Long memory and mean reversion in real exchange rates in Latin America

This article examines the long-run Purchasing Power Parity (PPP) hypothesis for 12 Latin American Real Effective Exchange Rates (REERs) using fractional integration techniques. The empirical results, applying parametric approaches, provide evidence of mean reversion in the REERs in the cases of Nicaragua, Belize, Costa Rica, Guyana and Paraguay and lack of it for the remaining seven countries. Employing semiparametric methods, the evidence of mean reversion covers the following countries: Belize, the Dominican Republic, Ecuador and Mexico. Thus, only for Belize and Guyana do we obtain consistent evidence of mean reversion in the real exchange rates. At the other extreme, lack of mean reversion, and thus, lack of PPP, is obtained with both methods in Bolivia, Brazil, Colombia and Venezuela. For the remaining six countries, the results are ambiguous. The results for the PPP theory in Belize and Guyana may show the importance of promoting policies based on exchange rate flexibility and economic liberalization to reach a long-run stability scenario that leads to greater international competitiveness and lower external vulnerability.     

Testing of the mean reversion parameter in continuous time models

In this paper we use the approximate bias expressions developed in Yu (2012) and Bao et al. (2013) to improve the testing of the ordinary least squares or quasi-maximum likelihood estimator of the mean reversion parameter in continuous time models. We follow the approach given in Iglesias and Phillips (2005) and Chambers (2013), where if we bias correct the estimated mean reversion parameter, we can improve on the small sample properties of the testing procedure. Simulation results confirm the usefulness of this approach using a t$t$-statistic in this setting in the near unit root situation when the mean reversion parameter is approaching its lower bound. Therefore we always recommend bias correcting when applying a t$t$-statistic in practice in this context.     

Generalized long memory and mean reversion of the real exchange rate

Definitive evidence regarding a rapid mean reversion of the real exchange rate is not present when using standard linear methodology, including unit root tests and fractional integration. To consider the robustness of these results, we use an encompassing model, the Gegenbauer AutoRegressive Moving Average (GARMA) model, which nests as special cases the existing linear methods. The GARMA model accommodates a complete notion of persistence and allows shocks to dissipate slowly in a cyclical manner. We find evidence supporting a weak version of purchasing power parity, where equilibrium errors are long memory with strongly persistent cycles. However, this new form of cyclical mean reversion is likely too slow to be economically meaningful. The inability to find a strong equilibrium attractor process, using a very general encompassing linear methodology provides support for the recent models that allow for a nonlinear attraction process and for shifting real exchange rate equilibria.     

Revisiting the mean reversion of inflation rates for 22 OECD countries

This study applies a flexible Fourier stationary test, proposed by Becker et al. (2006) to investigate the mean reversion of inflation in 22 OECD countries over the period of 1961 to 2011. While traditional unit root tests give us mixed results, empirical results from our flexible Fourier stationary test indicate that mean reversion of inflation holds in all 22 OECD countries. Our results have important policy implications for the 22 OECD countries under study.     

Parity reversion persistence in real exchange rates: middle income country case

This article investigates purchasing power parity (PPP) in the specific context of middle income countries. To circumvent the low power of traditional stationarity tests (Augmented Dickey-Fuller and Phillips-Perron tests), it performs variance ratio and fractional integration tests in addition to Perron's test that accounts for potential structural changes in real exchange rate processes. Beyond estimating half-life shocks to PPP, this article attempts to explain these estimates using a set of country specific variables as suggested by economic theory. The evidence suggests that reversion to parity tends to be faster in high inflation countries and that productivity improvement leads to a higher level of persistence. Openness to trade tends to reduce the extent of deviations from parity but this result does not appear to be statistically robust. Evidence shows also that deviations are less persistent under a fixed exchange rate regime and under unrestricted capital mobility.     

Mean reversion in target zones: a re-examination of some ERM exchange rates

The theoretical literature on exchange rate behaviour in target zones predicts that the exchange rate would be mean reverting. This article empirically investigates this theoretical prediction in the case of the German mark bilateral exchange rates. Using a recently developed unit root test, this article provides evidence that is generally negative to the idea of mean reversion. It shows that all bilateral exchange rates under investigation appear to be unit root processes with the exception of the Dutch guilder/German mark rate.     

Parity reversion in the Asian real exchange rates: new evidence from the local-persistent model

This article investigates the time-series properties of 13 Asian real exchange rates (RERs) vis-à-vis the US dollar. The half-life point estimates drawn from the local-persistent model are all less than 2 years, with a finite upper bound. There is no evidence to indicate that the Asian financial crisis has altered the speed of the purchasing power parity (PPP) adjustments. We find that the persistence of RERs over the last three decades remains unchanged in majority of the cases. Given the fairly rapid speed of adjustments and their corresponding confidence intervals, we conclude that the PPP puzzle does not exist in these countries.     

New tests for stationarity and parity reversion: Evidence on New Zealand real exchange rates

The present paper discusses the stochastic stationarity of New Zealand exchange rates in light of new time series methods and new tests. The question of whether the real exchange rates have a unit root or are mean reverting is set in the general framework of fractionally integrated models. The estimates sustain the claim that New Zealand real exchange series are not stationary. However, it is shown that nonstationarity is compatible with parity reversion in the framework of fractional unit-root models.     

Testing for random walk in euro exchange rates using the subsampling approach

This study utilizes variance ratio tests based on the subsampling approach to test the behaviour of euro-based exchange rates markets. Results are mixed, although the random walk behaviour is dominant among the three major currencies namely the Japanese yen, the US dollar and the British pound.     

Irreversibility,mean reversion,and investment timing

This paper examines the effect of irreversibility on investment under mean reversion. We develop a continuous-time model wherein a risk-neutral firm is endowed with a perpetual option to invest in a project at any time by incurring a fixed investment cost at that instant. The project, once undertaken, generates a stream of cash flows that are governed by a mean-reverting stochastic process. The firm is then allowed to liquidate its project at any time to partially recover the fixed investment cost. The recovery rate of the fixed investment cost inversely gauges the degree of irreversibility of investment. Using a real options approach, we derive an analytical solution to the value of the firm that is analogous with an American compound option. We show that greater irreversibility of investment induces the firm to raise its investment trigger, thereby deferring the undertaking of the project. We further show that greater irreversibility of investment has a detrimental effect that makes the firm less valuable.     

Using mean reversion as a measure of persistence

This paper suggests a new scalar measure of persistence together with a companion estimator, which has the advantage of not requiring the specification and estimation of a model for the series under investigation. The statistical properties of the companion estimator are established, which allow tests of hypotheses to be performed, under very general conditions. The use of the new measure is illustrated by re-evaluating persistence of inflation for the United States and the Euro Area. The conclusions for the United States do not differ significantly from what has been found in previous empirical studies. However, for the Euro Area we find evidence of a significant break occurring in 2001/2002, such that persistence becomes virtually nil for the period that follows the launch of the euro and the implementation of a common monetary policy by the European Central Bank.     

Growth and value hybrid valuation model based on mean reversion

This article proposes a novel valuation model, growth and value hybrid model, to estimate the stock price. This proposed model combines the essence of the asset-based approach, the income-based approach, and the principle of mean reversion to develop the theoretical closed-form formula consisting of three coefficients: value coefficient, value support coefficient and growth coefficient. Regression analysis is employed to fit market data to determine these coefficients. Moreover, this study proposes the double sorting method to build the quantile regression models of the formula to estimate the stock price at a specific quantile. The results show that the predictive capability of the hybrid valuation model is superior to the model without using value support coefficient, which supports the assumption that the PBR is not associated with the ROE when the ROE is less than a threshold. In different time periods of the stock market, no significant difference exists on the value support coefficient. However, the variations of the value coefficient and the growth coefficient are significant.     

Real exchange rates in emerging economies

We analyse the role of various investment margins in explaining the real exchange rate appreciation recorded in European transition countries. We present a model that introduces a quality investment margin and show that the margin is needed for replicating the observed pace of real exchange rate appreciation.     

Testing for the effect of current-account ‘news’ on exchange rates: A critique

Dornbusch (1980) has observed a correlation between unexpected exchange-rate changes and unexpected current account balances, which he interprets as evidence in favor of the ‘news’ hypothesis of exchange-rate determination. It is shown here that his test is flawed by simultaneity problem.     

On exchange rates and efficiency

Summary This paper analyzes an exchange economy in which several assets serve as stores of value and where agents have completely heterogeneous preferences and endowments. It describes the set of perfect foresight equilibria in which all assets have positive prices. There are international policies with determinate exchange rates if the world economy satisfies a strong efficiency criterion. Also, the corresponding equilibrium allocations are in the core of the world economy for certain international policies. Hence, a system of fixed exchange rates can support efficient allocations to the extent that countries agree on a division of seigniorage in the creation of international reserves.I would like to thank an annonymous referee, Suchan Chae, Mike Woodford, Ken Kasa, Helen Popper, Kathryn Marshall, and seminar participants at the University of Kansas, the Federal Reserve board, the 1990 meetings of the Western Economic Association, the University of Western Ontario, the University of Chicago, the University of Pennsylvania, Purdue University, and Victoria University of Wellington for comments on earlier drafts.     

Reverse shooting of exchange rates

Reverse shooting of the exchange rate has been put forward in this paper by scrutinizing the adjustment and evolution of the exchange rate towards its new long-run equilibrium level following a change in money supply. Joint and sequential effects of covered interest rate parity and the sticky price on the rise, from the short-term through the long-run horizon, results in a feature of reverse shooting of the exchange rate. Regardless of what the immediate response of the exchange rate to the change in money supply can be argued for, reverse shooting homogenizes the evolution path of exchange rate adjustment and movement from different views.     

Real exchange rates and competitiveness

This paper examines indicators of competitiveness. It analyses the conceptual foundations of conventional measures of the real exchange rate and finds that inferences about competitiveness from these indicators require strong, and in many cases implausible, assumptions. Based on this analysis some alternative measures are proposed and their use is illustrated using data from Europe. Given the usefulness of standardised indicators, four simple charts are proposed; these help solve some conundrums in the European data and provide the basis for a richer set of inferences about competitiveness.This paper has benefited from discussions with Bob Traa, from comments by Lars Svensson and many colleagues in the International Monetary Fund (IMF), and from the analysis inMarston (1986). The views expressed are those of the authors and should not be construed as representing the position of the IMF.     

Interest rates,exchange rates,and aggregate supply

The paper discusses fiscal policy incorporating interest-rate and exchange-rate effects on aggregate supply. It is shown how the familiar aggregate supply-aggregate demand framework can be used in the presence of endogenously determined interest rates and exchange rates.     

Threshold,smooth transition and mean reversion in inflation: New evidence from European countries

Knowing the absence or presence of a unit root in inflation is helpful not only in distinguishing between different economic hypotheses but is also important to monetary authorities in implementing the policies of disinflation. Using data for fourteen European countries, this study investigates the issue of nonstationarity in inflation by considering the possibility of nonlinearity. In particular, we consider the properties of a threshold, smooth transition and structural break in testing for a unit root in the inflation rates. By and large, the results support the view that the inflation rates of the European countries are characterized by a unit root process based on the conventional linear unit root tests. However, the results of the nonlinear unit root tests show that the inflation rates are characterized by nonlinear mean reversion after considering the nonlinear properties of the threshold, smooth transition and structural break. The mean reversion in inflation favors the hypothesis of, for example, the natural rate of inflation and the sticky-price model and implies that shocks only have transitory effects.     

Deviations and mean reversion to purchasing power parity in the Asian currency crisis of 1997

This study analyses the process of mean reversion towards purchasing power parity (PPP) for a sample of Asian countries around the 1997 crisis. It is found that appreciation relative to PPP is evident prior to the 1997 crash period. Correction occurs from 1997 onwards, a period marked by extreme movements in exchange rates with both appreciation and depreciation relative to the PPP rate over relatively short periods. The key result of this paper is that although reversion towards PPP is apparent for mean, though not statistically significant, it is clear that there is a substantial, statistically significant change in variance from 1997 onwards. This result has implications both for economic modelling of crash periods and for appropriate choice of statistical tests.