IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/38147.html
   My bibliography  Save this paper

A conditional directional distance function approach for measuring regional environmental efficiency: Evidence from the UK regions

Author

Listed:
  • Halkos, George
  • Tzeremes, Nickolaos

Abstract

This paper, by using conditional directional distance functions as introduced by Simar and Vanhems [J. Econometrics 166 (2012) 342-354] modifies the model by Färe and Grosskopf [Eur. J. Operat. Res. 157 (2004) 242-245], examines the link between regional environmental efficiency and economic growth. The proposed model using conditional directional distance functions incorporates the effect of regional economic growth on regions’ environmental efficiency levels. The results from the UK regional data reveal that economic growth has a negative effect on regions’ environmental performance up to a certain GDP per capita level, where after that point the effect becomes positive. This indicates the existence of a Kuznets type relationship between the UK regions’ environmental performance and economic growth.

Suggested Citation

  • Halkos, George & Tzeremes, Nickolaos, 2012. "A conditional directional distance function approach for measuring regional environmental efficiency: Evidence from the UK regions," MPRA Paper 38147, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:38147
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/38147/1/MPRA_paper_38147.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Wang, Ke & Lu, Bin & Wei, Yi-Ming, 2013. "China’s regional energy and environmental efficiency: A Range-Adjusted Measure based analysis," Applied Energy, Elsevier, vol. 112(C), pages 1403-1415.
    2. Daraio, Cinzia & Simar, Leopold & Wilson, Paul, 2010. "Testing whether two-stage estimation is meaningful in non-parametric models of production," LIDAM Discussion Papers ISBA 2010031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Rolf Färe & Shawna Grosskopf, 2007. "A Comment on Weak Disposability in Nonparametric Production Analysis," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 91(2), pages 535-538.
    4. Ali, Agha Iqbal & Lerme, Catherine S. & Seiford, Lawrence M., 1995. "Components of efficiency evaluation in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 80(3), pages 462-473, February.
    5. Simar, Léopold & Vanhems, Anne, 2012. "Probabilistic characterization of directional distances and their robust versions," Journal of Econometrics, Elsevier, vol. 166(2), pages 342-354.
    6. Bădin, Luiza & Daraio, Cinzia & Simar, Léopold, 2012. "How to measure the impact of environmental factors in a nonparametric production model," European Journal of Operational Research, Elsevier, vol. 223(3), pages 818-833.
    7. Fare, R. & Grosskopf, S. & Hernandez-Sancho, F., 2004. "Environmental performance: an index number approach," Resource and Energy Economics, Elsevier, vol. 26(4), pages 343-352, December.
    8. Halkos, George Emm. & Tzeremes, Nickolaos G., 2009. "Exploring the existence of Kuznets curve in countries' environmental efficiency using DEA window analysis," Ecological Economics, Elsevier, vol. 68(7), pages 2168-2176, May.
    9. Picazo-Tadeo, Andrés J. & Beltrán-Esteve, Mercedes & Gómez-Limón, José A., 2012. "Assessing eco-efficiency with directional distance functions," European Journal of Operational Research, Elsevier, vol. 220(3), pages 798-809.
    10. repec:ebl:ecbull:v:17:y:2006:i:1:p:1-7 is not listed on IDEAS
    11. Feldstein, Martin S & Foot, David K, 1971. "The Other Half of Gross Investment: Replacement and Modernization Expenditures," The Review of Economics and Statistics, MIT Press, vol. 53(1), pages 49-58, February.
    12. Selden Thomas M. & Song Daqing, 1994. "Environmental Quality and Development: Is There a Kuznets Curve for Air Pollution Emissions?," Journal of Environmental Economics and Management, Elsevier, vol. 27(2), pages 147-162, September.
    13. Managi, Shunsuke, 2006. "Are there increasing returns to pollution abatement? Empirical analytics of the Environmental Kuznets Curve in pesticides," Ecological Economics, Elsevier, vol. 58(3), pages 617-636, June.
    14. Cinzia Daraio & Léopold Simar, 2005. "Introducing Environmental Variables in Nonparametric Frontier Models: a Probabilistic Approach," Journal of Productivity Analysis, Springer, vol. 24(1), pages 93-121, September.
    15. Gene M. Grossman & Alan B. Krueger, 1995. "Economic Growth and the Environment," The Quarterly Journal of Economics, Oxford University Press, vol. 110(2), pages 353-377.
    16. Sahoo, Biresh K. & Luptacik, Mikulas & Mahlberg, Bernhard, 2011. "Alternative measures of environmental technology structure in DEA: An application," European Journal of Operational Research, Elsevier, vol. 215(3), pages 750-762, December.
    17. Sarkis, Joseph & Cordeiro, James J., 2012. "Ecological modernization in the electrical utility industry: An application of a bads–goods DEA model of ecological and technical efficiency," European Journal of Operational Research, Elsevier, vol. 219(2), pages 386-395.
    18. Fare, Rolf & Grosskopf, Shawna & Tyteca, Daniel, 1996. "An activity analysis model of the environmental performance of firms--application to fossil-fuel-fired electric utilities," Ecological Economics, Elsevier, vol. 18(2), pages 161-175, August.
    19. De Witte, K. & Verschelde, M., 2010. "Estimating and explaining efficiency in a multilevel setting: A robust two-stage approach," Working Papers 17, Top Institute for Evidence Based Education Research.
    20. Epstein, L. & Denny, M., 1980. "Endogenous capital utilization in a short-run production model : Theory and an empiral application," Journal of Econometrics, Elsevier, vol. 12(2), pages 189-207, February.
    21. Fare, Rolf & Grosskopf, Shawna, 2004. "Modeling undesirable factors in efficiency evaluation: Comment," European Journal of Operational Research, Elsevier, vol. 157(1), pages 242-245, August.
    22. Watanabe, Michio & Tanaka, Katsuya, 2007. "Efficiency analysis of Chinese industry: A directional distance function approach," Energy Policy, Elsevier, vol. 35(12), pages 6323-6331, December.
    23. Badin, Luiza & Daraio, Cinzia & Simar, Léopold, 2010. "Optimal bandwidth selection for conditional efficiency measures: A data-driven approach," European Journal of Operational Research, Elsevier, vol. 201(2), pages 633-640, March.
    24. Park, Byeong U. & Simar, Léopold & Zelenyuk, Valentin, 2008. "Local likelihood estimation of truncated regression and its partial derivatives: Theory and application," Journal of Econometrics, Elsevier, vol. 146(1), pages 185-198, September.
    25. Atakelty Hailu & Terrence S. Veeman, 2001. "Non-parametric Productivity Analysis with Undesirable Outputs: An Application to the Canadian Pulp and Paper Industry," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 83(3), pages 605-616.
    26. Daraio, Cinzia & Simar, Leopold, 2006. "A robust nonparametric approach to evaluate and explain the performance of mutual funds," European Journal of Operational Research, Elsevier, vol. 175(1), pages 516-542, November.
    27. Zhou, P. & Ang, B.W. & Poh, K.L., 2006. "Slacks-based efficiency measures for modeling environmental performance," Ecological Economics, Elsevier, vol. 60(1), pages 111-118, November.
    28. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
    29. Simar, Leopold & Wilson, Paul W., 2007. "Estimation and inference in two-stage, semi-parametric models of production processes," Journal of Econometrics, Elsevier, vol. 136(1), pages 31-64, January.
    30. Korhonen, Pekka J. & Luptacik, Mikulas, 2004. "Eco-efficiency analysis of power plants: An extension of data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 154(2), pages 437-446, April.
    31. Sueyoshi, Toshiyuki & Goto, Mika, 2011. "Methodological comparison between two unified (operational and environmental) efficiency measurements for environmental assessment," European Journal of Operational Research, Elsevier, vol. 210(3), pages 684-693, May.
    32. Léopold Simar & Paul Wilson, 2011. "Two-stage DEA: caveat emptor," Journal of Productivity Analysis, Springer, vol. 36(2), pages 205-218, October.
    33. Jeffery Racine & Jeffrey Hart & Qi Li, 2006. "Testing the Significance of Categorical Predictor Variables in Nonparametric Regression Models," Econometric Reviews, Taylor & Francis Journals, vol. 25(4), pages 523-544.
    34. Bian, Yiwen & Yang, Feng, 2010. "Resource and environment efficiency analysis of provinces in China: A DEA approach based on Shannon's entropy," Energy Policy, Elsevier, vol. 38(4), pages 1909-1917, April.
    35. Jeffrey Racine, 2008. "Nonparametric econometrics: a primer (in Russian)," Quantile, Quantile, issue 4, pages 7-56, March.
    36. Seok-Oh Jeong & Byeong Park & Léopold Simar, 2010. "Nonparametric conditional efficiency measures: asymptotic properties," Annals of Operations Research, Springer, vol. 173(1), pages 105-122, January.
    37. Cinzia Daraio & Léopold Simar, 2007. "Conditional nonparametric frontier models for convex and nonconvex technologies: a unifying approach," Journal of Productivity Analysis, Springer, vol. 28(1), pages 13-32, October.
    38. Zaim, Osman, 2004. "Measuring environmental performance of state manufacturing through changes in pollution intensities: a DEA framework," Ecological Economics, Elsevier, vol. 48(1), pages 37-47, January.
    39. Zhang, Xing-Ping & Cheng, Xiao-Mei & Yuan, Jia-Hai & Gao, Xiao-Jun, 2011. "Total-factor energy efficiency in developing countries," Energy Policy, Elsevier, vol. 39(2), pages 644-650, February.
    40. Taskin, Fatma & Zaim, Osman, 2000. "Searching for a Kuznets curve in environmental efficiency using kernel estimation," Economics Letters, Elsevier, vol. 68(2), pages 217-223, August.
    41. Timo Kuosmanen, 2005. "Weak Disposability in Nonparametric Production Analysis with Undesirable Outputs," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 87(4), pages 1077-1082.
    42. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
    43. Zhou, Peng & Poh, Kim Leng & Ang, Beng Wah, 2007. "A non-radial DEA approach to measuring environmental performance," European Journal of Operational Research, Elsevier, vol. 178(1), pages 1-9, April.
    44. George EMM. Halkos & Nickolaos G. Tzeremes, 2011. "Modelling Regional Welfare Efficiency Applying Conditional Full Frontiers," Spatial Economic Analysis, Taylor & Francis Journals, vol. 6(4), pages 451-471, July.
    45. Seifert, Lawrence M. & Zhu, Joe, 1998. "Identifying Excesses and Deficits in Chinese Industrial Productivity (1953-1990): a Weighted Data Envelopment Analysis Approach," Omega, Elsevier, vol. 26(2), pages 279-296, April.
    46. Shi, Guang-Ming & Bi, Jun & Wang, Jin-Nan, 2010. "Chinese regional industrial energy efficiency evaluation based on a DEA model of fixing non-energy inputs," Energy Policy, Elsevier, vol. 38(10), pages 6172-6179, October.
    47. Robert E. O'Connor & Richard J. Bord & Brent Yarnal & Nancy Wiefek, 2002. "Who Wants to Reduce Greenhouse Gas Emissions?," Social Science Quarterly, Southwestern Social Science Association, vol. 83(1), pages 1-17, March.
    48. Managi, Shunsuke & Jena, Pradyot Ranjan, 2008. "Environmental productivity and Kuznets curve in India," Ecological Economics, Elsevier, vol. 65(2), pages 432-440, April.
    49. 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.
    50. Rolf Färe & Shawna Grosskopf, 2003. "Nonparametric Productivity Analysis with Undesirable Outputs: Comment," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 85(4), pages 1070-1074.
    51. Rajiv D. Banker & Ram Natarajan, 2008. "Evaluating Contextual Variables Affecting Productivity Using Data Envelopment Analysis," Operations Research, INFORMS, vol. 56(1), pages 48-58, February.
    52. Osman Zaim & Fatma Taskin, 2000. "A Kuznets Curve in Environmental Efficiency: An Application on OECD Countries," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 17(1), pages 21-36, September.
    53. Taskin, Fatma & Zaim, Osman, 2001. "The role of international trade on environmental efficiency: a DEA approach," Economic Modelling, Elsevier, vol. 18(1), pages 1-17, January.
    54. Reinhard, Stijn & Knox Lovell, C. A. & Thijssen, Geert J., 2000. "Environmental efficiency with multiple environmentally detrimental variables; estimated with SFA and DEA," European Journal of Operational Research, Elsevier, vol. 121(2), pages 287-303, March.
    55. McDonald, John, 2009. "Using least squares and tobit in second stage DEA efficiency analyses," European Journal of Operational Research, Elsevier, vol. 197(2), pages 792-798, September.
    56. Racine, Jeff, 1997. "Consistent Significance Testing for Nonparametric Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(3), pages 369-378, July.
    57. Racine, Jeffrey S., 2008. "Nonparametric Econometrics: A Primer," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(1), pages 1-88, March.
    58. Zofio, Jose L. & Prieto, Angel M., 2001. "Environmental efficiency and regulatory standards: the case of CO2 emissions from OECD industries," Resource and Energy Economics, Elsevier, vol. 23(1), pages 63-83, January.
    59. Atakelty Hailu, 2003. "Nonparametric Productivity Analysis with Undesirable Outputs: Reply," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 85(4), pages 1075-1077.
    60. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    61. Sueyoshi, Toshiyuki & Goto, Mika, 2012. "Data envelopment analysis for environmental assessment: Comparison between public and private ownership in petroleum industry," European Journal of Operational Research, Elsevier, vol. 216(3), pages 668-678.
    62. George Halkos & Nickolaos Tzeremes, 2012. "Measuring German regions’ environmental efficiency: a directional distance function approach," Letters in Spatial and Resource Sciences, Springer, vol. 5(1), pages 7-16, March.
    63. Timo Kuosmanen & Victor Podinovski, 2008. "Weak Disposability in Nonparametric Production Analysis: Reply to Färe and Grosskopf," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 91(2), pages 539-545.
    64. Zhou, P. & Ang, B.W. & Wang, H., 2012. "Energy and CO2 emission performance in electricity generation: A non-radial directional distance function approach," European Journal of Operational Research, Elsevier, vol. 221(3), pages 625-635.
    65. Hoff, Ayoe, 2007. "Second stage DEA: Comparison of approaches for modelling the DEA score," European Journal of Operational Research, Elsevier, vol. 181(1), pages 425-435, August.
    66. Fare, Rolf, et al, 1989. "Multilateral Productivity Comparisons When Some Outputs Are Undesirable: A Nonparametric Approach," The Review of Economics and Statistics, MIT Press, vol. 71(1), pages 90-98, February.
    67. Seiford, Lawrence M. & Zhu, Joe, 2002. "Modeling undesirable factors in efficiency evaluation," European Journal of Operational Research, Elsevier, vol. 142(1), pages 16-20, October.
    68. Sueyoshi, Toshiyuki & Goto, Mika, 2011. "Measurement of Returns to Scale and Damages to Scale for DEA-based operational and environmental assessment: How to manage desirable (good) and undesirable (bad) outputs?," European Journal of Operational Research, Elsevier, vol. 211(1), pages 76-89, May.
    69. Valentin Zelenyuk & Vitaliy Zheka, 2006. "Corporate Governance and Firm’s Efficiency: The Case of a Transitional Country, Ukraine," Journal of Productivity Analysis, Springer, vol. 25(1), pages 143-157, April.
    70. Macpherson, Alexander J. & Principe, Peter P. & Smith, Elizabeth R., 2010. "A directional distance function approach to regional environmental-economic assessments," Ecological Economics, Elsevier, vol. 69(10), pages 1918-1925, August.
    71. Cazals, Catherine & Florens, Jean-Pierre & Simar, Leopold, 2002. "Nonparametric frontier estimation: a robust approach," Journal of Econometrics, Elsevier, vol. 106(1), pages 1-25, January.
    72. Daniel Tyteca, 1997. "Linear Programming Models for the Measurement of Environmental Performance of Firms—Concepts and Empirical Results," Journal of Productivity Analysis, Springer, vol. 8(2), pages 183-197, May.
    73. Rajiv D. Banker & Richard C. Morey, 1986. "Efficiency Analysis for Exogenously Fixed Inputs and Outputs," Operations Research, INFORMS, vol. 34(4), pages 513-521, August.
    74. Seiford, Lawrence M. & Zhu, Joe, 2005. "A response to comments on modeling undesirable factors in efficiency evaluation," European Journal of Operational Research, Elsevier, vol. 161(2), pages 579-581, March.
    75. Guo, Xiao-Dan & Zhu, Lei & Fan, Ying & Xie, Bai-Chen, 2011. "Evaluation of potential reductions in carbon emissions in Chinese provinces based on environmental DEA," Energy Policy, Elsevier, vol. 39(5), pages 2352-2360, May.
    76. Baris K. Yörük & Osman Zaim, 2006. "The Kuznets curve and the effect of international regulations on environmental efficiency," Economics Bulletin, AccessEcon, vol. 17(1), pages 1-7.
    77. Brajer, Victor & Mead, Robert W. & Xiao, Feng, 2011. "Searching for an Environmental Kuznets Curve in China's air pollution," China Economic Review, Elsevier, vol. 22(3), pages 383-397, September.
    Full references (including those not matched with items on IDEAS)

    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. Halkos, George & Tzeremes, Nickolaos, 2011. "Regional environmental efficiency and economic growth: NUTS2 evidence from Germany, France and the UK," MPRA Paper 33698, University Library of Munich, Germany.
    2. George Halkos & Nickolaos Tzeremes, 2014. "Measuring the effect of Kyoto protocol agreement on countries’ environmental efficiency in CO 2 emissions: an application of conditional full frontiers," Journal of Productivity Analysis, Springer, vol. 41(3), pages 367-382, June.
    3. Halkos, George & Tzeremes, Nickolaos, 2012. "Regional economic growth and environmental efficiency in greenhouse emissions: A conditional directional distance function approach," MPRA Paper 40015, University Library of Munich, Germany.
    4. Halkos, George & Tzeremes, Nickolaos, 2011. "A conditional full frontier modelling for analyzing environmental efficiency and economic growth," MPRA Paper 32839, University Library of Munich, Germany.
    5. George Halkos & Nickolaos Tzeremes, 2013. "National culture and eco-efficiency: an application of conditional partial nonparametric frontiers," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 15(4), pages 423-441, October.
    6. George Halkos & George Papageorgiou, 2016. "Spatial environmental efficiency indicators in regional waste generation: a nonparametric approach," Journal of Environmental Planning and Management, Taylor & Francis Journals, vol. 59(1), pages 62-78, January.
    7. Halkos, George E. & Tzeremes, Nickolaos G., 2014. "Public sector transparency and countries’ environmental performance: A nonparametric analysis," Resource and Energy Economics, Elsevier, vol. 38(C), pages 19-37.
    8. Sueyoshi, Toshiyuki & Yuan, Yan & Goto, Mika, 2017. "A literature study for DEA applied to energy and environment," Energy Economics, Elsevier, vol. 62(C), pages 104-124.
    9. Halkos, George & Sundström, Aksel & Tzeremes, Nickolaos, 2013. "Environmental performance and quality of governance: A non-parametric analysis of the NUTS 1-regions in France, Germany and the UK," MPRA Paper 48890, University Library of Munich, Germany.
    10. George Halkos & Aksel Sundström & Nickolaos Tzeremes, 2015. "Regional environmental performance and governance quality: a nonparametric analysis," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 17(4), pages 621-644, October.
    11. Halkos, George & Tzeremes, Nickolaos, 2013. "An additive two-stage DEA approach creating sustainability efficiency indexes," MPRA Paper 44231, University Library of Munich, Germany.
    12. George E. Halkos & Shunsuke Managi, 2017. "Measuring the Effect of Economic Growth on Countries’ Environmental Efficiency: A Conditional Directional Distance Function Approach," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 68(3), pages 753-775, November.
    13. George Halkos & Nickolaos Tzeremes, 2012. "Measuring German regions’ environmental efficiency: a directional distance function approach," Letters in Spatial and Resource Sciences, Springer, vol. 5(1), pages 7-16, March.
    14. Halkos, George & Tzeremes, Nickolaos, 2011. "Kuznets curve and environmental performance: evidence from China," MPRA Paper 34312, University Library of Munich, Germany.
    15. Cordero Ferrera, Jose Manuel & Alonso Morán, Edurne & Nuño Solís, Roberto & Orueta, Juan F. & Souto Arce, Regina, 2013. "Efficiency assessment of primary care providers: A conditional nonparametric approach," MPRA Paper 51926, University Library of Munich, Germany.
    16. Halkos, George & Tzeremes, Nickolaos, 2011. "Does the Kyoto Protocol Agreement matters? An environmental efficiency analysis," MPRA Paper 30652, University Library of Munich, Germany.
    17. Halkos, George & Polemis, Michael, 2016. "The good, the bad and the ugly? Balancing environmental and economic impacts towards efficiency," MPRA Paper 72132, University Library of Munich, Germany.
    18. Cordero, José Manuel & Alonso-Morán, Edurne & Nuño-Solinis, Roberto & Orueta, Juan F. & Arce, Regina Sauto, 2015. "Efficiency assessment of primary care providers: A conditional nonparametric approach," European Journal of Operational Research, Elsevier, vol. 240(1), pages 235-244.
    19. Halkos, George E. & Tzeremes, Nickolaos G., 2013. "Economic growth and environmental efficiency: Evidence from US regions," Economics Letters, Elsevier, vol. 120(1), pages 48-52.
    20. Leleu, Hervé, 2013. "Shadow pricing of undesirable outputs in nonparametric analysis," European Journal of Operational Research, Elsevier, vol. 231(2), pages 474-480.

    More about this item

    Keywords

    Regional environmental performance; Directional distance function; Conditional measures; U.K. regions;
    All these keywords.

    JEL classification:

    • R10 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - General
    • Q50 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • Q56 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Environment and Development; Environment and Trade; Sustainability; Environmental Accounts and Accounting; Environmental Equity; Population Growth
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

    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:pra:mprapa:38147. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.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.