Maximum entropy and Bayesian approaches to the ratio problem

Maximum entropy and Bayesian approaches provide superior estimates of a rat io of parameters, as this paper illustrates using the classic Nerlove model of agricultural supply. Providing extra information in the supports for th e underlying parameters for generalized maximum entropy (GME) estimators or as an analytically derived prior distribution in Zellner's minimum expecte d loss (MELD) estimators and Bayesian, method of moments (BMOM) estimators helps substantially. Simulations illustrate that GME, MELO, and BMOM estima tors with "conservative" priors have much smaller mean square errors and av erage biases than do standard ordinary least squares or MELD and BMOM estim ators with uninformative priors. In addition, a new estimator of the struct ural agricultural supply model provides estimates of parameters that cannot be obtained directly using traditional, reduced-form approaches. (C) 2001 Published by Elsevier Science S.A.