Bond Term Premium Analysis in the Presence of Multiple Regimes

Abstract

This papers addresses whether observed violations in the Liquidity Preference Hypothesis (LPH) can be explained by the presence of multiple regimes in the term premia. The investigation proceeds by directly testing the LPH via a series of inequality tests which allow the moments to be conditioned on observable information using an instrumental variables approach. The apparent rejection of the LPH is then investigated by modelling the term premia over time using a simple Bayesian Markov mixture model. The results suggest the presence of time varying term premia and multiple regimes which may explain the violations of the LPH. The Liquidity Preference Hypothesis (LPH) states that the ex ante return on government bonds is a monotonically increasing function of time to maturity. In other words, conditional on all available information, the expected holding period return on a 10 year bond should be greater than that of a 7 year bond which is greater than that of a 5 year bond and so on. The intuition underpinning the LPH is that longer maturity bonds are more risky than shorter maturity and therefore a risk premium is included in the expected holding period return (see Hicks (1946) and Kessel (1965)). Therefore tests of the LPH amount to testing a series of inequality restrictions on the set of risk premiums. Tests of the LPH have fallen into two broad categories. Firstly, unconditional tests of the LPH have been conducted by Fama (1984), McCulloch (1987) and Richardson, Page 2 Richardson and Smith (1992) with mixed results. Moreover, the power of these tests is questionable as the econometrician is discarding information available to the economic agents. The LPH makes inferences about the monotonicity of conditional expected returns; so unconditional tests lack the power to fully test the theory. Secondly, the theory relates ex ante returns, which are unobservable. Many econometricians have attempted to address this issue by forming expectations models and testing the fitted values of the expected returns (see Fama (1986), Fama and Bliss (1987), Stambaugh (1988), Fama and French (1989) and Klemkosky and Pilotte (1992)). However, when the tests of the LPH are complicated with an expectations model it is difficult to decipher the true implications. That is, it is necessary to consider the joint statistical properties of both the LPH test and the expectations model. This complication makes the test results difficult to interpret. More recently, statistical methods for testing inequality constraints have been developed. Boudoukh, Richardson, Smith and Whitelaw (1999) (hereafter BRSW) developed a test of inequality constraints allowing moments to be conditioned on observable information using an instrumental variables approach consistent with Hansen and Singleton (1982). This procedure overcomes the problem of unobservable ex ante risk premia and allows the econometrician to condition the returns on available information. This procedure was particularly applicable to tests of the LPH as it accounts for cross correlation ...