Generalized theory for measuring efficiency of individuals and groups. (English) Zbl 07905462
Summary: We present a cohesive generalized framework for an aggregation of the Nerlovian profit indicators and of the directional distance functions, frequently used in productivity and efficiency analysis in operations research and econometrics (e.g., via data envelopment analysis or stochastic frontier analysis). Our theoretical framework allows for greater flexibility than previous approaches, and embraces many other approaches as special cases. In the proposed aggregation scheme, the aggregation weights are mathematically derived from assumptions made about the optimization behavior and about the chosen directions of measurement. We also discuss various interesting special cases of popular directions, including the case of Debreu-Farrell-type efficiency.
MSC:
| 90B50 | Management decision making, including multiple objectives |
| 90C08 | Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) |
References:
| [1] | Blackorby, C.; Russell, RR, Aggregation of efficiency indices, Journal of Productivity Analysis, 12, 1, 5-20, 1999 |
| [2] | Bogetoft, P.; Wang, D., Estimating the potential gains from mergers, Journal of Productivity Analysis, 23, 2, 145-171, 2005 |
| [3] | Briec, W.; Dervaux, B.; Leleu, H., Aggregation of directional distance functions and industrial efficiency, Journal of Economics, 79, 3, 237-261, 2003 · Zbl 1058.91048 |
| [4] | Briec, W.; Dubois, M.; Mussard, S., Technical efficiency in firm games with constant returns to scale and \(\alpha \)-returns to scale, Annals of Operations Research, 304, 1-2, 35-62, 2021 · Zbl 1475.91129 |
| [5] | Chambers, R.; Chung, Y.; Färe, R., Profit, directional distance functions, and Nerlovian efficiency, Journal of Optimization Theory and Applications, 98, 2, 351-364, 1998 · Zbl 0909.90040 |
| [6] | Chambers, RG; Chung, Y.; Färe, R., Benefit and distance functions, Journal of Economic Theory, 70, 2, 407-419, 1996 · Zbl 0866.90027 |
| [7] | Charnes, A.; Cooper, W.; Rhodes, E., Measuring the efficiency of decision making units, European Journal of Operational Research, 2, 6, 429-444, 1978 · Zbl 0416.90080 |
| [8] | Cherchye, L.; De Rock, B.; Walheer, B., Multi-output profit efficiency and directional distance functions, Omega (Oxford), 61, 100-109, 2016 |
| [9] | Cooper, W.; Huang, Z.; Li, S.; Parker, B.; Pastor, J., Efficiency aggregation with enhanced Russell measures in data envelopment analysis, Socio-Economic Planning Sciences, 41, 1, 1-21, 2007 |
| [10] | Debreu, G., The coefficient of resource utilization, Econometrica, 19, 3, 273-292, 1951 · Zbl 0045.41404 |
| [11] | Färe, R.; Grosskopf, S.; Zelenyuk, V., Aggregation of cost efficiency: Indicators and indexes across firms, Academia Economic Papers, 32, 3, 395-411, 2004 |
| [12] | Färe, R.; Grosskopf, S.; Zelenyuk, V., Aggregation of Nerlovian profit indicator, Applied Economics Letters, 15, 11, 845-847, 2008 |
| [13] | Färe, R.; He, X.; Li, S.; Zelenyuk, V., A unifying framework for Farrell profit efficiency measurement, Operations Research, 67, 1, 183-197, 2019 · Zbl 1455.91132 |
| [14] | Färe, R.; Lovell, CK, Measuring the technical efficiency of production, Journal of Economic Theory, 19, 1, 150-162, 1978 · Zbl 0398.90012 |
| [15] | Färe, R.; Zelenyuk, V., On aggregate Farrell efficiencies, European Journal of Operational Research, 146, 3, 615-620, 2003 · Zbl 1037.90516 |
| [16] | Färe, R.; Zelenyuk, V., On Farrell’s decomposition and aggregation, International Journal of Business and Economics, 4, 2, 167-171, 2005 |
| [17] | Färe, R.; Zelenyuk, V., Extending Färe and Zelenyuk (2003), European Journal of Operational Research, 179, 2, 594-595, 2007 · Zbl 1131.90380 |
| [18] | Färe, R.; Zelenyuk, V., Profit efficiency: Generalization, business accounting and the role of convexity, Economics Letters, 196, 109483, 2020 · Zbl 1451.91066 |
| [19] | Farrell, MJ, The measurement of productive efficiency, Journal of the Royal Statistical Society. Series A (General), 120, 3, 253-290, 1957 |
| [20] | Førsund, FR; Hjalmarsson, L., Generalised Farrell measures of efficiency: An application to milk processing in Swedish dairy plants, The Economic Journal, 89, 354, 294-315, 1979 |
| [21] | Karagiannis, G., On structural and average technical efficiency, Journal of Productivity Analysis, 43, 3, 259-267, 2015 |
| [22] | Karagiannis, G.; Lovell, CAK, Productivity measurement in radial DEA models with a single constant input, European Journal of Operational Research, 251, 1, 323-328, 2015 · Zbl 1346.90591 |
| [23] | Koopmans, T., Three essays on the state of economic science, 1957, McGraw-Hill |
| [24] | Kuosmanen, T.; Cherchye, L.; Sipiläinen, T., The law of one price in data envelopment analysis: Restricting weight flexibility across firms, European Journal of Operational Research, 170, 3, 735-757, 2006 · Zbl 1091.90520 |
| [25] | Kuosmanen, T.; Kortelainen, M.; Sipiläinen, T.; Cherchye, L., Firm and industry level profit efficiency analysis using absolute and uniform shadow prices, European Journal of Operational Research, 202, 2, 584-594, 2010 · Zbl 1179.90111 |
| [26] | Li, S-K; Cheng, Y-S, Solving the puzzles of structural efficiency, European Journal of Operational Research, 180, 2, 713-722, 2007 · Zbl 1123.90325 |
| [27] | Li, S-K; Ng, YC, Measuring the productive efficiency of a group of firms, International Advances in Economic Research, 1, 4, 377-390, 1995 |
| [28] | Luenberger, DG, Benefit functions and duality, Journal of Mathematical Economics, 21, 5, 461-481, 1992 · Zbl 0766.90011 |
| [29] | Mayer, A.; Zelenyuk, V., Aggregation of Malmquist productivity indexes allowing for reallocation of resources, European Journal of Operational Research, 238, 3, 774-785, 2014 · Zbl 1338.91085 |
| [30] | Mayer, A.; Zelenyuk, V., The Palgrave Handbook of Economic Performance Analysis, Aggregation of individual efficiency measures and productivity indices, 527-557, 2019, Springer International Publishing |
| [31] | Mussard, S.; Peypoch, N., On multi-decomposition of the aggregate Malmquist productivity index, Economics Letters, 91, 3, 436-443, 2006 |
| [32] | Nesterenko, V.; Zelenyuk, V., Measuring potential gains from reallocation of resources, Journal of Productivity Analysis, 28, 1-2, 107-116, 2007 |
| [33] | Pachkova, EV, Restricted reallocation of resources, European Journal of Operational Research, 196, 3, 1049-1057, 2009 · Zbl 1176.90309 |
| [34] | Pham, M.; Simar, L.; Zelenyuk, V., Statistical inference for aggregation of Malmquist productivity indices, Operations Research, Forthcoming, 2023 · Zbl 07907217 · doi:10.1287/opre.2022.2424 |
| [35] | Raa, TT, Benchmarking and industry performance, Journal of Productivity Analysis, 36, 3, 285-292, 2011 |
| [36] | Russell, RR, Continuity of measures of technical efficiency, Journal of Economic Theory, 51, 2, 255-267, 1990 · Zbl 0715.90024 |
| [37] | Shephard, RW, Cost and production functions, 1953, Princeton University Press · Zbl 0052.15901 |
| [38] | Sickles, R.; Zelenyuk, V., Measurement of productivity and efficiency: Theory and practice, 2019, Cambridge University Press · Zbl 1409.91006 |
| [39] | Simar, L.; Wilson, PW, Statistical approaches for nonparametric frontier models: A guided tour, International Statistical Review, 83, 1, 77-110, 2015 · Zbl 07762797 |
| [40] | Simar, L.; Zelenyuk, V., Statistical inference for aggregates of Farrell-type efficiencies, Journal of Applied Econometrics, 22, 7, 1367-1394, 2007 |
| [41] | Simar, L.; Zelenyuk, V., Central limit theorems for aggregate efficiency, Operations Research, 166, 1, 139-149, 2018 · Zbl 1457.91211 |
| [42] | Walheer, B., Aggregation of metafrontier technology gap ratios: The case of European sectors in 1995-2015, European Journal of Operational Research, 269, 3, 1013-1026, 2018 · Zbl 1388.90059 |
| [43] | Walheer, B., Aggregating Farrell efficiencies with private and public inputs, European Journal of Operational Research, 276, 3, 1170-1177, 2019 · Zbl 1430.90353 |
| [44] | Zelenyuk, V., Aggregation of Malmquist productivity indexes, European Journal of Operational Research, 174, 2, 1076-1086, 2006 · Zbl 1103.90366 |
| [45] | Zelenyuk, V. (2022). Aggregation of efficiency and productivity: From firm to sector and higher levels. In S. C. Ray, R. G. Chambers, S. C. Kumbhakar (Eds.), Handbook of production economics. Springer, Singapore. doi:10.1007/978-981-10-3455-8_19 |
| [46] | Zelenyuk, V., Aggregation in efficiency and productivity analysis: A brief review with new insights and justifications for constant returns to scale, Journal of Productivity Analysis, Forthcoming, 2023 · doi:10.1007/s11123-023-00671-6 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
