IDEAS home Printed from https://ideas.repec.org/p/clg/wpaper/2013-15.html
   My bibliography  Save this paper

Undesirable Outputs and a Primal Divisia Productivity Index Based on the Directional Output Distance Function

Author

Listed:
  • Guohua Feng
  • Apostolos Serletis

    (University of Calgary)

Abstract

Despite their great popularity, all the conventional Divisia productivity indexes ignore undesirable outputs. The purpose of this study is to fill in this gap by proposing a primal Divisia-type productivity index that is valid in the presence of undesirable outputs. The new productivity index is derived by total differentiation of the directional output distance function with respect to a time trend and referred to as the Divisia–Luenberger productivity index. We also empirically compare the Divisia–Luenberger productivity index and a representative of the conventional Divisia productivity indexes–the radial-output-distance-function-based Feng and Serletis (2010) productivity index–using aggregate data on 15 OECD countries over the period 1981–2000. Our empirical results show that failure to take into account undesirable outputs not only leads to misleading rankings of countries both in terms of productivity growth and in terms of technological change, but also results in wrong conclusions concerning efficiency change.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Guohua Feng & Apostolos Serletis, "undated". "Undesirable Outputs and a Primal Divisia Productivity Index Based on the Directional Output Distance Function," Working Papers 2013-15, Department of Economics, University of Calgary.
  • Handle: RePEc:clg:wpaper:2013-15
    as

    Download full text from publisher

    File URL: https://econ.ucalgary.ca/sites/econ.ucalgary.ca.manageprofile/files/unitis/publications/1-4391341/Feng_and_Serletis.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fernandez C. & Koop G. & Steel M.F.J., 2002. "Multiple-Output Production With Undesirable Outputs: An Application to Nitrogen Surplus in Agriculture," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 432-442, June.
    2. van den Broeck, Julien & Koop, Gary & Osiewalski, Jacek & Steel, Mark F. J., 1994. "Stochastic frontier models : A Bayesian perspective," Journal of Econometrics, Elsevier, vol. 61(2), pages 273-303, April.
    3. Melvyn A. Fuss, 1994. "Productivity Growth in Canadian Telecommunications," Canadian Journal of Economics, Canadian Economics Association, vol. 27(2), pages 371-392, May.
    4. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
    5. Feng, Guohua & Serletis, Apostolos, 2010. "A primal Divisia technical change index based on the output distance function," Journal of Econometrics, Elsevier, vol. 159(2), pages 320-330, December.
    6. William A. Barnett, 2004. "Tastes and Technology: Curvature Is Not Sufficient for Regularity," Contributions to Economic Analysis, in: Functional Structure and Approximation in Econometrics, pages 429-433, Emerald Group Publishing Limited.
    7. Chambers, Robert G. & Fare, Rolf & Grosskopf, Shawna, 1996. "Productivity Growth in APEC Countries," Working Papers 197843, University of Maryland, Department of Agricultural and Resource Economics.
    8. O'Donnell, Christopher J. & Coelli, Timothy J., 2005. "A Bayesian approach to imposing curvature on distance functions," Journal of Econometrics, Elsevier, vol. 126(2), pages 493-523, June.
    9. Atkinson, Scott E. & Dorfman, Jeffrey H., 2005. "Bayesian measurement of productivity and efficiency in the presence of undesirable outputs: crediting electric utilities for reducing air pollution," Journal of Econometrics, Elsevier, vol. 126(2), pages 445-468, June.
    10. Diewert, W. Erwin & Fox, Kevin J., 2008. "On the estimation of returns to scale, technical progress and monopolistic markups," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 174-193, July.
    11. Mahlberg, Bernhard & Sahoo, Biresh K., 2011. "Radial and non-radial decompositions of Luenberger productivity indicator with an illustrative application," International Journal of Production Economics, Elsevier, vol. 131(2), pages 721-726, June.
    12. William A. Barnett & Michael Wolfe, 2004. "Semi-nonparametric Bayesian Estimation of the Asymptotically Ideal Production Model1," Contributions to Economic Analysis, in: Functional Structure and Approximation in Econometrics, pages 303-349, Emerald Group Publishing Limited.
    13. D. W. Jorgenson & Z. Griliches, 1967. "The Explanation of Productivity Change," Review of Economic Studies, Oxford University Press, vol. 34(3), pages 249-283.
    14. Bert M. Balk, 2005. "Divisia price and quantity indices: 80 years after," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(2), pages 119-158, May.
    15. Trivedi, P K, 1981. "Some Discrete Approximations to Divisia Integral Indices," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(1), pages 71-77, February.
    16. Fare, Rolf & Grosskopf, Shawna & Noh, Dong-Woon & Weber, William, 2005. "Characteristics of a polluting technology: theory and practice," Journal of Econometrics, Elsevier, vol. 126(2), pages 469-492, June.
    17. Barnett, William A. & Lee, Yul W. & Wolfe, Michael D., 1985. "The three-dimensional global properties of the minflex laurent, generalized leontief, and translog flexible functional forms," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 3-31.
    18. Färe, Rolf & Grosskopf, Shawna & Hayes, Kathy J. & Margaritis, Dimitris, 2008. "Estimating demand with distance functions: Parameterization in the primal and dual," Journal of Econometrics, Elsevier, vol. 147(2), pages 266-274, December.
    19. Färe, Rolf & Grosskopf, Shawna & Pasurka, Carl A., 2007. "Environmental production functions and environmental directional distance functions," Energy, Elsevier, vol. 32(7), pages 1055-1066.
    20. Martin, Robert E., 1986. "Externality regulation and the monopoly firm," Journal of Public Economics, Elsevier, vol. 29(3), pages 347-362, April.
    21. Fernandez, Carmen & Osiewalski, Jacek & Steel, Mark F. J., 1997. "On the use of panel data in stochastic frontier models with improper priors," Journal of Econometrics, Elsevier, vol. 79(1), pages 169-193, July.
    22. Star, Spencer & Hall, Robert E, 1976. "An Approximate Divisia Index of Total Factor Productivity," Econometrica, Econometric Society, vol. 44(2), pages 257-263, March.
    23. Krishna G. Iyer & Alicia N. Rambaldi & Kam Ki Tang, 2008. "Efficiency externalities of trade and alternative forms of foreign investment in OECD countries," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(6), pages 749-766.
    24. Pethig, Rudiger, 2006. "Non-linear production, abatement, pollution and materials balance reconsidered," Journal of Environmental Economics and Management, Elsevier, vol. 51(2), pages 185-204, March.
    25. Bert Balk & Rolf Färe & Shawna Grosskopf & Dimitris Margaritis, 2008. "Exact relations between Luenberger productivity indicators and Malmquist productivity indexes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(1), pages 187-190, April.
    26. Edward R. Morey, 1986. "An Introduction to Checking, Testing, and Imposing Curvature Properties: The True Function and the Estimated Function," Canadian Journal of Economics, Canadian Economics Association, vol. 19(2), pages 207-235, May.
    27. Frank Gollop & Gregory P. Swinand, 2001. "Total Resource Productivity. Accounting for Changing Environmental Quality," NBER Chapters, in: New Developments in Productivity Analysis, pages 587-608, National Bureau of Economic Research, Inc.
    28. Ayres, Robert U & Kneese, Allen V, 1969. "Production , Consumption, and Externalities," American Economic Review, American Economic Association, vol. 59(3), pages 282-297, June.
    29. Caves, Douglas W & Christensen, Laurits R, 1980. "The Relative Efficiency of Public and Private Firms in a Competitive Environment: The Case of Canadian Railroads," Journal of Political Economy, University of Chicago Press, vol. 88(5), pages 958-976, October.
    30. W.A. Barnett & J.M. Binner, 2004. "The Global Properties of the Minflex Laurent, Generalized Leontief, and Translog Flexible Functional Forms," Contributions to Economic Analysis, in: Functional Structure and Approximation in Econometrics, pages 79-97, Emerald Group Publishing Limited.
    31. Rolf Färe & Shawna Grosskopf, 2000. "Theory and Application of Directional Distance Functions," Journal of Productivity Analysis, Springer, vol. 13(2), pages 93-103, March.
    32. Pittman, Russell W, 1983. "Multilateral Productivity Comparisons with Undesirable Outputs," Economic Journal, Royal Economic Society, vol. 93(372), pages 883-891, December.
    33. Koutsomanoli-Filippaki, Anastasia & Margaritis, Dimitris & Staikouras, Christos, 2009. "Efficiency and productivity growth in the banking industry of Central and Eastern Europe," Journal of Banking & Finance, Elsevier, vol. 33(3), pages 557-567, March.
    34. Fare, Rolf & Shawna Grosskopf & Mary Norris & Zhongyang Zhang, 1994. "Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries," American Economic Review, American Economic Association, vol. 84(1), pages 66-83, March.
    35. Byung M. Jeon & Robin C. Sickles, 2004. "The role of environmental factors in growth accounting," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(5), pages 567-591.
    36. Robert G. Chambers, 2002. "Exact nonradial input, output, and productivity measurement," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(4), pages 751-765.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wei Huang & Bernhard Bruemmer, 2017. "Balancing economic revenue and grazing pressure of livestock grazing on the Qinghai–Tibetan–Plateau," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 61(4), pages 645-662, October.
    2. Haoran Yang & Yaoben Lin & Yang Hu & Xueqing Liu & Qun Wu, 2022. "Influence Mechanism of Industrial Agglomeration and Technological Innovation on Land Granting on Green Total Factor Productivity," Sustainability, MDPI, vol. 14(6), pages 1-17, March.
    3. Shen, Zhiyang & Wu, Haitao & Bai, Kaixuan & Hao, Yu, 2022. "Integrating economic, environmental and societal performance within the productivity measurement," Technological Forecasting and Social Change, Elsevier, vol. 176(C).
    4. Boussemart, Jean Philippe & Leleu, Hervé & Shen, Zhiyang, 2015. "Environmental growth convergence among Chinese regions," China Economic Review, Elsevier, vol. 34(C), pages 1-18.
    5. Tai-Hsin Huang & Yi-Huang Chiu & Chih-Ying Mao, 2021. "Imposing Regularity Conditions to Measure Banks’ Productivity Changes in Taiwan Using a Stochastic Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 28(2), pages 273-303, June.
    6. Getu Hailu, 2023. "Reflections on technological progress in the agri‐food industry: Past, present, and future," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 71(1), pages 119-141, March.
    7. Emir Malikov & Subal C. Kumbhakar & Mike G. Tsionas, 2016. "A Cost System Approach to the Stochastic Directional Technology Distance Function with Undesirable Outputs: The Case of us Banks in 2001–2010," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(7), pages 1407-1429, November.
    8. Atkinson, Scott E. & Tsionas, Mike G., 2016. "Directional distance functions: Optimal endogenous directions," Journal of Econometrics, Elsevier, vol. 190(2), pages 301-314.
    9. Kun Lv & Shurong Yu & Dian Fu & Jingwen Wang & Chencheng Wang & Junbai Pan, 2022. "The Impact of Financial Development and Green Finance on Regional Energy Intensity: New Evidence from 30 Chinese Provinces," Sustainability, MDPI, vol. 14(15), pages 1-29, July.
    10. Pang, Rui-Zhi & Deng, Zhong-Qi & Hu, Jin-li, 2015. "Clean energy use and total-factor efficiencies: An international comparison," Renewable and Sustainable Energy Reviews, Elsevier, vol. 52(C), pages 1158-1171.
    11. Emir Malikov & Subal C. Kumbhakar & Efthymios G. Tsionas, 2015. "Bayesian Approach to Disentangling Technical and Environmental Productivity," Econometrics, MDPI, vol. 3(2), pages 1-23, June.
    12. Deng, Zhongqi & Jiang, Nan & Pang, Ruizhi, 2021. "Factor-analysis-based directional distance function: The case of New Zealand hospitals," Omega, Elsevier, vol. 98(C).
    13. Safiullah, Md & Shamsuddin, Abul, 2022. "Technical efficiency of Islamic and conventional banks with undesirable output: Evidence from a stochastic meta-frontier directional distance function," Global Finance Journal, Elsevier, vol. 51(C).
    14. Huang, Wei & Bruemmer, Bernhard & Huntsinger, Lynn, 2016. "Incorporating measures of grassland productivity into efficiency estimates for livestock grazing on the Qinghai-Tibetan Plateau in China," Ecological Economics, Elsevier, vol. 122(C), pages 1-11.
    15. Bilel Jarraya & Hatem Afi & Anis Omri, 2023. "Analyzing the Profitability and Efficiency in European Non-Life Insurance Industry," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-25, June.
    16. Haiyan Deng & Ge Bai & Kristiaan Kerstens & Zhiyang Shen, 2023. "Comparing green productivity under convex and nonconvex technologies: Which is a robust approach consistent with energy structure?," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 44(8), pages 4377-4394, December.
    17. Huang, Tai-Hsin & Chung, Ming-Tai, 2017. "Do undesirables matter on the examination of banking efficiency using stochastic directional distance functions," The Quarterly Review of Economics and Finance, Elsevier, vol. 65(C), pages 194-211.
    18. Holzer, Jorge & DePiper, Geret, 2019. "Intertemporal quota arbitrage in multispecies fisheries," Journal of Environmental Economics and Management, Elsevier, vol. 93(C), pages 185-207.
    19. Safiullah, Md, 2020. "Bank governance and crisis-period efficiency: A multinational study on Islamic and conventional banks," Pacific-Basin Finance Journal, Elsevier, vol. 62(C).
    20. Deng, Zhongqi & Song, Shunfeng & Jiang, Nan & Pang, Ruizhi, 2023. "Sustainable development in China? A nonparametric decomposition of economic growth," China Economic Review, Elsevier, vol. 81(C).
    21. Lindikaya W. Myeki & Nicolette Matthews & Yonas T. Bahta, 2023. "Decomposition of Green Agriculture Productivity for Policy in Africa: An Application of Global Malmquist–Luenberger Index," Sustainability, MDPI, vol. 15(2), pages 1-17, January.
    22. Ruomeng Zhou & Yunsheng Zhang, 2023. "Measurement of Urban Green Total Factor Productivity and Analysis of Its Temporal and Spatial Evolution in China," Sustainability, MDPI, vol. 15(12), pages 1-32, June.
    23. Yaozu Xue, 2022. "Evaluation analysis on industrial green total factor productivity and energy transition policy in resource-based region," Energy & Environment, , vol. 33(3), pages 419-434, May.
    24. Zhongqi Deng & Qianyu Zhao & Helen X. H. Bao, 2020. "The Impact of Urbanization on Farmland Productivity: Implications for China’s Requisition–Compensation Balance of Farmland Policy," Land, MDPI, vol. 9(9), pages 1-24, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tai-Hsin Huang & Yi-Huang Chiu & Chih-Ying Mao, 2021. "Imposing Regularity Conditions to Measure Banks’ Productivity Changes in Taiwan Using a Stochastic Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 28(2), pages 273-303, June.
    2. Guohua Feng & Chuan Wang & Apostolos Serletis, 2018. "Shadow prices of $$\hbox {CO}_{2}$$ CO 2 emissions at US electric utilities: a random-coefficient, random-directional-vector directional output distance function approach," Empirical Economics, Springer, vol. 54(1), pages 231-258, February.
    3. Chambers, Robert & Färe, Rolf & Grosskopf, Shawna & Vardanyan, Michael, 2013. "Generalized quadratic revenue functions," Journal of Econometrics, Elsevier, vol. 173(1), pages 11-21.
    4. Feng, Guohua & Zhang, Xiaohui, 2012. "Productivity and efficiency at large and community banks in the US: A Bayesian true random effects stochastic distance frontier analysis," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 1883-1895.
    5. Jeanneaux, Philippe & Latruffe, Laure, 2016. "Modelling pollution-generating technologies in performance benchmarking: Recent developments, limits and future prospects in the nonparametric frameworkAuthor-Name: Dakpo, K. Hervé," European Journal of Operational Research, Elsevier, vol. 250(2), pages 347-359.
    6. Emir Malikov & Subal C. Kumbhakar & Efthymios G. Tsionas, 2015. "Bayesian Approach to Disentangling Technical and Environmental Productivity," Econometrics, MDPI, vol. 3(2), pages 1-23, June.
    7. Feng, Guohua & Serletis, Apostolos, 2010. "A primal Divisia technical change index based on the output distance function," Journal of Econometrics, Elsevier, vol. 159(2), pages 320-330, December.
    8. Holtkamp, A.M. & Brummer, B., 2018. "Environmental efficiency of smallholder rubber production," 2018 Conference, July 28-August 2, 2018, Vancouver, British Columbia 277518, International Association of Agricultural Economists.
    9. Huang, Tai-Hsin & Chung, Ming-Tai, 2017. "Do undesirables matter on the examination of banking efficiency using stochastic directional distance functions," The Quarterly Review of Economics and Finance, Elsevier, vol. 65(C), pages 194-211.
    10. Emir Malikov & Raushan Bokusheva & Subal C. Kumbhakar, 2018. "A hedonic-output-index-based approach to modeling polluting technologies," Empirical Economics, Springer, vol. 54(1), pages 287-308, February.
    11. Graham, Mary, 2009. "Developing a social perspective to farm performance analysis," Ecological Economics, Elsevier, vol. 68(8-9), pages 2390-2398, June.
    12. Kumar Mandal, Sabuj & Madheswaran, S., 2010. "Environmental efficiency of the Indian cement industry: An interstate analysis," Energy Policy, Elsevier, vol. 38(2), pages 1108-1118, February.
    13. Njuki, Eric & Bravo-Ureta, Boris, 2014. "A Bayesian Approach to Analyzing the Economic Costs of Environmental Regulation in U.S. Dairy Farming," Working Papers 33, University of Connecticut, Department of Agricultural and Resource Economics, Charles J. Zwick Center for Food and Resource Policy.
    14. Wei Huang & Bernhard Bruemmer, 2017. "Balancing economic revenue and grazing pressure of livestock grazing on the Qinghai–Tibetan–Plateau," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 61(4), pages 645-662, October.
    15. Feng, Guohua & Serletis, Apostolos, 2008. "Productivity trends in U.S. manufacturing: Evidence from the NQ and AIM cost functions," Journal of Econometrics, Elsevier, vol. 142(1), pages 281-311, January.
    16. Murty, Sushama & Robert Russell, R. & Levkoff, Steven B., 2012. "On modeling pollution-generating technologies," Journal of Environmental Economics and Management, Elsevier, vol. 64(1), pages 117-135.
    17. Yang, Fuxia & Yang, Mian & Nie, Hualin, 2013. "Productivity trends of Chinese regions: A perspective from energy saving and environmental regulations," Applied Energy, Elsevier, vol. 110(C), pages 82-89.
    18. Feng, Guohua & Serletis, Apostolos, 2010. "Efficiency, technical change, and returns to scale in large US banks: Panel data evidence from an output distance function satisfying theoretical regularity," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 127-138, January.
    19. Ayouba, Kassoum & Boussemart, Jean-Philippe & Lefer, Henri-Bertrand & Leleu, Hervé & Parvulescu, Raluca, 2022. "An indirect, Luenberger approach to price performance," International Journal of Production Economics, Elsevier, vol. 244(C).
    20. Forsund, Finn R., 2009. "Good Modelling of Bad Outputs: Pollution and Multiple-Output Production," International Review of Environmental and Resource Economics, now publishers, vol. 3(1), pages 1-38, August.

    More about this item

    JEL classification:

    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • O47 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Empirical Studies of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:clg:wpaper:2013-15. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Department of Economics (email available below). General contact details of provider: https://edirc.repec.org/data/declgca.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.