Estimating a nonlinear rational expectations commodity price model with unobservable state variables

This paper is concerned with the estimation of a model in which a possibly serially correlated stochastic process, the ‘harvest’ of an agricultural commodity, generates a competitive price in a market comprising both final consumers and risk-neutral speculators who can store the commodity at a cost in the anticipation of profit. Because storage cannot be negative, the relationship between prices and harvests is inherently nonlinear and is an unpromising candidate for a linear-quadratic model, or for linearization more generally. Instead, we calculate numerically a policy function in which price is a function of two unobservable state variables, the harvest and current availability, and we use the result to fit the price data.