A semiparametric factor model of interest rates and tests of the affine term structure

Many continuous-time term structure of interest rate models assume a factor structure where the drift and volatility functions are affine functions of the state-variable process. These models involve very specific parametric choices of factors and functional specifications of the drift and volatilit y. Moreover, under the affine term structure restrictions not all factors n ecessarily affect interest rates at all maturities simultaneously. This cla ss of so-called affine models covers a wide variety of existing empirical a s well as theoretical models in the literature. In this paper we take a ver y agnostic approach to the specification of these diffusion functions and t est implications of the affine term structure restrictions. We do not test a specific model among the class of affine models per se. Instead, the affi ne term structure restrictions we test are based on the derivatives of the responses of interest rates to the factors. We also test how many and which factors affect a particular rate. These tests are conducted within a frame work which models interest rates as functions of "fundamental'' factors, an d the responses of interest rates to these factors are estimated with nonpa rametric methods. We consider two sets of factors, one based on key macroec onomic variables, and one based on interest rate spreads. In general, despi te their common use we find that the empirical evidence does not support th e restrictions imposed by affine models. Besides testing the affine structu re restrictions we also uncover a set of fundamental factors which appear r emarkably robust in explaining interest rate dynamics at the long and short maturities we consider.