IDEAS home Printed from https://ideas.repec.org/a/pal/genrir/v48y2023i1d10.1057_s10713-022-00074-x.html
   My bibliography  Save this article

Probability weighting and insurance demand in a unified framework

Author

Listed:
  • Johannes G. Jaspersen

    (LMU Munich)

  • Richard Peter

    (University of Iowa)

  • Marc A. Ragin

    (University of Georgia)

Abstract

We provide a comprehensive analysis of the impact of probability weighting on optimal insurance demand in a unified framework. We identify decreasing relative overweighting as a new local condition on the probability weighting function that is useful for comparative static analysis. We discuss the effects of probability weighting on coinsurance, deductible choice, insurance demand for low-probability, high-impact risks versus high-probability, low-impact risks, and insurance demand in the presence of nonperformance risk. Probability weighting can make better or worse predictions than expected utility depending on the insurance demand problem at hand.

Suggested Citation

  • Johannes G. Jaspersen & Richard Peter & Marc A. Ragin, 2023. "Probability weighting and insurance demand in a unified framework," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 48(1), pages 63-109, March.
    • Handle: RePEc:pal:genrir:v:48:y:2023:i:1:d:10.1057_s10713-022-00074-x
    DOI: 10.1057/s10713-022-00074-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1057/s10713-022-00074-x
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1057/s10713-022-00074-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ghossoub, Mario, 2019. "Optimal insurance under rank-dependent expected utility," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 51-66.
    2. Cummins, J David & Mahul, Olivier, 2003. "Optimal Insurance with Divergent Beliefs about Insurer Total Default Risk," Journal of Risk and Uncertainty, Springer, vol. 27(2), pages 121-138, October.
    3. WilliamT Harbaugh & Kate Krause & Lise Vesterlund, 2010. "The Fourfold Pattern of Risk Attitudes in Choice and Pricing Tasks," Economic Journal, Royal Economic Society, vol. 120(545), pages 595-611, June.
    4. Chateauneuf, Alain & Cohen, Michele & Meilijson, Isaac, 2004. "Four notions of mean-preserving increase in risk, risk attitudes and applications to the rank-dependent expected utility model," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 547-571, August.
    5. Daniel J. Clarke, 2016. "A Theory of Rational Demand for Index Insurance," American Economic Journal: Microeconomics, American Economic Association, vol. 8(1), pages 283-306, February.
    6. Segal, Uzi, 1990. "Two-Stage Lotteries without the Reduction Axiom," Econometrica, Econometric Society, vol. 58(2), pages 349-377, March.
    7. Ian Jewitt, 1989. "Choosing Between Risky Prospects: The Characterization of Comparative Statics Results, and Location Independent Risk," Management Science, INFORMS, vol. 35(1), pages 60-70, January.
    8. Reinhard Selten & Abdolkarim Sadrieh & Klaus Abbink, 1999. "Money Does Not Induce Risk Neutral Behavior, but Binary Lotteries Do even Worse," Theory and Decision, Springer, vol. 46(3), pages 213-252, June.
    9. Jianming Xia & Xun Yu Zhou, 2016. "Arrow–Debreu Equilibria For Rank-Dependent Utilities," Mathematical Finance, Wiley Blackwell, vol. 26(3), pages 558-588, July.
    10. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    11. Shawn Cole & Xavier Gine & Jeremy Tobacman & Petia Topalova & Robert Townsend & James Vickery, 2013. "Barriers to Household Risk Management: Evidence from India," American Economic Journal: Applied Economics, American Economic Association, vol. 5(1), pages 104-135, January.
    12. Levon Barseghyan & Francesca Molinari & Ted O'Donoghue & Joshua C. Teitelbaum, 2013. "The Nature of Risk Preferences: Evidence from Insurance Choices," American Economic Review, American Economic Association, vol. 103(6), pages 2499-2529, October.
    13. repec:dau:papers:123456789/2348 is not listed on IDEAS
    14. Mark Browne & Christian Knoller & Andreas Richter, 2015. "Behavioral bias and the demand for bicycle and flood insurance," Journal of Risk and Uncertainty, Springer, vol. 50(2), pages 141-160, April.
    15. Shapira, Zur & Venezia, Itzhak, 2008. "On the preference for full-coverage policies: Why do people buy too much insurance?," Journal of Economic Psychology, Elsevier, vol. 29(5), pages 747-761, November.
    16. Ulrich Schmidt & Chris Starmer & Robert Sugden, 2008. "Third-generation prospect theory," Journal of Risk and Uncertainty, Springer, vol. 36(3), pages 203-223, June.
    17. Mohammed Abdellaoui & Aurelien Baillon & Laetitia Placido & Peter P. Wakker, 2011. "The Rich Domain of Uncertainty: Source Functions and Their Experimental Implementation," American Economic Review, American Economic Association, vol. 101(2), pages 695-723, April.
    18. Doherty, Neil A & Eeckhoudt, Louis, 1995. "Optimal Insurance without Expected Utility: The Dual Theory and the Linearity of Insurance Contracts," Journal of Risk and Uncertainty, Springer, vol. 10(2), pages 157-179, March.
    19. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    20. Rachel J Huang & Pai-Ta Shih & Larry Y Tzeng, 2012. "Disappointment and the Optimal Insurance Contract," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 37(2), pages 258-284, September.
    21. Sarin, Rakesh & Wakker, Peter P, 1998. "Revealed Likelihood and Knightian Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 16(3), pages 223-250, July-Aug..
    22. Hong, Chew Soo & Karni, Edi & Safra, Zvi, 1987. "Risk aversion in the theory of expected utility with rank dependent probabilities," Journal of Economic Theory, Elsevier, vol. 42(2), pages 370-381, August.
    23. Fox, Craig R & Rogers, Brett A & Tversky, Amos, 1996. "Options Traders Exhibit Subadditive Decision Weights," Journal of Risk and Uncertainty, Springer, vol. 13(1), pages 5-17, July.
    24. Wakker, Peter P & Thaler, Richard H & Tversky, Amos, 1997. "Probabilistic Insurance," Journal of Risk and Uncertainty, Springer, vol. 15(1), pages 7-28, October.
    25. Anja Zimmer & Helmut Gründl & Christian D. Schade & Franca Glenzer, 2018. "An Incentive†Compatible Experiment on Probabilistic Insurance and Implications for an Insurer's Solvency Level," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(1), pages 245-273, March.
    26. Alberto Abadie & Javier Gardeazabal, 2003. "The Economic Costs of Conflict: A Case Study of the Basque Country," American Economic Review, American Economic Association, vol. 93(1), pages 113-132, March.
    27. Carole Bernard & Xuedong He & Jia-An Yan & Xun Yu Zhou, 2015. "Optimal Insurance Design Under Rank-Dependent Expected Utility," Mathematical Finance, Wiley Blackwell, vol. 25(1), pages 154-186, January.
    28. Chateauneuf, Alain & Dana, Rose-Anne & Tallon, Jean-Marc, 2000. "Optimal risk-sharing rules and equilibria with Choquet-expected-utility," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 191-214, October.
    29. G. Carlier & R. Dana, 2008. "Two-persons efficient risk-sharing and equilibria for concave law-invariant utilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(2), pages 189-223, August.
    30. Diecidue, Enrico & Wakker, Peter P., 2002. "Dutch books: avoiding strategic and dynamic complications, and a comonotonic extension," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 135-149, March.
    31. W. Chiu & Louis Eeckhoudt & Beatrice Rey, 2012. "On relative and partial risk attitudes: theory and implications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(1), pages 151-167, May.
    32. Ulrich Schmidt, 2016. "Insurance Demand Under Prospect Theory: A Graphical Analysis," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(1), pages 77-89, January.
    33. Matthew Rabin, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica, Econometric Society, vol. 68(5), pages 1281-1292, September.
    34. Bernasconi, Michele, 1994. "Nonlinear Preferences and Two-Stage Lotteries: Theories and Evidence," Economic Journal, Royal Economic Society, vol. 104(422), pages 54-70, January.
    35. Neil A. Doherty & Harris Schlesinger, 1990. "Rational Insurance Purchasing: Consideration of Contract Nonperformance," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 105(1), pages 243-253.
    36. Hui Li & Seth Neumuller & Casey Rothschild, 2021. "Optimal annuitization with imperfect information about insolvency risk," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(1), pages 101-130, March.
    37. Timo R. Lambregts & Paul Bruggen & Han Bleichrodt, 2021. "Correction to: Insurance decisions under nonperformance risk and ambiguity," Journal of Risk and Uncertainty, Springer, vol. 63(3), pages 255-255, December.
    38. Henry Stott, 2006. "Cumulative prospect theory's functional menagerie," Journal of Risk and Uncertainty, Springer, vol. 32(2), pages 101-130, March.
    39. Glenn W. Harrison & Jia Min Ng, 2018. "Welfare effects of insurance contract non-performance," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 39-76, May.
    40. Hui-Kuan Chung & Paul Glimcher & Agnieszka Tymula, 2019. "An Experimental Comparison of Risky and Riskless Choice—Limitations of Prospect Theory and Expected Utility Theory," American Economic Journal: Microeconomics, American Economic Association, vol. 11(3), pages 34-67, August.
    41. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    42. Segal, Uzi & Spivak, Avia, 1990. "First order versus second order risk aversion," Journal of Economic Theory, Elsevier, vol. 51(1), pages 111-125, June.
    43. Ryan, Matthew J., 2006. "Risk aversion in RDEU," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 675-697, September.
    44. Meyer, Jack & Ormiston, Michael B, 1999. "Analyzing the Demand for Deductible Insurance," Journal of Risk and Uncertainty, Springer, vol. 18(3), pages 223-230, October.
    45. Arthur Snow, 2011. "Ambiguity aversion and the propensities for self-insurance and self-protection," Journal of Risk and Uncertainty, Springer, vol. 42(1), pages 27-43, February.
    46. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    47. Michael Braun & Alexander Muermann, 2004. "The Impact of Regret on the Demand for Insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 71(4), pages 737-767, December.
    48. Chakravarty, Surajeet & Kelsey, David, 2015. "Sharing ambiguous risks," Journal of Mathematical Economics, Elsevier, vol. 56(C), pages 1-8.
    49. Nathalie Etchart-Vincent, 2004. "Is Probability Weighting Sensitive to the Magnitude of Consequences? An Experimental Investigation on Losses," Journal of Risk and Uncertainty, Springer, vol. 28(3), pages 217-235, May.
    50. Craig McIntosh & Felix Povel & Elisabeth Sadoulet, 2019. "Utility, Risk and Demand for Incomplete Insurance: Lab Experiments with Guatemalan Co-Operatives," The Economic Journal, Royal Economic Society, vol. 129(622), pages 2581-2607.
    51. Michal W. Krawczyk & Stefan T. Trautmann & Gijs Kuilen, 2017. "Catastrophic risk: social influences on insurance decisions," Theory and Decision, Springer, vol. 82(3), pages 309-326, March.
    52. Timo R. Lambregts & Paul Bruggen & Han Bleichrodt, 2021. "Insurance decisions under nonperformance risk and ambiguity," Journal of Risk and Uncertainty, Springer, vol. 63(3), pages 229-253, December.
    53. MOSSIN, Jan, 1968. "Aspects of rational insurance purchasing," LIDAM Reprints CORE 23, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    54. John David Cummins & Olivier Mahul, 2003. "Optimal insurance with divergent beliefs about total default risk," Post-Print hal-01952121, HAL.
    55. Chateauneuf, Alain & Dana, Rose-Anne & Tallon, Jean-Marc, 2000. "Optimal risk-sharing rules and equilibria with Choquet-expected-utility," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 191-214, October.
    56. Epper, Thomas & Fehr-Duda, Helga, 2017. "A Tale of Two Tails: On the Coexistence of Overweighting and Underweighting of Rare Extreme Events," Economics Working Paper Series 1705, University of St. Gallen, School of Economics and Political Science.
    57. W Henry Chiu, 2012. "Risk Aversion, Downside Risk Aversion and Paying for Stochastic Improvements," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 37(1), pages 1-26, March.
    58. George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, vol. 42(12), pages 1676-1690, December.
    59. Andreas Friedl & Katharina Lima de Miranda & Ulrich Schmidt, 2014. "Insurance demand and social comparison: An experimental analysis," Journal of Risk and Uncertainty, Springer, vol. 48(2), pages 97-109, April.
    60. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    61. Peter, Richard & Ying, Jie, 2020. "Do you trust your insurer? Ambiguity about contract nonperformance and optimal insurance demand," Journal of Economic Behavior & Organization, Elsevier, vol. 180(C), pages 938-954.
    62. Botond Koszegi & Matthew Rabin, 2007. "Reference-Dependent Risk Attitudes," American Economic Review, American Economic Association, vol. 97(4), pages 1047-1073, September.
    63. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    64. Johannes G. Jaspersen, 2016. "Hypothetical Surveys And Experimental Studies Of Insurance Demand: A Review," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(1), pages 217-255, January.
    65. Goetz von Peter & Sebastian von Dahlen & Sweta C Saxena, 2012. "Unmitigated disasters? New evidence on the macroeconomic cost of natural catastrophes," BIS Working Papers 394, Bank for International Settlements.
    66. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    67. David Alary & Christian Gollier & Nicolas Treich, 2013. "The Effect of Ambiguity Aversion on Insurance and Self‐protection," Economic Journal, Royal Economic Society, vol. 123(12), pages 1188-1202, December.
    68. Mahul, Olivier & Wright, Brian D., 2007. "Optimal coverage for incompletely reliable insurance," Economics Letters, Elsevier, vol. 95(3), pages 456-461, June.
    69. Dionne, Georges & Li, Jingyuan, 2014. "When can expected utility handle first-order risk aversion?," Journal of Economic Theory, Elsevier, vol. 154(C), pages 403-422.
    70. Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-1280, November.
    71. Justin Sydnor, 2010. "(Over)insuring Modest Risks," American Economic Journal: Applied Economics, American Economic Association, vol. 2(4), pages 177-199, October.
    72. Saurabh Bhargava & George Loewenstein & Justin Sydnor, 2017. "Choose to Lose: Health Plan Choices from a Menu with Dominated Option," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(3), pages 1319-1372.
    73. Zimmer, Anja & Schade, Christian & Gründl, Helmut, 2009. "Is default risk acceptable when purchasing insurance? Experimental evidence for different probability representations, reasons for default, and framings," Journal of Economic Psychology, Elsevier, vol. 30(1), pages 11-23, February.
    74. repec:dau:papers:123456789/5461 is not listed on IDEAS
    75. Susan Laury & Melayne McInnes & J. Swarthout, 2009. "Insurance decisions for low-probability losses," Journal of Risk and Uncertainty, Springer, vol. 39(1), pages 17-44, August.
    76. Jan V. Hansen & Rasmus H. Jacobsen & Morten I. Lau, 2016. "Willingness To Pay For Insurance In Denmark," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(1), pages 49-76, January.
    77. Tsanakas, Andreas & Christofides, Nicos, 2006. "Risk Exchange with Distorted Probabilities," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 219-243, May.
    78. Vickie Bajtelsmit & Jennifer Coats & Paul Thistle, 2015. "The effect of ambiguity on risk management choices: An experimental study," Journal of Risk and Uncertainty, Springer, vol. 50(3), pages 249-280, June.
    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. Mankaï, Selim & Marchand, Sébastien & Le, Ngoc Ha, 2024. "Valuing insurance against small probability risks: A meta-analysis," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 109(C).

    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. Peter, Richard & Ying, Jie, 2020. "Do you trust your insurer? Ambiguity about contract nonperformance and optimal insurance demand," Journal of Economic Behavior & Organization, Elsevier, vol. 180(C), pages 938-954.
    2. Ghossoub, Mario & He, Xue Dong, 2021. "Comparative risk aversion in RDEU with applications to optimal underwriting of securities issuance," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 6-22.
    3. Glenn W. Harrison & Jia Min Ng, 2018. "Welfare effects of insurance contract non-performance," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 39-76, May.
    4. Glenn W. Harrison & Jia Min Ng, 2019. "Behavioral insurance and economic theory: A literature review," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 22(2), pages 133-182, July.
    5. Biener, Christian & Landmann, Andreas & Santana, Maria Isabel, 2019. "Contract nonperformance risk and uncertainty in insurance markets," Journal of Public Economics, Elsevier, vol. 175(C), pages 65-83.
    6. Mankaï, Selim & Marchand, Sébastien & Le, Ngoc Ha, 2024. "Valuing insurance against small probability risks: A meta-analysis," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 109(C).
    7. Aurélien Baillon & Aleli Kraft & Owen O’Donnell & Kim Wilgenburg, 2022. "A behavioral decomposition of willingness to pay for health insurance," Journal of Risk and Uncertainty, Springer, vol. 64(1), pages 43-87, February.
    8. Markus Huggenberger & Peter Albrecht, 2022. "Risk pooling and solvency regulation: A policyholder's perspective," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(4), pages 907-950, December.
    9. Vieider, Ferdinand M. & Truong, Nghi & Martinsson, Peter & Pham Khanh Nam & Martinsson, Peter, 2013. "Risk preferences and development revisited: A field experiment in Vietnam," Discussion Papers, WZB Junior Research Group Risk and Development SP II 2013-403, WZB Berlin Social Science Center.
    10. Lampe, Immanuel & Würtenberger, Daniel, 2020. "Loss aversion and the demand for index insurance," Journal of Economic Behavior & Organization, Elsevier, vol. 180(C), pages 678-693.
    11. Peter Brooks & Simon Peters & Horst Zank, 2014. "Risk behavior for gain, loss, and mixed prospects," Theory and Decision, Springer, vol. 77(2), pages 153-182, August.
    12. Louis R. Eeckhoudt & Roger J. A. Laeven, 2021. "Probability Premium and Attitude Towards Probability," Papers 2105.00054, arXiv.org.
    13. Kpegli, Yao Thibaut & Corgnet, Brice & Zylbersztejn, Adam, 2023. "All at once! A comprehensive and tractable semi-parametric method to elicit prospect theory components," Journal of Mathematical Economics, Elsevier, vol. 104(C).
    14. Diecidue, Enrico & Schmidt, Ulrich & Zank, Horst, 2009. "Parametric weighting functions," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1102-1118, May.
    15. Immanuel Lampe & Daniel Würtenberger, 2019. "Loss Aversion And The Demand For Index Insurance," Working Papers on Finance 1907, University of St. Gallen, School of Finance.
    16. Thomas Epper & Helga Fehr-Duda, 2012. "The missing link: unifying risk taking and time discounting," ECON - Working Papers 096, Department of Economics - University of Zurich, revised Oct 2018.
    17. Benjamin L. Collier & Daniel Schwartz & Howard C. Kunreuther & Erwann O. Michel‐Kerjan, 2022. "Insuring large stakes: A normative and descriptive analysis of households' flood insurance coverage," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(2), pages 273-310, June.
    18. Ghossoub, Mario, 2019. "Optimal insurance under rank-dependent expected utility," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 51-66.
    19. Jinrui Pan & Craig S. Webb & Horst Zank, 2019. "Delayed probabilistic risk attitude: a parametric approach," Theory and Decision, Springer, vol. 87(2), pages 201-232, September.
    20. Alex Gershkov & Benny Moldovanu & Philipp Strack & Mengxi Zhang, 2023. "Optimal Insurance: Dual Utility, Random Losses and Adverse Selection," ECONtribute Discussion Papers Series 242, University of Bonn and University of Cologne, Germany.

    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:pal:genrir:v:48:y:2023:i:1:d:10.1057_s10713-022-00074-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.palgrave-journals.com/ .

    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.