Regime-switching purchasing power parity in Latin America: Monte Carlo unit root tests with dynamic conditional score

We suggest a Monte Carlo simulation-based unit root test of the purchasing power parity theory for Latin American countries. Under the null hypothesis, we use a Markov regime-switching (MS) model with unit root in the conditional location and MS volatility dynamics. Under the alternative hypothesis, the proposed test incorporates Markov regime-switching autoregressive moving average (MS-ARMA) plus MS volatility dynamics. Under both the null and alternative hypotheses, one of the volatility models estimated is Beta-t-EGARCH, which is a recent dynamic conditional score volatility model. We use data on real effective exchange rate time series for 14 Latin American countries. For each country, we estimate by Monte Carlo simulation the critical values of the unit root test. We provide an economic discussion of the unit root test results and also study the robustness of MS-ARMA plus MS volatility with respect to smooth transition autoregressive models with Fourier function.     

Nonlinear Mean-Reversion in Real Exchange Rates: Toward a Solution To the Purchasing Power Parity Puzzles

We fit nonlinearly mean-reverting models to real dollar exchange rates over the post-Bretton Woods period, consistent with a theoretical literature on transactions costs in international arbitrage. The half lives of real exchange rate shocks, calculated through Monte Carlo integration, imply faster adjustment speeds than hitherto recorded. Monte Carlo simulations reconcile our results with the large empirical literature on unit roots in real exchange rates by showing that when the real exchange rate is nonlinearly mean reverting, standard univariate unit root tests have low power, while multivariate tests have much higher power to reject a false null hypothesis.     

Decomposing the persistence of real exchange rates

We propose a new methodology for decomposing the persistence of deviations from purchasing power parity (PPP). By directly comparing the impulse response function (IRF) of a vector autoregressive (VAR) model, where the real exchange rate is Granger caused by a set of candidate variables, with the IRF of the equivalent ARMA model for the real exchange rate, we capture the effects of the Granger-causing variables on the half-life of deviations from PPP. Our empirical results for a set of 20 industrial countries suggest that on average around 50% of the persistence of real exchange rates can be attributed to nominal interest rate differentials, inflation differentials and relative business cycle position with the numenaire country. Finally, we provide confidence intervals for the contributions of the aforementioned variables to the persistence of deviations from PPP by means of Monte Carlo simulations.     

Examining the evidence of purchasing power parity by recursive mean adjustment

This paper revisits the empirical evidence of purchasing power parity under the current float by recursive mean adjustment (RMA) proposed by So and Shin (1999). We first report superior power of the RMA-based unit root test in finite samples relative to the conventional augmented Dickey–Fuller (ADF) test via Monte Carlo experiments for 16 linear and nonlinear autoregressive data generating processes. We find that the more powerful RMA-based unit root test rejects the null hypothesis of a unit root for 16 out of 20 current float real exchange rates relative to the US dollar, while the ADF test rejects only 5 at the 10% significance level. We also find that the computationally simple RMA-based asymptotic confidence interval can provide useful information regarding the half-life of the real exchange rate.     

What do we know about real exchange rate nonlinearities?

Nonlinear modeling of adjustments to purchasing power parity has recently gained much attention. However, a huge body of the empirical literature applies ESTAR models and neglects the existence of other competing nonlinear models. Among these, the Markov Switching AR model has a strong substantiation in international finance. Our contribution to the literature is fivefold: First, ESTAR and MSAR models from a unit root perspective are compared. To this end, a new unit root test against MSAR is proposed as the second contribution. Thirdly, the case of misspecified alternatives in a Monte Carlo setup with real world parameter constellations is studied. The ESTAR unit root test is not indicative, while the MSAR unit test is robust. Fourthly, the case of correctly specified alternatives is considered and low power of the ESTAR but not for the MSAR unit root test is observed. Fifthly, an empirical application to real exchange rates suggests that they may indeed be explained by Markov Switching dynamics rather than ESTAR.     

Evolutionary game dynamics and distributed recency-weighted learning

This paper presents a relationship between evolutionary game dynamics and distributed recency-weighted Monte Carlo learning. After reviewing some existing theories of replicator dynamics and agent-based Monte Carlo learning, we provide proofs of the formulation-level equivalence between these two models. The relationship will be revealed not only from a theoretical viewpoint, but also by computational simulations of the models. As a consequence, macro dynamic patterns generated by distributed micro-decisions can be explained by parameters defined at an individual level. In particular, given the equivalent formulations, we investigate how the rate of agents’ recency weighting in learning affects the emergent evolutionary game dynamic patterns. An increase in this rate negatively affects the inertia, making the evolutionary stability condition more strict, and positively affecting the evolutionary speed toward equilibrium.JEL Classification: C63, C73Supervisions and advice given by Arthur J. Caplan have greatly contributed to this paper. I am also grateful to the anonymous reviewers for their valuable comments redirecting my presentation to a more appropriate one.     

A reappraisal of the evidence on PPP: a systematic investigation into MA roots in panel unit root tests and their implications

Panel unit root tests of real exchange rates—as opposed to univariate tests—usually reject non-stationarity. These tests, however, could be biased if the real exchange rate contained MA roots. Indeed, two independent arguments claim that the real exchange rate, being a sum of a stationary and a non-stationary component, is possibly an ARIMA (1, 1, 1) process. Monte Carlo simulations show how systematic changes in the parameters of the components, of the test equation and of the correlation matrix affect the size of first and second-generation panel unit root tests. Two components of the real exchange rate—the real exchange rate of a single good and a weighted sum of relative prices—are constructed from the data for a panel of countries. Computation of the relevant parameters reveals that panel unit root tests of the real exchange rate are severely oversized, usually much more so than simple augmented Dickey-Fuller tests. Thus, the evidence for purchasing power parity from first and second-generation panel unit root tests may be merely due to extreme size biases.     

The real exchange rate and the black market exchange rate in developing countries

This article tests for the validity of the Purchasing power parity (PPP) theory using both the black market and the official exchange rates for panels with cross sectional dependency. The test is conducted using a newly developed, nonlinear IV panel unit root test that properly handles cross-sectional dependency for thirty-seven developing countries. We find that the null of joint unit root hypothesis is rejected for the whole panel, using the black market exchange rate, and for sub-panels of African and high inflation countries, using either exchange rate. The black market-based real exchange rates are, therefore, shown to provide stronger evidence for the purchasing power parity theory than do the official rates. This finding is consistent with the observation that black market exchange rates better represent market forces and thus are more relevant when testing for the validity of the PPP theory in developing countries.     

Exchange rates dynamics revisited: a panel data test of the fractional integration order

We test the possibility that exchange rates from nine developed countries have a unit root against the alternate possibility that they are fractionally integrated. Theoretically, exchange rates are only expected to follow a random walk under restrictive assumptions. However, most traditional unit root tests cannot reject a unit root in exchange rates, and time series tests that allow for fractional integration have given inconclusive results. To increase the power of the test of the integration order we develop two panel data tests of the fractional integration order. Monte Carlo simulations show that these tests are correctly sized and have relatively high power compared to other similar tests. Moreover, our empirical results show that we can reject a unit root in exchange rates with a high probability, but the integration order is close to one. This indicates that exchange rates are mean-reverting, although the reversion is slow, resulting in long swings.     

Testing for a unit root with covariates against nonlinear alternatives

This paper proposes a new procedure for testing the unit root null against stationary but nonlinear alternatives. This test can be viewed as a generalization of the one developed by Kapetanios et al. (2003) (the KSS test) by incorporating stationary covariates. The asymptotic distribution of the test is derived and the asymptotic critical values are tabulated. A set of Monte Carlo simulations show that our test generally achieves large power improvements over the KSS test. An illustrated empirical application indicates that our proposed test is able to unveil more evidence than the KSS test in favor of no unit root of real exchange rates in 15 Asian countries.     

External debt and real exchange rates’ adjustment in the euro area: new evidence from a nonlinear NATREX model

In this article, we revisit medium- to long-run real exchange rate determination within the euro area, focusing on the role of external debt. Accordingly, we rely on the NATural Real EXchange rate (NATREX) approach which provides an explicit framework of the external debt–real exchange rates nexus. In particular, given the indebtedness levels reached by the euro area economies, we investigate potential nonlinearity in real exchange rates dynamics, according to the level of the external debt. Our results evidence that during the monetary union, gross and net external debt positions of the euro area countries have exerted pressures on real exchange rate dynamics within the area. Moreover, we find that, beyond a threshold reached by the external debt, euro area countries are found to be in a vulnerable position, leading to an unavoidable adjustment process. Nevertheless, the adjustment process, while effective, is found to be low and occurs slowly.     

GLS detrending-based unit root tests in nonlinear STAR and SETAR models

We extend GLS detrending procedure to testing for unit roots against STAR and SETAR alternatives. Monte Carlo simulations and applications to DM/Yen real exchange rates demonstrate that GLS detrending-based nonlinear unit root tests are more powerful than OLS detrending-based counterparts.     

A simple unit root test against asymmetric STAR nonlinearity with an application to real exchange rates in Nordic countries

Existing tests of the unit root hypothesis against the alternative hypothesis of exponential smooth transition autoregressive (ESTAR) nonlinearity implicitly assume symmetry under the alternative. This paper proposes a simple unit root test against the alternative of symmetric or asymmetric ESTAR nonlinearity. In the event that the unit root hypothesis is rejected, a simple test of symmetric versus asymmetric ESTAR nonlinearity is also proposed. The asymptotic distributions of the test statistics are straightforward to establish and finite-sample performance is studied with Monte Carlo simulations. An empirical application involving the real exchange rates of four Nordic countries against the U.S. dollar illustrates the usefulness of the new tests.     

Real exchange rates,economic performance,and trade balances in the central european free trade association

The relationships between real exchange rates dynamics, domestic economic growth, and external economic positions are examined for four East European countries: Poland, Hungary, Slovakia, and the Czech Republic. Results show that in Poland the dynamic of the trade balance is independent of both the real exchange rate and industrial production. In both Hungary and Slovakia, trade balances appear to have strong autonomous components, albeit in circumstances where the influence of real exchange rates and industrial production dynamics cannot be entirely denied. The Czech Republic's situation is, however, substantially different from its Central European Free Trade Assocation partners. The growing trade balance deficit appears to be determined by both the continuing real appreciation of the Czech currency and a mildly accelerating industrial production growth. Both are the consequence of accelerating capital inflow.     

Median-unbiased estimation of structural change models: an application to real exchange rate persistence

Measuring deviations from purchasing power parity has been the subject of extensive investigation. The most common practice in empirical research for measuring real exchange rate persistence is to estimate univariate autoregressive (AR) time series models and calculate the half-life, defined as the number of periods for a unit shock to a time series to decay by 50%. In the presence of structural change, there are two potential biases in the parameter estimates of AR models: (1) a downward small sample median-bias and (2) an upward bias, which occurs when structural change is present and ignored. We conduct a variety of Monte Carlo simulations and demonstrate that the existence of structural change causes a substantial increase in the small sample bias documented in Andrews (1993). We then propose an extension of median-unbiased estimation, which explicitly accounts for structural change, and apply these methods to estimate half-lives of several long-horizon real exchange rates analysed by Lothian and Taylor (1996) and Taylor (2002). The upward bias from neglecting structural change dominates the downward median-bias for these real exchange rates. When structural change is present and accounted for, the median-unbiased half-lives towards a changing mean decrease and the confidence intervals tighten.     

Quantile nonlinear unit root test with covariates and an application to the PPP hypothesis

In this article, we employ the methods initiated by Hansen (1995) to develop new quantile nonlinear unit root tests with covariates. The limiting distributions of our proposed tests are derived, which are dependent on nuisance parameter reflecting the correlation between the equation error and the covariates. To deal with this inferential difficulty, two alternative procedures based on either consistent estimate of the nuisance parameter or bootstrap implementation of the test are proposed. Monte Carlo simulations show that the proposed tests perform very well in finite samples and large power gains can be achieved by including correlated covariates in the testing equation. The proposed tests are applied to the PPP hypothesis. The empirical results indicate that the real exchange rates are not constant unit root processes.     

Threshold Dynamics of Short-term Interest Rates: Empirical Evidence and Implications for the Term Structure

This paper studies a nonlinear one-factor term structure model in discrete time. The short-term interest rate follows a self-exciting threshold autoregressive (SETAR) process that allows for shifts in the intercept and the variance. In comparison with a linear model, we find empirical evidence in favour of the threshold model for Germany and the US. Based on the estimated short-rate dynamics we derive the implied arbitrage-free term structure of interest rates. Since analytical solutions are not feasible, bond prices are computed by means of Monte Carlo integration. The resulting term structure captures stylized facts of the data. In particular, it implies a nonlinear relation between long rates and the short rate.     

The Target Zone Model, Non-Linearity and Mean Reversion: is the Honeymoon Really Over?

We estimate a target zone model for three ERM exchange rates for 1983–6 and 1987–91 by the method of simulated moments, taking account of the continuous time specification by using daily data with the interruptions of holidays and weekends. Specification tests are unable to reject the model. The estimates imply, however, an essentially linear relationship between the exchange rate and the fundamentals, with a very limited 'honeymoon effect'. Using Monte Carlo simulations, calibrated on the estimates, we find that standard tests for mean reversion of the exchange rate would largely reject the target zone model when, in fact, it held.     

Determinants of the real exchange rate in the long-run for developing and emerging countries: a theoretical and empirical approach

This paper presents a new framework for the determinants of real exchange in the long-run in developing and emerging countries (DECs). We assume that currencies should be regarded as an asset. In consequence, dealers in the foreign exchange market play a crucial role on its dynamics. To set our model, we connect the model developed by Kaltenbrunner, which is grounded on chapter 17 of the General Theory, with productivity’s differential effect. By doing so, it states that even short-run factors and monetary variables affect the long-run real exchange rate. Moreover, it points out that the hierarchical nature of the international monetary system is crucial to understand exchange rate movements in DECs. Besides presenting such theoretical approach, our contribution is to test it empirically for 45 DECs from 1990 to 2008 by applying econometric techniques appropriate for panel data. We use a new data-set, which comprises, among other variables, foreign portfolio flow, interest rate differential, external vulnerability measures, and international liquidity, on annual basis. The empirical results endorse this framework. Overall, it shows the primacy of financial factors as determinants of the long-run real exchange rate and points to the endogenous and self-perpetuating nature of international monetary system hierarchy.     

Fractionalization and long-run economic growth: webs and direction of association between the economic and the social -- South Africa as a time series case study

In this paper it is considered that the relationship between nominal exchange rate and prices depends on the nature of the shocks impacting the economy. In order to identify the sources of nominal exchange rate and relative price fluctuations we impose long-run restrictions on the dynamics of these variables through a 2-variable and 3-variable SVAR, respectively. This methodology is applied to data on the Spanish economy and find that supply and real demand shocks move nominal exchange rates and relative prices in opposite directions. Nominal shocks, however, move both variables in the same direction. Thus, in this case, only under nominal shocks may exchange rate depreciations fuel inflation.