© Anik Djuraidah, Ismail Pranata. Article available under the CC BY-SA 4.0 licence
ARTICLE
ABSTRACT
Technical efficiency measures the performance of an observation unit in generating outputs effectively. The stochastic production frontier (SPF), which is a commonly used method for this purpose, determines how close a unit is to achieving maximum output based on its inputs. However, the outliers in the data can distort the accuracy of SPF models. To address this issue, various error distribution modifications like gamma, Student’s-t, Weibull and Rayleigh distributions have been proposed. However, there is limited research comparing these distributions in handling outliers. This study describes a simulation conducted to compare five SPF models: Normal-half Normal, Normal-Gamma, Normal-Weibull, Normal-Rayleigh, and Student’s-t-half Normal. Applying simulated data across nine scenarios with varying data amounts and outlier percentages, the findings demonstrate that the SPF Student’s t-half Normal model provides the most accurate prediction of technical efficiency. Using a heavy-tailed distribution, such as the Student's t distribution, for the disturbance component is more effective in handling outliers in the response variable than modifying the inefficiency of the component distribution.
KEYWORDS
robust, outlier, simulation, stochastic production frontier, technical efficiency.
REFERENCES
Aigner, D. J., Chu, S. F., (1968). On estimating the industry production function. American Economic Review, 58(4), pp. 826–839.
Aigner, D., Lovell, C. A. K. and Schmidt, P., (2023). Reprint of: Formulation and estimation of stochastic frontier production function models. J. Econometrics, 234(S), pp. 15–24. doi: 10.1016/j.jeconom.2023.01.
Behr, A., (2015). Production and efficiency analysis with R. Springer, Cham.
Campos, M. S., Costa, M. A., Gontijo, T. S., Lopes-Ahn, A. L., (2022). Robust stochastic frontier analysis applied to the Brazilian electricity distribution benchmarking method. Decis. Anal., 3, 100051. doi:/10.1016/j.dajour.2022.100051.
Coelli, T., (1995). Estimators and hypothesis tests for a stochastic frontier function: A Monte Carlo analysis. Journal of Productivity Analysis, 6(3), pp. 247–268. doi: 10.1007/BF01076978.
Coelli, T. J., Rao, D. S. P., O’Donnell, C. J. and Battese, G.E., (2005). An introduction to efficiency and productivity analysis. Springer, Boston, MA, USA.
Dakpo, K. H., Desjeux, Y. and Latruffe, L., (2022). {sfaR}: Stochastic frontier analysis using R.
Greene, W. H., (1990). A gamma-distributed stochastic frontier model. J. Econometrics, 46, pp. 141–163.
Greene, W. H., (2003). Simulated likelihood estimation of the normal-gamma stochastic frontier function. Journal of Productivity Analysis, 19, pp. 179–190.
Hajargasht, G., (2015). Stochastic frontiers with a Rayleigh distribution. Journal of Productivity Analysis, 44(2), pp 199-208. doi: 10.1007/s11123-014-0417-8.
Jondrow, J., Knox Lovell, C., Materov, I. S., Schmidt, P., (1982). On the estimation of technical inefficiency in the stochastic frontier production function model. J. Econometrics., 19(2-3), 233-238. Doi: 10.1016/0304-4076(82)90004-5.
Kumbhakar, C. S., Wang, J. H. and Horncastle, P. A., (2015). A practitioner’s guide to stochastic frontier analysis using Stata. Cambridge University Press, New York.
Mariyono, J., (2006). Geographical distribution of technical efficiency in Indonesian rice production during the period of 1979-1994. Ekon. Pembang., 11, pp. 33–48.
Meeusen, W., Van Den Broeck, J., (1977). Efficiency estimation from Cobb-Douglas production function with composed error. International Economic Review (Philadelphia), 18.
Mutz, R., Bornmann, L. and Daniel, H.-D., (2017). Are there any frontiers of research performance? Efficiency measurement of funded research projects with the Bayesian stochastic frontier analysis for count data. JOI, 11(3), pp. 613–628. doi: 10.1016/j.joi.2017.04.009.
Nurwulan, R., Djuraidah, A. and Fitrianto, A., (2022). Handling outliers in the stochastic frontier model using Cauchy and Rayleigh distributions to measure technical efficiency of rice farming business. Indonesian Journal of Artificial Intelligence and Data Mining, 5(2), pp. 98–110.
O’Donnell, C. J., (2018). Productivity and efficiency analysis. Springer, Singapore.
Pranata, I., Djuraidah, A. and Aidi, M., (2023). Robust stochastic production frontier to estimate technical efficiency of rice farming in Sulawesi Selatan. Barekeng Journal of Mathematics and Applications, 17(1). doi: 10.30598/barekengvol17iss1pp0391-0400.
Sakouvogui, K., Shaik, S., Doetkott, C. and Magel, R., (2021). Sensitivity analysis of stochastic frontier analysis models. Monte Carlo Methods and Applications, 27 (1), pp. 71-90. doi: 10.1515/mcma-2021-2083.
Sartono, B. , (2005). Pembangkitan bilangan acak untuk simulasi Monte Carlo nonparametrik. Forum Statistika dan Komputasi, 10, pp. 8–11.
Train, K., (2009). Discrete choice methods with simulation. 2nd ed. Cambridge University Press, Cambridge.
Tsionas, G. E., (2007). Efficiency measurement with the Weibull stochastic frontier. Oxford Bulletin of Economics and Statistics, 69(5), pp. 693–706. doi: 10.1111/j.1468- 0084.2007.
Wheat, P., Stead, A. D. and Greene, W. H., (2019). Robust stochastic frontier analysis: A Student’s t-half normal model with application to highway maintenance costs in England. Journal of Productivity Analysis, 51(1), pp. 21–38. doi: 10.1007/s11123- 018-0541-y.
Zulkarnain, R., Djuraidah, A., Sumertajaya, I. M. and Indahwati, (2021). Utilization of Student’s-T distribution to handle outliers in technical efficiency measurement. Media Statistika, 14(1), pp. 56–67.