A Birth‐Death Markov Chain Monte Carlo Method to Estimate the Number of States in a State‐Contingent Production Frontier Model
提出一种生灭马尔可夫链蒙特卡罗方法，内生估计菲律宾水稻农场生产前沿中未观测环境状态的数量，发现后验中位数为3个状态，且相比固定状态数模型拟合更优。
In this article we estimate 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 research that 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 provide 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 demonstrates that using a state‐independent dummy time trend instead of a state‐contingent linear time trend leads to slightly smaller differences in state mean output levels, although input elasticities remain state‐contingent.