Estimation of Dynamic Stochastic Frontier Model using Likelihood-based Approaches

Lai, Hung-pin and Kumbhakar, Subal C. (2018): Estimation of Dynamic Stochastic Frontier Model using Likelihood-based Approaches.

Abstract

Almost all the existing panel stochastic frontier models treat technical efficiency as static. Consequently there is no mechanism by which an inefficient producer can improve its efficiency over time. The main objective of this paper is to propose a panel stochastic frontier model that allows the dynamic adjustment of persistent technical inefficiency. The model also includes transient inefficiency which is assumed to be heteroscedastic. We consider three likelihood-based approaches to estimate the model: the full maximum likelihood (FML), pairwise composite likelihood (PCL) and quasi-maximum likelihood (QML) approaches. Moreover, we provide Monte Carlo simulation results to examine and compare the finite sample performances of the three above-mentioned likelihood-based estimators. Finally, we provide an empirical application to the dynamic model.

• Item Type: MPRA Paper
• Language: English
• Keywords: Technical inefficiency, panel data, copula, full maximum likelihood estimation, pairwise composite likelihood estimation, quasi-maximum likelihood estimation
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C23 - Panel Data Models ; Spatio-temporal Models; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C24 - Truncated and Censored Models ; Switching Regression Models ; Threshold Regression Models; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation

References

Ahn, S. C., D.H. Good and R. C. Sickles. (2000). "Estimation of long-run inefficiency levels: a dynamic frontier approach." Econometric Reviews, 19(4): 461-492.

Amsler, C., A. Prokhorov, and P. Schmidt. (2014). Using copulas to model time dependence in stochastic frontier models." Econometric Reviews, 33(5–6):497–522.

Arnold, B. C. and D. Strauss (1991). "Pseudolikelihood estimation: some examples." Sankhyā: The Indian Journal of Statistics, Series B. 53(2): 233-243.

Battese, G. E. and T. J. Coelli (1992). "Frontier production functions, technical efficiency and panel data: with application to paddy farmers in India." Journal of Productivity Analysis. 3: 153-169.

Belotti, F. and G. Ilardi (2017). "Consistent inference in fixed-effects stochastic frontier models." Journal of Econometrics, forthcoming.

Chandler, R. E. and Bate, S. (2007), "Inference for clustered data using theindependence log-likelihood", Biometrika, 94(1), 167-183.

Cornwell, C., P. Schmidt, and R. Sickles. (1990). "Production frontiers with cross-sectional and time-series variation in efficiency levels." Journal of Econometrics, 46: 185-200.

Cox, D. R. and N. Reid (2004). "A note on pseudolikelihood constructed from marginal densities." Biometrika. 91(3): 729-737.

Emvalomatis, G. (2012). "Adjustment and unobserved heterogeneity in dynamic stochastic frontier models." Journal of Productivity Analysis. 37: 7-16.

Filippini, M., and Greene, W.H., (2016), “Persistent and Transient Productive Inefficiency: A Maximum Simulated Likelihood Approach." Journal of Productivity Analysis, 45:187-196.

Geweke, J. (1989), “Bayesian inference in econometric models using Monte Carlo integration”. Econometrica. 57: 1317–1339.

González-Farías, G, J. A. Dominguez-Molina, and A.K. Gupta (2004). "The closed skew normal distribution." In Skew-elliptical distribution and their applications: A journey beyond normality. M.G. Genton (ed), Chapman and Hall/CRC Press.

Hajivassiliou, V., and D. McFadden (1998). The method of simulated scores for the estimation of LDV models. Econometrica, 66: 863–896.

Keane, M. P. (1994). A computationally practical simulation estimator for panel data. Econometrica, 62: 95–116.

Kumar, S. and R. R. Russell (2002). "Technological change, technological catch-up, and capital deepening: relative contributions to growth and convergence." American Economic Review. 92(3): 527-548.

Kumbhakar, S. C. (1987). "The specification of technical and allocative inefficiency in stochastic production and profit frontiers." Journal of Econometrics, 34(3): 335-348.

Kumbhakar, S. C. (1990). "Production frontiers, panel data, and time-varying Technical inefficiency." Journal of Econometrics. 46(1-2): 201-211.

Kumbhakar, S. C. and H.-J. Wang (2005). "Estimation of growth convergence using a stochastic production frontier approach." Economics Letters. 88: 300-305.

Lee, Y. and P. Schmidt (1993). "A production frontier model with flexible temporal variation in technical efficiency." The Measurement of Productive Efficiency: Techniques and Applications,Oxford University Press.

Mardia, K. V., et al. (2009). "Maximum likelihood estimation using composite likelihoods for closed exponential families." Biometrika. 96(4): 975-982.

Pitt, M. M. and L.-F. Lee (1981). "The measurement and sources of technical inefficiency in the Indonesian weaving industry." Journal of Development Economics. 9: 43-64.

Renard, D., et al. (2004). "A pairwise likelihood approach to estimation in multilevel probit models." Computational Statistics & data. 44(4): 649-667.

Schmidt, P. and R. C. Sickles (1984). "Production frontiers and panel data." Journal of Business & Economic Statistics. 2(4): 367-374.

Schweizer, B. and A. Sklar (1983), Probability Metric Spaces, Elsevier Science, New York.

Sklar, A. (1959), “Fonctions de Répartition à n Dimensions et Leurs Marges,” Publications de l’Institut de Statistique de L’Université de Paris, 8: 229-31.

Tsionas, E. G. (2006). "Inference in Dynamic Stochastic frontier models." Journal of Applied Econometrics, 21: 669-676.

Varin, C. and P. Vidoni (2005)."A note on composite likelihood inference and model selection. " Biometrika, 92(3): 519–528.