A Non-Linear Macroeconomic Term Structure Model

Abstract

This model uses three implicit states (Core CPI, the unemployment rate, and the quarterly growth rate of non-farm payrolls) which follow a multivariate continuous-time Ornstein-Uhlenbeck (OU) process.  The instantaneous risk-free rate (Fed Funds) is set using a policy rule (following Black (1995)) which is affine in the implicit states with a lower bound at one basis point.  The policy rule is fixed throughout the sample period from November, 1985 through March, 2013.  While the policy rule is fixed throughout the sample, the economy responds differently when Fed Funds are stuck at their minimum (the Zero Period) than it does when the Fed can use Fed Funds more effectively to influence the economy (the Normal Period). The implicit state OU processes have different coefficients, both physical and risk neutral, in the two response periods.  While market participants may know the implicit states, an econometrician must estimate from them market and macroeconomic data. I estimate the implicit states and the OU processes parameters by maximizing the joint conditional likelihood that the implicit states are close to the government states estimates; that the model accurately determines the yield curve; and that the actual one-month returns are forecasted by the model.  The data are monthly estimates of the state variables published by the government, month-end zero coupon yield curves with maturities from 2 to 30 years published by the Fed, and one month returns for the benchmark 2, 10, and 30 year Treasury zeros calculated from the month-end yield curves from November, 1985 through March, 2013.  Over the entire sample the root mean square error (RMSE) in fitting yield curves is only 4.6 basis points.  I find conditional yield curve responses to changes in the state variables, which are significantly different from the unconditional factors.  The model is tested out-of-sample by fitting Treasury Inflation Protected Securities. I find ample profit opportunities.