| This dissertation is an empirical investigation of competing classes of models of the short-term interest rate. The short-term interest rate is a key element in all term-structure models. This work generates evidence for a best fitting model from both the smooth continuous-time specifications (e.g. Hansen and Scheinkman (1995), and Ait-Sahalia (1996)) and the discrete-time regime switching specifications (Hamilton (1988), and Gray (1996)). The best fitting models within each class are then compared to one another using the Schwarz (BIC) criterion.; The estimation is carried out on three-month interest rates for the United States, the United Kingdom, Germany, and Japan. By looking at a panel of four countries, the paper generates independent cross-country evidence on the contrasts between the smooth continuous-time models and the discrete-time regime switching specifications. The main finding is that a regime switching square-root model provides a good fit to all of the series and outperforms the continuous-time models.; Within the discrete-time class of models, the starting point is an AR(1) with various forms for the conditional heteroskedasticity. The volatility is permitted to have both a level effect and a GARCH structure. The data are tested for the presence of a second regime. The test indicates that a two-regime model provides a better fit than a single regime specification. Hence the models are expanded to include a second regime. All of the popular discrete models for the short-term interest rate are nested in this structure. Since the errors are assumed to be conditionally normal, the models are estimated by maximum likelihood.; The estimation procedure for the continuous time models is the Efficient Method of Moments (EMM). The EMM procedure starts with the projection of the interest rate series onto a Hermite expansion that closely approximates the observed data. The scores from this auxiliary model provide the conditional moment restrictions for a GMM estimation which is the second step of the procedure.; The continuous-time class of models estimated includes single and multi-factor (stochastic volatility) models. The starting point is the constant elasticity of variance specification of Chan et al. (1992). This model is expanded by including an unseen stochastic volatility process. For all countries, only the models that include the stochastic volatility factor are able to pass the chi-square goodness-of-fit tests.; The Hermite expansion is also used as the basis for the comparison of the non-nested models. A long simulation from the continuous-time models is reprojected onto the Hermite expansion. The reprojected density provides a close approximation to the transitional densities of the structural model and thus can be used to compute the likelihood of the continuous-time models, which is otherwise unavailable. The regime-switching square-root models easily surpass the best fitting continuous time models. |
