Abstract: We study the behaviour of the exchange rate in a target zone in the case where a realignment may occur at the edges of the band. We show, in contrast to the previous result, that the stabilising property of the target zone may remain, even when the credibility is very low. Full text available here.
Abstract: We study the behaviour of the interest rate differential in a non-sustainable exchange rate target zone. We show that the relation between the interest rate differential and the fundamentals before the speculative attack is dependent on the expected post-attack monetary policy. Full text available here.
Abstract: This study tests Krugman's model on exchange rate target zones using four old EMS exchange rates (those of the currencies of Belgium, France, Italy and the Netherlands against the Deutsche mark). Although a vast theoretical literature is available, there are very few empirical studies testing the main results of Krugman's model, namely the honeymoon effect, smooth pasting, and the overall S-curved relationship between fundamental and exchange rate. The present study supports the honeymoon effect but does not find any evidence in support of smooth pasting, nor of an S-curved relationship between the exchange rate and fundamentals for the Belgian franc, French franc and Italian lira against the Deutsche mark. The Dutch guilder very closely follows movements in the Deutsche mark throughout the period 1981-90. End of month exchange rates and Euro-currency interest rates data are used.
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Abstract: This paper examines exchange rate determination in a target zone regime when the bounds can be fixed for an extended period but are subject to occasional jumps. In this case, the behaviour of the endogenous variable is affected by the agents' expectations about both the occurence and the size of the jump. Empirical results using data for the French franc / Deutsche mark exchange rate provide support for the nonlinear model with time-varying realignment probability and indicate that the agents correctly anticipated most of the observed changes in the central parity.
Abstract: This paper is concerned with the solution and estimation of a simple class of linear rational expectation (RE) models with current expectations of the endogenous variables when there a priori bounds on the dependent variable. We show that for plausible values of the parameters, the model has a unique RE solution. We first consider the exact maximum likelihood estimation of such a limited dependent rational expectation (LD-RE) model and perform a number of Monte Carlo experiments to shed light on the small sample properties of a number of alternative estimators. The results clearly illustrate the importance of taking proper account of the limited nature of the dependent variable and its expectations in the estimation of the parameters of the LD-RE models. We then extend the analysis to a 2-limit situation where the dependent variable is within a band, prove the existence and uniqueness of the RE equilibrium for this case, and present an empirical application to the Deutsche mark / French frank exchange rate within the ERM of the EMS.
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Abstract: This paper examines limited-dependent rational expectations (LD-RE) models containing future expectations of the dependent variable. Limited dependence is of a two-limit tobit variety which may, for example, arise as a result of a policy of imposing limits on the movement of the dependent variable by means of marginal as well as intramarginal interventions. We show that when the forcing variables are serially independent the model has an analytical solution which can be computed by backward recursion. With serially correlated forcing variables, we discuss an approximate solution method, as well as a numerically exact method that, in principle, can be implemented by stochastic simulation, although in practice it is limited by available computational capacity. The paper discusses some properties of the approximate solutions and reports the results of a limited number of Monte Carlo experiments in order to illustrate the computational feasibility of using the exact solution when the fundamentals are serially independent and the approximate solution when they are serially correlated.
Abstract: The purpose of this paper is to implement empirically a variant of the new theory of exchange rate targeting, suitable for high inflation small open economies. The theory formulates an expectations induced relationship between the exchange rate and the fundamental subject to random shocks and target zone constraints on rates of depreciation. The empirical analysis identifies the roles played by policy and market fundamentals in foreign exchange markets, and estimates the key parameters of the exchange rate dynamic equation.
Abstract: Existing empirical analyses of target zone models in EMS data are flawed. They fail to allow for the multilateral nature of EMS institutions. This paper outlines briefly the shortcomings of existing tests, focusing on the so-called fat-tailed distribution result.
Abstract: This book investigates the determinants of exchange rates and evaluates the main options for policy makers in limiting exchange rate fluctuations.
Abstract: The probabilities of realignments between the Danish krone and the Deutsche mark are investigated for the 1979 - 1995 period. Two multivariate systems are estimated. In the I(1) systems, the deviations from the cointegration relations are used as explanatory variables when determining the probabilities of exchange rate changes. It is found that real imbalances in the economy have to a large extent determined the probabilities of central parity changes. Furthermore, the probabilities of central parity changes have been significantly lower after 1983.
Abstract: The paper provides a continuous time model of the dynamic behaviour of exchange rates and interest rates when exchange rates are managed within a target zone with the possibility of realignments. In the case of a realignment, the exchange rate jumps to a shadow exchange rate. The timing of realignments is modeled by a Cox process with an intensity that depends on the location of the exchange rate in the target zone band as well as the distance to the shadow exchange rate. We set up an approximate maximum likelihood estimation approach and provide parameter estimates for six ERM target zones. Moreover, in the empirical analysis we filter out the shadow exchange rates and investigate which fundamental macroeconomic factors are able to explain the short run and long run behaviour of the filtered shadow exchange rates. Working paper available here.
Abstract: On Wednesday 16th September 1992, after a rise of two percentage points in interest rates and the announcement of a further three percentage point rise for the following day had failed to stem heavy selling pressure on sterling against the currencies of the ERM, sterling's membership of the ERM was suspended with no firm indication of a return date. This paper looks at the behaviour of interest rates and expected inflation implied by the prices of conventional and index linked government securities for a period of five weeks including that Wednesday. This allows us to judge the macroeconomic consequences of the shift in the exchange rate regime as implied by the behaviour of financial markets, and how those markets incorporate new information.
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Abstract: Realignment expectations which measure exchange rate credibility are analysed for European exchange rates, using daily financial data since the inception of the EMS. It is difficult to find economically meaningful relationships between realignment expectations and macroeconomic variables, although there are signs that lower inflation improves credibility. Statistically, many movements to realignment expectations are common to ERM participants. There were few indications of poor ERM credibility before late August 1992; the dimensions of the currency crisis of September 1992 appear to have taken both policy-makers and private agents largely by surprise.
Abstract: An empirical model of time-varying realignment risk in an exchange rate target zone is developed. Expected rates of devaluation are estimated as the difference between interest rate differentials and estimated expected rates of depreciation within the exchange rate band, using French franc / Deutsche mark data during the EMS. The behaviour of estimated expected rates of depreciation accord well with the theoretical model of Bertola-Svensson. We are also able to predict actual realignments with some success. (originally NBER Working Paper No. 3685, April 1991)
Abstract: This paper examines the recent credibility of the currencies participating in the ERM since 1987, focusing on sterling in 1992. It shows that there is little market evidence that sterling's credibility was in serious doubt until mid-September, 1992.
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Abstract: This paper uses a panel of data from 22 countries between 1967 and 1992 to explain exchange rate volatility, focusing on potential trade-offs between fixed exchange rates, independent monetary policy, and capital mobility. The author uses monetary models to parameterize monetary divergence and factor analysis to measure capital mobility. Exchange rate volatility is loosely linked to both monetary divergence and the degree of capital mobility. Interestingly, exchange rate volatility is significantly correlated with the width of the explicitly declared exchange rate band, even after taking monetary divergence and capital mobility into account.
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Abstract: In recent years, economic modelling has seen a significant shift from deterministic models to stochastic ones. Because of the prevalence of imperfect information and rational expectations, bounded and unbounded stochastic models now play an important role in both micro- and macro-economics, as well as the full ambit of financial models. This chapter illustrates how Mathematica can be used to model and simulate a variety of stochastic problems. Particular attention is focused upon exchange rate target zones and the theory of irreversible investment under uncertainty.
Abstract: This paper models expected future values of Gaussian stochastic processes that are bounded by reflecting barriers. Such expectations are of course crucial to any model with forward looking agents. The approach is illustrated by applying it to an exchange rate target zone. By adopting a distributional approach, the formal analysis can be both simple and somewhat elegant. In doing so, we show that the first moments of folded and censored distributions are related in a surprisingly neat way. The setting is discrete-time, though where appropriate, we extend the analysis to the continuous-time analogue of reflected Brownian motion.
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Abstract: This paper presents a model of exchange rate behaviour in a multilateral target zone. The model produces new economic insights beyond the well-known bilateral model of Krugman (1991), which is obtained as a special case. The paper also introduces a new class of stochastic processes in economics, namely multidimensional reflected diffusion processes. Two main features characterise the economics of exchange rates in a multilateral target zone. (i) The restrictions on interventions imposed by cross-currency constraints: when one country changes its money supply, say because its exchange rate with a second country has hit its band, all exchange rates involving the currency of that particular country will be affected, regardless of their position within their respective bands. (ii) Cooperation in sharing the intervention burden: in general, the exchange rate between any two countries will depend on the fundamentals of third countries in a multilateral target zone. This is because if the monetary authorities intervene together, a shock in the fundamentals of any country will induce a revision of the expectation of future interventions of other countries. The model reverts the counterfactual predictions of the bilateral model that the exchange rate steady-state density should be U-shaped and that its volatility should be a decreasing function of the distance of the exchange rate to the limits of its band. Thus, accounting for the multilateral feature of real-world target zones allows us to reconcile target zone models with the most salient empirical features of exchange rate behaviour.
Abstract: The presence of farm programmes should directly affect the expectations of producers. This paper analyses the formation of price expectations when price supports constitute an effective lower bound on the distribution of expectations. We first investigate what the expected price would be if the usual rational expectations formula is used. This leads to a relationship that is not estimable. We suggest two alternatives - one based on a tobit approximation and the other based on a perfect prediction of when the support is going to be effective. Using a simplified model of the US corn market, the methodology is demonstrated and compared to an alternative method of using futures prices as the expectation of harvest price.
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Abstract: Often, a policy authority may switch policy rules when an economic variable crosses a boundary. Many economic models suggest that agents' current behaviour might be affected by the anticipation of such a switch. This note studies the price of an asset which is a claim to a stream of payoffs which follow a Wiener process to an absorbing barrier.
Abstract: The gold - exchange standard in India 1893-1913 was characterised by a narrow target zone for the exchange rate, a wide annual range for the international interest-rate differential, and negative (seasonal) autocorrelation in interest rates. These properties are consistent with a standard target zone model in which fundamentals are negatively autocorrelated on a Markov chain.
Abstract: The decision on when to make an irreversible investment is considered as a trade-off between the instantaneous size of the net benefit and the time at which it is obtained. The benefit can be larger by waiting longer, but then it will also have to be more discounted. Smooth pasting arises as a first-order condition for maximum expected profit. The relationship to the standard approach is illustrated by a geometric Brownian price process. Full text available here.
Abstract: This paper is a selective survey of new or recent methods to extract information about market expectations from asset prices for monetary policy purposes. Traditionally, interest rates and forward exchange rates have been used to extract expected means of future interest rates, exchange rates and inflation. More recently, these methods have been refined to rely on implied forward interest rates, so as to extract expected future time-paths. Very recently, methods have been designed to extract not only the means but the whole (risk neutral) probability distribution from a set of option prices.
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Abstract: This paper presents a modified version of the Garman-Kohlhagen formula for pricing European currency options. The specific option pricing formula is derived in an economy where the evolvement of exchange rates display mean reverting behaviour. In specific, the dynamics of the logarithm of the exchange rate is modelled by an Ornstein-Uhlenbeck process. In order to find option prices, a continuous-time equilibrium set-up similar to the discrete-time scenario in Rubinstein (1976) is used. Domestic and foreign interest rates and their dynamics are determined endogenously in the equilibrium model. We obtain a closed form option pricing formula on the same form as the Garman-Kohlhagen / Black-Scholes formula except that the volatility as a function of time to maturity has a different functional form. This option pricing result suggests that in an economy with implicit target zones, the Garman-Kohlhagen formula will tend to overprice options with long maturities relatively to options with short maturities. The option pricing result in this paper is related to option pricing results in models that allow for stochastic interest rate behaviour. We show how the same option pricing result alternatively can be derived using the no-arbitrage approach used in Hilliard, Madura and Tucker taking the interest rate spread as exogenous to the model.
Abstract: One view of exchange rate realignments is that they undermine the credibility of a fixed exchange rate by creating expectations of further realignments. This paper presents an alternative model where the private sector attaches a higher probability to a realignment when there is spare capacity in the economy. The model shows that a realignment can enhance the credibility of the fixed rate by reducing the level of spare capacity. However, it is also shown that if realignment expectations are formed in this way, a fixed rate system may seriously destabilise the economy.
Abstract: The focus of academic discussions of exchange rate policy has shifted in recent years. The new literature on exchange rate regime choice emphasizes considerations relating to the problems of credibility in exchange rate targeting and the connections between exchange rate regime choices and choices of monetary and fiscal policy. Arguments for exchange rate targeting are reviewed. Under most circumstances and for most countries, a system of freely floating exchange rates is likely to be a better choice than attempting to peg the exchange rate.
Abstract: Many recent papers suggest that the basic flex-price target zone model does not perform well empirically. This paper investigates the testable implications of a sticky-price target zone model and finds that, to a limited extent, it has better empirical performance than the simplest flex-price model. However (in terms of nominal variables) the sticky-price model is found to be observationally equivalent to the flex-price model when the latter is extended to include intramarginal intervention and realignments.
Abstract: Recent papers have analysed the effects of Britain's return to gold in 1925. One line of argument has been that the return to gold was a state contingent regime switch. An alternative view is that it was time contingent. This paper shows that these approaches are not mutually exclusive. The solution for the exchange rate is derived in a model where a switch to a fixed rate takes place either when a state contingent trigger is reached or at a fixed time, whichever is the sooner. State contingent and time contingent elements are thus combined within the same model.
Abstract: An exchange rate target zone is analysed in a model where the economy is disturbed by shocks to money demand and goods demand. The stabilising properties of a target zone are compared to those of fixed and flexible exchange rate regimes. It is found that a target zone offers a compromise between these two extremes. It is also shown that, when there are shocks to both money and goods demand, a target zone is better than either a fixed rate or a floating rate in the sense that it minimises the variance of output and prices.
Abstract: Under the assumption of no arbitrage, the credibility of an exchange rate target zone is tested by whether domestic interest rates fall within "rate of return bands" between the maximum and minimum home currency rate of return on a foreign investment in the absence of a devaluation. Under the assumption of uncovered interest parity, credibility is tested by whether expected future exchange rates fall within the exchange rate band. These tests are applied to data on the Swedish target zone from January 1987 through August 1990.
Abstract: The term structure of interest rate differentials is derived in a model of a small open economy with a target zone exchange rate regime. For given time to maturity the interest rate differential is decreasing in the exchange rate, and for given exchange rate the interest rate differential's absolute value and its instantaneous variability are both decreasing in the time to maturity. Devaluation / realignment risks are incorporated and imply upward shifts of the interest rate differentials. Several implications of the theory are found to be broadly consistent with data on Swedish exchange rates and interest differentials for the period 1986-1989.
Abstract: For narrow exchange rate bands, and for reasonable parameter values, the interest rate differential's asymptotic (unconditional) variability is increasing in the width of the exchange rate band; whereas for wide exchange rate bands it is slowly decreasing in the exchange rate band. The interest rate differential's instantaneous (conditional) variability is decreasing in the width of the exchange rate band. A narrow target zone differs from a completely fixed exchange rate regime in that the interest rate differential's instantaneous standard deviation is high and even increases when the zone narrows.
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Abstract: The foreign exchange risk premium in an exchange rate target zone is derived, when the exchange rate is heteroskedastic within the band and there is a separate devaluation risk. The risk premium is then the sum of two separate risk premia, arising from uncertainty about exchange rate movements within the band and from uncertainty about devaluations. Both real and nominal risk premia are considered. Real and nominal risk premia from movements within the band are very small. Real and nominal risk premia from devaluations are larger but still relatively small proportions of the interest rate differential.
Abstract: This paper presents estimates of devaluation expectations for six ERM currencies relative to the Deutsche mark, for the period March 1979 - April 1992. Both the 'simplest test' and the 'drift adjustment' method are used. The simplest test adjusts interest rate differentials for the maximum and minimum expected rate of depreciation within the exchange rate band; the drift adjustment method adjusts interest rate differentials by the estimated expected rate of depreciation within the band. The latter method gives more precise estimates, especially for short horizons, and allows statistical inference and hypothesis testing. Expected rates of devaluation have generally fallen during the period. Still, some devaluation expectations relative to the Deutsche mark remain in 1992, except for the Belgian / Luxembourg franc and the Netherlands guilder. Expected rates of devaluation have fluctuated more than interest rate differentials.
Abstract: This paper discusses what I have learned from last year's currency crises in the ERM and the Nordic countries about fixed exchange rates as a means to achieve price stability. After discussing an explanation for the crises, the paper concludes that fixed exchange rates are not a shortcut to price stability. Monetary stability and credibility have to be built at home and cannot easily be imported from abroad. Fixed exchange rates are more fragile and difficult to maintain than previously thought. They may even be in conflict with price stability, by inducing a procyclical destabilising monetary policy, and by inducing an inflation bias. Building monetary credibility is even more important with flexible exchange rates.
Abstract: The paper argues that the reason real world fixed exchange rate regimes usually have finite bands, instead of completely fixed exchange rates between realignments, is that exchange rate bands, counter to the textbook result, give central banks some monetary independence, even with free international capital mobility. The nature and amount of monetary independence is specified, informally and in a formal model, and quantified with Swedish krona data. Altogether the amount of monetary independence appears sizeable. For instance, an increase in the Swedish krona band from zero to about 2 percent may reduce the krona interest rate's standard deviation by about a half.
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Abstract: This paper studies the credibility of a target zone considering the existence of heterogeneous expectations in the foreign exchange market. In general, we consider two types of agents: credible and non-credible agents (i.e. fundamentalists). One of the main results of the model is the possibility of collapse of a target zone as a function of expectations. This implies the existence of an endogenous realignment risk.
Abstract: The target zone model presented here encompasses a realignment probability that increases as the fundamental deviates from the centre of the band. The analysis is carried out for cases where the fundamental follows either a Brownian motion or an Ornstein-Uhlenbeck process. The simplest version of the model yields tractable results, which prove to be robust when its most restrictive assumption is relaxed. The solution obtained is dubbed the "steeper S", in accordance with its most relevant feature.
Abstract: A currency board arrangement (CBA) is supposed to be robust against attacks. Currency substitution complicates life, with controversial implications for floating versus fixed exchange rate regimes. After reporting evidence of currency substitution in Hong Kong, a monetary model incorporating currency substitution is used to estimate the shadow exchange rate and the probability of speculative attack on the Hong Kong dollar. A decomposition analysis of a Markov-switching model indicates that the no-attack regime was the most durable one. This implies that Hong Kong's quasi CBA was relatively robust against speculative attacks and currency substitution.
Abstract: The author presents an overview of exchange rate systems and exchange rate theories, grouping the various theories according to the time period for which their explanation is relevant.
Abstract: Weekly rates of the EMS vis-a-vis the Deutsche mark from April 1979 to March 1991 are modelled as a combined MA(1) - GARCH(1,1) jump process. The moving average part accounts for mean reversion required for the rates to stay inside the target zone. The generalised autoregressive conditional heteroskedasticity part accounts for changing volatility, whereas the jump process models parity changes and other erratic movements. Using an adjusted Pearson chi-squared goodness of fit test, we find similar results for the Bernoulli and the Poisson jump processes. In those cases in which the Bernoulli-normal distribution does not pass the goodness of fit test, a mixture of three normals does. Finally, the MA(1) - GARCH(1,1) Bernoulli jump models are jointly estimated assuming a constant contemporaneous correlation matrix for the disturbances and a common jump probability for all the currencies.
Abstract: The dynamics of weekly excess returns of an investment in a foreign currency against that in the Deutsche mark are studied for four EMS currencies. For most of the period 1979-1990, the interest differentials within the EMS have been higher than the realised depreciations relative to the Deutsche mark. Two explanations for the existence of excess returns are found. The first is uncertainty, measured by the conditional standard deviation, which is influenced to a large extent by the inflation differential. The second source is the continuously changing perceived realignment risk, which causes the returns to be negatively correlated and induces a positive relationship between the returns and the position of the spot rate in the fluctuation band.
Abstract: Discussion on previous article
Abstract: EU monetary integration was reinforced in the 1980s when macroeconomic convergence and a dominant role of the German Bundesbank created the basis for relatively stable exchange rates and increasing EU trade volumes. The analysis here focuses on the EMS crisis of 1992/93, the topic of optimum currency areas and the problem of fiscal policies and regional stabilisation in Europe, the US and Canada. This book gives an assessment of the EMS developments and shows how financial market liberalisation as well as the EU single market project affect the process of economic and monetary union. The role of currency substitution and problems of the Bundesbank's monetary policy control in a changing international system are evaluated.
Abstract: This paper looks at the effect on the exchange rate, in a target zone regime, of changing the width of the band. The main result of the paper is that the exchange rate moves in the same direction as the closest edge of the band does. This effect is stronger, the closer the exchange rate is to the edges of the band.
Abstract: This paper develops a target zone model for the exchange rate where the expected realignment is an increasing function of the distance of the exchange rate from the central parity, as a percentage of the width of the band. In this framework, the interest rate differential increases with the deviation of the exchange rate from the central parity when the exchange rate is close to the central parity, and it decreases when the exchange rate is close to the edges of the band. Finally, the paper looks at the evidence from the EMS, and finds partial support for the implications of the model.
Abstract: This paper studies the Mexican and Israeli experiences with a target zone. The first part of the paper develops a model of exchange rate determination under a target zone regime with stochastic realignments and examines the conditions under which the adoption of the target zone, instead of a fixed exchange rate, reduces the volatility of the interest rate differential. We conclude that, if the variance of the expected realignment is sufficiently large, then the target zone will be useful. The second part of the paper is an empirical study that shows that the target zone regime helped reduce interest rate variability in Israel and Mexico by absorbing part of the shocks to the expected realignment with movements of the exchange rate inside the band.
Abstract: The European Monetary System (EMS) has been credited with immediately enhancing the credibility of monetary policy among its member countries. However, there is little empirical evidence to support this view. This study provides evidence from exchange rate data that political actions taken to support the EMS enhanced credibility over time. Fiscal austerity programs undertaken in support of the EMS by many members were found to improve the credibility of the exchange rate arrangement. Further, empirical results were sensitive to the specification of the estimating equations, and varied dramatically if risk premia (discounts) were absent from estimating equations.
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Abstract: This paper discusses the choice of exchange rate regime. It is argued that in general floating is undesirable, because of the extreme weakness of the economic mechanism that holds the exchange rate close to a level consistent with the fundamentals. Of the alternatives, fixed rates can occasionally make sense, where several conditions are all satisfied. But under current conditions of high capital mobility the more prudent choice will in most cases be a system of limited flexibility, in the form of a 'crawling band' (a wide band that is adjusted in small steps so as to keep it in line with the fundamentals, but is defended in the traditional ways) or possibly a 'monitoring band' (a wide band with similar properties, which is defended only when the rate goes outside the band).
Abstract: This paper examines the (long-run) intra-zonal elasticities between the spot exchange rates of the Deutsche mark and other major ERM currencies (French franc, Belgian franc, Dutch guilder, Danish krone, Italian lira and British pound) under the EMS. The findings show that under the fixed-but-adjustable rate system, the hypothesis of no cointegration can be rejected for all chosen ERM currency pairs and unit restriction on zonal elasticities can be accepted for almost all cointegrated currency pairs. On the other hand, under the fixed-rate system, Danish krone, Italian lira and British pound fail the cointegration test and the zonal elasticities for all cointegrated currency pairs are rejected to be unity. The study signifies less intense linkages of the ERM currencies without parity realignments. Finally, the Deutsche mark took the role of error-correcting process for one cointegrated currency pair under the fixed-but-adjustable-rate system, and it performed the same role for two pairs under the fixed-rate system. Hence, Deutsche mark should not be assumed a priori statistically exogenous under the EMS.
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Abstract: This paper examines the role of an exchange rate target zone system in the presence of a persistent exchange rate misalignment caused by economic fundamentals such as 'fads', as compared to fixed rate and free floating systems. Output variations in each of the regimes and the relationship between the band width and variance of the shocks are also investigated.
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