Maximum entropy and Bayesian approaches to the ratio problem

Maximum entropy and Bayesian approaches provide superior estimates of a ratio of parameters, as this paper illustrates using the classic Nerlove model of agricultural supply. Providing extra information in the supports for the underlying parameters for generalized maximum entropy (GME) estimators or as an analytically derived prior distribution in Zellner’s minimum expected loss (MELO) estimators and Bayesian method of moments (BMOM) estimators helps substantially. Simulations illustrate that GME, MELO, and BMOM estimators with "conservative" priors have much smaller mean square errors and average biases than do standard ordinary least squares or MELO and BMOM estimators with uninformative priors. In addition, a new estimator of the structural agricultural supply model provides estimates of parameters that cannot be obtained directly using traditional, reduced-form approaches.