A normal-Weighted Exponential Stochastic Frontier Model
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Date
2022-06-15
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A.A.U
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 decreases. Moreover, a real data application is performed, and it is about
estimation of carbon efficiency of manufacturing firms in Africa. We have estimated an input
requirement production function, using fuel consumption as 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 is differences in carbon efficiency
estimates of manufacturing firms. Using a normal-half normal stochastic frontier model, a carbon
efficiency of manufacturing firms in Africa gives an estimate ranging between 1.002344
(99.8984%) and 1.002362 (99.8976%). For a normal-exponential stochastic frontier model the range of
carbon inefficiency estimates are between 1.074752 (97.5092%) and 1.090364 (96.3126%). Similarly, for
a normal-weighted exponential stochastic frontier model the carbon inefficiency estimates are between
1.122895 (95.0907%) and 1.237519 (91.1602%). 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 a multiple
linear regression on carbon inefficiency estimates to see the determinants. In all three stochastic frontier
models: top manager work experience, obstacle to access finance, firm size, export status, and foreign
ownership are the key determinants.