Do asymmetric and nonlinear adjustments explain the forward premium anomaly?IntroductionUncovered interest rate parity and nonlinearityDynamic logistic UIP regressionEmpirical resultsSimulation evidence on the anomalyConclusionAcknowledgementReferencesDo asymmetric and nonlinear adjustments explainthe forward premium anomaly?Richard T. Bailliea,b,c,*, Rehim Kilic¸daDepartment of Economics, Michigan State University, East Lansing, MI 48824-1024, USAbDepartment of Finance, Michigan State University, East Lansing, MI 48824-1024, USAcDepartment of Economics, Queen Mary University of London, London E1 4NS, UKdSchool of Economics, Georgia Institute of Technology, 781 Marietta Street, Atlanta, GA 30332-0615, USAAbstractThis paper explores some of the asymmetries and nonlinearities in an attempt to throw light on the forwardpremium anomaly, where spot exchange rate returns are typically found to be negatively correlated with thelagged interest rate differential and lead to an apparent rejection of Uncovered Interest Parity (UIP). The ap-proach in this paper is motivated by some recent theoretical literature on the limits to speculation and hys-teresis. The paper estimates Logistic Smooth Transition Dynamic Regression (LSTR) models witha variety of transition variables, including the lagged forward premium, monetary and income fundamentalsand also variables associated with time varying risk premium, including the conditional variances of somefundamentals. Results are reported for nine different currencies. Many of the estimated LSTR models provideevidence for the existence of an outer regime that is consistent with UIP. Estimation of the standard forwardpremium regression on observations falling in these regimes across the sample is moderately supportive ofUIP holding in the outer regime. A simulation experiment also suggests that an LSTR dgp can produce dataconsistent with the anomaly. However, parameter estimation issues leads to considerable uncertainty with theestimated transition functions and hence imprecise definitions of regimes. The results are an interesting stepin the direction of understanding the nonlinear dimension of the problem without fully resolving the anomaly.Ó 2005 Elsevier Ltd. All rights reserved.JEL classification: C22; F31; F41Keywords: Forward premium anomaly; Uncovered Interest Parity; Nonlinearity; LSTR models* Corresponding author. Department of Economics and Department of Finance, Michigan State University, MarshallHall, East Lansing, MI 48824-1024, USA. Tel.: þ1 517 355 1864; fax: þ1 517 432 1068.E-mail addresses: [email protected] (R.T. Baillie), [email protected] (R. Kilic¸).0261-5606/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.jimonfin.2005.10.002Journal of International Money and Finance 25 (2006) 22e47www.elsevier.com/locate/econbase1. IntroductionThe theory of uncovered interest rate parity (UIP) states that the expected return, or rate of ap-preciation on a currency equals the interest rate differential, or equivalently the forward premium.One popular method for testing the theory has been to regress the rate of appreciation of the spotrate on the lagged forward premium. A test for UIP is then to test if the slope coefficient is unity, theintercept zero and the residuals serially uncorrelated. The forward premium anomaly is the wide-spread empirical finding of a negative slope coefficient in the above regression, so that the rate ofappreciation of the spot exchange rate is negatively correlated with the lagged forward premium.This phenomenon has been consistently found for most freely floating currencies in the currentfloat and appears robust to the choice of numeraire currency. Hence the forward premium anomalyimplies that the country with the highest interest rate will have an appreciating currency, and nota depreciating currency, as implied by the theory of UIP.Many possible theories have been proposed to attempt to explain the anomaly. For example,considerable previous work has modeled time dependent risk premia, e.g., Hodrick (1987,1989) and Mark and Wu (1997). Other work has considered possible peso problems, segmentedmarkets and heterogenous trading behavior; and excellent surveys of the forward premiumanomaly and suggested resolutions have been provided by Hodrick (1987) and Engel (1996).More recent work has emphasized the econometric issues involving unbalanced regressionswhere the approximate martingale spot returns are being regressed on the lagged forward pre-mium, which is highly autocorrelated and possibly a long memory process. These issues areanalyzed by Baillie and Bollerslev (2000) and Maynard and Phillips (2001). Baillie and Boller-slev (2000) also show that the magnitude and sign of the estimated slope coefficient in the for-ward premium regression appears to be slowly time varying, particularly in small sample sizes.This current paper also deals with some of the econometric aspects of the anomaly and fo-cuses on some nonlinear and asymmetric aspects of the relationship. The need for such an ap-proach can be justified from several theoretical papers that consider transaction costs fromclosing arbitrage conditions in financial markets. Also, some recent applied research, e.g. Ban-sal and Dahlquist (2000), has found the size and extent of the anomaly to be related to the in-terest rate differential. A convenient starting point for the focus of this paper, is the logisticsmooth transition dynamic regression (LSTR) model, which is related to the LSTAR and othernonlinear models introduced by Granger and Terasvirta (1993) and Terasvirta (1994). Suchmodels have begun to be extensively applied to various issues in financial economics. Thisstudy estimates LSTR models for a variety of transition variables, including the forward pre-mium, money supply differentials, income differentials, combinations of fundamentals, squaredforward premium and conditional variances of fundamentals that are theoretically postulated tobe important elements of the time varying risk premium. For some currencies and some tran-sition variables, the estimated LSTR models appear to show the existence of two major re-gimes, with an inner regime that is consistent with the forward premium anomaly, and anouter regime where the conditions associated with UIP cannot be rejected.The results for nine currencies are generally supportive of the proposition that nonlinearity isan important aspect of the forward premium anomaly, with a