Nonparametric Estimation of the Short Rate Diffusion from a Panel of Yields

Abstract:     
Chapman and Pearson (2000) document that the nonparametric drift function estimator proposed by Stanton (1997) for the short rate diffusion can produce spurious nonlinearities due to the persistent dependence of interest rate data and limited sampling period. In this paper, we propose a nonparametric estimator of the short rate diffusion that can greatly reduce the bias of the Stanton estimator. The proposed estimator uses a panel of yields with different maturities instead of a single time series of short rate observations. It is implemented in two steps. In the first step, we pool all the yields together and obtain a nonparametric "pooled" estimator of the drift function. Ideally, if the drift functions of interest rates with different maturities were identical, then the optimal estimator of the short rate drift function would simply pool the data of all the yields. In practice, while the drift functions of interest rates with different maturities may be similar in functional shape, they are unlikely to be identical. Therefore in the second step, we correct the bias of the pooled estimator using a nonparametric correction factor. The advantage of the two-step procedure is that when the pooled estimator of the drift function is similar to the drift function of the short rate in functional shape, the correction factor is a smooth function and much easier to estimate nonparametrically. Our simulations confirm that the proposed method significantly attenuates the spurious nonlinearities of the Stanton drift function estimator. We estimate the US short rate diffusion process using a panel of six Treasury yields with maturities ranging from 3 months to 10 years, and show that the proposed method has both significant economic implications and substantial efficiency gain. With observations of the panel of yields over the past 50 years, the new drift function estimator has the same efficiency as the Stanton estimator implemented with 145 years of daily short rate observations.

Keywords: drift function, nonparametric estimation, panel of yields

Working Paper Series