A dynamic model of the U.S. cotton market with rational expectations
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This study presents a dynamic rational expectations model for the U.S. cotton market. The dynamic decision rules are derived from the cotton farmer and miller optimization problems; and the equilibrium movements of prices, production, land allocation, and mill consumption are solved analytically. The dynamic element in the cotton farmer and miller problems come from the cost functions. In the cotton cost function a sequential adjustment cost is used while a quadratic cost function is used in the cotton yarns cost function. These optimal decision rules are derived as functions of past values of these decision variables, expectations of future product prices, and other exogenous variables. Assuming rational expectations and knowing the orders of the Markov-processes for the relevant state variables and the disturbances, closed-form regression equations representing decision rules and stochastic processes are obtained. Then, the VAR approach and Granger-causality test are used to obtain information which help to forecast the relevant state variables at the first stage of estimation. With the specific assumption on the errors, a dynamic mill demand for cotton is estimated by using the method of nonlinear least squares and tested by using the likelihood ratio. The empirical results provide some support for the specific model. Furthermore, the empirical model provides a framework for policy evaluation.