Empirical tests of interest rate model pricing kernels

Abstract

This paper estimates and tests consumption-based pricing kernels used in common equilibrium interest rate term structure models. In contrast to previous papers that use return orthogonality conditions, estimation in this paper is accomplished using moment conditions from a consumption-based option pricing equation and market prices of interest rate options. This methodology is more sensitive to preference misspecification over states associated with large changes in consumption than previous techniques. In addition, this methodology provides a large set of natural moment conditions to use in estimation and testing compared to an arbitrary choice of return orthogonality conditions (e.g. instruments selected) used in GMM estimation. Eurodollar futures option prices and an estimated joint model of quarterly aggregate consumption and three month Eurodollar rates suggest are used to estimate and test pricing kernels based on logarithmic, power, and exponential utility functions. Using the market prices of interest rate options, evidence is found which is consistent with the equity premium puzzle; very high levels of risk aversion are needed to justify the observed premium associated with an investment position positively correlated with aggregate consumption. In addition, evidence is found which is consistent with the riskfree rate puzzle: at high levels of risk-aversion for power or exponential utility, negative rates of time preference are needed to fit the observed low riskless interest rates. These results suggest that typical term structure models are misspecified in terms of assumed preferences. This may have deleterious effects on model estimates of the interest rate term structure estimates and interest rate option prices.