A Birth-Death Markov Chain Monte Carlo Method to Estimate the Number of States in a State-Contingent Production Frontier Model

This article estimates a state-contingent production frontier for a group of farms while endogenously estimating the number of states of nature induced by unobserved environmental variables. This estimation is conducted by using a Birth-Death Markov Chain Monte Carlo method. State-contingent output is estimated conditioned on an observed input vector and an a priori unknown number of unobserved states, each of which is modeled as a component of a mixture of Gaussian distributions. In a panel data application, state-independent dummy variables are used to control for time effects. The model is applied to 44 rice farms in the Philippines operating between 1990 and 1997. The endogenous estimation procedure indicates a unimodal posterior probability distribution on the number of states with a median of three states. The estimated posterior coefficient values and their economic implications are compared to those of previous work, which had assumed a fixed number of states determined exogenously. Goodness of fit testing is performed for the first time for a state-contingent production model. The results indicate satisfactory fit and also provided insights regarding the degree of estimation error reduction achieved by utilizing a distribution for the number of states instead of a point estimate. All of our models show significant improvement in terms of Mean Squared Error of in-sample predictions against previous work. This application also demonstrated that the use of a state-independent dummy time trend, instead of a state-contingent linear time trend, led to slightly smaller differences in state mean output levels, although input-elasticities remain state-contingent