A Normal-Weighted Exponential Stochastic Frontier Model

Abstract

This thesis introduces a new stochastic frontier model called a normal-weighted exponential
stochastic frontier model. We have derived a closed form log-likelihood function and JLMS
inefficiency estimator of a normal-weighted exponential stochastic frontier model. In addition, we
have derived the gradient and hessian matrix of a normal-weighted exponential stochastic frontier
model. A Monte Carlo (MC) simulation is carried out to verify the correctness of the derivations,
of a normal-weighted exponential stochastic frontier model, and to study the finite sample
properties of maximum likelihood estimator. Our simulation result shows that a normal-weighted
exponential stochastic frontier model performs well compared to a normal-exponential stochastic
frontier model. In our simulation result, it shows that as sample size increases, the bias and
standard errors decrease. Furthermore, a real-world data application is carried out, with the goal
of estimating the carbon efficiency of African manufacturing firms. We have estimated an inputrequirement production function, using fuel consumption as a dependent variable and output and
other inputs as independent variables. Our estimated result shows that the estimates of coefficients
are the same across models. However, there are differences in the carbon efficiency estimates of
manufacturing firms. We have used the carbon efficiency estimates to rank African countries, and
Egypt is the most carbon efficient country in Africa. We have also run multiple linear regressions
on carbon inefficiency estimates to see the determinants. In all three stochastic frontier models,
top manager work experience, obstacles to accessing finance, firm size, export status, and foreign
ownership are the key determinants.