Nonparametric, Stochastic Frontier Models with Multiple Inputs and Outputs

References

• Aigner, D., Lovell, C. A. K., and Schmidt, P. (1977), “Formulation and Estimation of Stochastic Frontier Production Function Models,” Journal of Econometrics, 6, 21–37. DOI: 10.1016/0304-4076(77)90052-5.
   Google Scholar
• Akhavein, J. D., Berger, A. N., and Humphrey, D. B. (1997), “The Effects of Megamergers on Efficiency and Prices: Evidence from a Bank Profit Function,” Review of Industrial Organization, 12, 95–139.
   Web of Science ®Google Scholar
• Battese, G. E., and Corra, G. S. (1977), “Estimation of a Production Frontier Model: With Application to the Pastoral Zone Off Eastern Australia,” Australian Journal of Agricultural Economics, 21, 169–179. DOI: 10.1111/j.1467-8489.1977.tb00204.x.
   Web of Science ®Google Scholar
• Berger, A. N., and Mester, L. J. (1997), “Inside the Black Box: What Explains Differences in the Efficiencies of Financial Institutions?” Journal of Banking and Finance, 21, 895–947. DOI: 10.1016/S0378-4266(97)00010-1.
   Web of Science ®Google Scholar
• Chambers, R. G., Chung, Y., and Färe, R. (1996), “Benefit and Distance Functions,” Journal of Economic Theory, 70, 407–419. DOI: 10.1006/jeth.1996.0096.
   Web of Science ®Google Scholar
• Chambers, R. G., Chung, Y., and Färe, R. (1998), “Profit, Directional Distance Functions, and Nerlovian Efficiency,” Journal of Optimization Theory and Applications, 98, 351–364.
   Web of Science ®Google Scholar
• Coelli, T. (1995), “Estimators and Hypothesis Tests for a Stochastic Frontier Function: A Monte Carlo Analysis,” Journal of Productivity Analysis, 6, 247–268. DOI: 10.1007/BF01076978.
   Web of Science ®Google Scholar
• Coelli, T., and Perelman, S. (1996), “Efficiency Measurement, Multiple-Output Technologies and Distance Functions: With Application to European Railways,” CREPP working paper 96/05, University of Liège, Belgium.
   Google Scholar
• Cuesta, R. A., and Orea, L. (2002), “Mergers and Technical Efficiency in Spanish Savings Banks: A Stochastic Distance Function Approach,” Journal of Banking and Finance, 26, 2231–2247. DOI: 10.1016/S0378-4266(01)00184-4.
   Web of Science ®Google Scholar
• Daouia, A., Florens, J. P., and Simar, L. (2020), “Robust Frontier Estimation from Noisy Data: A Tikhonov Regularization Approach,” Econometrics and Statistics, 14, 1–23. DOI: 10.1016/j.ecosta.2018.07.003.
   Web of Science ®Google Scholar
• Daraio, C., and Simar, L. (2007), Advanced Robust and Nonparametric Methods in Efficiency Analysis, New York: Springer.
   Google Scholar
• Fan, J., and Gijbels, I. (1996), Local Polynomial Modelling and Its Applications, London: Chapman and Hall.
   Google Scholar
• Fan, Y., Li, Q., and Weersink, A. (1996), “Semiparametric Estimation of Stochastic Production Frontier Models,” Journal of Business and Economic Statistics, 14, 460–468.
   Web of Science ®Google Scholar
• Färe, R., Grosskopf, S., and Margaritis, D. (2008), “Productivity and Efficiency: Malmquist and More,” in The Measurement of Productive Efficiency (2nd ed.), eds. H. Fried, C. A. K. Lovell, and S. Schmidt, pp. 522–621, Oxford: Oxford University Press.
   Google Scholar
• Florens, J. P., Simar, L., and Van Keilegom, I. (2020), “Estimation of the Boundary of a Variable Observed with Symmetric Error,” Journal of the American Statistical Association, 115, 425–441. DOI: 10.1080/01621459.2018.1555093.
   Web of Science ®Google Scholar
• Hafner, C. M., Manner, H., and Simar, L. (2018), “The “Wrong Skewness” Problems in Stochastic Frontier Models: A New Approach,” Econometric Reviews, 37, 380–400.
   Web of Science ®Google Scholar
• Hall, P., and Simar, L. (2002), “Estimating a Changepoint, Boundary or Frontier in the Presence of Observation Error,” Journal of the American Statistical Association, 97, 523–534. DOI: 10.1198/016214502760047050.
   Web of Science ®Google Scholar
• Henderson, D. J., and Parmeter, C. F. (2015), Applied Nonparametric Econometrics, New York: Cambridge University Press.
   Google Scholar
• Jondrow, J., Lovell, C. A. K., Materov, I. S., and Schmidt, P. (1982), “On the Estimation of Technical Inefficiency in the Stochastic Frontier Production Model,” Journal of Econometrics, 19, 233–238. DOI: 10.1016/0304-4076(82)90004-5.
   Web of Science ®Google Scholar
• Kneip, A., Simar, L., and Van Keilegom, I. (2015), “Frontier Estimation in the Presence of Measurement Error with Unknown Variance,” Journal of Econometrics, 184, 379–393. DOI: 10.1016/j.jeconom.2014.09.012.
   Web of Science ®Google Scholar
• Kneip, A., Simar, L., and Wilson, P. W. (2008), “Asymptotics and Consistent Bootstraps for DEA Estimators in Non-parametric Frontier Models,” Econometric Theory, 24, 1663–1697. DOI: 10.1017/S0266466608080651.
   Web of Science ®Google Scholar
• Kumbhakar, S. C., Park, B. U., Simar, L., and Tsionas, E. G. (2007), “Nonparametric Stochastic Frontiers: A Local Likelihood Approach,” Journal of Econometrics, 137, 1–27. DOI: 10.1016/j.jeconom.2006.03.006.
   Web of Science ®Google Scholar
• Kumbhakar, S. C., Parmeter, C. F., and Zelenyuk, V. (2020), “Stochastic Frontier Analysis: Foundations and Advances i,” in Handbook of Production Economics, eds. S. C. Ray, R. Chambers, and S. Kumbhakar, pp. 1–40, Singapore: Springer.
   Google Scholar
• Kuosmanen, T., and Johnson, A. (2017), “Modeling Joint Production of Multiple Outputs in StoNED: Directional Distance Function Approach,” European Journal of Operational Research, 262, 792–801. DOI: 10.1016/j.ejor.2017.04.014.
   Web of Science ®Google Scholar
• Kuosmanen, T., and Kortelainen, M. (2012), “Stochastic Non-smooth Envelopment of Data: Semi-parametric Frontier Estimation Subject to Shape Constraints,” Journal of Productivity Analysis, 38, 11–28. DOI: 10.1007/s11123-010-0201-3.
   Web of Science ®Google Scholar
• Lang, S. (1964), A Second Course in Calculus, Reading, MA: Addison-Wesley Publishing Company, Inc.
   Google Scholar
• Li, Q., and Racine, J. (2007), Nonparametric Econometrics, Princeton, NJ: Princeton University Press.
   Google Scholar
• Lovell, C. A. K. (1993), “Production Frontiers and Productive Efficiency,” in The Measurement of Productive Efficiency: Techniques and Applications, eds. H. Fried, C. A. K. Lovell, and S. Schmidt, pp. 3–67, Oxford: Oxford University Press, Inc.
   Google Scholar
• Malikov, E., Kumbhakar, S. C., and Tsionas, M. G. (2016), “A Cost System Approach to the Stochastic Directional Technology Distance Functions with Undesirable Outputs: The Case of US Banks in 2011–2010,” Journal of Applied Econometrics, 31, 1407–1429. DOI: 10.1002/jae.2491.
   Web of Science ®Google Scholar
• Masry, E. (1996), “Multivariate Local Polynomial Regression for Time Series: Uniform Strong Consistency and Rates,” Journal of Time Series Analysis, 17, 571–599. DOI: 10.1111/j.1467-9892.1996.tb00294.x.
   Google Scholar
• Meeusen, W., and van den Broeck, J. (1977), “Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error,” International Economic Review, 18, 435–444. DOI: 10.2307/2525757.
   Web of Science ®Google Scholar
• Olson, J. A., Schmidt, P., and Waldman, D. M. (1980), “A Monte Carlo Study of Estimators of Stochastic Frontier Production Functions,” Journal of Econometrics, 13, 67–82. DOI: 10.1016/0304-4076(80)90043-3.
   Web of Science ®Google Scholar
• Park, B. U., Simar, L., and Zelenyuk, V. (2015), “Categorical Data in Local Maximum Likelihood: Theory and Application to Productivity Analysis,” Journal of Productivity Analysis, 43, 199–214. DOI: 10.1007/s11123-014-0394-y.
   Web of Science ®Google Scholar
• Parmeter, C. F., and Zelenyuk, V (2019), “Combining the Virtues of Stochastic Frontier and Data Envelopment Analysis,” Operations Research, 67, 1628–1658. DOI: 10.1287/opre.2018.1831.
   Web of Science ®Google Scholar
• Prokhorov, A., Tran, K. C., and Tsionas, M. G. (2021), “Estimation of Semi- and Nonparametric Stochastic Frontier Models with Endogenous Regressors,” Empirical Economics, 60, 3043–3068. DOI: 10.1007/s00181-020-01941-0.
   Web of Science ®Google Scholar
• Richmond, J. (1974), “Estimating the Efficiency of Production,” International Economic Review, 15, 515–521. DOI: 10.2307/2525875.
   Google Scholar
• Serra, T., Lansink, A. O., and Stefanou, S. E. (2011), “Measurement of Dynamic Efficiency: A Directional Distance Function Parametric Approach,” American Journal of Agricultural Economics, 93, 756–767. DOI: 10.1093/ajae/aaq175.
   Web of Science ®Google Scholar
• Sickles, R. C., and Zelenyuk, V. (2019), Measurement of Productivity and Efficiency, Cambridge, UK: Cambridge University Press.
   Google Scholar
• Simar, L. (2007), “How to Improve the Performances of DEA/FDH Estimators in the Presence of Noise,” Journal of Productivity Analysis, 28, 183–201. DOI: 10.1007/s11123-007-0057-3.
   Web of Science ®Google Scholar
• Simar, L., Van Keilegom, I., and Zelenyuk, V. (2017), “Nonparametric least squares methods for stochastic frontier models,” Journal of Productivity Analysis, 47, 189–204. DOI: 10.1007/s11123-016-0474-2.
   Web of Science ®Google Scholar
• Simar, L., and Wilson, P. W. (2010), “Estimation and Inference in Cross-Sectional, Stochastic Frontier Models,” Econometric Reviews, 29, 62–98. DOI: 10.1080/07474930903324523.
   Web of Science ®Google Scholar
• Simar, L., and Wilson, P. W. (2013), “Estimation and Inference in Nonparametric Frontier Models: Recent Developments and Perspectives,” Foundations and Trends in Econometrics, 5, 183–337.
   Google Scholar
• Simar, L., and Wilson, P. W. (2015), “Statistical Approaches for Non-parametric Frontier Models: A Guided Tour,” International Statistical Review, 83, 77–110.
   Web of Science ®Google Scholar
• Simar, L., and Zelenyuk, V. (2011), “Stochastic FDH/DEA Estimators for Frontier Analysis,” Journal of Productivity Analysis, 36, 1–20. DOI: 10.1007/s11123-010-0170-6.
   Web of Science ®Google Scholar
• Simper, R., Hall, M. J. B., Liu, W., Zelenyuk, V., and Zhou, Z. (2017), “How Relevant is the Choice of Risk Management Control Variable to Non-parametric Bank Profit Efficiency Analysis? The Case of South Korean Banks,” Annals of Operations Research, 250, 105–127. DOI: 10.1007/s10479-015-1946-x.
   Web of Science ®Google Scholar
• Sun, K., and Salim, R. (2020), “A Semiparametric Stochastic Input Distance Frontier Model with Application to the Indonesian Banking Industry,” Journal of Productivity Analysis, 54, 139–156. DOI: 10.1007/s11123-020-00589-3.
   Web of Science ®Google Scholar
• Wheat, P., Greene, W., and Smith, A. (2014), “Understanding Prediction Intervals for Firm Specific Inefficiency Scores from Parametric Stochastic Frontier Models,” Journal of Productivity Analysis, 42, 55– 65. DOI: 10.1007/s11123-013-0346-y.
   Web of Science ®Google Scholar
• Wheelock, D. C., and Wilson, P. W. (2001), “New Evidence on Returns to Scale and Product Mix Among U.S. Commercial Banks,” Journal of Monetary Economics, 47, 653–674. DOI: 10.1016/S0304-3932(01)00059-9.
   Web of Science ®Google Scholar
• Wheelock, D. C., and Wilson, P. W. (2012), “Do Large Banks have Lower Costs? New Estimates of Returns to Scale for U.S. Banks,” Journal of Money, Credit, and Banking, 44, 171–199.
   Web of Science ®Google Scholar
• Wheelock, D. C., and Wilson, P. W. (2018), “The Evolution of Scale-Economies in U.S. Banking,” Journal of Applied Econometrics, 33, 16–28.
   Web of Science ®Google Scholar
• Wilson, P. W. (2018), “Dimension Reduction in Nonparametric Models of Production,” European Journal of Operational Research, 267, 349–367. DOI: 10.1016/j.ejor.2017.11.020.
   Web of Science ®Google Scholar