Panel Stochastic Frontier Analysis with Dependent Error Terms

Abstract

In presence of panel data, technical efficiency is used to compare the performances of Decision-Making Units (DMUs). The novelty of this paper is the consideration of the dependence between the two error terms in the case of panel data and the introduction of time effect models in the Stochastic Frontier Analysis (SFA). Hence, our SFA model considers the balanced panel case, several models describing the evolution of the inefficiency over time and the dependence between the two error terms. The inefficiency and noise terms being dependent, a copula function which reflects the dependence between them is included in their joint density. The model is estimated by maximum likelihood and the Akaike Information Criterion (AIC) is used for model selection. Moreover, a likelihood ratio test is performed for the nested models. A bootstrap algorithm is proposed for statistical inference on the Technical Efficiency (TE) measures. Results for Moroccan policy of the production and sales of drinking water from 2001 to 2007 identify the most and least efficient provinces, and a generally positive trend of estimated TE measures.

Keywords

• Bootstrap
• Copulas
• Efficiency
• Panel data
• Stochastic frontier analysis

References

1. Battese, G.E. and T.J. Coelli (1988). Prediction of firm level technical efficiencies with a generalized frontier production function and panel data. Journal of Econometrics, 38(3), 387-399.
2. Battese, G.E. and T.J. Coelli (1992). Frontier Production Functions, Technical Efficiency and Panel Data: With Application to Paddy Farmers in India. The Journal of Productivity Analysis, 3(1), 153-169.
3. Battese, G.E. and T.J. Coelli (1995). A Model for Technical Inefficiency Effects in a Stochastic Frontier Production Function for Panel Data. Empirical Economics, 20, 325- 332.
4. Battese, G.E., A. Heshmati, and L. Hjalmarsson (2000). Efficiency of labour use in Swedish39 International Econometric Review (IER) banking industry: a stochastic frontier approach. Empirical Economics, 25(4), 623- 640.
5. Battese, G.E., T.J. Coelli, and T.C. Colby (1989). Estimation of Frontier Production Functions and the Efficiencies of Indian Farms Using Panel Data from ICRISAT’s Village LevelStudies. JournalofQuantitativeEconomics, 5(2), 327-348.
6. Bhat, C. and N. Eluru (2009). A Copula-Based Approach to Accommodate Residential SelfSelection Effects in Travel Behavior Modeling. Transportation Research, Part B, 43(7), 749-765.
7. Coelli, T.J. (1995). Estimators and hypothesis tests for a stochastic frontier function: A Monte Carlo analysis. Journal of Productivity Analysis, 6(3), 247-268.
8. Coelli, T.J. (1996). A Guide to FRONTIER, Version 4.1: A Computer Program for Stochastic Frontier Production and Cost Function Estimation. Centre for efficiency and Productivity Analysis, CEPA Working Paper 96/07, Department of Econometrics, University of New England.

9. Cornwell, C., P. Schmidt, and R.C. Sickles (1990). Production frontiers with cross-sectional and time-series variation in efficiency levels. Journal of Econometrics, 46(1-2), 185- 200.
10. Daraio, C. and L. Simar (2007). Advanced Robust and Nonparametric Methods in Efficiency Analysis: Methodology and Applications. Springer.
11. De Witte, K. and R.C. Marques (2008). Designing incentives in local public utilities, an international comparison of the drinking water sector. Social Science Research Network SSRN 1084807.
12. Efron, B. (1982). The jackknife, the bootstrap, and other resampling plans. CBMS-NSF Regional Conference Series in Applied Mathematics, #38. Philadelphia: SIAM.
13. El Mehdi, R. and C.M. Hafner (2014a). Local government efficiency: The case ofMoroccan municipalities. AfricanDevelopmentReview, 26(1),88-101.
14. El Mehdi, R. and C.M. Hafner (2014b). Inference in stochastic frontier analysis with dependent error terms. Mathematics and Computers in Simulation (MATCOM), 102(C), 104-116.
15. Faria, R.C., G.S. Souza, and T.B. Moreira (2005). Public versus private water utilities: Empirical evidence for brazilian companies. Economics Bulletin, 8(2), 1-7.
16. Gallant, A. Ronald (1984). The fourier flexible form. American Journal of Agricultural40 International Econometric Review (IER) Economics, 66(2), 204-208.
17. Jondrow, J., C. A. Knox Lovell, I. S. Materov, and P. Schmidt (1982). On the estimation of technical inefficiency in the stochastic frontier production function model. Journal of Econometrics, 19(2-3), 233-238.
18. Kim, S. and Y.H. Lee (2006). The productivity debate of East Asia revisited: a stochastic frontier approach. AppliedEconomics, Taylorand FrancisJournals, 38(14), 1697-1706.
19. Kumbhakar, S.C. (1990). Production frontiers, panel data, and time-varying technical inefficiency. Journal of Econometrics, 46(1-2), 201- 211.
20. Kumbhakar, S.C. and C.A. Knox Lovell (2000). Stochastic Frontier Analysis. First edition. Cambridge University Press, United Kingdom.
21. Lee, Y.H. and P. Schmidt (1993). A Production Frontier Model with Flexible Temporal Variation in Technical Inefficiency. The Measurement of Productive Efficiency: Techniques and Applications. Edited by H. Fried, C.A.K. Lovell and S. Schmidt, Oxford University Press, pp. 237-255.
22. Nelsen, R. B. (1999). An Introduction to Copulas. First edition. Springer, New York.
23. Sampaio, A., C. Barros, and J. Ramajo (2005). Technical Inefficiency in Municipal Water Distribution Service: A Case Study for Portugal. Anales de Economia Aplicada, XIX Reuni´ on Anual. Edi¸ c˜ oes Asepelt (Associa¸ c˜ ao de Economia Aplicada) Espanha Badajoz.
24. Schmidt, P. and R.C. Sickles (1984). Production frontiers and panel data. Journal of Business & Economic Statistics, 2(4), 367-374.
25. Simar, L. and P.W. Wilson (2010). Inferences from cross-sectional, stochastic frontier models. Econometric Reviews, 29(1), 62-98.
26. Smith, M.D. (2008). Stochastic frontier models with dependent error components. The Econometrics Journal, 11(1), 172-192.
27. Tupper, H.C. and M. Resende (2004). Efficiency and regulatory issues in the Brazilian water and sewage sector: an empirical study. Utilities Policy, 12(1), 29-40.
28. Vishwakarma, A. and M. Kulshrestha (2010). Stochastic Production Frontier Analysis of Water Supply Utility of Urban Cities in the State of Madhya Pradesh, India. International Journal of EnvironmentalSciences, 1(3), 357-367.