A Jump-diffusion Model for Exchange Rates in a Target Zone

We propose a simple jump-diffusion model for an exchange rate target zone. The model captures most stylized facts from the existing target zone models while remaining analytically tractable. The model is based on a modified two-limit version of the C OX , I NGERSOLL and R OSS (1985) model. In the model the exchange rate is kept within the band because the variance decreases as the exchange rate approaches the upper or lower limits of the band. We also consider an extension of the model with parity adjustments, which are modeled as Poisson jumps. Estimation of the model is by GMM based on conditional moments. We derive prices of currency options in our model, assuming that realignment jump risk is idiosyncratic. Throughout, we apply the theory to EMS exchange rate data. We show that, after the EMS crisis of 1993, currencies remain in an implicit target zone which is narrower than the officially announced target zones.     

The Theory of Exchange Rate Target Zones

The theory of exchange rate target zones focuses on the role of exchange rate expectations in determining exchange rate behaviour and interest rate differentials in currency bands. This paper analyses earlier models of the target zone research programme as well as more recent developments including endogenous realignment expectations, price rigidities and alternative monetary feedback rules by means of a unified approach. Target zones may be the cause of stabilizing or destabilizing exchange rate expectations, the determinants of which crucially depend on the within-band central bank policy as well as the credibility of the central banks' commitment to defend the target zone. The paper closes with a discussion of the relative merits of implementing a target zone and some suggestions for further research.     

An EMS target zone model in discrete time

The discrete time analogue of the continuous time Krugman target zone model is developed in order to capture the typical volatility clusters and fat-tailed distributed innovations of exchange rates. It is shown that under these more general stochastic conditions the S-shaped relation between exchange rate and fundamentals is preserved, but is less pronounced. The model is tested for its S-shape and stochastic properties. Two clearly distinct sets of EMS currencies are detected on the basis of the curvature features. One-step-ahead realignment probabilities are used as an alternative evaluation method. © 1998 John Wiley & Sons, Ltd.     

A univariate analysis of EMS exchange rates using a target zone model

The models in the literature on exchange-rate target zones imply a non-linear time series model for the exchange rate. We show how the parameters of such models can be estimated and develop Maximum Likelihood and Method of Simulated Moments estimators for the target zone model of Krugman (1991). The Maximum Likelihood estimator is based on a computationally attractive approximation to the exact predictive density of the continuous time model. Monte Carlo experiments are used to assess the properties of this estimator. In the empirical part we estimate the model with data on recent EMS exchange rates. We find that the Krugman (1991) target zone model is not able to explain the full observed kurtosis and conditional heteroscedasticity of the exchange-rate returns.     

EXCHANGE RATE TARGET ZONES: A SURVEY OF THE LITERATURE

This work selectively reviews the literature on exchange rate target zones and their theoretical and empirical methodologies and examines whether they can be used to clarify to what extent this type of exchange rate regime could contribute to greater exchange rate stability. We discuss the main contributions of the first and second generations of exchange rate target zone models. In an attempt to reconcile the poor empirical performance of the Krugman model with the reality of exchange rate target zone regimes, this line of research integrates target zones with alternative underlying economic models, such as imperfect credibility, intra‐marginal interventions and sticky price models. It was thus possible to understand the correlations observed between the exchange rate, its fundamentals determinants and the interest rate differential, and to explain the fact that the statistical distribution of the exchange rate is hump shaped rather than U shaped. This implies that the initial emphasis of target zone models on nonlinearities, ‘honeymoon effect’, ‘smooth pasting’ and marginal interventions has vanished. Exchange rate target zones are better described as similar to managed floating regimes with intra‐marginal interventions, with some marginal interventions when the exchange rate reaches the edges of the floating band.     

Why the Pound Should be Devalued Inside the ERM

I believe the choice of DM2.95 as a central rate for sterling's entry into the ERM was a major mistake of macroeconomic policy, on a par with monetary targeting and underestimatingtlle late 1980s' consumer-led boom. Indeed it was a belief that we were about to make this mistake that led me to undertake, with colleagues at the National Institute of Economic and Social Research, a detailed and unique study of the choice facing policy makers. I shall have more to say on that study below. Shortly after entry I wrote: "The danger is that the government will attempt to defend the present exchange rate bands at all costs. As a result it may produce, or fail to prevent, a recession on the same scale as 1980-81. (Wren-Lewis, 1990, emphasis added). I fear that much of this has come to pass, but we still have a chance to retrieve something.
To propose a devaluation of sterling within the ERM requires three distinct arguments. The first is that we entered the ERM at a real exchange rate which was above a level required to produce a sustainable current account of the balance of payments. The second is that this matters, and in particular that it has prevented the government from taking steps to counteract the recession. The third is that the gains in adjusting, through a realignment, to a lower rate now outweigh the loss of credibility that would be involved. I shall consider each point in turn.¹     

Managed Floating as a Monetary Policy Strategy

Although there seems to be a broad consensus among economists that purely floating or completely fixed exchange rates (the so-called corner solutions) are the only viable alternatives of exchange rate management, many countries do not behave according to this paradigm and adopt a strategy within the broad spectrum of exchange rate regimes that is limited by the two corner solutions. Many of these intermediate regimes are characterized by significant foreign exchange market interventions and a certain degree of exchange rate flexibility with non-preannounced exchange rate targets. While academic research in this area usually concentrates on some specific aspects of intermediate regimes (such as the effectiveness of interventions or institutional aspects), managed floating has rarely been analyzed as a comprehensive monetary policy strategy. In this paper, we present a monetary policy framework in which central banks simultaneously use the exchange rate and the interest rate as operating targets of monetary policy. We explain the mechanics of foreign exchange market interventions and sterilization and we explain why a central bank has an interest of controlling simultaneously the two operating targets. We derive the monetary policy rules for the two operating targets from a simple open economy macro model in which the uncovered interest parity condition and the monetary conditions index play a central role.     

Economic policies on Slovenia's road to the euro area

On 1 January 2007, Slovenia was the first new EU member state to enter the euro area. Since June 2004, the Slovenian tolar participated in the exchange rate mechanism ERM-II with a central parity of 239.64 against the euro. This parity was also the conversion rate upon euro area accession. Applying a macroeconometric model of Slovenia, this paper analyses the macroeconomic effects of different conversion rates. These simulations are compared to a scenario with flexible exchange rates. The best results are obtained with the actual conversion rate. In addition, it is shown that the labour market performance can be significantly improved by cutting non-wage labour costs.     

The credibility of the Colombian exchange rate target zone: Its impact over the volatility of interest rate differentials

This paper analyzes the credibility of Colombia’s exchange rate target zone, and in particular its impact on the volatility of interest rate differentials. Bertola and Caballeros’ (1995) model of a target zone with imperfect credibility is used to derive the impact of a reduction in credibility over the variance of the interest rate differential. It is theoretically shown, that as credibility decreases the variance of the interest rate differential increases. This theoretical argument is used to estimate credibility in Colombia’s exchange rate target zone. Using a SWARCH model, the probability of being in a regime with high interest rate volatility is estimated, and is related with events in the exchange rate market. Results suggest that there is evidence of lack of credibility even before the recent international financial turmoil was triggered.     

Estimation Bias and Inference in Overlapping Autoregressions: Implications for the Target‐Zone Literature*

Samples with overlapping observations are used for the study of uncovered interest rate parity, the predictability of long‐run stock returns and the credibility of exchange rate target zones. This paper quantifies the biases in parameter estimation and size distortions of hypothesis tests of overlapping linear and polynomial autoregressions, which have been used in target‐zone applications. We show that both estimation bias and size distortions of hypothesis tests are generally larger, if the amount of overlap is larger, the sample size is smaller, and autoregressive root of the data‐generating process is closer to unity. In particular, the estimates are biased in a way that makes it more likely that the predictions of the Bertola–Svensson model will be supported. Size distortions of various tests also turn out to be substantial even when using a heteroskedasticity and autocorrelation‐consistent covariance matrix.     

A statistical identity linking folded and censored distributions

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.     

Exchange Rate Policy: Is this where we came in?

In the second issue of Economic Outlook (April 1977) we published an article entitled "Why the exchange rate must be set free". In this Viewpoint we recall the arguments we presented then and consider their relevance to the present debate about exchange rate policy. We conclude that circumstances now are rather different from those in 1977 and that the choice between monetary targeting and exchange rate targeting is not as simple as it appeared then. Nevertheless we do believe that in the circumstances of recent month it was correct to let the exchange rate rise above its unofficial "ceiling" of DM3 rather than to pursue a specific exchange rate target.     

Forecast Summary

The outlook is conditioned by our assumption that sterling enters the ERM, probably in the autumn, at a central DM parity not very different from the current rate and that this exchange rate is held over the medium term. Fiscal and monetary policy have to be made consistent with a stable pound, which rules out tax cuts and restricts the fall in base rates to 12 per cent. The benefits of the ERM are to be seen in a reduction in the underlying rate of inflation to below 5 per cent by 1992. But ERM participation is not costless. The downside is four years of output growth averaging below 2 per cent and higher unemployment. The ERM offers the possibility of low inflation and steady growth in the second half of the 1990s: it is not a 'quick fix' for the current problems facing the UK economy.     

Bond market co-movements,expected inflation and the GBP-USD equilibrium real exchange rate

Since the end of the fixed rates in 1973 and after the European Monetary System (EMS) sterling dismissal in 1992, the value of the pound has undergone large cyclical fluctuations on average. Of particular interest to policy makers is the understanding of whether such movements are consistent with the lack or not of a correction mechanism to some long-run equilibrium. The purpose of the present study is to understand those dynamics, how the external value of the British sterling (GBP) relative to the US dollar (USD) evolved during the recent floating experiences, and what have been the driving forces. In this paper we assume the real exchange rate to be determined by forces relating to the goods and capital market in a general equilibrium framework. This entails testing the purchasing power parity (PPP) and the uncovered interest parity (UIP) together. In doing so, we model inflation expectations explicitly. Our findings have two important implications, both for monetary policy. First, we show that some of the observed changes in the bilateral real exchange rate cannot be solely attributed to changes in inflation rates, but, also to capital markets. Secondly, we find a weaker behavior of the US bond rate on international markets, possibly explained by the special US dollar status of World reserve currency.     

Money stock targeting and money supply: A closer examination of the data

In a recent paper Mercenier and Sekkat (1988) use a linear-quadratic model to examine the willingness of a monetary authority in a small open economy to target its exchange rate. Based on their empirical results, the authors conclude that the Bank of Canada has displayed a willingness to use the money supply to target the Canada—US exchange rate. We re-examine their empirical results using a different estimation approach and with different assumptions about the forcing process of the exogeneous variables. We also extend the sample period to include more recent observations. While we find some weak evidence to support their conclusion, the results, in general, suggest that a linear-quadratic model may not be a particularly useful representation of the assumed exchange rate targeting by a monetary authority.     

Forecast Summary

The forecast illustrates the costs and benefits of joining the ERM at the relatively high central parity of DM2.95. It shows that, providing the government does keep the pound within its wide 6 per cent EMS band, retail price inflation can be brought down to the average European level of 3 per cent by the mid 1990s. But there is a cost in terms of lower output and rising unemployment. GDP growth is expected to slow to about 1 1/2per cent this year and next and to average 2 per cent or slightly more from 1992 onwards. This is less than the rate of growth of productive potential and implies a weak labour market with unemployment rising steadily bock above 2 million. The forecast assumes a $25 oil price; in an alternative we sketch out the implications of a rise in the price to $45 for a limited period.     

Nonlinear adjustment,purchasing power parity and the role of nominal exchange rates and prices

Although the literature on purchasing power parity (PPP) is rich in controversy, the relative contribution of prices and nominal exchange rates to real exchange rate movements which restore PPP disequilibria has rarely been put under any close scrutiny. This paper as a first step applies a cointegrated VAR framework to test for stationary real exchange rates and linear adjustments in prices and nominal exchange rates. As a second step, ESTR error correction models are fitted to test whether nonlinear error correctional behaviour characterizes the data. The results clearly indicate that the nominal exchange rate is responsible for the nonlinear mean reverting behaviour in real exchange rates and also mainly drives overall adjustment. Applying dynamic stochastic simulations based on the estimated models, this study also confirms recent results that the half-life times of real exchange rate shocks are significantly smaller than the consensus benchmark of 3–5 years.     

An objective function for simulation based inference on exchange rate data

The assessment of models of financial market behaviour requires evaluation tools. When complexity hinders a direct estimation approach, e.g., for agent based microsimulation models, simulation based estimators might provide an alternative. In order to apply such techniques, an objective function is required, which should be based on robust statistics of the time series under consideration. Based on the identification of robust statistics of foreign exchange rate time series in previous research, an objective function is derived. This function takes into account stylized facts about the unconditional distribution of exchange rate returns and properties of the conditional distribution, in particular, autoregressive conditional heteroscedasticity and long memory. A bootstrap procedure is used to obtain an estimate of the variance-covariance matrix of the different moments included in the objective function, which is used as a base for the weighting matrix. Finally, the properties of the objective function are analyzed for two different agent based models of the foreign exchange market, a simple GARCH-model and a stochastic volatility model using the DM/US-$ exchange rate as a benchmark. It is also discussed how the results might be used for inference purposes. Research has been supported by the DFG grant WI 20024/2-1/2. We are indebted to two anonymous referees of this journal, Leigh Tesfatsion, Patrick Burns and other participants of the CEF’06 conference in Limassol for helpful comments on preliminary versions of this paper.     

Forecast Summary

Even if output recovers in the second quarter (as we expect), it looks as if there will be no increase in GDP this year in comparison with 1991. This reflects the weak start to the year, in which non-oil output registered its seventh successive quarterly decline. Through the year (fourth quarter to fourth quarter), however, we expect GDP to rise 1.5 per cent, laying the basis for a stronger recovery in 1993. Even so, it is not until late next year that output returns to its previous peak Paradoxically, we have raised our forecast of domestic demand from February (on a milder stock rundown) but imports are taking a disproportionate amount of the extra demand, holding back domestic output and aggravating the current account deficit. From nearly £9bn this year, we see the deficit rising to over £14bn by the middle of the decade, equivalent to 1³/4 per cent of GDP. While this is disappointing, it should be relatively easily financed even with lower interest rates providing the pound is held at its present DM 2.95 parity. we assume no ERM realignment which underpins a further drop in inflation to 4 per cent later this year and to 3-3 1/2 per cent by the mid 1990s. The weakness of output means that unemployment continues to rise for another 12 months, peaking in the middle of 1993 at three million, and that public sector finances will move still further into deficit - we project a PSBR this year of £30bn and a peak of £34bn in 1993-4, equivalent to 5 1/4 per cent of GDP.     

Carry-trades on the yen and the Swiss franc: are they different?

Using monthly data from 1986 to 2009 for 11 major currencies against the U.S. dollar (USD), we find that interest rate differentials between nine of these currencies are generally positive (sample mean of 0.86%) but are strongly negative for Japan (mean of ?2.78%) and for Switzerland (mean of ?2.22%). Investigating empirical models of nominal exchange rate changes we find for all panels that about 2% of real exchange rate misalignments are corrected in the following month. We also find important differences across samples and for the two carry-trade currencies the key results are as follows. First, interest rate differentials have a negative impact on exchange rates: higher paying currencies should appreciate, contrary to the ex-ante uncovered interest rate parity (UIP) condition. We find that this result is very robust to money supply (M1) differentials serving as instrumental variables to inflation rates. In addition, these two currencies depreciate slightly when money supply (M1) differentials increase. Second, dummy variables for periods of market turmoil suggest a particularly strong appreciation of these currencies against the USD, consistent with the unwinding of carry-trade activities.