Exchange Rates and Fundamentals: Evidence from Long‐Horizon Regression Tests*

This article considers the long‐run relationship between nominal exchange rates and fundamentals from a different perspective. We apply a long‐horizon regression approach proposed by Fisher and Seater (1993) and find evidence supporting the explanatory power of exchange rate models. In particular, the Taylor‐rule model outperforms other conventional models. We then use the inverse power function (IPF) proposed by Andrews (1989) to investigate the power of the Fisher–Seater test. The IPF analysis provides additional evidence supporting exchange rate models.     

Prewhitening Bias in HAC Estimation*

Heteroskedasticity and autocorrelation consistent (HAC) estimation commonly involves the use of prewhitening filters based on simple autoregressive models. In such applications, small sample bias in the estimation of autoregressive coefficients is transmitted to the recolouring filter, leading to HAC variance estimates that can be badly biased. The present paper provides an analysis of these issues using asymptotic expansions and simulations. The approach we recommend involves the use of recursive demeaning procedures that mitigate the effects of small‐sample autoregressive bias. Moreover, a commonly used restriction rule on the prewhitening estimates (that first‐order autoregressive coefficient estimates, or largest eigenvalues, >0.97 be replaced by 0.97) adversely interferes with the power of unit‐root and [ Kwiatkowski, Phillips, Schmidt and Shin (1992) Journal of Econometrics, Vol. 54, pp. 159–178] (KPSS) tests. We provide a new boundary condition rule that improves the size and power properties of these tests. Some illustrations of the effects of these adjustments on the size and power of KPSS testing are given. Using prewhitened HAC estimates and the new boundary condition rule, the KPSS test is consistent, in contrast to KPSS testing that uses conventional prewhitened HAC estimates [ Lee, J. S. (1996) Economics Letters, Vol. 51, pp. 131–137].     

The Impact of Short‐ and Long‐run Exchange Rate Uncertainty on Investment: A Panel Study of Industrial Countries*

We examine the relationship between aggregate investment and exchange rate uncertainty in the G7, using panel estimation and decomposition of volatility derived from the components generalized autoregressive conditionally heteroscedastic (GARCH) model. Our dynamic panel approach takes account of potential cross‐sectional heterogeneity, which can lead to bias in estimation. We find that for a poolable subsample of European countries, it is the transitory and not the permanent component of volatility which adversely affects investment. To the extent that short‐run uncertainty in the CGARCH model characterizes higher frequency shocks generated by volatile short‐term capital flows, these are most deleterious for investment.     

Further Evidence on PPP Adjustment Speeds: the Case of Effective Real Exchange Rates and the EMS*

Two different approaches intend to resolve the ‘puzzling’ slow convergence to purchasing power parity (PPP) reported in the literature [see Rogoff (1996) , Journal of Economic Literature, Vol. 34.] On the one hand, there are models that consider a non‐linear adjustment of real exchange rate to PPP induced by transaction costs. Such costs imply the presence of a certain transaction band where adjustment is too costly to be undertaken. On the other hand, there are models that relax the ‘classical’ PPP assumption of constant equilibrium real exchange rates. A prominent theory put together by Balassa (1964, Journal of Political Economy, Vol. 72) and Samuelson (1964 Review of Economics and Statistics, Vol. 46) , the BS effect, suggests that a non‐constant real exchange rate equilibrium is induced by different productivity growth rates between countries. This paper reconciles those two approaches by considering an exponential smooth transition‐in‐deviation non‐linear adjustment mechanism towards non‐constant equilibrium real exchange rates within the EMS (European Monetary System) and effective rates. The equilibrium is proxied, in a theoretically appealing manner, using deterministic trends and the relative price of non‐tradables to proxy for BS effects. The empirical results provide further support for the hypothesis that real exchange rates are well described by symmetric, nonlinear processes. Furthermore, the half‐life of shocks in such models is found to be dramatically shorter than that obtained in linear models.     

Weak Identification of Forward‐looking Models in Monetary Economics*

Recently, single‐equation estimation by the generalized method of moments (GMM) has become popular in the monetary economics literature, for estimating forward‐looking models with rational expectations. We discuss a method for analysing the empirical identification of such models that exploits their dynamic structure and the assumption of rational expectations. This allows us to judge the reliability of the resulting GMM estimation and inference and reveals the potential sources of weak identification. With reference to the New Keynesian Phillips curve of Galí and Gertler [Journal of Monetary Economics (1999) Vol. 44, 195] and the forward‐looking Taylor rules of Clarida, Galí and Gertler [Quarterly Journal of Economics (2000) Vol. 115, 147], we demonstrate that the usual ‘weak instruments’ problem can arise naturally, when the predictable variation in inflation is small relative to unpredictable future shocks (news). Hence, we conclude that those models are less reliably estimated over periods when inflation has been under effective policy control.     

Measuring Conditional Persistence in Nonlinear Time Series*

The persistence properties of economic time series have been a primary object of investigation in a variety of guises since the early days of econometrics. Recently, work on nonlinear modelling for time series has introduced the idea that persistence of a shock at a point in time may vary depending on the state of the process at that point in time. This article suggests investigating the persistence of processes conditioning on their history as a tool that may aid parametric nonlinear modelling. In particular, we suggest that examining the nonparametrically estimated derivatives of the conditional expectation of a variable with respect to its lag(s) may be a useful indicator of the variation in persistence with respect to its past history. We discuss in detail the implementation of the measure and present a Monte Carlo investigation. We further apply the persistence analysis to real exchange rates.     

GMM Estimation with Non‐causal Instruments*

This note provides a warning against careless use of the generalized method of moments (GMM) with time series data. We show that if time series follow non‐causal autoregressive processes, their lags are not valid instruments, and the GMM estimator is inconsistent. Moreover, endogeneity of the instruments may not be revealed by the J‐test of overidentifying restrictions that may be inconsistent and has, in general, low finite‐sample power. Our explicit results pertain to a simple linear regression, but they can easily be generalized. Our empirical results indicate that non‐causality is quite common among economic variables, making these problems highly relevant.     

The Yen Real Exchange Rate may be Stationary after all: Evidence from Non‐linear Unit‐root Tests*

The empirical literature that tests for purchasing power parity (PPP) by focusing on the stationarity of real exchange rates has so far provided, at best, mixed results. The behaviour of the yen real exchange rate has most stubbornly challenged the PPP hypothesis and deepened this puzzle. This paper contributes to this discussion by providing new evidence on the stationarity of bilateral yen real exchange rates. We employ a non‐linear version of the augmented Dickey–Fuller test, based on an exponentially smooth‐transition autoregressive model (ESTAR) that enhances the power of the tests against mean‐reverting non‐linear alternative hypotheses. Our results suggest that the bilateral yen real exchange rates against the other G7 and Asian currencies were mean reverting during the post‐Bretton Woods era. Thus, the real yen behaviour may not be so different after all but simply perceived to be so because of the use of a restrictive alternative hypothesis in previous tests.     

Exchange Rate Pass‐through to Trade Prices: The Role of Nonlinearities and Asymmetries*

A standard assumption in the empirical literature is that exchange rate pass‐through is both linear and symmetric. This study tests these assumptions for export and import prices in the G7 economies. It focuses on non‐linearities in the reaction of profit margins to exchange rate movements, which may arise from the presence of price rigidities and switching costs. Nonlinearities are characterized by augmenting a standard linear model with polynomial functions of the exchange rate and with interactive dummy variables. The results suggest that nonlinearities and especially asymmetries cannot be ignored, although their magnitude varies noticeably across countries.     

The Relative Price of Non‐traded Goods under Imperfect Competition*

We consider the role of imperfect competition in explaining the relative price of non‐traded to traded goods within the Balassa–Samuelson framework. Under imperfect competition in these two sectors, relative prices depend on both productivity and mark‐up differentials. We test this hypothesis using a panel of sectors for 12 OECD countries. The empirical evidence suggests that relative price movements are well explained by productivity and mark‐up differentials.     

General‐to‐Specific Model Selection Procedures for Structural Vector Autoregressions*

Structural vector autoregressive (SVAR) models have emerged as a dominant research strategy in empirical macroeconomics, but suffer from the large number of parameters employed and the resulting estimation uncertainty associated with their impulse responses. In this paper, we propose general‐to‐specific (Gets) model selection procedures to overcome these limitations. It is shown that single‐equation procedures are generally efficient for the reduction of recursive SVAR models. The small‐sample properties of the proposed reduction procedure (as implemented using PcGets) are evaluated in a realistic Monte Carlo experiment. The impulse responses generated by the selected SVAR are found to be more precise and accurate than those of the unrestricted VAR. The proposed reduction strategy is then applied to the US monetary system considered by Christiano, Eichenbaum and Evans (Review of Economics and Statistics, Vol. 78, pp. 16–34, 1996) . The results are consistent with the Monte Carlo and question the validity of the impulse responses generated by the full system.     

Regression‐based Tests for a Change in Persistence*

We show that the minimal forward (reverse) recursive unit tests of Banerjee, Lumsdaine and Stock [Journal of Business and Economics Statistics (1992) Vol. 10, pp. 271–288] are consistent against the alternative of a change in persistence from I(0) to I(1) [I(1) to I(0)]. However, these statistics are also shown to diverge for series which are I(0) throughout. Consequently, a rejection by these tests does not necessarily imply a change in persistence. We propose a further test, based on the ratio of these statistics, which is consistent against changes either from I(0) to I(1), or vice versa, yet does not over‐reject against constant I(0) series. Consistent breakpoint estimators are proposed.     

Forecast Encompassing and Parameter Estimation*

A desirable property of a forecast is that it encompasses competing predictions, in the sense that the accuracy of the preferred forecast cannot be improved through linear combination with a rival prediction. In this paper, we investigate the impact of the uncertainty associated with estimating model parameters in‐sample on the encompassing properties of out‐of‐sample forecasts. Specifically, using examples of non‐nested econometric models, we show that forecasts from the true (but estimated) data generating process (DGP) do not encompass forecasts from competing mis‐specified models in general, particularly when the number of in‐sample observations is small. Following this result, we also examine the scope for achieving gains in accuracy by combining the forecasts from the DGP and mis‐specified models.     

Nonlinear models for strongly dependent processes with financial applications

This paper is motivated by recent evidence that many univariate economic and financial time series have both nonlinear and long memory characteristics. Hence, this paper considers a general nonlinear, smooth transition regime autoregression which is embedded within a strongly dependent, long memory process. A time domain MLE$MLE$ with simultaneous estimation of the long memory, linear AR$AR$ and nonlinear parameters is shown to have desirable asymptotic properties. The Bayesian and Hannan–Quinn information criteria are shown to provide consistent model selection procedures. The paper also considers an alternative two step estimator where the original time series is fractionally filtered from an initial semi-parametric estimate of the long memory parameter. Simulation evidence indicates that the time domain MLE$MLE$ is generally superior to the two step estimator. The paper also includes some applications of the methodology and estimation of a fractionally integrated, nonlinear autoregressive-ESTAR$ESTAR$ model to forward premium and real exchange rates.     

A Simple Panel‐CADF Test for Unit Roots*

In this paper, we propose a simple extension to the panel case of the covariate‐augmented Dickey–Fuller (CADF) test for unit roots developed in Hansen (1995) . The panel test we propose is based on a P values combination approach that takes into account cross‐section dependence. We show that the test has good size properties and gives power gains with respect to other popular panel approaches. An empirical application is carried out for illustration purposes on international data to test the purchasing power parity (PPP) hypothesis.     

Contemporaneous threshold autoregressive models: Estimation,testing and forecasting

This paper proposes a contemporaneous smooth transition threshold autoregressive model (C-STAR) as a modification of the smooth transition threshold autoregressive model surveyed in Teräsvirta [1998. Modelling economic relationships with smooth transition regressions. In: Ullah, A., Giles, D.E.A. (Eds.), Handbook of Applied Economic Statistics. Marcel Dekker, New York, pp. 507–552.], in which the regime weights depend on the ex ante probability that a latent regime-specific variable will exceed a threshold value. We argue that the contemporaneous model is well suited to rational expectations applications (and pricing exercises), in that it does not require the initial regimes to be predetermined. We investigate the properties of the model and evaluate its finite-sample maximum likelihood performance. We also propose a method to determine the number of regimes based on a modified Hansen [1992. The likelihood ratio test under nonstandard conditions: testing the Markov switching model of GNP. Journal of Applied Econometrics 7, S61–S82.] procedure. Furthermore, we construct multiple-step ahead forecasts and evaluate the forecasting performance of the model. Finally, an empirical application of the short term interest rate yield is presented and discussed.     

Variance Estimation for Generalized Entropy and Atkinson Inequality Indices: the Complex Survey Data Case*

We derive the sampling variances of generalized entropy and Atkinson indices when estimated from complex survey data, and show how they can be calculated straightforwardly using widely available software. We also show that, when the same approach is used to derive variance formulae for the independent and identically distributed case, it leads to estimators that are simpler than those proposed before. Both cases are illustrated with a comparison of income inequality in Britain and Germany.     

The Analysis of Seasonal Long Memory: The Case of Spanish Inflation*

This paper describes semiparametric techniques recently proposed for the analysis of seasonal or cyclical long memory and applies them to a monthly Spanish inflation series. One of the conclusions is that this series has long memory not only at the origin but also at some but not all seasonal frequencies, suggesting that the fractional difference operator (1−L¹²)^d should be avoided. Moreover, different persistent cycles are observed before and after the first oil crisis. Whereas the cycles seem stationary in the former period, we find evidence of a unit root after 1973, which implies that a shock has a permanent effect. Finally, it is shown how to compute the exact impulse responses and the coefficients in the autoregressive expansion of parametric seasonal long memory models. These two quantities are important to assess the impact of aleatory shocks such as those produced by a change of economic policy and for forecasting purposes, respectively.     

The ACR Model: A Multivariate Dynamic Mixture Autoregression*

This paper proposes and analyses the autoregressive conditional root (ACR) time‐series model. This multivariate dynamic mixture autoregression allows for non‐stationary epochs. It proves to be an appealing alternative to existing nonlinear models, e.g. the threshold autoregressive or Markov switching class of models, which are commonly used to describe nonlinear dynamics as implied by arbitrage in presence of transaction costs. Simple conditions on the parameters of the ACR process and its innovations are shown to imply geometric ergodicity, stationarity and existence of moments. Furthermore, consistency and asymptotic normality of the maximum likelihood estimators are established. An application to real exchange rate data illustrates the analysis.     

Regression Models with Data‐based Indicator Variables*

Ordinary least squares estimation of an impulse‐indicator coefficient is inconsistent, but its variance can be consistently estimated. Although the ratio of the inconsistent estimator to its standard error has a t‐distribution, that test is inconsistent: one solution is to form an index of indicators. We provide Monte Carlo evidence that including a plethora of indicators need not distort model selection, permitting the use of many dummies in a general‐to‐specific framework. Although White's (1980) heteroskedasticity test is incorrectly sized in that context, we suggest an easy alteration. Finally, a possible modification to impulse ‘intercept corrections’ is considered.