FEDERAL RESERVE BANK OF ST. LOUIS REVIEW JULY/AUGUST 2007 327 Commentary

There is a single, exogenous, stochastic, and perishable endowment good. The endowment grows at the rate xt, with stochastic volatility vt: Hence, the endowment process is characterized by a parameter vector φx,φv,θx,θv,σv. There is a representative agent with Epstein-Zin preferences. The advantages of this preference structure, with its property of separating relative risk aversion from the elasticity of intertemporal substitution, are well known. The preference parameter vector is β,ρ,α . The pricing kernel is the intertemporal marginal rate of substitution in consumption, denoted logmt+1. The price of default-free discount bonds can be determined recursively through an arbitrage-free restriction of the form With this structure for the endowment process and the preferences, the model can be mapped into the Duffie-Kan affine term-structure model with two factors. In particular, the authors guess a form of the value function and then verify that this guess is a solution. The value function then implies the form of the real pricing kernel. The process by which the authors relate the deeper preference and endowment parameters to the b E m bt n t t t n (