Using Copulas to Model Time Dependence in Stochastic Frontier Models
AbstractWe consider stochastic frontier models in a panel data setting where there is dependence over time. Current methods of modelling time dependence in this setting are either unduly restrictive or computationally infeasible. Some impose restrictive assumptions on the nature of dependence such as the "scaling" property. Others involve T-dimensional integration, where T is the number of cross-sections, which may be large. Moreover, no known multivariate distribution has the property of having commonly used, convenient marginals such as normal/half-normal. We show how to use copulas to resolve these issues. The range of dependence we allow for is unrestricted and the computational task involved is easy compared to the alternatives. Also, the resulting estimators are more efficient than those that assume independence over time. We propose two alternative specifications. One applies a copula function to the distribution of the composed error term. This permits the use of MLE and GMM. The other applies a copula to the distribution of the one-sided error term. This allows for a simulated MLE and improved estimation of inefficiencies. An application demonstrates the usefulness of our approach.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Concordia University, Department of Economics in its series Working Papers with number 11002.
Date of creation: Aug 2011
Date of revision:
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Artem Prokhorov & Peter Schmidt, 2009.
"Likelihood Based Estimation in a Panel Setting: Robustness, Redundancy and Validity of Copulas,"
09002, Concordia University, Department of Economics.
- Prokhorov, Artem & Schmidt, Peter, 2009. "Likelihood-based estimation in a panel setting: Robustness, redundancy and validity of copulas," Journal of Econometrics, Elsevier, vol. 153(1), pages 93-104, November.
- Horrace, William C., 2005. "Some results on the multivariate truncated normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 209-221, May.
- Kumbhakar, Subal C., 1990. "Production frontiers, panel data, and time-varying technical inefficiency," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 201-211.
- Wen-Jen Tsay & Cliff J. Huang & Tsu-Tan Fu & I-Lin Ho, 2009. "Maximum Likelihood Estimation of Censored Stochastic Frontier Models: An Application to the Three-Stage DEA Method," IEAS Working Paper : academic research 09-A003, Institute of Economics, Academia Sinica, Taipei, Taiwan.
- Greene, William, 2005. "Reconsidering heterogeneity in panel data estimators of the stochastic frontier model," Journal of Econometrics, Elsevier, vol. 126(2), pages 269-303, June.
- Jondrow, James & Knox Lovell, C. A. & Materov, Ivan S. & Schmidt, Peter, 1982. "On the estimation of technical inefficiency in the stochastic frontier production function model," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 233-238, August.
- Wei Wang & Christine Amsler & Peter Schmidt, 2011. "Goodness of fit tests in stochastic frontier models," Journal of Productivity Analysis, Springer, vol. 35(2), pages 95-118, April.
- Wang, Hung-Jen, 2006. "Stochastic frontier models," MPRA Paper 31079, University Library of Munich, Germany.
- Caudill, Steven B & Ford, Jon M & Gropper, Daniel M, 1995. "Frontier Estimation and Firm-Specific Inefficiency Measures in the Presence of Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 105-11, January.
- William C. Horrace & Peter Schmidt, 2002. "Confidence Statements for Efficiency Estimates from Stochastic Frontier Models," Econometrics 0206006, EconWPA.
- Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
- Peter Schmidt & Antonio Alvarez & Christine Amsler, 2004.
"Interpreting and testing the scaling property in models where inefficiency depends on firm characteristics,"
Econometric Society 2004 Far Eastern Meetings
520, Econometric Society.
- Antonio Alvarez & Christine Amsler & Luis Orea & Peter Schmidt, 2006. "Interpreting and Testing the Scaling Property in Models where Inefficiency Depends on Firm Characteristics," Journal of Productivity Analysis, Springer, vol. 25(3), pages 201-212, 06.
- Pitt, Mark M. & Lee, Lung-Fei, 1981. "The measurement and sources of technical inefficiency in the Indonesian weaving industry," Journal of Development Economics, Elsevier, vol. 9(1), pages 43-64, August.
- Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Economics Department).
If references are entirely missing, you can add them using this form.