Term spread regressions of the rational expectations hypothesis of the term structure allowing for risk premium effects

Abstract

This paper suggests a new empirical methodology of testing the predictions of the term spread between long and short-term interest rates about future changes of the former allowing for term premium effects, according to the rational expectations hypothesis of the term structure. To capture the effects of a time-varying term premium on the term spread, the paper relies on an empirically attractive affine Gaussian dynamic term structure model which assumes that the term structure of interest rates is spanned by three unobserved state variables. To retrieve accurate values of these variables from interest rates series, the paper suggests a new method which can overcome the effects of measurement (or pricing) errors inherent in these series on the estimates of the model. This method is assessed by a Monte Carlo study. Ignoring these errors will lead to biased estimates of term structure models. The empirical results of the paper provide support for the suggested term structure model. They show that this model can efficiently capture the time-varying term premium effects embodied in long-term interest rates, which can explain the failures of term spread to forecast future changes in long-term rates.Keywords: affine term structure model; principal components; rational expectations hypothesis of the term structure of interest rates; time-varying term premium. JEL classifications: G12; E43.

Real term structure forecasts of consumption growth

“…The principal component factors which will be retrieved by our analysis, denoted as pc it , will be employed in the estimation procedure of our GDTSM in order to minimize possible measurement errors effects in real rates R t (τ) on the estimates of state variables x it . As noted by Joslin and et al (2011), and Argyropoulos and Tzavalis (2015), this can happen because pc it constitute well diversified portfolios of interest rates R t (τ), which diversify away any measurement errors inherent in them. Finally, we estimate and test the GDTSM.…”

“…The first set (see Panels A of the tables) relies on estimates of state variables x it retrieved from the data by inverting relationship X t = D K (τ) −1 (Z t − A K (τ)), following the standard method of Pearson and Sun (denoted as P-S). The second set of estimates replaces the observed values of vector Z t in relationship X t = D k (τ) − 1 (Z t − A K (τ)) with their predicted (projected) values on principal component factors pc 1t and pc 2t , i.e., X t = D k (τ) −1 (E(Z t |PC t − A K (τ)), where PC t = (pc 1t , pc 2t )′ (see Panels B of the tables), following the modification of the P-S method suggested by Argyropoulos and Tzavalis (2015). These constitute the predicted values of the following regressions:…”

Essays on forecasting interest rates, economic activity and inflation, based on factor models of the yield curve

“…To test for unit root tests in interest rates R t ( ), we will carry out a second generation of ADF tests, known as e¢ cient ADF (E-ADF) test (see, e.g., Elliott et al [55], Elliott [54], and Ng and Perron [91]) 6 . These tests are designed to have maximum power against stationary alternatives which are local to unity.…”

“…where denotes the local parameter of the alternative hypothesis against which the unit root hypothesis is tested. Then, we will estimate the following regression of the quasi-di¤erenced interest rates series d(R t ( )j ) on the quasi-di¤erences of the vector of deterministic components 6 Evidence provided in the literature on unit root tests of interest rates series is mixed. Earlier studies of this literature based on single time series unit root tests, such as the standard ADF test, can not reject the null hypothesis of a unit root (see, e.g., Hall et al [67]).…”

“…This test is designed to have maximum power against stationary alternatives to unit root hypothesis which are local to unity. Thus, it can improve the power performance of the standard ADF statistic often used in practice to test for a unit root in R t ( ): 6 Values of E-ADF unit root test statistic are reported in Table 1. This is done for real interest rates R t ( ), with maturity intervals ={1, 3, 6, 12, 24, 36, 48, 60} months.…”