A double-copula stochastic frontier model with dependent error components and correction for sample selection

In the standard stochastic frontier model with sample selection, the two components of the error term are assumed to be independent, and the joint distribution of the unobservable in the selection equation and the symmetric error term in the stochastic frontier equation is assumed to be bivariate normal. In this paper, we relax these assumptions by using two copula functions to model the dependences between the symmetric and inefficiency terms on the one hand, and between the errors in the sample selection and stochastic frontier equation on the other hand. Several families of copula functions are investigated, and the best model is selected using the Akaike Information Criterion (AIC). The methodology was applied to a sample of 200 rice farmers from Northern Thailand. The main findings are that (1) the double-copula stochastic frontier model outperforms the standard model in terms of AIC, and (2) the standard model underestimates the technical efficiency scores, potentially resulting in wrong conclusions and recommendations. We propose a stochastic frontier model with self-selection, based on two copulas.The model is estimated using maximum simulated likelihood.Several copula families are considered; the best model is selected using AIC.The model was applied to cross-sectional rice production data.Our model provides more reliable estimates of technical efficiency scores.

[1]  Hung T. Nguyen,et al.  Modeling volatility and dependency of agricultural price and production indices of Thailand: Static versus time-varying copulas , 2013, Int. J. Approx. Reason..

[2]  R. Nelsen.  An Introduction to Copulas (Springer Series in Statistics) , 2006 .

[3]  W. Greene,et al.  A stochastic frontier model with correction for sample selection , 2008 .

[4]  G. S. Maddala,et al.  Limited-dependent and qualitative variables in econometrics: Two-stage estimation methods , 1983 .

[5]  Murray D Smith,et al.  Modeling Sample Selection Using Archimedean Copulas , 2003 .

[6]  S. Rahman,et al.  Energy productivity and efficiency of maize accounting for the choice of growing season and environmental factors: An empirical analysis from Bangladesh , 2013 .

[7]  J. Heckman.  Sample selection bias as a specification error , 1979 .

[8]  D. Solís,et al.  The impact of high value markets on smallholder productivity in the Ecuadorean Sierra: A Stochastic Production Frontier approach correcting for selectivity bias , 2014 .

[9]  Songsak Sriboonchitta,et al.  Production efficiency of Jasmine rice producers in Northern and North-eastern Thailand , 2009 .

[10]  R. Nelsen.  An Introduction to Copulas , 1998 .

[11]  Murray D. Smith,et al.  Stochastic Frontier Models with Dependent Error Components , 2008 .

[12]  Bernhard Brümmer,et al.  Productive efficiency of specialty and conventional coffee farmers in Costa Rica: Accounting for technological heterogeneity and self-selection , 2012 .

[13]  Brian D. Johnson,et al.  Is the Magic Still There? The Use of the Heckman Two-Step Correction for Selection Bias in Criminology , 2007 .

[14]  A. U.S.,et al.  FORMULATION AND ESTIMATION OF STOCHASTIC FRONTIER PRODUCTION FUNCTION MODELS , 2001 .

[15]  Chih-Chiang Wu,et al.  The economic value of range-based covariance between stock and bond returns with dynamic copulas ☆ , 2011 .

[16]  Rosalba Radice,et al.  Computational Statistics and Data Analysis , 2022 .

[17]  Thierry Denoeux,et al.  Modeling dependence between error components of the stochastic frontier model using copula: Application to intercrop coffee production in Northern Thailand , 2015, Int. J. Approx. Reason..

[18]  William H. Greene,et al.  Simulated Likelihood Estimation of the Normal-Gamma Stochastic Frontier Function , 2000 .

[19]  Christian Cech,et al.  Copula-Based Top-Down Approaches in Financial Risk Aggregation , 2006 .