Using Proxies for the Short Rate : When are Three Months Like an Instant?

The dynamics of the unobservable quot;shortquot; or quot;instantaneousquot; rate of interest are frequently estimated using a proxy. We show how the biases resulting from this practice (the quot;proxy problemquot;) are related to the derivatives of the proxy with respect to the short rate and the (inverse) function from the proxy to the short rate.Analytic results show that the proxy problem is not economically significant for single-factor affine models, for parameter values consistent with U.S. data. In addition, for the two-factor affine model of Longstaff and Schwartz (1992), the proxy problem is only economically significant for pricing discount bonds with maturities of more than five years. We also describe two different procedures which can be used to assess the magnitude of the proxy problem in more general interest rate models. Numerical evaluation of a nonlinear single-factor model suggests that the proxy problem can significantly affect both estimates of the diffusion function and discount bond prices