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Another look at productivity growth in industrialized countries

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Abstract

This paper discusses early work on productivity change by Färe and Grosskopf and their co-authors. We illustrate the use of recent statistical results by revisiting and updating Färe et al. (1994, AER). We analyze 17 OECD countries, estimating productivity change and its sources as measured by Malmquist indices and various decompositions. We describe and use recent theoretical results to make inferences, thereby quantifying what is learned from the data as opposed to merely providing point estimates.

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Notes

  1. Note that this is a pointed cone (i.e., \({{{\mathcal{C}}}}({{{\Psi }}}^{t})\) includes {(0, 0)}). Moreover, conical hulls are necessarily convex; e.g., see Hiriart-Urruty and Lemaréchal (1993, pp. 101–102).

  2. Country i is scale-efficient in period 1 if \(\gamma ({Z}_{i}^{1}| {{{\mathcal{C}}}}({{{\Psi }}}^{1}))=\gamma ({Z}_{i}^{1}| {{{\Psi }}}^{1})\). Otherwise, the country is scale-inefficient. See Wheelock and Wilson (1999) for discussion.

  3. The assumptions can also be stated in terms of the output, hyperbolic and directional measures of efficiency, and the results of Kneip et al. (2015) extend to those measures after trivial (but tedious) changes in notation in Kneip et al. (2015).

  4. Färe et al. (1985) make no mention of how (3.4) might be computed. Ray (2001) proposes what amounts to a delta-method approximation that can be computed using linear programming methods, but this can introduce substantial errors. Wilson (2011) provides a simple algorithm for computing (3.4) that does not rely on non-linear programming, and this method is implemented in the FEAR package for R described by Wilson (2008). See Wilson (2011) for additional discussion.

  5. See, for example, Spanos (2019) for detailed discussion of the difference between estimators and estimates. Korostelev et al. (1995a, b) are the first papers to analyze the differences and relations between Ψt and estimators of Ψt.

  6. In their Table 3, Färe et al. (1994) report technical efficiency estimates for each of the 17 countries examined in 1979, 1983 and 1988. The technical efficiency estimates are computed while imposing CRS. As such, the estimates are valid iff globally CRS holds in each year, while the VRS-DEA estimators are consistent regardless of whether CRS holds.

  7. The theory developed by Kneip et al. (2021) explicitly allows for dependence of a given country’s input-output quantities across time, but require independence of the country’s input-output quantities from those of other countries in other periods. Cross-sectional, spatial dependence and how to deal with it in the present context remain unresolved issues left for future research. In Table 2, dependence across time is preserved in the bootstrap world by drawing pairs of input-output observations for specific countries.

  8. The FEAR package is available at https://pww.people.clemson.edu/Software/FEAR/fear.html for free use for academic research.

References

  • Adelman D (2022) An efficient frontier approach to scoring and ranking hospital performance. Operations Res 68:762–792

    Google Scholar 

  • Apon AW, Ngo LB, Payne ME, Wilson PW (2015) Assessing the effect of high performance computing capabilities on academic research output. Empirical Econ 48:283–312

    Google Scholar 

  • Badunenko O, Henderson DJ, Houssa R (2014) Significant drivers of growth in Africa. J Prod Anal 42:339–354

    Google Scholar 

  • Banker RD, Charnes A, Cooper WW (1984) Some models for estimating technical and scale inefficiencies in data envelopment analysis. Manag Sci 30:1078–1092

    Google Scholar 

  • Boissoa D, Grosskopf S, Hayes K (2000) Productivity and efficiency in the US: effects of business cycles and public capital. Regional Sci Urban Econ 30:663–681

    Google Scholar 

  • Bou-Hamad I, Anouze AL, Osman IH (2022) A cognitive analytics management framework to select input and output variables for data envelopment analysis modeling of performance efficiency of banks using random forest and entropy of information. Ann Operat Res 308:63–92

    Google Scholar 

  • Caves DW, Christensen LR, Diewert WE (1982) The economic theory of index numbers and the measurement of input, output and productivity. Econometrica 50:1393–1414

    Google Scholar 

  • Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Operat Res 2:429–444

    Google Scholar 

  • Charnes A, Cooper WW, Rhodes E (1981) Evaluating program and managerial efficiency: an application of data envelopment analysis to program follow through. Manag Sci 27:668–697

    Google Scholar 

  • Chen C-M, Delmas MA (2012) Measuring eco-inefficiency: a new frontier approach. Operat Res 60:1064–1079

    Google Scholar 

  • Chen C-M, Zhu J (2011) Efficient resource allocation via efficiency bootstraps: an application to R&D project budgeting. Operat Res 59:729–741

    Google Scholar 

  • Chiu C-R, Chang M-C, Hu J-L (2022) Energy intensity improvement and energy productivity changes: an analysis of BRICS and G7 countries. J Product Anal 57:297–311

    Google Scholar 

  • Cook WD, Zhu J (2011) Multiple variable proportionality in data envelopment analysis. Operat Res 59:1023–1032

    Google Scholar 

  • Daraio C, Simar L, Wilson PW (2018) Central limit theorems for conditional efficiency measures and tests of the ‘separability condition’ in non-parametric, two-stage models of production. Econom J 21:170–191

    Google Scholar 

  • Daraio C, Simar L, Wilson PW (2021) Quality as a latent heterogeneity factor in the efficiency of universities. Econ Modell 99:105485

    Google Scholar 

  • Domazlicky BR, Weber WL (1997) Total factor productivity in the contiguous United States, 1977–1986. J Regional Sci 37:213–233

    Google Scholar 

  • Färe R. Fundamentals of Production Theory (Springer-Verlag, Berlin, 1988).

  • Färe R, Grosskopf S, Lindgren B, Roos P (1992) Productivity changes in Swedish pharmacies 1980–1989: a non-parametric Malmquist approach. J Product Anal 3:85–101

    Google Scholar 

  • Färe R, Grosskopf S, Lovell CAK. The Measurement of Efficiency of Production (Kluwer-Nijhoff Publishing, Boston, 1985).

  • Färe R, Grosskopf S, Norris M (1997) Productivity growth, technical progress, and efficiency change in industrialized countries: Reply. Am Econ Rev 87:1040–1043

    Google Scholar 

  • Färe R, Grosskopf S, Norris M, Zhang Z (1994) Productivity growth, technical progress, and efficiency change in industrialized countries. Am Econ Rev 84:66–83

    Google Scholar 

  • Farrell MJ (1957) The measurement of productive efficiency. J R Stat Soc A 120:253–281

    Google Scholar 

  • Feenstra RC, Inklaar R, Timmer MP (2015) The next generation of the penn world table. Am Econ Rev 105:3150–3182

    Google Scholar 

  • Gerami J, Mozaffari MR, Wanke PF, Correa HL (2022) Improving information reliability of non-radial value efficiency analysis: an additive slacks based measure approach. Eur J Operat Res 298:967–978

    Google Scholar 

  • Gilbert A, Wilson PW (1998) Effects of deregulation on the productivity of Korean banks. J Econ Bus 50:133–155

    Google Scholar 

  • Henriques CO, Neves ME, Castelão L, Nguyen DK (2022) Assessing the performance of exchange traded funds in the energy sector: a hybrid DEA multiobjective linear programming approach. Ann Operat Res 313:341–365

    Google Scholar 

  • Hiriart-Urruty J, Lemaréchal C. Convex Analysis and Minimization Algorithms I (Springer-Verlag GmbH, Berlin, 1993).

  • Hu S, Kim HH. Research on urban innovation efficiency of Guangdong-Hong Kong-Macao Greater Bay Area based on DEA-Malmquist model Published online, 22 February 2022. Available at https://doi.org/10.1007/s10479-022-04577-8 (2022).

  • Jeon BM, Sickles RC (2006) The role of environmental factors in growth accounting. J Appl Econom 19:567–591

    Google Scholar 

  • Johnson AL, McGinnis LF (2009) The hyperbolic-oriented efficiency measure as a remedy to infeasibility of super efficiency models. J Operat Res Soc 60:1511–1517

    Google Scholar 

  • Kalinichenko O, Amado CAF, Santos SP (2022) Exploring the potential of data envelopment analysis for enhancing pay-for-performance programme design in primary health care. Eur J Operat Res 298:1084–1100

    Google Scholar 

  • Kneip A, Simar L, Wilson PW (2008) Asymptotics and consistent bootstraps for DEA estimators in non-parametric frontier models. Econom Theory 24:1663–1697

    Google Scholar 

  • Kneip A, Simar L, Wilson PW (2011) A computationally efficient, consistent bootstrap for inference with nonparametric DEA estimators. Comput Econ 38:483–515

    Google Scholar 

  • Kneip A, Simar L, Wilson PW (2015) When bias kills the variance: central limit theorems for DEA and FDH efficiency scores. Econom Theory 31:394–422

    Google Scholar 

  • Kneip A, Simar L, Wilson PW (2016) Testing hypotheses in nonparametric models of production. J Bus Econ Stat 34:435–456

    Google Scholar 

  • Kneip A, Simar L, Wilson PW (2021) Inference in dynamic, nonparametric models of production: central limit theorems for Malmquist indices. Econom Theory 37:537–572

    Google Scholar 

  • Kneip A, Simar L, Wilson PW (2022) Conical FDH estimators of general technologies, with applications to returns to scale and Malmquist productivity indices LIDAM Discussion Paper ISBA 2022/24; available at http://hdl.handle.net/2078.1/264666.

  • Korostelev A, Simar L, Tsybakov AB (1995) Efficient estimation of monotone boundaries. Ann Stat 23:476–489

    Google Scholar 

  • Korostelev A, Simar L, Tsybakov AB (1995) On estimation of monotone and convex boundaries. Publications de l’Institut de Statistique de l’Université de Paris XXXIX 1:3–18

    Google Scholar 

  • Kumar S, Russell R (2002) Technological change, technological catch-up, and capital deepening: relative contributions to growth and convergence. Am Econ Rev 92:527–548

    Google Scholar 

  • Le TL, Lee P-P, Peng KC, Chung RH (2019) Evaluation of total factor productivity and environmental efficiency of agriculture in nine East Asian countries. Agric Econ 65:249–258

    Google Scholar 

  • Lovell CAK (2003) The decomposition of Malmquist productivity indexes. J Product Anal 20:437–458

    Google Scholar 

  • Malmquist S (1953) Index numbers and indifference surfaces. Trabajos de Estatística y de Investigación Operativa 4:209–242

    Google Scholar 

  • Mendelová V (2022) Decomposition of technical efficiency under fixed proportion technologies: an application of data envelopment analysis. J Product Anal 57:1–22

    Google Scholar 

  • Naderi A (2022) Efficiency measurement of higher education units using multilevel frontier analysis. J Product Anal 57:79–92

    Google Scholar 

  • O’Loughlin CT, Wilson PW (2021) Benchmarking the performance of U.S. municipalities. Empir Econ 60:2665–2700

    Google Scholar 

  • Pachar N, Darbari JD, Govindan K, Jha PC (2022) Sustainable performance measurement of indian retail chain using two-stage network DEA. Ann Operat Res 315:1477–1515

    Google Scholar 

  • Podinovski VV, Bouzdine-Chameeva T (2013) Weight restrictions and free production in data envelopment analysis. Operat Res 61:426–437

    Google Scholar 

  • Radovanović S, Savi c G, Delibašić B, Suknović M (2022) FairDEA-removing disparate impact from efficiency scores. Eur J Operat Res 301:1088–1098

    Google Scholar 

  • Ray SC (2001) On an extended decomposition of the Malmquist productivity index Unpublished working paper, Department of Economics, University of Connecticut.

  • Ray SC, Desli E (1997) Productivity growth, technical progress, and efficiency change in industrialized countries: comment. Am Econ Rev 87:1033–1039

    Google Scholar 

  • Russell RR. Theoretical productivity indices. In Grifell-Tatjé E, Lovell CAK, Sickles RC (eds.) The Oxford Handbook of Productivity Analysis, 101–138 (Oxford University Press, New York, 2018).

  • Şahin B, İlgün G (2019) Assessment of the impact of public hospital associations (PHAs) on the efficiency of hospitals under the ministry of health in Turkey with data envelopment analysis. Health Care Manag Sci 22:437–446

    Google Scholar 

  • Sarac SB, Atici KB, Ulucan A (2022) Elasticity measurement on multiple levels of DEA frontiers: an application to agriculture. J Product Anal 57:313–324

    Google Scholar 

  • Shephard RW. Theory of Cost and Production Functions (Princeton University Press, Princeton, 1970).

  • Simar L, Wilson PW (1998) Productivity growth in industrialized countries Discussion Paper #9810, Institut de Statistique, Université Catholique de Louvain, Louvain-la-Neuve, Belgium.

  • Simar L, Wilson PW (1998) Sensitivity analysis of efficiency scores: how to bootstrap in nonparametric frontier models. Manag Sci 44:49–61

    Google Scholar 

  • Simar L, Wilson PW (1999) Estimating and bootstrapping Malmquist indices. Eur J Operat Res 115:459–471

    Google Scholar 

  • Simar L, Wilson PW (2011) Inference by the m out of n bootstrap in nonparametric frontier models. J Product Anal 36:33–53

    Google Scholar 

  • Simar L, Wilson PW (2019) Central limit theorems and inference for sources of productivity change measured by nonparametric Malmquist indices. Eur J Operat Res 277:756–769

    Google Scholar 

  • Simar L, Wilson PW. New tools for evaluating the performance of health-care providers using dea and fdh estimators. In Grosskopf, S., Valdmanis, V. & Zelenyuk, V. (eds.) The Cambridge Handbook of Productivity, Efficiency & Effectivenss in Health Care (Cambridge University Press, Cambridge, UK, 2023). Forthcoming.

  • Simar L, Wilson PW (2023) Nonparametric, stochastic frontier models with multiple inputs and outputs. J Bus Econ Stat. Forthcoming.

  • Spanos A. Probability Theory and Statistical Inference: Econometric Modeling with Observational Data (Cambridge University Press, Cambridge, 2019).

  • Summers R, Heston A (1991) The penn world table (mark 5): an expanded set of international comparisons, 1950–1987. Quarterly J Econ 106:1–41

    Google Scholar 

  • Taleba M, Khalidb R, Ramlib R, Ghasemi MR, Ignatius J (2022) An integrated bi-objective data envelopment analysis model for measuring returns to scale. Eur J Operat Res 296:967–979

    Google Scholar 

  • Walheer B (2022) Global Malmquist and cost Malmquist indexes for group comparison. J Product Anal 58:75–93

    Google Scholar 

  • Wheelock DC, Wilson PW (1999) Technical progress, inefficiency, and productivity change in U. S. banking, 1984–1993. J Money Credit Banking 31:212–234

    Google Scholar 

  • Wilson PW (2008) FEAR: a software package for frontier efficiency analysis with R. Socio-Econ Planning Sci 42:247–254

    Google Scholar 

  • Wilson PW. Asymptotic properties of some non-parametric hyperbolic efficiency estimators. In Van Keilegom I, Wilson PW (eds.) Exploring Research Frontiers in Contemporary Statistics and Econometrics, 115–150 (Springer-Verlag, Berlin, 2011).

  • Wilson PW, Zhao S. Investigating the performance of Chinese banks over 2007–2014. Ann Operat Res. Online publication avaialble at https://doi.org/10.1007/s10479-022-04925-8 (2022).

  • Yu M-M, Seeb KF, Hsiao B (2022) Integrating group frontier and metafrontier directional distance functions to evaluate the efficiency of production units. Eur J Operat Res 301:254–276

    Google Scholar 

  • Zhang Z, Liao H (2022) A stochastic cross-efficiency DEA approach based on the prospect theory and its application in winner determination in public procurement tenders Published online, 24 February 2022. Available at https://doi.org/10.1007/s10479-022-04539-0.

  • Zofío JL, Lovell CAK (2001) Graph efficiency and productivity measures: an application to US agriculture. Appl Econ 33:1433–1442

    Google Scholar 

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Acknowledgements

A preliminary version of the work in this paper was presented at the 17th European Workshop on Efficiency and Productity (EWEPA XVII) held in Porto, Portugal 27–29 June, 2022.

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  1. Institut de Statistique, Biostatistique, et Sciences Actuarielles (ISBA), LIDAM, Université Catholique de Louvain-la-Neuve, Voie du Roman Pays 20, B 1348, Louvain-la-Neuve, Belgium

    Léopold Simar

  2. Department of Economics and School of Computing, Clemson University, Clemson, SC, USA

    Paul W. Wilson

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Simar, L., Wilson, P.W. Another look at productivity growth in industrialized countries. J Prod Anal 60, 257–272 (2023). https://doi.org/10.1007/s11123-023-00689-w

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