A simple closed-form approximation for the cumulative distribution function of the composite error of stochastic frontier models

This paper derives an analytic closed-form formula for the cumulative distribution function (cdf) of the composite error of the stochastic frontier analysis (SFA) model. Since the presence of a cdf is frequently encountered in the likelihood-based analysis with limiteddependent and qualitative varia...

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Bibliographic Details
Published inJournal of productivity analysis Vol. 39; no. 3; pp. 259 - 269
Main Authors Tsay, Wen-Jen, Huang, Cliff J., Fu, Tsu-Tan, Ho, I.-Lin
Format Journal Article
LanguageEnglish
Published Boston Spring Science+Business Media 01.06.2013
Springer US
Springer Nature B.V
Subjects
Accounting/Auditing
Approximation
Censorship
Cumulative distribution functions
Dependent variables
Econometrics
Economic models
Economic statistics
Economic theory
Economics
Economics and Finance
Estimating techniques
Mathematical independent variables
Maximum likelihood estimation
Maximum likelihood estimators
Maximum likelihood method
Microeconomics
Minimum wage
Modeling
Operations Research/Decision Theory
Performance evaluation
Production functions
Stochastic models
Studies
Variables
Wages
Wages & salaries
Censored stochastic frontier model
C13
C46
Stochastic frontier analysis
Cumulative distribution function
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Summary:This paper derives an analytic closed-form formula for the cumulative distribution function (cdf) of the composite error of the stochastic frontier analysis (SFA) model. Since the presence of a cdf is frequently encountered in the likelihood-based analysis with limiteddependent and qualitative variables as elegantly shown in the classic book of Maddala (Limited-dependent and qualitative variables in econometrics. Cambridge University Press, Cambridge, 1983), the proposed methodology is useful in the framework of the stochastic frontier analysis. We apply the formula to the maximum likelihood estimation of the SFA models with a censored dependent variable. The simulations show that the finite sample performance of the maximum likelihood estimator of the censored SFA model is very promising. A simple empirical example on the modeling of reservation wage in Taiwan is illustrated as a potential application of the censored SFA.
ISSN:0895-562X
1573-0441
DOI:10.1007/s11123-012-0283-1