- Email: [email protected]
Target zone credibility and economic fundamentals
Economic Modelling 20 Ž2003. 791᎐807
Target zone credibility and economic fundamentals Marco Tronzano a , Zacharias Psaradakis b,U , Martin Solaa,c a b
Dipartimento di Economia e Metodi Quantitati¨ i, Uni¨ ersita ´ degli studi di Geno¨ a, Italy School of Economics, Mathematics and Statistics, Birkbeck College, 7᎐15 Gresse Street, London W1T 1LL, UK c Departamento de Economıa, ´ Uni¨ ersidad Torcuato Di Tella, Buenos Aires, Argentina
Accepted 15 April 2002
Abstract This paper investigates empirically the relationship between target zone credibility and economic fundamentals using French monthly data for the period 1991:6 to 1998:9. The econometric framework is one which allows expected devaluation Žproxied by the interest rates differential . to stochastically switch between a ‘high’ and a ‘low’ phase according to the outcome of a Markov process. The transition probabilities of the Markov process are assumed to vary over time as functions of various monetary and real macroeconomic variables. Our findings suggest that expected devaluation is significantly influenced by foreign reserves and the deviations of the exchange rate from the EMS central parity, whereas the effects of real variables are weak at best. 䊚 2002 Elsevier Science B.V. All rights reserved. JEL classifications: C22; F31 Keywords: Credibility; Regime-switching model; Target zone; Transition probabilities
U
Corresponding author. Tel.: q44-20-76316415; fax: q44-20-76316416. E-mail address: [email protected] ŽZ. Psaradakis..
0264-9993r03r$ - see front matter 䊚 2002 Elsevier Science B.V. All rights reserved. doi:10.1016rS0264-9993Ž02.00009-3
792
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
1. Introduction Since the last official realignment of the French FrancrDeutschemark ŽFFrDM. parity in January 1987, French inflation and interest rates exhibited a remarkable convergence towards the corresponding German rates. By mid-1991 convergence had been achieved, and the exchange rate mechanism ŽERM. of the European Monetary System ŽEMS. appeared to be successful in managing exchange rates. However, attacks on several currencies in 1992 led to the suspension of the Pound Sterling and the Italian Lira from the ERM and the widening of the target-zone bands of the remaining ERM currencies. As the crisis took place when the macroeconomic policies of most of the country members were regarded to be consistent with the exchange rate agreement, this raises the question of whether the speculative attacks were fundamentals-driven or simply self-fulfilling prophesies. The answer to the above question has important policy implications. Suppose, for instance, that speculative attacks can basically be explained in terms of economic policies inconsistent with the maintenance of a fixed parity, or in terms of large adverse macroeconomic shocks which may temporarily negatively affect policy-makers’ incentives to satisfy the above commitment. In this case, there might be some room to prevent further pressures on ‘weak’ currencies through policy measures that correct the main macroeconomic imbalances and promote faster convergence towards more ‘virtuous’ countries. If, conversely, exchange rate crises can mainly be ascribed to self-fulfilling elements, unrelated to market fundamentals, efforts towards a more rigorous stance in macroeconomic policies and increased convergence will ultimately prove futile, the only effective way to prevent further attacks being represented by the introduction of some measures of capital control. In this paper we investigate whether the ERM crisis can, for the case of France, be considered to be driven by economic fundamentals. In particular we examine whether expected devaluation of the FFrDM parity, proxied by the interest rates differential, can be explained by pressures in the real sector of the economy Žsee, e.g. Drazen and Masson, 1994. or by pressures in the monetary sector Žas in the traditional speculative attacks literature .. Since we are interested in crisis-type periods, we consider the French experience after convergence has been achieved, and we study episodes of temporary divergence of the interest rates.1 The relationship between expected devaluation and macroeconomic fundamentals is analysed within a non-linear econometric framework where the interest rates differential is a discontinuous function of macroeconomic variables Žcf. Bertola and Caballero, 1992.. In this context, it is assumed that the shifts between ‘high’ and ‘low’ expected devaluation are stochastic but autocorrelated, governed by a twostate Markov process. The transition probabilities of the latter are allowed to vary
1
The study of the convergence process itself requires a completely different framework of analysis and is beyond the scope of the present paper.
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
793
over time as functions of relevant macroeconomic variables. The effects of monetary variables Žtypically related to speculative attacks analyses . as well as real variables Žas in escape-clause approaches to currency crises. are examined. As mentioned before, the interest rates differential is used here as a proxy for the expected rate of devaluation. There is little doubt that such a proxy is far from perfect and the ‘drift adjustment’ method of Bertola and Svensson Ž1993. provides a more appropriate proxy for many applications.2 In our case, the drift-adjustment method gave results that are qualitatively similar to those obtained with the interest rates differential. This is not surprising since, in periods of high interest rates differentials, it is typically true that the differences between interest differentials and expected rates of realignment are not substantial Žcf. Jeanne and Masson, 1997.. Moreover, even if this is untrue during periods of low interest rates differentials, it is unlikely that the use of the latter proxy would lead to wrong separation of the regimes. In view of the similarity of the results obtained using the two alternative measures of credibility, and given the adverse effects that the use of a generated variable like the expected rate of realignment is likely to have on the finite-sample properties of estimators and test statistics for Markov-switching models Žsee Psaradakis and Sola, 1998, 1999., we decided to concentrate on the analysis of the dynamics of the interest rate differential. The remainder of the paper proceeds as follows. Section 2 describes the statistical models used to characterise the dynamics of interest rates differential. Section 3 discusses the macroeconomic variables considered in the analysis and their relation to the theoretical literature. Section 4 presents and discusses the estimation results of Markov-switching models with time-varying transition mechanisms, focusing on the information content of the various macrovariables. Section 5 summarises and concludes.
2. Econometric models and inference In this paper, the dynamics of the nominal interest rates differential Ž rt . between France and Germany are modelled using the following autoregressive specification: m
rt y Ž st . s
Ý j
rtyj y Ž styj . q Ž st . t ,
Ž t s 1,...,T .
Ž1.
js1
In Eq. Ž1., st is a random variable in 0, 14 that indicates the unobservable ‘state’ or ‘regime’ operative at date t, t 4 are independent and identically distributed random variables with zero mean and unit variance, and Ž⭈. and Ž⭈., respec-
2
This is certainly true when the focus of the analysis are the non-linear relationships between exchange rates and fundamentals implied by target zone models of exchange rate dynamics.
794
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
tively, represent a mean and standard deviation shift function. These functions are parameterised linearly as
Ž st . s ␣ 0 q ␣ 1 st and
Ž st . s 0 Ž 1 y st . q 1 st We normalise by defining state 1 to be the state with the higher mean Žachieved by setting ␣ 1 ) ␣ 0 .. It is further assumed that t 4 is independent of st 4 . Regarding the regime indicators st 4 , we assume that nature selects regime at date t with a probability that depends on what regime the process was in at date t y 1, and this probability varies over time as a function of some economic variableŽs.. Thus, following Diebold et al. Ž1994., the stochastic process st 4 is specified to be a non-homogeneous Markov chain with state space 0, 14 and transition mechanism: Pr st s 0 < sty1 s 0, z ty1 4 ' qt s exp Ž c 0 q  0 z ty1 . r w 1 q exp Ž c 0 q  0 z ty1 .x Pr st s 1 < sty1 s 1, z ty1 4 ' pt s exp Ž c1 q  1 z ty1 . r w 1 q exp Ž c1 q  1 z ty1 .x Pr st s 1 < sty1 s 0, z ty1 4 s 1 y qt
Ž2.
Pr st s 0 < sty1 s 1, z ty1 4 s 1 y pt where z t is a variable that affects the state transition probabilities. The model in Eqs. Ž1. and Ž2. extends the standard linear autoregressive specification by allowing the mean and conditional variance of rt to be functions of the Žstochastically chosen. regime that controls the process at date t. Since d ptrd z ty1 has the same sign as  1 ,  1 ) 0 Ž  1 - 0. implies that an increase in z ty1 increases Ždecreases. the probability of remaining in state 1. Similarly,  0 ) 0 Ž  0 - 0. implies that an increase in z ty1 will increase Ždecrease. the probability of remaining in state 0.3 An alternative specification for the transition mechanism governing st 4 replaces z ty1 in Eq. Ž2. by z t Žsee, e.g. Piard, 1999.. ln this case, however, z t needs to be strictly exogenous for the analysis to be correct. In addition to its implications for statistical inference, any violation of exogeneity in this framework makes the interpretation of results extremely problematic; after all, if z t and rt are jointly determined, one can hardly argue that z t helps to predict state transitions. Another important issue is the possible existence of feedback effects: whenever z ty1 cannot be considered exogenous, its effects on the transition probabilities may 3
The familiar Markov model with time-invariant transition mechanism may be obtained from Eqs. Ž1. and Ž2. by imposing the restriction  0 s  1 s 0.
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
795
arise because of induced changes in rty1. Therefore, in order to use this methodology to assess the forecasting ability of z ty1 , it is advisable to start with a general model for the transition mechanism and test whether rty1 has significant effects. In other words, Eq. Ž2. needs to be replaced by: Pr st s 0 < sty1 s 0, z ty1 ,rty1 4 s exp Ž c 0 q  0 z ty1 q d 0 rty1 . r w 1 q exp Ž c 0 q  0 z ty1 q d 0 rty1 .x Pr st s 1 < sty1 s 1, z ty1 ,rty1 4 s exp Ž c1 q  1 z ty1 q d1 rty1 . r w 1 q exp Ž c1 q  1 z ty1 q d1 rty1 .x Pr st s 1 < sty1 s 0, z ty1 ,rty1 4 s 1 y Pr st s 0 < sty1 s 0, z ty1 ,rty1 4 Pr st s 0 < sty1 s 1, z ty1 ,rty1 4 s 1 y Pr st s 1 < sty1 s 1, z ty1 ,rty1 4 This strategy was adopted in our empirical analysis but, since we found the coefficients d 0 and d1 to always be insignificantly different from zero for our data, we only report results obtained when the transition mechanism is specified as in Eq. Ž2.. Statistical inference in the context of a Markov-switching model like Eqs. Ž1. and Ž2. can proceed by making use of a variant of the non-linear filtering algorithm discussed in Hamilton Ž1994, §22.4.. This gives as a by-product the log-likelihood function T
L Ž . s
Ý
log f Ž rt < Fty1 ; .
Ž3.
tsmq1
where Ft s r 1 , z1 , . . . rt , z t 4 and f Ž rt < Fty1; . represents the conditional density of rt given the set of information that is available at date t y 1. The maximum likelihood estimates may then be found by numerically maximising Eq. Ž3. with respect to the underlying structural parameters . Furthermore, since another by-product of the filter is the joint conditional probability Pr st , sty1 , . . . ,stym < Ft 4 , inferences about the unobserved regimes st 4 may be made on the basis of the filter probabilities Pr st s 1 < Ft ; ˆ4 , computed as Pr st s 1 < Ft ;ˆ 4 s
1
Ý
i1s0
1
...
Ý
i m s0
Pr st s 1,sty1 s i1 ,...,stym s i m < Ft ;ˆ 4
where ˆ stands for the maximum likelihood estimate of .
796
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
3. Macroeconomic fundamentals Many papers have explored the links between target zone credibility and macroeconomic fundamentals. Although these rely upon different theoretical approaches, there appears to be a consensus about the significant potential effects of macroeconomic variables on the credibility of a quasi-fixed exchange rate commitment.4 The theoretical justification for using the chosen variables in our analysis lies both with the speculative-attack and with the escape-clause explanations of exchange rate crises. The former considers the crises as a result of the pursuing of domestic policies incompatible with the exchange rate policy, while the latter incorporates the influence of different random shock on policy-makers incentives to devalue the domestic currency.5 Our goal is to investigate whether the empirical evidence is consistent with the speculative attack or the escape-clause explanation of the exchange rate crisis. If no empirical support for any of these alternative theories is found, the evidence could be interpreted as favouring the self-fulfilling explanation for the currency crises. Note, however, that our approach only provides indirect evidence on the empirical relevance of the latter hypothesis, and does not constitute a direct test of the type discussed, for instance, in Jeanne Ž1997., Jeanne and Masson Ž1997.. The variables considered in the analysis may be classified into the following two groups: Ža. Žb.
Real ¨ ariables: industrial production Ž IP .; trade balance ŽTB .; real exchange rate Ž REX .; unemployment rate ŽUN .. Monetary ¨ ariables: foreign reserves Ž RES .; change in real debt Ž DB .; growth rate of M1 Ž M1.; growth rate of M 2 Ž M 2.; differential between domestic and foreign rates of M1 expansion Ž M y M U .; domestic inflation rate Ž P .; inflation differential Ž P y P U .; deviations of nominal FFrDM exchange rate from EMS central parity Ž DEV ..
For the real variables IP and REX, we consider both their growth rates and an estimate of their cyclical component obtained by application of the popular Hodrick᎐Prescott ŽHP. filter with smoothing parameter equal to 14 400 Žsee Hodrick and Prescott, 1997.. The variables TB and UN are considered in their raw form as well as in deviation from the HP trend.
4
The links between target zone credibility and macrovariables, within the drift-adjustment approach, are considered in Caramazza Ž1993., Lindberg et al. Ž1993., Halikias Ž1994., Rose and Svensson Ž1994.and Thomas Ž1994.. For other approaches see Drazen and Masson Ž1994., Edin and Vredin Ž1993., Chen and Giovannini Ž1994., Tronzano Ž1994., Jeanne Ž1997., Masson Ž1995., Mizrach Ž1995., Siklos and Tarajos Ž1996., Jeanne and Masson Ž1998., Martinez-Peria Ž1998., Piard Ž1999., among others. 5 Blackburn and Sola Ž1993. provide a survey of the theoretical literature on speculative attacks. The strategic exchange rate policy literature is surveyed in Tronzano Ž1996., while the escape clause approach to currency crises is also discussed in Jeanne Ž1995..
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
797
The significance of the real variables Žchange in industrial production, trade balance, real exchange rate, unemployment rate. in the transition probabilities may be interpreted in terms of the escape-clause literature on exchange rate pegs.6 The significance, in the transition probability functions, of the rates of monetary expansion and the inflation rates Žboth in domestic and relative terms., and the change in real debt may, on the other hand, be interpreted in terms of the analyses asset-marketrspeculative-attack of exchange rate determination and currency crises.7 Regarding foreign reserves, we recognise that since the same pressures which would make a speculative attack more likely to occur would also force a country to loose reserves, one might argue that the latter should be considered endogenous and uninformative about the nature of the exchange rate crisis. Nevertheless, reserves, along with other variables, play a crucial role in the identification of the type of the speculative attack. If one found that, together with other monetary variables, reserves are significant predictors of a shift to a state of nature which is associated with a speculative attack, one could conclude that the attack was fundamentals-driven. If, on the other hand, reserves are not significant predictors, but real macroeconomic variables are, an escape-clause explanation of the crisis is more pertinent. Finally, if foreign reserves and the position of the exchange rate in the band are significant, but other monetary or real variables are not, one can conclude that the crisis was self-fulfilling. We also consider the deviations of the nominal exchange rate from the EMS central parity as a variable potentially influencing the credibility of the FFrDM target zone. Imperfectly credible target zone models, in which the interest rates differential is positively correlated with movements of the nominal exchange rate towards the upper Žweak. edge of the band ŽBertola and Caballero, 1992., find strong support both from casual observation of the EMS experience and from more rigorous statistical testing. Many realignments of the FFrDM parity have indeed taken place when the domestic currency was near the upper limit of its fluctuation band. Therefore, the. position of the FFrDM inside the band is regarded as being an important variable in influencing the probability of a realignment Žsee Caramazza, 1993; Thomas, 1994; Chen and Giovannini, 1994; Mizrach, 1995; Werner, 1995..8
6
According to this literature, although authorities can credibly commit to defending a given parity, the occurrence of negative real shocks can optimally induce them to devalue the domestic currency. These shocks typically affect aggregate domestic demand Žproxied here by a change in industrial production., the economy’s external position Žproxied by the trade balance ., or competitiveness Žreal exchange rate.. 7 According to the speculative attacks literature, an overly expansionary monetary policy, possibly induced by increasing fiscal imbalances, will eventually force the collapse of a fixed exchange rate system. 8 The interpretation of empirical findings associated to this variable requires, however, proper qualifications, since the position of the exchange rate within the hand has sometimes been used as an auxiliary instrument of monetary policy.
798
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
Table 1 Granger-causality tests a Variable
F-statistic
IP ŽG. IP ŽHP. TB ŽG. TB ŽHP. REX ŽG. REX ŽHP. UN UN ŽHP. RES DB M1 M2 M y MU P P y PU DEV
1.235 Ž0.296. 0.108 Ž0.897. 0.241 Ž0.787. 0.323 Ž0.725. 0.175 Ž0.840. 1.708 Ž0.188. 0.517 Ž0.598. 1.796 Ž0.172. 7.524 Ž0.001. 0.266 Ž0.767. 0.776 Ž0.464. 1.057 Ž0.352. 0.619 Ž0.541. 1.088 Ž0.342. 0.083 Ž0.920. 4.043 Ž0.021.
a
All statistics are based on regressions with two lags of the interest rate differential and of the relevant macrovariable. The entries ŽG. and ŽHP. beside the name of a variable indicate growth rates and deviations from the HP trend, respectively. Numbers in parentheses are P-values.
4. Empirical findings and discussion This section presents the results of our analysis. We start by discussing the linear Granger-causality patterns between interest rates differential and the chosen macrovariables. The results from the Markov-switching models with a time-varying transition mechanism follow. Throughout we use monthly data covering the period from 1991:6 to 1998:9. 4.1. Granger-causality tests As a preliminary step in our analysis, we examine the predictive content of the real and monetary variables discussed in Section 3 for the interest rates differential. To do so, we employ the conventional test for Granger-causality in two-variable systems. The results of standard F-tests of the hypothesis that each of the macrovariables is Granger non-causal for the interest rates differential are summarised in Table 1 where and in the sequel, the entries Ž G . and Ž HP . beside the name of a variable indicate growth rates and deviations from the HP trend, respectivelyx. ln agreement with other findings in the literature, most of the macrovariables do not seem to be useful linear predictors, the only exceptions being foreign reserves and the deviations from central parity. However, it must be borne in mind that such tests are designed to detect linear relationships between variables. The
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
799
Table 2 Maximum likelihood estimation results for model 1᎐2 Žreal variables. a
␣0 ␣1 0 1 c0 c1 0 1 1 L QŽ20. Q2 Ž20.
␣0 ␣1 0 1 c0 c1 0 1 1 L QŽ20. Q2 Ž20.
IP ŽG.
TB
REX ŽG.
UN
0.321 Ž0.057. 1.259 Ž0.207. 0.171 Ž0.015. 1.267 Ž0.205. 3.966 Ž0.996. 2.392 Ž0.932. y0.765 Ž0.624. 0.343 Ž0.636. 0.620 Ž0.076.
0.319 Ž0.059. 1.263 Ž0.278. 0.171 Ž0.016. 1.269 Ž0.266. 3.486 Ž0.943. 2.021 Ž1.019. 0.010 Ž0.749. y0.064 Ž1.038. 0.619 Ž0.081.
0.322 Ž0.057. 1.258 Ž0.201. 0.170 Ž0.015. 1.266 Ž0.204. 11.22 Ž5.924. 2.969 Ž1.201. y8.761 Ž5.862. 1.185 Ž0.875. 0.621 Ž0.075.
0.139 Ž0.059. 1.263 Ž0.272. 0.171 Ž0.016. 1.269 Ž0.281. 0.274 Ž0.036. 5.951 Ž2.021. 0.281 Ž1.192. y0.349 Ž1.989. 0.619 Ž0.082.
51.99 3.412 0.645
51.12 4.005 0.641
IP ŽHP.
TB ŽHP.
REX ŽHP.
UN ŽHP.
0.321 Ž0.057. 1.254 Ž0.202. 0.170 Ž0.015. 1.268 Ž0.204. 5.406 Ž1.666. 3.846 Ž1.675. y1.395 Ž0.741. 0.931 Ž0.625. 0.621 Ž0.075.
1.734 Ž0.268. y1.378 Ž0.232. 1.276 Ž0.241. 0.286 Ž0.025. y0.169 Ž0,042. 2.890 Ž0.569. 0.466 Ž7.578. 0.001 Ž0.001. 0.675 Ž0.060.
0.322 Ž0.057. 1.259 Ž0.204. 0.170 Ž0.015. 1.267 Ž0.204. 3.930 Ž1.311. 1.317 Ž0.954. y2.307 Ž1.586. 1.252 Ž0.720. 0.625 Ž0.075.
0.321 Ž0.057. 1.248 Ž0.206. 0.170 Ž0.015. 1.272 Ž0.205. 4.847 Ž1.760. 2.062 Ž0.724. 1.703 Ž0.980. y0.111 Ž0.209. 0.619 Ž0.075.
54.79 3.139 0.341
52.25 10.42 8.186
58.45 2.185 0.904
55.79 7.742 1.764
51.35 3.712 0.664
54.26 8.364 0.724
a The entries ŽG. and ŽHP. beside the name of a variable indicate growth rates and deviations from the HP trend, respectively. Numbers in parentheses are asymptotic standard errors.
econometric framework employed in the sequel is undoubtedly more appropriate for the analysis of non-linear dynamics. 4.2. Marko¨ -switching models The results from fitting Eqs. Ž1. and Ž2. with m s 1 to the interest rates differential data are reported in Tables 2 and 3.9 We also give the outcome of tests 9
Maximum likelihood estimates were obtained using a quasi-Newton algorithm that approximates the Hessian according to the Broyden᎐Fletcher᎐Goldfarb᎐Shanno update computed from numerical derivatives. Asymptotic standard errors were calculated from the inverse of the outer-product-of-thegradient estimate of the information matrix.
800
Table 3 Maximum likelihood estimation results for model 1᎐2 Žmonetary variables. a
␣1 0 1 c0 c1
0 1 1
L QŽ20. Q2 Ž20. a
DB
M1
0.321 Ž0.057. 1.256 Ž0.208. 0.171 Ž0.015. 1.267 Ž0.205. y9.427 Ž4.159. 2.450 Ž1.016. 10.08 Ž5.001. y0.262 Ž1.495. 0.620 Ž0.076.
0.320 Ž0.058. 1.256 Ž0.224. 0.171 Ž0.016. 1.273 Ž0.207. 3.803 Ž0.979. 1.994 Ž0.752. y0.265 Ž0.416. 0.287 Ž0.275. 0.618 Ž0.077.
0.321 Ž0.059. 1.254 Ž0.275. 0.171 Ž0.016. 1.267 Ž0.281. 3.982 Ž1.567. 2.389 Ž1.204. 0.653 Ž1.347. y0.533 Ž0.807. 0.619 Ž0.079.
52.66 2.683 0.415
51.84 4.026 0.621
53.31 1.757 0.464
Numbers in parentheses are asymptotic standard errors.
M y MU
P
P y PU
DEV
0.321 Ž0.060. 1.254 Ž0.274. 0.171 Ž0.016. 1.267 Ž0.263. 3.811 Ž1.790. 2.413 Ž1.299. 1.113 Ž3.862. y0.814 Ž1.424. 0.619 Ž0.078.
0.321 Ž0.057. 1.257 Ž0.212. 0.171 Ž0.015. 1.265 Ž0.205. 5.151 Ž1.751. 2.227 Ž0.790. 1.053 Ž0.706. y0.588 Ž0.353. 0.620 Ž0.077.
0.320 Ž0.058. 1.261 Ž0.213. 0.171 Ž0.015. 1.268 Ž0.205. 4.927 Ž1.704. 1.737 Ž0.801. y6.001 Ž4.842. 2.818 Ž4.108. 0.620 Ž0.076.
0.322 Ž0.058. 1.255 Ž0.278. 0.170 Ž0.015. 1.267 Ž0.263. 4.635 Ž2.352. 2.044 Ž1.020. y6.623 Ž4.389. y0.364 Ž4.773. 0.620 Ž0.080.
0.321 Ž0.057. 1.255 Ž0.207. 0.171 Ž0.015. 1.268 Ž0.205. 5.992 Ž1.790. 3.354 Ž1.638. y31.52 Ž14.77. y12.99 Ž13.79. 0.620 Ž0.075.
53.54 1.767 0.675
54.13 1.738 0.706
52.29 2.480 0.550
52.85 3.772 0.447
M2
53.87 2.259 0.300
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
␣0
RES
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
801
for linear and non-linear temporal dependence in the estimated residuals, based on the Ljung᎐Box portmanteau Q statistics for the first 20 autocorrelations of the standardised residuals and of their squares. These statistics, respectively denoted by QŽ20. and Q2 Ž20., have asymptotic 2 distributions with 20 d.f. under the null hypothesis of independence Žsee Ljung and Box, 1978; McLeod and Li, 1983.. To make the discussion easier, we label state 0 Žlow interest rates differential . as the credible state and state 1 Žhigh interest rates differential . as the non-credible state.10 4.2.1. Real ¨ ariables Table 2 gives the results for the case of the real variables, namely industrial production, the trade balance, the real exchange rate and the unemployment rate. As explained before, the use of these variables can be justified in terms of the escape-clause literature, which emphasises the influence of real shocks on policymakers decisions to quit the commitment to a fixed exchange rate parity. In contrast to studies that lend support to models underlining the relevance of real variables for the credibility of a fixed exchange rate policy Že.g. Caramazza, 1993; Chen and Giovannini, 1994; Isard, 1994; Thomas, 1994; Jeanne, 1997; Mizrach, 1995., we find all four real variables Žas well as their cyclical components. to have a statistically insignificant effect on the probability of remaining in a credible or non-credible regime. This is also reflected in plots of the estimated transition probabilities pt and qt Žnot shown. which display little variation over time. There appears, therefore, that there is little support in the data for escapeclause explanations of the French ERM crisis. 4.2.2. Monetary ¨ ariables Maximum likelihood estimates from Markov-switching models with monetary variables used as the forcing macrovariables are recorded in Table 3. The fitted models appear to be well identified, having parameters that are significant in most cases and standardised residuals which exhibit the signs of linear or non-linear temporal dependence. The maximum likelihood estimates provide no evidence that real debt, money expansion, inflation, or inflation differentials affect the transition probabilities, with both  0 and  1 being insignificantly different from zero for all six macrovariables Žrecall also that Granger non-causality was not rejected either for these variables.. In contrast, foreign reserves exert a significant influence on the state transition probabilities, an increase in reserves leading to an increased probability of remaining in a credible regime Ž  0 is significantly positive. Žcf. Caramazza, 1993; Chen and Giovannini, 1994; Spaventa, 1994; Thygesen, 1994; Tronzano, 1994..
10
It is worth noting that our results are robust with respect to different values of m. We prefer to work with the parsimonious first-order models since their residuals exhibit no sign of serial correlation.
802
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
More insights about the effects of reserves can be inferred from the plots shown in Fig. 1. The top panel of the figure gives the filter probability of being in a non-credible state at each date of the sample, while the lower panel shows the time-varying transition probabilities pt and qt along with a time plot of foreign reserves. The probability of remaining in a credible state Ž qt . displays much variability, with a sharp change occurring in the early months of 1995. It is also clear that decreases in reserves in 1993 and 1995 were both followed by a decreased probability of remaining in a credible regime, while the opposite is true for the increases in reserves that took place during the last 2 years of the sample. 4.2.3. De¨ iations from the EMS central parity We finally turn to the influence of nominal exchange, rate deviations from the official EMS central parity. The inclusion of this variable in the analysis is motivated by the consideration that realignments have often occurred with EMS currencies trading near the weak edge of their intervention bands. This variable is meant to capture intangible market sentiments about target zone credibility ŽCaramazza, 1993., possibly uncorrelated with standard macroeconomic fundamentals ŽThomas, 1994.. The effects of nominal exchange rate deviations are, however, particularly difficult to interpret, since their influence upon credibility is, in principle, largely indeterminate. If the band were fully credible, as in Krugman Ž1991., movements towards the upper limit Ži.e. positive deviations from the central parity. will prompt an expected exchange rate appreciation, thus producing a negative relationship with the nominal interest rates differential.11 On the other hand, models with imperfectly credible bands, as in Bertola and Caballero Ž1992., imply that positive deviations from the central parity will negatively affect credibility, giving rise to a positive correlation with the nominal interest rates differential. On purely empirical grounds, a similar dichotomy is implied by the existence of different periods in the EMS history. The early years have been characterised by an extreme turbulence, and huge bilateral exchange rate jumps Žfrequently preceding official EMS realignments.; in this context, it is quite natural to interpret large positive deviations from the central parity as anticipatory speculative build-ups, possibly leading to an official parity change. Conversely, between February 1987 and the September 1992 currency crisis, no further realignment took place, so that there is a widespread consensus that EMS credibility significantly increased along this period Žsee Bekaert and Gray, 1996.. The estimates in the last column of Table 3 suggest that a depreciation of the FFrDM exchange rate with respect to the EMS central parity decreases the probability of remaining in a credible state Ž  0 is significantly negative.. On the
11 Although this mean-reverting behaviour is consistent with EMS data, fully credible target zone models imply strong restrictions on the conditional distribution of exchange rate changes, which have largely been rejected Žsee Flood et al., 1991; Smith and Spencer, 1992..
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
Fig. 1. Estimated filter and transition probabilities.
803
804
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
other hand, movements of the exchange rate towards the weak edge of the French target zone do not exert any appreciable impact on the probability of staying in a non-credible regime. On the whole, our results suggest that the mere existence of a fluctuation band does not, per se, provide a solid anchor to stabilise private sector expectations. Fig. 2 plots the filter probabilities associated with the non-credible regime, as well as the time-varying transition probabilities, when nominal exchange rate deviations are the forcing macrovariable. The enlargement of the exchange rate band since August 1993 marks the beginning of a consistent credibility rebound, as signalled by a decrease in the probability of remaining in the credible regime Ž qt . . This trend, which is clearly associated with increased deviations from central parity, is soon reversed but is again interrupted during the early months of 1995 by renewed exchange rate pressures motivated by tensions on international financial markets and uncertainties stemming from the domestic political situation. It is also apparent from Fig. 2 that the French Franc has consistently been trading in the upper half of the exchange rate band.
5. Summary This paper analysed the 1992᎐1993 exchange rate crisis of the ERM using Markov regime-switching models with transition probabilities that are time-varying, depending on different driving macroeconomic variables. We employed this methodology to investigate whether monetary and real variables had any anticipatory signal about the crisis and whether changes in the expected devaluation, proxied by the interest rates differential, had been triggered by any of these variables. Using French monthly data for the period from 1991:6 to 1998:9, we found no evidence that real variables have played an important role. On the other hand, both linear Granger-causality tests and Markov-switching models reveal foreign exchange reserves and deviations of the exchange rate from the official EMS central parity to have significant predictive power for the increases in the expected devaluation. This evidence provides limited support for the standard speculative attack interpretation of the collapse of the target zone.
Acknowledgements We wish to thank John Driffill, Morten Ravn and an anonymous referee for helpful comments on an earlier version of the paper. We are also grateful to Sylviane Piard for her valuable suggestions and help with the data.
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
Fig. 2. Estimated filter and transition probabilities.
805
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
806
Appendix A: Data appendix
All data were extracted from DATASTREAM. The definitions of the series and the mnemonics are listed below.
DATASTREAM
IP: TB: REX: UN: RES: DB: M1: M 2: M y MU: P: r:
Industrial production index ŽFRI66..CE.. Visible trade balance ŽFRVISBALB.. Real effective exchange rate ŽFBI . . . REUF.. Unemployment rate ŽFRTOTUN%E.. Official reserves ŽFRRESERV.. Government debt ŽFRI88B . . . A.. Money supply M1 ŽFRM1RMNYB.. Money supply M2 ŽFRM2RMNYB.. M1 differential ŽFRM1RMNYB᎐BDOCM1MNB.. Log-difference of CPI ŽFRCP . . . F.. 1-month Euro-FrancrEuro-Marc differential ŽECFR1M᎐ECWGM1M..
References Bekaert, G., Gray, S.F., 1996. Target zones and exchange rates: an empirical investigation. NBER Working Paper no. 5445, Cambridge, Massachusetts. Bertola, G., Caballero, R.J., 1992. Tirget zones and realignments. Am. Econ. Rev. 82, 520᎐536. Bertola, G., Svensson, L.E.O, 1993. Stochastic devaluation risk and the empirical fit of target zone models. Rev. Econ. Stud. 60, 689᎐712. Blackburn, K., Sola, M., 1993. Speculative currency attacks and balance of payments crises. J. Econ. Surv. 7, 119᎐144. Caramazza, F., 1993. French᎐German interest rate differentials and time-varying realignment risk. IMF Staff Pap. 40, 567᎐583. Chen, Z., Giovannini, A., 1994. The credibility of adjustable parities: the experience of the European Monetary System. In: Kenen, P.B., Papadia, F., Saccomanni, F. ŽEds.., The International Monetary System, Chapter 7. Cambridge University Press, Cambridge. Diebold, F.X., Lee, J.H., Weinbach, G.C., 1994. Regime switching with time-varying transition probabilities. In: Hargreaves, C. ŽEd.., Nonstationary Time Series Analysis and Cointegration, Chapter 10. Oxford University Press, Oxford. Drazen, A., Masson, P.R., 1994. Credibility of policies versus credibility of policy-makers. Q. J. Econ. 109, 735᎐754. Edin, P.A., Vredin, A., 1993. Devaluation risk in target zones: evidence from the Nordic countries. Econ. J. 103, 161᎐175. Flood, R.P., Rose, A.K., Mathieson, D.J., 1991. An empirical exploration of exchange rate target zones. Carnegie᎐Rochester Conf. Ser. Publ. Policy 35, 7᎐65. Halikias, I., 1994. Testing the credibility of Belgium’s exchange rate policy. IMF Staff Pap. 41, 350᎐366. Hamilton, J.D., 1994. Time Series Analysis. Princeton University Press, Princeton. Hodrick, R.J., Prescott, E.C., 1997. Post-war U.S. business cycles: an empirical investigation. J. Money Credit Banking 29, 1᎐16. Isard, P., 1994. Realignment expectations, forward rate bias, and intervention in an optimizing model of exchange rate adjustment. IMF Staff Pap. 41, 435᎐459.
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
807
Jeanne, O., 1995. Models of Currency Crises: a Tentative Synthesis with Special Reference to the 1992᎐93 EMS Crises, mimeo. Ecole Nationale des Ponts et Chaussees-Ceras, Paris. ´ Jeanne, O., 1997. Are currency crises self-fulfilling? A test. J. Int. Econ. 43, 263᎐286. Jeanne, O., Masson, P., 1997. Was the French Franc Crisis a Sunspot Equilibrium? mimeo. Ecole Nationale des Ponts et Chaussees-Ceras, Paris. ´ Jeanne, O., Masson, P., 1998. Currency Crises, Sunspots and Markov-Switching Regimes, mimeo. Research Department, International Monetary Fund, Washington DC. Krugman, P., 1991. Target zones and exchange rate dynamics. Q. J. Econ. 106, 669᎐682. Lindberg, H., Soderlind, P., Svensson, L.E.O., 1993. Devaluation expectations: the Swedish Krona ¨ 1985᎐92. Econ. J. 103, 1170᎐1179. Ljung, G.M., Box, G.E.P., 1978. On a measure of lack of fit in time series models. Biometrika 65, 297᎐303. Martinez-Peria, M.S., 1998. A Regime Switching Approach to the Study of Speculative Attacks: a Focus on the EMS Crises, mimeo. Department of Economics, University of California at Berkeley. Masson, P.R., 1995. Gaining and losing credibility: the case of the United Kingdom. Econ. J. 105, 571᎐582. McLeod, A.I., Li, W.K., 1983. Diagnostic checking ARMA time series models using squared-residual autocorrelations. J. Time Ser. Anal. 4, 269᎐273. Mizrach, B., 1995. Target zone models with stochastic realignments: an econometric evaluation. J. Int. Money Financ. 14, 641᎐657. Piard, S., 1999. New Empirical Evidence on the French Currency Crises, mimeo, Department of Economics, London Guildhall University. Psaradakis, Z., Sola, M., 1998. Finite-sample properties of the maximum likelihood estimator in autoregressive models with Markov switching. J. Econom. 86, 369᎐386. Psaradakis, Z., Sola, S., 1999. Generated Regressors and Markov-Switching Models, mimeo, Department of Economics, Birkbeck College, University of London. Rose, A.K., Svensson, L.E.O., 1994. European exchange rate credibility before the fall. Eur. Econ. Rev. 38, 1185᎐1216. Siklos, P.L., Tarajos, R., 1996. Fundamentals and devaluation expectations in target zones: some new evidence from the ERM. Open Econ. Rev. 7, 35᎐59. Smith, G.W., Spencer, M.G., 1992. Estimation and testing in models of exchange rate target zones and process switching. In: Krugman, P., Miller, M. ŽEds.., Exchange Rate Targets and Currency Bands, Chapter 11. Cambridge University Press, Cambridge. Spaventa, L., 1994. Discussion. In: Kenen, P.B., Papadia, F., Saccomanni, F. ŽEds.., The International Monetary System. Cambridge University Press, Cambridge. Thomas, A.H., 1994. Expected devaluation and economic fundamentals. IMF Staff Pap. 41, 262᎐285. Thygesen, N., 1994. Discussion. In: Kenen, P.B., Papadia, F., Saccomanni, F. ŽEds.., The International Monetary System. Cambridge University Press, Cambridge. Tronzano, M., 1994. Assessing the credibility of a target zone: an alternative approach applied to France Ž1988᎐1993.. Discussion Paper no. 18r94. Department of Economies, Birkbeck College, University of London. Tronzano, M., 1996. Time Consistency of Macroeconomic Policy in an Open Economy: a Survey of the Theoretical Literature, mimeo, Department of Economics, Birkbeck College, University of London. Werner, A.M., 1995. Exchange rate, target zones, realignments and the interest rate differential: theory and evidence. J. Int. Econ. 39, 353᎐367.
Target zone credibility and economic fundamentals Marco Tronzano a , Zacharias Psaradakis b,U , Martin Solaa,c a b
Dipartimento di Economia e Metodi Quantitati¨ i, Uni¨ ersita ´ degli studi di Geno¨ a, Italy School of Economics, Mathematics and Statistics, Birkbeck College, 7᎐15 Gresse Street, London W1T 1LL, UK c Departamento de Economıa, ´ Uni¨ ersidad Torcuato Di Tella, Buenos Aires, Argentina
Accepted 15 April 2002
Abstract This paper investigates empirically the relationship between target zone credibility and economic fundamentals using French monthly data for the period 1991:6 to 1998:9. The econometric framework is one which allows expected devaluation Žproxied by the interest rates differential . to stochastically switch between a ‘high’ and a ‘low’ phase according to the outcome of a Markov process. The transition probabilities of the Markov process are assumed to vary over time as functions of various monetary and real macroeconomic variables. Our findings suggest that expected devaluation is significantly influenced by foreign reserves and the deviations of the exchange rate from the EMS central parity, whereas the effects of real variables are weak at best. 䊚 2002 Elsevier Science B.V. All rights reserved. JEL classifications: C22; F31 Keywords: Credibility; Regime-switching model; Target zone; Transition probabilities
U
Corresponding author. Tel.: q44-20-76316415; fax: q44-20-76316416. E-mail address: [email protected] ŽZ. Psaradakis..
0264-9993r03r$ - see front matter 䊚 2002 Elsevier Science B.V. All rights reserved. doi:10.1016rS0264-9993Ž02.00009-3
792
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
1. Introduction Since the last official realignment of the French FrancrDeutschemark ŽFFrDM. parity in January 1987, French inflation and interest rates exhibited a remarkable convergence towards the corresponding German rates. By mid-1991 convergence had been achieved, and the exchange rate mechanism ŽERM. of the European Monetary System ŽEMS. appeared to be successful in managing exchange rates. However, attacks on several currencies in 1992 led to the suspension of the Pound Sterling and the Italian Lira from the ERM and the widening of the target-zone bands of the remaining ERM currencies. As the crisis took place when the macroeconomic policies of most of the country members were regarded to be consistent with the exchange rate agreement, this raises the question of whether the speculative attacks were fundamentals-driven or simply self-fulfilling prophesies. The answer to the above question has important policy implications. Suppose, for instance, that speculative attacks can basically be explained in terms of economic policies inconsistent with the maintenance of a fixed parity, or in terms of large adverse macroeconomic shocks which may temporarily negatively affect policy-makers’ incentives to satisfy the above commitment. In this case, there might be some room to prevent further pressures on ‘weak’ currencies through policy measures that correct the main macroeconomic imbalances and promote faster convergence towards more ‘virtuous’ countries. If, conversely, exchange rate crises can mainly be ascribed to self-fulfilling elements, unrelated to market fundamentals, efforts towards a more rigorous stance in macroeconomic policies and increased convergence will ultimately prove futile, the only effective way to prevent further attacks being represented by the introduction of some measures of capital control. In this paper we investigate whether the ERM crisis can, for the case of France, be considered to be driven by economic fundamentals. In particular we examine whether expected devaluation of the FFrDM parity, proxied by the interest rates differential, can be explained by pressures in the real sector of the economy Žsee, e.g. Drazen and Masson, 1994. or by pressures in the monetary sector Žas in the traditional speculative attacks literature .. Since we are interested in crisis-type periods, we consider the French experience after convergence has been achieved, and we study episodes of temporary divergence of the interest rates.1 The relationship between expected devaluation and macroeconomic fundamentals is analysed within a non-linear econometric framework where the interest rates differential is a discontinuous function of macroeconomic variables Žcf. Bertola and Caballero, 1992.. In this context, it is assumed that the shifts between ‘high’ and ‘low’ expected devaluation are stochastic but autocorrelated, governed by a twostate Markov process. The transition probabilities of the latter are allowed to vary
1
The study of the convergence process itself requires a completely different framework of analysis and is beyond the scope of the present paper.
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
793
over time as functions of relevant macroeconomic variables. The effects of monetary variables Žtypically related to speculative attacks analyses . as well as real variables Žas in escape-clause approaches to currency crises. are examined. As mentioned before, the interest rates differential is used here as a proxy for the expected rate of devaluation. There is little doubt that such a proxy is far from perfect and the ‘drift adjustment’ method of Bertola and Svensson Ž1993. provides a more appropriate proxy for many applications.2 In our case, the drift-adjustment method gave results that are qualitatively similar to those obtained with the interest rates differential. This is not surprising since, in periods of high interest rates differentials, it is typically true that the differences between interest differentials and expected rates of realignment are not substantial Žcf. Jeanne and Masson, 1997.. Moreover, even if this is untrue during periods of low interest rates differentials, it is unlikely that the use of the latter proxy would lead to wrong separation of the regimes. In view of the similarity of the results obtained using the two alternative measures of credibility, and given the adverse effects that the use of a generated variable like the expected rate of realignment is likely to have on the finite-sample properties of estimators and test statistics for Markov-switching models Žsee Psaradakis and Sola, 1998, 1999., we decided to concentrate on the analysis of the dynamics of the interest rate differential. The remainder of the paper proceeds as follows. Section 2 describes the statistical models used to characterise the dynamics of interest rates differential. Section 3 discusses the macroeconomic variables considered in the analysis and their relation to the theoretical literature. Section 4 presents and discusses the estimation results of Markov-switching models with time-varying transition mechanisms, focusing on the information content of the various macrovariables. Section 5 summarises and concludes.
2. Econometric models and inference In this paper, the dynamics of the nominal interest rates differential Ž rt . between France and Germany are modelled using the following autoregressive specification: m
rt y Ž st . s
Ý j
rtyj y Ž styj . q Ž st . t ,
Ž t s 1,...,T .
Ž1.
js1
In Eq. Ž1., st is a random variable in 0, 14 that indicates the unobservable ‘state’ or ‘regime’ operative at date t, t 4 are independent and identically distributed random variables with zero mean and unit variance, and Ž⭈. and Ž⭈., respec-
2
This is certainly true when the focus of the analysis are the non-linear relationships between exchange rates and fundamentals implied by target zone models of exchange rate dynamics.
794
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
tively, represent a mean and standard deviation shift function. These functions are parameterised linearly as
Ž st . s ␣ 0 q ␣ 1 st and
Ž st . s 0 Ž 1 y st . q 1 st We normalise by defining state 1 to be the state with the higher mean Žachieved by setting ␣ 1 ) ␣ 0 .. It is further assumed that t 4 is independent of st 4 . Regarding the regime indicators st 4 , we assume that nature selects regime at date t with a probability that depends on what regime the process was in at date t y 1, and this probability varies over time as a function of some economic variableŽs.. Thus, following Diebold et al. Ž1994., the stochastic process st 4 is specified to be a non-homogeneous Markov chain with state space 0, 14 and transition mechanism: Pr st s 0 < sty1 s 0, z ty1 4 ' qt s exp Ž c 0 q  0 z ty1 . r w 1 q exp Ž c 0 q  0 z ty1 .x Pr st s 1 < sty1 s 1, z ty1 4 ' pt s exp Ž c1 q  1 z ty1 . r w 1 q exp Ž c1 q  1 z ty1 .x Pr st s 1 < sty1 s 0, z ty1 4 s 1 y qt
Ž2.
Pr st s 0 < sty1 s 1, z ty1 4 s 1 y pt where z t is a variable that affects the state transition probabilities. The model in Eqs. Ž1. and Ž2. extends the standard linear autoregressive specification by allowing the mean and conditional variance of rt to be functions of the Žstochastically chosen. regime that controls the process at date t. Since d ptrd z ty1 has the same sign as  1 ,  1 ) 0 Ž  1 - 0. implies that an increase in z ty1 increases Ždecreases. the probability of remaining in state 1. Similarly,  0 ) 0 Ž  0 - 0. implies that an increase in z ty1 will increase Ždecrease. the probability of remaining in state 0.3 An alternative specification for the transition mechanism governing st 4 replaces z ty1 in Eq. Ž2. by z t Žsee, e.g. Piard, 1999.. ln this case, however, z t needs to be strictly exogenous for the analysis to be correct. In addition to its implications for statistical inference, any violation of exogeneity in this framework makes the interpretation of results extremely problematic; after all, if z t and rt are jointly determined, one can hardly argue that z t helps to predict state transitions. Another important issue is the possible existence of feedback effects: whenever z ty1 cannot be considered exogenous, its effects on the transition probabilities may 3
The familiar Markov model with time-invariant transition mechanism may be obtained from Eqs. Ž1. and Ž2. by imposing the restriction  0 s  1 s 0.
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
795
arise because of induced changes in rty1. Therefore, in order to use this methodology to assess the forecasting ability of z ty1 , it is advisable to start with a general model for the transition mechanism and test whether rty1 has significant effects. In other words, Eq. Ž2. needs to be replaced by: Pr st s 0 < sty1 s 0, z ty1 ,rty1 4 s exp Ž c 0 q  0 z ty1 q d 0 rty1 . r w 1 q exp Ž c 0 q  0 z ty1 q d 0 rty1 .x Pr st s 1 < sty1 s 1, z ty1 ,rty1 4 s exp Ž c1 q  1 z ty1 q d1 rty1 . r w 1 q exp Ž c1 q  1 z ty1 q d1 rty1 .x Pr st s 1 < sty1 s 0, z ty1 ,rty1 4 s 1 y Pr st s 0 < sty1 s 0, z ty1 ,rty1 4 Pr st s 0 < sty1 s 1, z ty1 ,rty1 4 s 1 y Pr st s 1 < sty1 s 1, z ty1 ,rty1 4 This strategy was adopted in our empirical analysis but, since we found the coefficients d 0 and d1 to always be insignificantly different from zero for our data, we only report results obtained when the transition mechanism is specified as in Eq. Ž2.. Statistical inference in the context of a Markov-switching model like Eqs. Ž1. and Ž2. can proceed by making use of a variant of the non-linear filtering algorithm discussed in Hamilton Ž1994, §22.4.. This gives as a by-product the log-likelihood function T
L Ž . s
Ý
log f Ž rt < Fty1 ; .
Ž3.
tsmq1
where Ft s r 1 , z1 , . . . rt , z t 4 and f Ž rt < Fty1; . represents the conditional density of rt given the set of information that is available at date t y 1. The maximum likelihood estimates may then be found by numerically maximising Eq. Ž3. with respect to the underlying structural parameters . Furthermore, since another by-product of the filter is the joint conditional probability Pr st , sty1 , . . . ,stym < Ft 4 , inferences about the unobserved regimes st 4 may be made on the basis of the filter probabilities Pr st s 1 < Ft ; ˆ4 , computed as Pr st s 1 < Ft ;ˆ 4 s
1
Ý
i1s0
1
...
Ý
i m s0
Pr st s 1,sty1 s i1 ,...,stym s i m < Ft ;ˆ 4
where ˆ stands for the maximum likelihood estimate of .
796
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
3. Macroeconomic fundamentals Many papers have explored the links between target zone credibility and macroeconomic fundamentals. Although these rely upon different theoretical approaches, there appears to be a consensus about the significant potential effects of macroeconomic variables on the credibility of a quasi-fixed exchange rate commitment.4 The theoretical justification for using the chosen variables in our analysis lies both with the speculative-attack and with the escape-clause explanations of exchange rate crises. The former considers the crises as a result of the pursuing of domestic policies incompatible with the exchange rate policy, while the latter incorporates the influence of different random shock on policy-makers incentives to devalue the domestic currency.5 Our goal is to investigate whether the empirical evidence is consistent with the speculative attack or the escape-clause explanation of the exchange rate crisis. If no empirical support for any of these alternative theories is found, the evidence could be interpreted as favouring the self-fulfilling explanation for the currency crises. Note, however, that our approach only provides indirect evidence on the empirical relevance of the latter hypothesis, and does not constitute a direct test of the type discussed, for instance, in Jeanne Ž1997., Jeanne and Masson Ž1997.. The variables considered in the analysis may be classified into the following two groups: Ža. Žb.
Real ¨ ariables: industrial production Ž IP .; trade balance ŽTB .; real exchange rate Ž REX .; unemployment rate ŽUN .. Monetary ¨ ariables: foreign reserves Ž RES .; change in real debt Ž DB .; growth rate of M1 Ž M1.; growth rate of M 2 Ž M 2.; differential between domestic and foreign rates of M1 expansion Ž M y M U .; domestic inflation rate Ž P .; inflation differential Ž P y P U .; deviations of nominal FFrDM exchange rate from EMS central parity Ž DEV ..
For the real variables IP and REX, we consider both their growth rates and an estimate of their cyclical component obtained by application of the popular Hodrick᎐Prescott ŽHP. filter with smoothing parameter equal to 14 400 Žsee Hodrick and Prescott, 1997.. The variables TB and UN are considered in their raw form as well as in deviation from the HP trend.
4
The links between target zone credibility and macrovariables, within the drift-adjustment approach, are considered in Caramazza Ž1993., Lindberg et al. Ž1993., Halikias Ž1994., Rose and Svensson Ž1994.and Thomas Ž1994.. For other approaches see Drazen and Masson Ž1994., Edin and Vredin Ž1993., Chen and Giovannini Ž1994., Tronzano Ž1994., Jeanne Ž1997., Masson Ž1995., Mizrach Ž1995., Siklos and Tarajos Ž1996., Jeanne and Masson Ž1998., Martinez-Peria Ž1998., Piard Ž1999., among others. 5 Blackburn and Sola Ž1993. provide a survey of the theoretical literature on speculative attacks. The strategic exchange rate policy literature is surveyed in Tronzano Ž1996., while the escape clause approach to currency crises is also discussed in Jeanne Ž1995..
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
797
The significance of the real variables Žchange in industrial production, trade balance, real exchange rate, unemployment rate. in the transition probabilities may be interpreted in terms of the escape-clause literature on exchange rate pegs.6 The significance, in the transition probability functions, of the rates of monetary expansion and the inflation rates Žboth in domestic and relative terms., and the change in real debt may, on the other hand, be interpreted in terms of the analyses asset-marketrspeculative-attack of exchange rate determination and currency crises.7 Regarding foreign reserves, we recognise that since the same pressures which would make a speculative attack more likely to occur would also force a country to loose reserves, one might argue that the latter should be considered endogenous and uninformative about the nature of the exchange rate crisis. Nevertheless, reserves, along with other variables, play a crucial role in the identification of the type of the speculative attack. If one found that, together with other monetary variables, reserves are significant predictors of a shift to a state of nature which is associated with a speculative attack, one could conclude that the attack was fundamentals-driven. If, on the other hand, reserves are not significant predictors, but real macroeconomic variables are, an escape-clause explanation of the crisis is more pertinent. Finally, if foreign reserves and the position of the exchange rate in the band are significant, but other monetary or real variables are not, one can conclude that the crisis was self-fulfilling. We also consider the deviations of the nominal exchange rate from the EMS central parity as a variable potentially influencing the credibility of the FFrDM target zone. Imperfectly credible target zone models, in which the interest rates differential is positively correlated with movements of the nominal exchange rate towards the upper Žweak. edge of the band ŽBertola and Caballero, 1992., find strong support both from casual observation of the EMS experience and from more rigorous statistical testing. Many realignments of the FFrDM parity have indeed taken place when the domestic currency was near the upper limit of its fluctuation band. Therefore, the. position of the FFrDM inside the band is regarded as being an important variable in influencing the probability of a realignment Žsee Caramazza, 1993; Thomas, 1994; Chen and Giovannini, 1994; Mizrach, 1995; Werner, 1995..8
6
According to this literature, although authorities can credibly commit to defending a given parity, the occurrence of negative real shocks can optimally induce them to devalue the domestic currency. These shocks typically affect aggregate domestic demand Žproxied here by a change in industrial production., the economy’s external position Žproxied by the trade balance ., or competitiveness Žreal exchange rate.. 7 According to the speculative attacks literature, an overly expansionary monetary policy, possibly induced by increasing fiscal imbalances, will eventually force the collapse of a fixed exchange rate system. 8 The interpretation of empirical findings associated to this variable requires, however, proper qualifications, since the position of the exchange rate within the hand has sometimes been used as an auxiliary instrument of monetary policy.
798
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
Table 1 Granger-causality tests a Variable
F-statistic
IP ŽG. IP ŽHP. TB ŽG. TB ŽHP. REX ŽG. REX ŽHP. UN UN ŽHP. RES DB M1 M2 M y MU P P y PU DEV
1.235 Ž0.296. 0.108 Ž0.897. 0.241 Ž0.787. 0.323 Ž0.725. 0.175 Ž0.840. 1.708 Ž0.188. 0.517 Ž0.598. 1.796 Ž0.172. 7.524 Ž0.001. 0.266 Ž0.767. 0.776 Ž0.464. 1.057 Ž0.352. 0.619 Ž0.541. 1.088 Ž0.342. 0.083 Ž0.920. 4.043 Ž0.021.
a
All statistics are based on regressions with two lags of the interest rate differential and of the relevant macrovariable. The entries ŽG. and ŽHP. beside the name of a variable indicate growth rates and deviations from the HP trend, respectively. Numbers in parentheses are P-values.
4. Empirical findings and discussion This section presents the results of our analysis. We start by discussing the linear Granger-causality patterns between interest rates differential and the chosen macrovariables. The results from the Markov-switching models with a time-varying transition mechanism follow. Throughout we use monthly data covering the period from 1991:6 to 1998:9. 4.1. Granger-causality tests As a preliminary step in our analysis, we examine the predictive content of the real and monetary variables discussed in Section 3 for the interest rates differential. To do so, we employ the conventional test for Granger-causality in two-variable systems. The results of standard F-tests of the hypothesis that each of the macrovariables is Granger non-causal for the interest rates differential are summarised in Table 1 where and in the sequel, the entries Ž G . and Ž HP . beside the name of a variable indicate growth rates and deviations from the HP trend, respectivelyx. ln agreement with other findings in the literature, most of the macrovariables do not seem to be useful linear predictors, the only exceptions being foreign reserves and the deviations from central parity. However, it must be borne in mind that such tests are designed to detect linear relationships between variables. The
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
799
Table 2 Maximum likelihood estimation results for model 1᎐2 Žreal variables. a
␣0 ␣1 0 1 c0 c1 0 1 1 L QŽ20. Q2 Ž20.
␣0 ␣1 0 1 c0 c1 0 1 1 L QŽ20. Q2 Ž20.
IP ŽG.
TB
REX ŽG.
UN
0.321 Ž0.057. 1.259 Ž0.207. 0.171 Ž0.015. 1.267 Ž0.205. 3.966 Ž0.996. 2.392 Ž0.932. y0.765 Ž0.624. 0.343 Ž0.636. 0.620 Ž0.076.
0.319 Ž0.059. 1.263 Ž0.278. 0.171 Ž0.016. 1.269 Ž0.266. 3.486 Ž0.943. 2.021 Ž1.019. 0.010 Ž0.749. y0.064 Ž1.038. 0.619 Ž0.081.
0.322 Ž0.057. 1.258 Ž0.201. 0.170 Ž0.015. 1.266 Ž0.204. 11.22 Ž5.924. 2.969 Ž1.201. y8.761 Ž5.862. 1.185 Ž0.875. 0.621 Ž0.075.
0.139 Ž0.059. 1.263 Ž0.272. 0.171 Ž0.016. 1.269 Ž0.281. 0.274 Ž0.036. 5.951 Ž2.021. 0.281 Ž1.192. y0.349 Ž1.989. 0.619 Ž0.082.
51.99 3.412 0.645
51.12 4.005 0.641
IP ŽHP.
TB ŽHP.
REX ŽHP.
UN ŽHP.
0.321 Ž0.057. 1.254 Ž0.202. 0.170 Ž0.015. 1.268 Ž0.204. 5.406 Ž1.666. 3.846 Ž1.675. y1.395 Ž0.741. 0.931 Ž0.625. 0.621 Ž0.075.
1.734 Ž0.268. y1.378 Ž0.232. 1.276 Ž0.241. 0.286 Ž0.025. y0.169 Ž0,042. 2.890 Ž0.569. 0.466 Ž7.578. 0.001 Ž0.001. 0.675 Ž0.060.
0.322 Ž0.057. 1.259 Ž0.204. 0.170 Ž0.015. 1.267 Ž0.204. 3.930 Ž1.311. 1.317 Ž0.954. y2.307 Ž1.586. 1.252 Ž0.720. 0.625 Ž0.075.
0.321 Ž0.057. 1.248 Ž0.206. 0.170 Ž0.015. 1.272 Ž0.205. 4.847 Ž1.760. 2.062 Ž0.724. 1.703 Ž0.980. y0.111 Ž0.209. 0.619 Ž0.075.
54.79 3.139 0.341
52.25 10.42 8.186
58.45 2.185 0.904
55.79 7.742 1.764
51.35 3.712 0.664
54.26 8.364 0.724
a The entries ŽG. and ŽHP. beside the name of a variable indicate growth rates and deviations from the HP trend, respectively. Numbers in parentheses are asymptotic standard errors.
econometric framework employed in the sequel is undoubtedly more appropriate for the analysis of non-linear dynamics. 4.2. Marko¨ -switching models The results from fitting Eqs. Ž1. and Ž2. with m s 1 to the interest rates differential data are reported in Tables 2 and 3.9 We also give the outcome of tests 9
Maximum likelihood estimates were obtained using a quasi-Newton algorithm that approximates the Hessian according to the Broyden᎐Fletcher᎐Goldfarb᎐Shanno update computed from numerical derivatives. Asymptotic standard errors were calculated from the inverse of the outer-product-of-thegradient estimate of the information matrix.
800
Table 3 Maximum likelihood estimation results for model 1᎐2 Žmonetary variables. a
␣1 0 1 c0 c1
0 1 1
L QŽ20. Q2 Ž20. a
DB
M1
0.321 Ž0.057. 1.256 Ž0.208. 0.171 Ž0.015. 1.267 Ž0.205. y9.427 Ž4.159. 2.450 Ž1.016. 10.08 Ž5.001. y0.262 Ž1.495. 0.620 Ž0.076.
0.320 Ž0.058. 1.256 Ž0.224. 0.171 Ž0.016. 1.273 Ž0.207. 3.803 Ž0.979. 1.994 Ž0.752. y0.265 Ž0.416. 0.287 Ž0.275. 0.618 Ž0.077.
0.321 Ž0.059. 1.254 Ž0.275. 0.171 Ž0.016. 1.267 Ž0.281. 3.982 Ž1.567. 2.389 Ž1.204. 0.653 Ž1.347. y0.533 Ž0.807. 0.619 Ž0.079.
52.66 2.683 0.415
51.84 4.026 0.621
53.31 1.757 0.464
Numbers in parentheses are asymptotic standard errors.
M y MU
P
P y PU
DEV
0.321 Ž0.060. 1.254 Ž0.274. 0.171 Ž0.016. 1.267 Ž0.263. 3.811 Ž1.790. 2.413 Ž1.299. 1.113 Ž3.862. y0.814 Ž1.424. 0.619 Ž0.078.
0.321 Ž0.057. 1.257 Ž0.212. 0.171 Ž0.015. 1.265 Ž0.205. 5.151 Ž1.751. 2.227 Ž0.790. 1.053 Ž0.706. y0.588 Ž0.353. 0.620 Ž0.077.
0.320 Ž0.058. 1.261 Ž0.213. 0.171 Ž0.015. 1.268 Ž0.205. 4.927 Ž1.704. 1.737 Ž0.801. y6.001 Ž4.842. 2.818 Ž4.108. 0.620 Ž0.076.
0.322 Ž0.058. 1.255 Ž0.278. 0.170 Ž0.015. 1.267 Ž0.263. 4.635 Ž2.352. 2.044 Ž1.020. y6.623 Ž4.389. y0.364 Ž4.773. 0.620 Ž0.080.
0.321 Ž0.057. 1.255 Ž0.207. 0.171 Ž0.015. 1.268 Ž0.205. 5.992 Ž1.790. 3.354 Ž1.638. y31.52 Ž14.77. y12.99 Ž13.79. 0.620 Ž0.075.
53.54 1.767 0.675
54.13 1.738 0.706
52.29 2.480 0.550
52.85 3.772 0.447
M2
53.87 2.259 0.300
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
␣0
RES
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
801
for linear and non-linear temporal dependence in the estimated residuals, based on the Ljung᎐Box portmanteau Q statistics for the first 20 autocorrelations of the standardised residuals and of their squares. These statistics, respectively denoted by QŽ20. and Q2 Ž20., have asymptotic 2 distributions with 20 d.f. under the null hypothesis of independence Žsee Ljung and Box, 1978; McLeod and Li, 1983.. To make the discussion easier, we label state 0 Žlow interest rates differential . as the credible state and state 1 Žhigh interest rates differential . as the non-credible state.10 4.2.1. Real ¨ ariables Table 2 gives the results for the case of the real variables, namely industrial production, the trade balance, the real exchange rate and the unemployment rate. As explained before, the use of these variables can be justified in terms of the escape-clause literature, which emphasises the influence of real shocks on policymakers decisions to quit the commitment to a fixed exchange rate parity. In contrast to studies that lend support to models underlining the relevance of real variables for the credibility of a fixed exchange rate policy Že.g. Caramazza, 1993; Chen and Giovannini, 1994; Isard, 1994; Thomas, 1994; Jeanne, 1997; Mizrach, 1995., we find all four real variables Žas well as their cyclical components. to have a statistically insignificant effect on the probability of remaining in a credible or non-credible regime. This is also reflected in plots of the estimated transition probabilities pt and qt Žnot shown. which display little variation over time. There appears, therefore, that there is little support in the data for escapeclause explanations of the French ERM crisis. 4.2.2. Monetary ¨ ariables Maximum likelihood estimates from Markov-switching models with monetary variables used as the forcing macrovariables are recorded in Table 3. The fitted models appear to be well identified, having parameters that are significant in most cases and standardised residuals which exhibit the signs of linear or non-linear temporal dependence. The maximum likelihood estimates provide no evidence that real debt, money expansion, inflation, or inflation differentials affect the transition probabilities, with both  0 and  1 being insignificantly different from zero for all six macrovariables Žrecall also that Granger non-causality was not rejected either for these variables.. In contrast, foreign reserves exert a significant influence on the state transition probabilities, an increase in reserves leading to an increased probability of remaining in a credible regime Ž  0 is significantly positive. Žcf. Caramazza, 1993; Chen and Giovannini, 1994; Spaventa, 1994; Thygesen, 1994; Tronzano, 1994..
10
It is worth noting that our results are robust with respect to different values of m. We prefer to work with the parsimonious first-order models since their residuals exhibit no sign of serial correlation.
802
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
More insights about the effects of reserves can be inferred from the plots shown in Fig. 1. The top panel of the figure gives the filter probability of being in a non-credible state at each date of the sample, while the lower panel shows the time-varying transition probabilities pt and qt along with a time plot of foreign reserves. The probability of remaining in a credible state Ž qt . displays much variability, with a sharp change occurring in the early months of 1995. It is also clear that decreases in reserves in 1993 and 1995 were both followed by a decreased probability of remaining in a credible regime, while the opposite is true for the increases in reserves that took place during the last 2 years of the sample. 4.2.3. De¨ iations from the EMS central parity We finally turn to the influence of nominal exchange, rate deviations from the official EMS central parity. The inclusion of this variable in the analysis is motivated by the consideration that realignments have often occurred with EMS currencies trading near the weak edge of their intervention bands. This variable is meant to capture intangible market sentiments about target zone credibility ŽCaramazza, 1993., possibly uncorrelated with standard macroeconomic fundamentals ŽThomas, 1994.. The effects of nominal exchange rate deviations are, however, particularly difficult to interpret, since their influence upon credibility is, in principle, largely indeterminate. If the band were fully credible, as in Krugman Ž1991., movements towards the upper limit Ži.e. positive deviations from the central parity. will prompt an expected exchange rate appreciation, thus producing a negative relationship with the nominal interest rates differential.11 On the other hand, models with imperfectly credible bands, as in Bertola and Caballero Ž1992., imply that positive deviations from the central parity will negatively affect credibility, giving rise to a positive correlation with the nominal interest rates differential. On purely empirical grounds, a similar dichotomy is implied by the existence of different periods in the EMS history. The early years have been characterised by an extreme turbulence, and huge bilateral exchange rate jumps Žfrequently preceding official EMS realignments.; in this context, it is quite natural to interpret large positive deviations from the central parity as anticipatory speculative build-ups, possibly leading to an official parity change. Conversely, between February 1987 and the September 1992 currency crisis, no further realignment took place, so that there is a widespread consensus that EMS credibility significantly increased along this period Žsee Bekaert and Gray, 1996.. The estimates in the last column of Table 3 suggest that a depreciation of the FFrDM exchange rate with respect to the EMS central parity decreases the probability of remaining in a credible state Ž  0 is significantly negative.. On the
11 Although this mean-reverting behaviour is consistent with EMS data, fully credible target zone models imply strong restrictions on the conditional distribution of exchange rate changes, which have largely been rejected Žsee Flood et al., 1991; Smith and Spencer, 1992..
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
Fig. 1. Estimated filter and transition probabilities.
803
804
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
other hand, movements of the exchange rate towards the weak edge of the French target zone do not exert any appreciable impact on the probability of staying in a non-credible regime. On the whole, our results suggest that the mere existence of a fluctuation band does not, per se, provide a solid anchor to stabilise private sector expectations. Fig. 2 plots the filter probabilities associated with the non-credible regime, as well as the time-varying transition probabilities, when nominal exchange rate deviations are the forcing macrovariable. The enlargement of the exchange rate band since August 1993 marks the beginning of a consistent credibility rebound, as signalled by a decrease in the probability of remaining in the credible regime Ž qt . . This trend, which is clearly associated with increased deviations from central parity, is soon reversed but is again interrupted during the early months of 1995 by renewed exchange rate pressures motivated by tensions on international financial markets and uncertainties stemming from the domestic political situation. It is also apparent from Fig. 2 that the French Franc has consistently been trading in the upper half of the exchange rate band.
5. Summary This paper analysed the 1992᎐1993 exchange rate crisis of the ERM using Markov regime-switching models with transition probabilities that are time-varying, depending on different driving macroeconomic variables. We employed this methodology to investigate whether monetary and real variables had any anticipatory signal about the crisis and whether changes in the expected devaluation, proxied by the interest rates differential, had been triggered by any of these variables. Using French monthly data for the period from 1991:6 to 1998:9, we found no evidence that real variables have played an important role. On the other hand, both linear Granger-causality tests and Markov-switching models reveal foreign exchange reserves and deviations of the exchange rate from the official EMS central parity to have significant predictive power for the increases in the expected devaluation. This evidence provides limited support for the standard speculative attack interpretation of the collapse of the target zone.
Acknowledgements We wish to thank John Driffill, Morten Ravn and an anonymous referee for helpful comments on an earlier version of the paper. We are also grateful to Sylviane Piard for her valuable suggestions and help with the data.
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
Fig. 2. Estimated filter and transition probabilities.
805
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
806
Appendix A: Data appendix
All data were extracted from DATASTREAM. The definitions of the series and the mnemonics are listed below.
DATASTREAM
IP: TB: REX: UN: RES: DB: M1: M 2: M y MU: P: r:
Industrial production index ŽFRI66..CE.. Visible trade balance ŽFRVISBALB.. Real effective exchange rate ŽFBI . . . REUF.. Unemployment rate ŽFRTOTUN%E.. Official reserves ŽFRRESERV.. Government debt ŽFRI88B . . . A.. Money supply M1 ŽFRM1RMNYB.. Money supply M2 ŽFRM2RMNYB.. M1 differential ŽFRM1RMNYB᎐BDOCM1MNB.. Log-difference of CPI ŽFRCP . . . F.. 1-month Euro-FrancrEuro-Marc differential ŽECFR1M᎐ECWGM1M..
References Bekaert, G., Gray, S.F., 1996. Target zones and exchange rates: an empirical investigation. NBER Working Paper no. 5445, Cambridge, Massachusetts. Bertola, G., Caballero, R.J., 1992. Tirget zones and realignments. Am. Econ. Rev. 82, 520᎐536. Bertola, G., Svensson, L.E.O, 1993. Stochastic devaluation risk and the empirical fit of target zone models. Rev. Econ. Stud. 60, 689᎐712. Blackburn, K., Sola, M., 1993. Speculative currency attacks and balance of payments crises. J. Econ. Surv. 7, 119᎐144. Caramazza, F., 1993. French᎐German interest rate differentials and time-varying realignment risk. IMF Staff Pap. 40, 567᎐583. Chen, Z., Giovannini, A., 1994. The credibility of adjustable parities: the experience of the European Monetary System. In: Kenen, P.B., Papadia, F., Saccomanni, F. ŽEds.., The International Monetary System, Chapter 7. Cambridge University Press, Cambridge. Diebold, F.X., Lee, J.H., Weinbach, G.C., 1994. Regime switching with time-varying transition probabilities. In: Hargreaves, C. ŽEd.., Nonstationary Time Series Analysis and Cointegration, Chapter 10. Oxford University Press, Oxford. Drazen, A., Masson, P.R., 1994. Credibility of policies versus credibility of policy-makers. Q. J. Econ. 109, 735᎐754. Edin, P.A., Vredin, A., 1993. Devaluation risk in target zones: evidence from the Nordic countries. Econ. J. 103, 161᎐175. Flood, R.P., Rose, A.K., Mathieson, D.J., 1991. An empirical exploration of exchange rate target zones. Carnegie᎐Rochester Conf. Ser. Publ. Policy 35, 7᎐65. Halikias, I., 1994. Testing the credibility of Belgium’s exchange rate policy. IMF Staff Pap. 41, 350᎐366. Hamilton, J.D., 1994. Time Series Analysis. Princeton University Press, Princeton. Hodrick, R.J., Prescott, E.C., 1997. Post-war U.S. business cycles: an empirical investigation. J. Money Credit Banking 29, 1᎐16. Isard, P., 1994. Realignment expectations, forward rate bias, and intervention in an optimizing model of exchange rate adjustment. IMF Staff Pap. 41, 435᎐459.
M. Tronzano et al. r Economic Modelling 20 (2003) 791᎐807
807
Jeanne, O., 1995. Models of Currency Crises: a Tentative Synthesis with Special Reference to the 1992᎐93 EMS Crises, mimeo. Ecole Nationale des Ponts et Chaussees-Ceras, Paris. ´ Jeanne, O., 1997. Are currency crises self-fulfilling? A test. J. Int. Econ. 43, 263᎐286. Jeanne, O., Masson, P., 1997. Was the French Franc Crisis a Sunspot Equilibrium? mimeo. Ecole Nationale des Ponts et Chaussees-Ceras, Paris. ´ Jeanne, O., Masson, P., 1998. Currency Crises, Sunspots and Markov-Switching Regimes, mimeo. Research Department, International Monetary Fund, Washington DC. Krugman, P., 1991. Target zones and exchange rate dynamics. Q. J. Econ. 106, 669᎐682. Lindberg, H., Soderlind, P., Svensson, L.E.O., 1993. Devaluation expectations: the Swedish Krona ¨ 1985᎐92. Econ. J. 103, 1170᎐1179. Ljung, G.M., Box, G.E.P., 1978. On a measure of lack of fit in time series models. Biometrika 65, 297᎐303. Martinez-Peria, M.S., 1998. A Regime Switching Approach to the Study of Speculative Attacks: a Focus on the EMS Crises, mimeo. Department of Economics, University of California at Berkeley. Masson, P.R., 1995. Gaining and losing credibility: the case of the United Kingdom. Econ. J. 105, 571᎐582. McLeod, A.I., Li, W.K., 1983. Diagnostic checking ARMA time series models using squared-residual autocorrelations. J. Time Ser. Anal. 4, 269᎐273. Mizrach, B., 1995. Target zone models with stochastic realignments: an econometric evaluation. J. Int. Money Financ. 14, 641᎐657. Piard, S., 1999. New Empirical Evidence on the French Currency Crises, mimeo, Department of Economics, London Guildhall University. Psaradakis, Z., Sola, M., 1998. Finite-sample properties of the maximum likelihood estimator in autoregressive models with Markov switching. J. Econom. 86, 369᎐386. Psaradakis, Z., Sola, S., 1999. Generated Regressors and Markov-Switching Models, mimeo, Department of Economics, Birkbeck College, University of London. Rose, A.K., Svensson, L.E.O., 1994. European exchange rate credibility before the fall. Eur. Econ. Rev. 38, 1185᎐1216. Siklos, P.L., Tarajos, R., 1996. Fundamentals and devaluation expectations in target zones: some new evidence from the ERM. Open Econ. Rev. 7, 35᎐59. Smith, G.W., Spencer, M.G., 1992. Estimation and testing in models of exchange rate target zones and process switching. In: Krugman, P., Miller, M. ŽEds.., Exchange Rate Targets and Currency Bands, Chapter 11. Cambridge University Press, Cambridge. Spaventa, L., 1994. Discussion. In: Kenen, P.B., Papadia, F., Saccomanni, F. ŽEds.., The International Monetary System. Cambridge University Press, Cambridge. Thomas, A.H., 1994. Expected devaluation and economic fundamentals. IMF Staff Pap. 41, 262᎐285. Thygesen, N., 1994. Discussion. In: Kenen, P.B., Papadia, F., Saccomanni, F. ŽEds.., The International Monetary System. Cambridge University Press, Cambridge. Tronzano, M., 1994. Assessing the credibility of a target zone: an alternative approach applied to France Ž1988᎐1993.. Discussion Paper no. 18r94. Department of Economies, Birkbeck College, University of London. Tronzano, M., 1996. Time Consistency of Macroeconomic Policy in an Open Economy: a Survey of the Theoretical Literature, mimeo, Department of Economics, Birkbeck College, University of London. Werner, A.M., 1995. Exchange rate, target zones, realignments and the interest rate differential: theory and evidence. J. Int. Econ. 39, 353᎐367.