Obtaining Point Estimates of State Variables from the Term Structure of Interest Rates

Abstract

We propose a novel two-stage procedure to obtain point estimates of the state variables that drive the term structure of interest rates. In the rst stage, we rst estimate the parameters of the pricing kernel by matching the unconditional moments of the data at each time to maturity with their model counterparts. Then, at each date, we estimate the value of the state variable that imposes the lowest cost in matching the modelled yield curve to the observed yields; bending energy is our choice of measure of the cost required for this curve matching exercise. The resulting estimates have three principal advantages over commonly-used proxies for the economic state of nature. This procedure provides high-frequency estimates of the state of nature, which could be extremely useful for explaining changes in other high-frequency economic variables. These estimates are also a more comprehensive summary of expected future investment opportunities since they take into account investor expectations over various maturities that are embedded in the yield curve. The estimates are also less ad-hoc, since they are based on an underlying model of the yield curve. We demonstrate the procedure for a single state variable a ne model of the yield curve. ∗I owe thanks to Gonzalo Rubio for helpful comments, and to IESE Business School, University of Navarra for support. All errors are mine. Address correspondence to nbulusu@iese.edu or to Av. Pearson 21, 08034 Barcelona, Spain.