Solving non-linear stochastic models by parameterizing expectations: An application to asset pricing with production

Abstract

A new algorithm called the parameterized expectations approach (PEA) for solving dynamic stochastic models under rational expectations is developed and its advantages and disadvantages are discussed. This algorithm can, in principle, approximate the true equilibrium arbitrarily well. Also, this algorithm works from the Euler equations, so that the equilibrium does not have to be cast in the form of a planner's problem. Monte--Carlo integration and the absence of grids on the state variables, cause the computation costs not to go up exponentially when the number of state variables or the exogenous shocks in the economy increase. \\ As an application we analyze an asset pricing model with endogenous production. We analyze its implications for time dependence of volatility of stock returns and the term structure of interest rates. We argue that this model can generate hump--shaped term structures.