A Simple Analytic Approximation Approach for Estimating the True Random Effects and True Fixed Effects Stochastic Frontier Models

This paper derives an analytic approximation formula for the likelihood function of the true random effects stochastic frontier model of Greene (2005) with a time span T = 2. Gaussian quadrature procedure and simulation-based method is not re- quired for the closed-form approach. Combining the analytic formula with a pairwise likelihood estimator (PLE), we easily can estimate the true random effects stochastic frontier models with T > 2. This analytic approximation approach is also applicable to the true fixed effects stochastic frontier model of Greene (2005) after the fixed effects parameters are eliminated from the pairwise differencing or first differencing operators. The Monte Carlo simulations confirm the promising performance of the analytic methodology under all the configurations generated from the true random effects and true fixed effects stochastic frontier models in this paper. The proposed method is applied to the World Health Organization's (WHO) panel data on national health care systems.