Domestic-foreign interest rate differentials: near unit roots and symmetric threshold models.

• Author: Strauss, Jack

1. Introduction

   The spread between domestic and foreign interest rates is an important variable that central banks consider in their policies at the macroeconomic level. It is also a variable of interest for investors in the foreign exchange market who are engaged in currency carry trade. A thorough understanding of the time series properties of interest rate differentials and their persistence across countries is, hence, of importance for both policymakers as well as investors.

   It has been documented that the time series behavior of interest rate differentials across countries is characterized by high persistence and heteroscedasticity when the data frequencies are monthly or higher. Studies such as Crowder (1995) find that conventional unit root tests possess low power in discerning whether the interest differential across economies follows a stationary or unit root process, particularly when the underlying process might be subject to nonlinearities. If interest rates possess nonlinearities that differ across economies, and transaction costs imply a band of arbitrage inaction, as suggested by Anderson (1997) and others (allowing these nonlinearities to persist), then interest rate differentials may follow a threshold process whereby the speed with which domestic and foreign interest rates revert to some value depends on the spread between domestic and foreign interest rates. In addition, changes in business cycle conditions and monetary policy may cause real interest rates and expected inflation to behave differently during different time periods. If business cycles and monetary policy responses are nonsynchronous, the interest differential and its persistence will also be affected. In this paper, we show the potential for nonlinear models; in particular, the threshold autoregressive (TAR) model that allows for heteroscedastic errors is better able to capture some important regularities in the cross-country interest rate differentials than linear models. While there are certainly numerous other nonlinear models one might choose to estimate, we chose to estimate a symmetric Band-TAR model based on the financial and economic underpinnings of the foreign exchange market, which are discussed in more detail in the literature below.

   The TAR framework assumes that the time series properties of interest rate differentials between economies differ depending on the level of the interest rate differential. When cross-country interest rate differentials exceed an estimated threshold band, the differential will exhibit a stationary mean-reverting behavior toward the band, while wandering as a non-stationary random walk when the interest rate differential lies within the threshold bands. The results of our paper show that the time series properties of cross-country interest differentials exhibit significant TAR nonlinearities that can characterize their (near) unit root behavior reported in the extant literature. The methodology used in the current paper applies and extends the framework of Gospodinov (2001, 2005) to allow for a symmetric Band-TAR process that allows for heteroscedastic errors and investigates monthly interest rate differentials between the United States and Canada, France, Germany, Japan, and the United Kingdom over the period 1974-2005. Specifically, we allow for a central band within which the interest rate differential follows a unit root process and a mean-reverting stationary process outside this central band. We find that TAR models can capture some of the important properties of movements in cross-country interest rate differentials over time.

2. Literature Review

   Many economic time series are strongly autocorrelated and can be modeled as linear (near) unit root or I(1) processes. One such series is the interest rate differential. Crowder (1995), for example, shows that cross-country interest rate differentials can be characterized by a high degree of persistence and conditional heteroscedasticity. He finds that in most cases the null of a unit root for interest rate differentials across countries cannot be rejected.

   As mentioned above, interest rate differentials are an important variable of interest to those engaged in carry trade, "a strategy where an investor borrows in a foreign country with lower interest rates than their home country and invests the funds in their domestic market, usually in fixed-income securities." (1) Ito (2002, p. 15) writes that the Japanese government has actively engaged and profited from "carrying (interest rate differential) profits from interventions during the ten year" and the "unwinding yen-carry trade positions." Ho, Guonan, and McCauley (2005) report that carry trade is used extensively in countries with tightly managed exchange rates, particularly in Asian economies. Chinn (2005) writes that "at the short horizon (one month, 3 months), the forex traders make plenty of money betting against this relationship (it's called the carry trade)."

   Wadhwani (1999, p. 13) relates uncovered interest parity (UIP) to the random walk hypothesis and finds that when the interest rate differential responds less than the percentage change in exchange rates (i.e., [beta] < 1) "carry trades make sense, because the advantage of holding the high-interest rate currency is only partially offset by a currency depreciation." (2) He finds that the more evidence in favor of the random walk hypothesis, the more support for carry trade, whereas the more evidence in support of UIP, the less potential for profit from carry trade. Chinn (2005) also finds that the greater the interest rate differential, the more likely one can profit, because this is when UIP is most likely to fail to hold. A recent Deutsche Bundesbank (2005) report examines the importance of carry trade on exchange rate dynamics and its relevance when UIP is weak. Following this logic, because of the existence of transactions costs, carry trade is unlikely to occur extensively when interest differentials are low but is likely to be prevalent when differences between interest rates across countries increase as the potential for profits rises. This activity leads to the interest rate differential narrowing, or mean reverting quickly, and hence can be modeled using a TAR framework. For example, Naug (2003, p. 132) writes in a Bank of Norway report that "Carry traders are interested in the krone as long as the interest differential is high; changes in the differential may not matter for these traders when the differential is low."

   Studies by Caner and Hansen (2001), Enders and Granger (1998), Gonzalez and Gonzalo (1999), Gospodinov (2001, 2005), and Lanne and Saikkonen (2002) argue that the apparent (near) unit root behavior of many financial and economic time series may be the result of omitted nonlinearity. Taylor (2001) demonstrates that if the true process is a threshold, then Said and Dickey (1984) Augmented Dickey Fuller (ADF) unit root tests will have an autoregressive coefficient biased toward one. For example, if the autoregressive (AR) representation of the interest rate differential switches between stationary and nonstationary regimes, then ADF unit root testing procedures will have difficulty in detecting mean reversion, and false inference may occur because of the size distortions induced by the misspecification. The above studies offer a number of examples to reinforce the investigation of nonlinear specifications. Gospodinov (2005) and Ang and Bekaert (2002a, b) show that short-term interest rates can exhibit significant nonlinear behavior that depends on term structure, business cycle phenomena, or the volatility ratio of long- and short-term interest rates. As mentioned, we show that the nonlinear behavior of the interest rate also manifests itself in the nonlinear behavior of the interest rate differential across countries; that is, the macroeconomic phenomena responsible for regime switching in the level of interest rate do not occur simultaneously in other economies.

   A central difficulty in modeling interest rates and interest differentials (e.g., at weekly or monthly frequencies) is that innovations are highly persistent and exhibit strong conditional heteroscedasticity. One approach is to employ nonparametric methods to estimate the drift and diffusion functions and construct tests for nonlinearity. The nonparametric procedures suggested in the recent literature (Ait-Sahalia 1996; Stanton 1997), however, are not appropriate for highly persistent series and can lead to severe size distortions (Conley et al. 1997; Pritsker 1998) and spurious results (Chapman and Pearson 2000). These estimators are biased in the extremes of the estimated function where there are only a few observations available. In addition, they depend crucially on the choice of the bandwidth (smoothing) parameter. For highly persistent data, the normal recommendations for an optimal bandwidth are not appropriate. Furthermore, Mark and Moh (2002) provide evidence for heavy tailed distributions in interest rate differentials and attribute this to "Big News."

   The estimation of regime switching (RS) models to characterize the movements of economic variables that exhibit near unit behavior has become increasingly popular in recent years. Two types of regime switching models that have been employed are Markov-switching (MS) models and threshold autoregressive (TAR) models. Gonzalez and Gonzalo (1999) and Caner and Hansen (2001) have considered TAR models as alternatives to linear (near) unit root models. Their model allows for a series to have a (near) unit root in one regime while being stationary in the other. If the first-order autoregressive coefficient is switching between two regimes, one that is stationary and the other nonstationary (or near unit root), then linear testing procedures will have difficulties detecting the mean reversion of the process. Caner and Hansen (2001) also derive statistical tests for testing their...