Measurement error corrected stochastic frontier analysis

Stochastic frontier analysis relies on the assumption that inputs are measured with negligible error, a condition often violated when proxies are necessary. We propose a stochastic frontier analysis framework that corrects for the use of proxies by developing a likelihood function for Cobb–Douglas and Translog production functions. For the latter, we apply a pseudo-maximum likelihood approach to handle the nuisance parameters in the model and a Monte Carlo integration scheme to handle integrals that cannot be solved analytically. Based on the Battese and Coelli (1992) model, we validate the framework with panel data. A simulation study shows that correcting for measurement errors caused by proxies substantially reduces bias and improves the accuracy of production function coefficients and technical efficiency estimates. An application to the Air Navigation Service Provider market in Europe highlights the effectiveness of the framework in addressing bias, particularly in estimating returns-to-scale.