[This article develops a rich class of discrete-time, nonlinear dynamic term structure models (DTSMs). Under the risk-neutral measure, the distribution of the state vector X t resides within a family of discrete-time affine processes that nests the exact discrete-time counterparts of the entire class of continuous-time models in Duffie and Kan (1996) and Dai and Singleton (2000). Under the historical distribution, our approach accommodates nonlinear (nonaffine) processes while leading to closed-form expressions for the conditional likelihood functions for zero-coupon bond yields. As motivation for our framework, we show that it encompasses many of the equilibrium models with habit-based preferences or recursive preferences and long-run risks. We illustrate our methods by constructing maximum likelihood estimates of a nonlinear discrete-time DTSM with habit-based preferences in which bond prices are known in closed form. We conclude that habit-based models, as typically parameterized in the literature, do not match key features of the conditional distribution of bond yields.]

Equilibrium, affine asset pricing models with Larry G. Epstein and Stanley E. Zin (1989)’s preferences typically generate time variation in risk premiums through time variation in the quantity of risks, with the market prices of risks (MPR) held constant. This is true of models with built in long-run consumption risks (LRR) (e.g., Ravi Bansal and Amir Yaron (2004), Bansal, Dana Kiku, and Yaron (2009)), as well as of the broader formulations in Bjorn Eraker and Ivan Shaliastovich (2008). For pricing bonds such formulations may be overly constrained as reduced form models suggest that it is time variation in the MPRs, more than stochastic yield volatilities, that resolve the expectations puzzles in bond markets. Constant MPRs are not an inherent feature of equilibrium pricing models with recursive preferences, but rather they arise as a consequence of the linearizations underlying the affine approximations to these models that have been explored empirically. The essential ingredients of these econometric formulations are (P1) recursive (Epstein-Zin) preferences, (P2) risk neutral (핈), affine pricing, and (P3) the assumption that the state of the economy is described by an affine process under the historical (핇) distribution. Key to achieving property (P2), given P1 and P3, is the assumption that the valuation ratio (the log “price/consumption” ratio) associated with the claim that pays aggregate consumption is an affine function of the state. We develop a dynamic term structure model with recursive preferences that preserves

This article develops a rich class of discrete-time, nonlinear dynamic term structure models (DTSMs). Under the risk-neutral measure, the distribution of the state vector Xt resides within a family of discrete-time affine processes that nests the exact discrete-time counterparts of the entire class of continuous-time models in Duffie and Kan (1996) and Dai and Singleton (2000). Under the historical distribution, our approach accommodates nonlinear (nonaffine) processes while leading to closed-form expressions for the conditional likelihood functions for zero-coupon bond yields. As motivation for our framework, we show that it encompasses many of the equilibrium models with habit-based preferences or recursive preferences and long-run risks. We illustrate our methods by constructing maximum likelihood estimates of a nonlinear discrete-time DTSM with habit-based preferences in which bond prices are known in closed form. We conclude that habit-based models, as typically parameterized in the literature, do not match key features of the conditional distribution of bond yields.