# TESTING THE EXPECTATIONS HYPOTHESIS OF THE TERM STRUCTURE OF INTEREST RATES IN THE PRESENCE OF A POTENTIAL REGIME SHIFT

*Markku Lanne*

No 294, Computing in Economics and Finance 2000 from Society for Computational Economics

**Abstract:**
According to the classical expectations hypothesis of the term structure of interest rates, long-term interest rates are determined by the expectations of the future short-term interest rate. This hypothesis is typically rejected, especially with U.S. data. One explanation that has recently been offered for this rejection is the presence of so called peso effects that influece the distribution of the typically used test statistics. The term 'peso effect' refers to potential regime shifts in the process of the short-term rate that occur less frequently in the actual sample than they should according to the probability distribution of the process. Even if there were not a single regime shift in the observed data, the fact that these shifts have a positive probability, affects the expectations that the market forms of the future short-term rates, and thus the data seems to be irreconcilable with the expectations hypothesis.Previous term structure literature has mainly attempted to take the effect of regime switches into account by testing the rational expectations restrictions within models with more than one regime, typically the so called Markov switching models. These models are not applicable, however, if no regime shift has actually occurred in the sample period. In this paper we consider a model where no regime shift has occurred but the agents form expectations based on a nonlinear model allowing for such shifts. The model consists of a term structure equation implied by the expectations hypothesis, a threshold autoregression for the short-term (m-period) interest rate, and the restriction that the upper regime never occurs in the sample. Thus in the sample the threshold autoregression reduces to an AR model, but presence of a threshold term affects expectations. The selection of the threshold variable can be based on statistical criteria; in our empirical application the lagged level of the short-term interest rate turned out to be the best. The expectations hypothesis can be tested by testing restrictions on the parameters of the term structure equation.The model can be estimated by maximum likelihood, given a method for computing the conditional expectation in the term structure equation. To this end we employ a common simulation method where, given, some fixed values of the parameters and initial values, a large number of realizations of the threshold autoregression for the short-term rate are simulated m(n/m-1) periods ahead (n is maturity of the longer-term rate), and the conditional expectations are obtained as averages over these realizations at each horizon. This is computationally burdensome (especially if n/m is large) since the simulation is required in the estimation at each iteration and for all observations t=1,...,T.The model is estimated and the expectations hypothesis is tested for monthly Eurodollar deposit rates for maturities 1, 3 and 6 months covering the period 1983:1-1999:6. Because we are assuming that no regime shifts have occurred in the sample, only the period after the abondonment of the 'new operating procedures' of the Federal Reserve in considered. The choice of maturities is dictated by the availability of data, and the computational complexity of our model which increases with the maturity of the longer-term interest rate. Classical regression based tests indicate rejection, while tests in the model allowing for potential regime shifts that have not realized in the sample period, lend support to the expectations hypothesis. The estimation results imply that the potential regime shift has affected the expectations concerning the longer-term interest rate only in a short period at the beginning of the sample where the interest rates were highest.

**Date:** 2000-07-05

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**Related works:**

Journal Article: Testing the Expectations Hypothesis of the Term Structure of Interest Rates in the Presence of a Potential Regime Shift (2003)

Working Paper: Testing the expectations hypothesis of the term structure of interest rates in the presence of a potential regime shift (1999)

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