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.     

Nonlinear adjustment in the real dollar–euro exchange rate: The role of the productivity differential as a fundamental

In this paper we analyze the influence of productivity differentials in the dynamics of the real dollar–euro exchange rate. Using nonlinear procedures for the estimation and testing of ESTAR models during the period 1970–2009 we find that the dollar–euro real exchange rate shows nonlinear mean reversion towards the fundamentals represented by the productivity differential. In addition, we provide evidence about the ability of this variable to capture the overvaluation and undervaluation of the dollar against the euro.     

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.     

Arbitrage costs and nonlinear adjustment in the G7 stock markets

This article aims to study stock price adjustments towards fundamentals due to the existence of arbitrage costs defined as the sum of transaction costs and a risky arbitrage premium associated with the uncertainty characterizing the fundamentals. Accordingly, it is shown that a two regime Smooth Transition Error Correction Model (STECM) is appropriate to reproduce the dynamics of stock price deviations from fundamentals in the G7 countries during the period 1969 to 2005. This model takes into account the interdependences or contagion effects between stock markets. Deviations appear to follow a quasi random walk in the central regime when prices are near fundamentals (i.e. when arbitrage costs are greater than expected arbitrage profits, the mean reversion mechanism is inactive), while they approach a white noise in the outer regimes (i.e. when arbitrage costs are lower than expected arbitrage profits, the mean reversion is active). Interestingly, as expected when arbitrage costs are heterogeneous, the estimated STECM shows that stock price adjustments are smooth and that the convergence speed depends on the size of the deviation. Finally, using two appropriate indicators proposed by Peel and Taylor (2000), both the magnitudes of under and overvaluation of stock price and the adjustment speed are calculated per date in the G7 countries. These indicators show that the dynamics of stock price adjustment are strongly dependent on both the date and the country under consideration.     

The Common Component in Forward Premiums: Evidence from the Asia–Pacific Region

We empirically analyze the behavior of the forward premium. Unlike previous research, we use data from Asia–Pacific countries and adopt a panel data approach that allows us to decompose the forward premium into common and idiosyncratic components. Our data suggest the presence of one common factor and the stationarity of both components for short maturities, leading to the conclusion of a stationary forward premium. In contrast, the stationarity of the premium is less supported by the longer maturity data. Furthermore, a large portion of the premium fluctuation is shown to be due to a common factor, particularly over the short time horizon, which in turn can be explained by economic developments in the USA.     

Non-linear cointegration and adjustment: an asymmetric exponential smooth-transition model for US interest rates

This paper seeks to extend the extant empirical evidence regarding asymmetric adjustment to equilibrium of short and long interest rates. Using an adaptation of the exponential smooth transition model to allow for sign asymmetry in the transition function, we show that equilibrium reversion exhibits two broad characteristics. First, small deviations are random, while large deviations are reverting. Second, deviations that arise when the long rate exceeds the short rate are characterised by quicker reversion than the opposite case. These results are consistent with the effects of arbitrage and central bank intervention. Finally, forecasting exercises support this model over alternate linear and non-linear specifications.      

Nonlinear adjustment to the mean reversion of consumption–income ratio

This study utilizes a flexible Fourier stationary test, proposed by Becker et al. (2006) to investigate the mean reversion of consumption–income ratio in 16 OECD countries from 1960 to 2010. Empirical results from our flexible nonlinear stationary test show that the mean reversion hypothesis is not rejected for 12 of the 16 OECD countries.     

The purchasing power parity puzzle is worse than you think

The ‘‘purchasing power parity puzzle’’ is the difficulty of reconciling very high short-term volatility of real exchange rates with very slow rates of mean reversion. The strongest evidence of slow mean reversion comes from least squares estimates of first-order autoregressive models of the long-horizon dollar-sterling real exchange rate. Using median-unbiased estimation methods, we show that these methods underestimate the half-lives of PPP deviations, and thus overestimate the speed of mean reversion. When the specification is amended to allow for serial correlation, the speed of mean reversion falls even further. This makes resolution of the purchasing power parity puzzle more problematic.First version received: May 2003/Final version received: July 2004We thank Lutz Kilian, James Lothian, Mark Taylor, and two anonymous referees for helpful comments and suggestions.     

A Theory of Exchange Rates and the Term Structure of Interest Rates

This paper defines the concepts of indirect and direct risk premium effects and analyzes their properties in an exchange rate model. In the model, these effects are endogenously determined in a rational expectations equilibrium. For the effect of an interest rate shock, they have the opposite signs and the indirect risk premium effect can dominate the direct risk premium effect under reasonable parameters. This means that domestic short‐term bonds and foreign bonds are complements in the model even though domestic long‐term bonds and foreign bonds are substitutes. This model, focusing on the indirect risk premium effect and on the term structure of interest rates, can be combined with a small sample bias approach to explain stylized facts about the forward premium anomaly, which is found for short‐term interest rates, but not for long‐term interest rates.     

Smooth transition,non-linearity and current account sustainability: Evidence from the European countries

In this paper we examine three types of nonlinearities, i.e., nonlinearity stemming from structural breaks, sign nonlinearity and size nonlinearity, for ten European countries and their importance to current account sustainability. For this purpose, we apply a battery of linear and nonlinear unit root tests. Our results show that the structural break nonlinearity and size nonlinearity are vital to the current account-GDP ratios of European countries in testing for the null hypothesis of a unit root. Nevertheless, the current account-GDP ratios of these countries do not exhibit the sign nonlinearity. That is, by taking account of the nonlinear trend, the threshold autoregressive and momentum threshold autoregressive models do not detect any asymmetry in the response of the current account imbalance to deviations from its long-run nonlinear trend.     

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.     

Some cautions on the use of nonlinear panel unit root tests: Evidence from a modified series-specific non-linear panel unit-root test

The purpose of this paper is to examine the relevance of applying nonlinear panel unit root test to examine the non-linear mean reversion behaviors of real exchange rates. We find that nonlinear panel unit root test may achieve lower power performance as compared to its alternative of linear panel unit test when the data generating process does not contain significant non-linear components. This finding post cautions to researchers in modeling and testing real exchanges behavior. We also develop a modified series-specific nonlinear panel unit root test and find evidence in favor of purchasing power parity hypothesis for China's four ASEAN trading partners in the period of February 1997 to August 2009.     

Asymmetry dynamics in real exchange rates: New results on East Asian currencies

This paper provides new evidence on the purchasing power parity (PPP) hypothesis in six East Asian countries. Based on nonlinear unit root tests, we discovered that the results are broadly consistent with the fact that real exchange rates (RERs) follow a nonlinear mean reversion process. We presented new evidence that the adjustment towards the PPP parity is asymmetric (LSTAR process) above and below the equilibrium value in all but one case — the Malaysian ringgit (MYR). The empirical results suggest that it is important that the conventional tests of PPP be amended to take account of asymmetries in the adjustment process in RERs.     

An Incomplete Markets Explanation of the Uncovered Interest Rate Parity Puzzle

A large literature attributes failure of uncovered interest rate parity (UIP) to the existence of a time‐varying risk premium. This paper presents a mechanism in a simple two‐country two‐good endowment economy with incomplete markets that generates sizeable deviations from UIP. In a parameterization where international wealth effects are important, liquidity constraints on an internationally traded bond and agents’ strong resulting precautionary motives successfully generates a time‐varying risk premium: countries that have accumulated large outstanding external positions have, being closer to the constraints, stronger precautionary motives and their asset carries a risk premium.     

Further evidence regarding nonlinear trend reversion of real GDP and the CPI

This paper examines whether the CPI and real GDP for the US exhibit nonlinear reversion to trend as recently concluded by Beechey and Österholm [Beechey, M. and Österholm, P., 2008. Revisiting the uncertain unit root in GDP and CPI: testing for nonlinear trend reversion. Economics Letters 100, 221-223]. The wild bootstrap is used to correct for non-normality and heteroscedasticity in a nonlinear unit root test. The use of ‘wild bootstrapped’ critical values affects test conclusions in some cases. Results also are sensitive to the sample period examined.     

Diverse beliefs and time variability of risk premia

Why do risk premia vary over time? We examine this problem theoretically and empirically by studying the effect of market belief on risk premia. Individual belief is taken as a fundamental primitive state variable. Market belief is observable; it is central to the empirical evaluation and we show how to measure it. Our asset pricing model is familiar from the noisy REE literature but we adapt it to an economy with diverse beliefs. We derive equilibrium asset prices and implied risk premium. Our approach permits a closed form solution of prices; hence we trace the exact effect of market belief on the time variability of asset prices and risk premia. We test empirically the theoretical conclusions. Our main result is that, above the effect of business cycles on risk premia, fluctuations in market belief have significant independent effect on the time variability of risk premia. We study the premia on long positions in Federal Funds Futures, 3- and 6-month Treasury Bills (T-Bills). The annual mean risk premium on holding such assets for 1?C12?months is about 40?C60 basis points and we find that, on average, the component of market belief in the risk premium exceeds 50% of the mean. Since time variability of market belief is large, this component frequently exceeds 50% of the mean premium. This component is larger the shorter is the holding period of an asset and it dominates the premium for very short holding returns of less than 2?months. As to the structure of the premium we show that when the market holds abnormally favorable belief about the future payoff of an asset the market views the long position as less risky hence the risk premium on that asset declines. More generally, periods of market optimism (i.e. ??bull?? markets) are shown to be periods when the market risk premium is low while in periods of pessimism (i.e. ??bear?? markets) the market??s risk premium is high. Fluctuations in risk premia are thus inversely related to the degree of market optimism about future prospects of asset payoffs. This effect is strong and economically very significant.     

Rethinking Long Memory and Structural Breaks in the Forward Premium

This paper documents new results that the ability of structural breaks to explain away non‐stationary long memory in the forward premium weakens considerably with higher‐frequency data. For daily data, removing structural breaks does not make non‐stationary long memory stationary, contrary to the evidence for monthly data reported in the recent literature. Simulating data on a daily basis, we show that using monthly data tends to overstate the importance of structural breaks, and obfuscate the true nature of persistence, in the forward premium. Our results thus corroborate earlier findings that long memory bears primary responsibility for the forward premium anomaly.     

Determinants of the premium in forward contracts

Whilst the benefits of forward contracting for goods and services have been extensively researched in terms of mitigating market power effects in spot markets, we analyse how the risk in spot price formation induces a counteracting premium in the contract prices. We consider and test a wide-ranging set of propositions, involving fundamental, behavioural, dynamic, market conduct and shock components, on a long data set from the most liquid of European electricity forward markets, the EEX. We show that part of what is conventionally regarded as the market price of risk in electricity is actually that of its underlying fuel commodity, gas; that market power has a double effect on prices, insofar as it increases spot prices and induces a forward premium; that oil price sentiment spills over and that the premium reacts to scarcity and the higher moments of spot price uncertainty. We observe that considerations of the scale and determinants of the forward premium are at least as important as the market power effects in spot market price formation when evaluating the efficiency of wholesale power trading.     

Nonlinear integration of London and Amsterdam stock markets in the 1700s

The financial markets in London and Amsterdam were some of the first to develop. Using threshold autoregressive models, we use data on two commonly traded stocks in these cities to show that the joint behaviour of the prices is consistent with the theory of arbitrage in the presence of transportation costs. The results suggest that prices converged more quickly as the price difference between the two markets increased. We also show that the threshold estimates are consistent between assets and across time. These results provide some of the earliest evidence of nonlinear mean reversion in asset prices in geographically separate financial markets.     

The efficiency of the london metal exchange: another look at the evidence

Recent evidence suggests that some markets on the London Metal Exchange do not exhibit the major characteristics of efficient markets: rationality and risk neutrality. In this note we ilustrate several shortcomings of recent work in this area. We suggest that one can be confident that the tin market exhibited a risk premium, that is, was inefficient, between 1976 and 1985. Reliable results on the efficiency of the lead, copper, aluminium, and nickel markets escape the Fama approach to testing the efficient markets hypothesis as it is currently employed.