Term structural models with regime-shifts as in Naik and Lee (1997), Evans (1998), and Bansal and Zhou (2002), capture the important feature that the aggregate economy is subject to discrete and persistent changes in the business cycle. The business cycle fluctuations together with the monetary policy response to them have significant impacts on not only the short interest rate, but also the entire term structure. Regime-switching term structure models represent a parsimonious way to introduce the nonlinear interactions between the business cycle effects and the term structure dynamics. Using the US treasury yield data from 1964 to 1995, Bansal and Zhou (2002) find that the model-implied regime changes usually lead or coincide with economic recessions. Therefore the term structure regimes seem to confirm and complement the real business cycles.
One important benchmark for comparing term structure models is the characterization of risk premiums on bonds of various maturities. The most common strategy for understanding bond risk premiums is to study deviations from the the so-called Expectations Hypothesis. One form of the violation that regression of yield changes on yield spreads produce negative slope coefficient instead of unity (Campbell and Shiller, 1991), has been addressed is many recent papers (see, Roberds and Whiteman (1999), Dai and Singleton (2002), and Bansal and Zhou (2002)). Another form of the violation of Expectations Hypothesis is that the forward rate can predict the excess bond return (Fama and Bliss, 1987). More recently, Cochrane and Piazzesi (2002) document that using multiple forward rates to predict bond excess returns generates very high predictability of bond excess returns—the adjusted R ’s from the regression being around 30%. Further, they show that the coefficients of multiple forward-rate regressors form a tent shape pattern related to the maturity of the forward rate. The size of the predictability and the tent shape pattern of the projection coefficients is quite puzzling and constitutes a challenge to term structure models.
The main contribution of this paper to provide an interpretation for the predictability evidence from the perspective of latent factor term structure models. When evaluating the plausibility of various term structure models it is important to not focus exclusively on the predictability issue; previous work (see Dai and Singleton (2000), Bansal and Zhou (2002), Ahn et al. (2002)) highlight the difficulties that many received models have in capturing the transition dynamics of yields (i.e. conditional volatility and conditional cross-correlation across yields). The predictability evidence, in conjunction with the transition dynamics constitutes a sufficiently rich set of data-features to discriminate across alternative term structure models and evaluate their plausibility. The main empirical finding of this paper is to show that the regime-shifts term structure models can simultaneously justify the nature of bond return predictability and the transition dynamics of yields. More specifically, we find that models with regime-shifts model can reproduce the high predictability and the tent shaped regression coefficients documented in Cochrane and Piazzesi (2002). Additionally, the regime-shifts term structure model reproduces the dynamics of conditional volatility and cross-correlation across yields. On the other hand, commonly used multi factor CIR and affine model cannot capture these dimensions of the data. Our overall evidence indicates that incorporating regime shifts are important for interpreting key aspects of treasury bonds markets data.
We use US treasury yield data from 1964 through 2001. The period from 1996 to 2000 poses a tough challenge for standard asset pricing models, with unprecedented long economic growth and bull market run. At the same time this stretch of the data has several economic recessions and periods of economic boom. Using the whole sample we find that the conditional correlation between the long and short yields vary over a range from about 40% to 80%. The conditional volatilities of the long and short yields also reveal very large variation. Despite this, when confronting the U.S. treasury yields data from 1964 to 2001, our regime-shifts model still stands out as the best performing candidate. The regime indicator is related to business cycles in the data; for example, the model-based regime indicator predicts the 2001-2002 recession.
To estimate various models under consideration we use the Efficient Method of Moments (EMM), developed in Bansal et al. (1995) and Gallant and Tauchen (1996). Tests of over-identifying restrictions based on the EMM method provide a way to compare different, potentially non-nested models. This estimation technique forces the model to confront several important aspects of the data, such as the conditional volatility and correlation across different yields. To generate diagnostic evidence to help discrimination across models, we rely on the reprojection methods developed by Gallant and Tauchen (1998). Our empirical evidence suggests that the benchmark CIR and affine model specifications with up to three factors are sharply rejected with p-values of zero. The only model specification that finds support in the data (with p-value of 1%) is our preferred two-factor regime switching model where the market price of risks depends on regime shifts. Our diagnostics of the various models show that the our preferred regime shifts model specification produces the smallest cross-sectional pricing errors across all the specifications considered in the paper. Using reprojections we compute the conditional correlations and volatility under the null of the various models. Our results show that only the regime-shifts models can capture the large variations in conditional correlations and conditional volatility that are observe in the data.
The remainder of this paper is organized in the following manner. Section 2 reviews the regime shifts term structure model developed in Bansal and Zhou (2002). Section 3 discusses the empirical estimation results, the specifications tests, and an array of diagnostics based on the conditional correlation and volatility. It also examines cross-sectional implications on pricing errors, violations of the expectation hypothesis of forward rate predictability and the link between regime classification and business cycles, especially the recent economic recession. Section 4 contains the concluding remarks.
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