2on the costs of higher inßation (ε > 0).1 There is no cost of realignment to the central bankerbecause it is the government that decides whether realignment occurs. Therefore, when thepolicy maker decides to devalue, exchange-rate policy is delegated to the central banker and∆e is determined such that ∂LBC∂∆e= 0, that is,Π = ∆e =ρ1+ ε+ ρ2(ρΠe + en) (4)The more the central banker is inßation averse (ε high), the smaller is the inßuence ofinßationary expectations and the employment target on the devaluation rate.Information available for the formation of inßation expectations is the same as that forthe policy maker except that private agents do not know the realignment cost C. Therefore,they cannot perfectly forecast the Þnal decision of the policy maker. If economic agentsexpect the maintenance of the peg, then Πe = 0. If they expect a devaluation, Πe = Π, thatis,Πe =ρ1+ εen (5)Inßation expectations increase with the inßationary bias en while they decrease with thecentral bankers degree of inßation aversion.2.2 The realignment condition and eﬀects of partial delegationWhen the government defends the peg, it follows that Π = ∆e = 0. When it proceeds to arealignment, Π is expressed by equation (4) . Inserting (1) into (2), the governments loss inthe two respective situations is found asLGFX =12(ρΠe + en) 2 (6)LGFL =ρ2 + (1+ ε)22 (1+ ε+ ρ2)2(ρΠe + en) 2 + C (7)1The delegation is partial as there is a cost to the government when a realignment occurs. To take thiscost into account, the decision as to whether to maintain the peg is left to the government, but the magnitudeof any realignment is delegated to the central banker.3This loss depends positively on inßation expectations and the inßationary bias. As a result,the policy maker will decide to devalue if LGFX − LGFL > 0, that is,ρ2 (1+ 2ε+ ρ2)2 (1+ ε+ ρ2)2(ρΠe + en)2 > C (8)This inequality indicates that the probability of realignment increases when expected inßa-tion and the inßationary bias are higher and when the realignment cost C is smaller.Taking into account inßation expectations, thresholds under which the government willdecide to devalue are equal toCWD1 =ρ2 (1+ 2ε+ ρ2)2 (1+ ε+ ρ2)2en2 (9)CWD2 =ρ2 (1+ 2ε+ ρ2)2 (1+ ε)2en2 (10)CWD1 is the threshold which prevails when private agents expect no devaluation (Πe = 0),whileCWD2 is the threshold which prevails when private agents expect a realignment (Πe = Π).Note that CWD1 and CWD2 are both positive and that CWD1 < CWD2 . At one threshold CWD2 ,as inßationary expectations are high, competitiveness and unemployment problems are sopainful that a devaluation occurs unless the realignment cost is very high. At the otherthreshold CWD1 , the policy maker will maintain the peg even if the realignment cost is low.Multiple equilibria occur between CWD1 and CWD2 . Therefore, if C belongs to this interval,the government can either defend the peg or realign. The decision depends on private agentsexpectations. This implies that crises are self-fulÞlling.We consider here delegation to a central banker who is more inßation averse than thegovernment. ε = 0 represents the case of no delegation as then government and centralbanker have exactly the same preferences and targets. Let CNDi , where i = 1, 2, denotethresholds obtained when the government does not delegate exchange-rate policy. Puttingε = 0 into (9) and (10),CND1 =ρ22 (1+ ρ2)en2 (11)CND2 =ρ2 (1+ ρ2)2en2 (12)Note that CND1 and CND2 are both positive and that for the same reasons as previouslyCND1 < CND2 . The comparison of these diﬀerent thresholds leads to the following proposition.4Proposition 1. Partial delegation of exchange-rate policy to a more inßation-averse centralbanker reduces the level of the thresholds.This proposition is conÞrmed by the following inequality.CWDi < CNDi where i = 1, 2 (13)So, whatever private agents expectations, with partial delegation to a more inßation-aversecentral banker, the probability of crisis is reduced. The policy maker maintains the peg whilethe cost of realignment is smaller. This result can be explained by the negative (downward)inßuence of partial delegation on expected inßation. As the cost of defending a Þxed ratedecreases when private agents expect its maintenance, the probability of crisis is reduced.This suggests that the eﬀect of partial delegation on the probability of crisis is more eﬀectivewhen private agents expect a future realignment. This idea is conÞrmed by the propositionbelow.Proposition 2. Partial delegation of exchange-rate policy to a more inßation-averse centralbanker decreases the gap between the two thresholds.This proposition gives additional information concerning the evolution of thresholds.Proposition 1 indicates that, with partial delegation, the probability of crisis is reduced ateach threshold. Proposition 2 speciÞes that the probability of crisis is reduced more at CWD2than at CWD1 . Therefore, as the peg is more fragile at CWD2 and the strategy of partialdelegation more eﬃcient, expectations of devaluation strengthen the need of implementingthis strategy. It is conÞrmed by the following inequality.CWD2 − CWD1 < CND2 − CND1 (14)As illustrated in Figure 1, the area of multiple equilibria is reduced. We write 1 when thegovernment devalues and 0 when it defends the peg. The Þrst number indicates the policymakers decision in the case of no delegation and the second number the policy makersdecision when exchange-rate policy is partially delegated to a more inßation-averse centralbanker.5Policy maker’s decision C1ND C2ND C Figure 1 C1WD C2WD (1,1) (1,1) (1,0) (1,1) (1,0) (0,1) (0,0) (1,0) (0,0) (0,0) Whether CWD2 ≶ CND1 depends on the value of ε. Using (9) and (10), we Þnd∂CWDi∂ε< 0 where i = 1, 2 (15)∂¡CWD2 − CWD1¢∂ε< 0 (16)Thus, we obtain the following proposition.Proposition 3. The more the central banker is inßation averse,i) the lower is the level of thresholds;ii) the smaller is the gap between the two thresholds.This last proposition means that, whatever inßation expectations, the probability of crisisdecreases with the central bankers degree of inßation aversion and that the magnitude ofthis reduction is higher when private agents expect a devaluation. If ε is very high, expectedinßation is close to zero (see (5)). Then, CWD1 is lower and the interval between CWD2and CWD1 substantially decreases. At the extreme, CWD1 is close to zero and CWD2 close toCWD1 . CWD2 then becomes smaller than CND1 . Self-fulÞlling crises are avoided. One thresholdremains at which the probability of crisis is considerably reduced.6References[1] Barro, R. and D. B. Gordon, 1983, A Positive Theory of Monetary Policy in a NaturalRate Model, Journal of Political Economy 91, 589-610.[2] Krugman, P., 1979, A Model of Balance of Payments Crises, Journal of Money, Creditand Banking 11, 311325.[3] Krugman, P., 1996, Are Currency Crises Self-FulÞlling?, NBER Annual Macroeconomics,345-378.[4] Krugman, P., 1998, Currency Crises, http://web.mit.edu/krugman/www/crises.html.[5] Kydland, F. and E. Prescott, 1977, Rules Rather than Discretion : the Inconsistency ofOptimal Plans, Journal of Political Economy 85, 473-491.[6] Loisel, O. et P. Martin, 2001, Coordination, Cooperation, Contagion and Currency Crises,Journal of International Economics 53, 399-419.[7] Obstfeld, M., 1994, The Logic of Currency Crises, Cahiers Economiques et Monétaires43, 189-213.[8] Rogoﬀ, K., 1985, The Optimal Degree of Commitment to an Intermediate MonetaryTarget, Quarterly Journal of Economics 100, 1169-1190.7

Partial delegation in a model of currency crisis

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