IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/25055.html
   My bibliography  Save this paper

Mortality Risk, Insurance, and the Value of Life

Author

Listed:
  • Daniel Bauer
  • Darius Lakdawalla
  • Julian Reif

Abstract

We develop a new framework for valuing health and longevity improvements that departs from conventional but unrealistic assumptions of full annuitization and deterministic health. Our framework can value the prevention of mortality and of illness, and it can quantify the effects of retirement policies on the value of life. We apply the framework to life-cycle data and generate new insights absent from the conventional approach. First, treatment is up to five times more valuable than prevention, even when both extend life equally. This asymmetry helps explain low observed investment in preventive care. Second, severe illness can significantly increase the value of statistical life, helping to reconcile theory with empirical findings that consumers value life-extension more in bleaker health states. Third, retirement annuities boost aggregate demand for life-extension. We calculate that Social Security adds $10.6 trillion (11 percent) to the value of post-1940 longevity gains and would add $127 billion to the value of a one percent decline in future mortality.

Suggested Citation

  • Daniel Bauer & Darius Lakdawalla & Julian Reif, 2018. "Mortality Risk, Insurance, and the Value of Life," NBER Working Papers 25055, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:25055
    Note: AG EH PE
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w25055.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Arthur, W B, 1981. "The Economics of Risks to Life," American Economic Review, American Economic Association, vol. 71(1), pages 54-64, March.
    2. Banks, James & Blundell, Richard & Tanner, Sarah, 1998. "Is There a Retirement-Savings Puzzle?," American Economic Review, American Economic Association, vol. 88(4), pages 769-788, September.
    3. Jesus Fernández-Villaverde & Dirk Krueger, 2007. "Consumption over the Life Cycle: Facts from Consumer Expenditure Survey Data," The Review of Economics and Statistics, MIT Press, vol. 89(3), pages 552-565, August.
    4. Dimitris Christelis & Dimitris Georgarakos & Tullio Jappelli & Maarten van Rooij, 2020. "Consumption Uncertainty and Precautionary Saving," The Review of Economics and Statistics, MIT Press, vol. 102(1), pages 148-161, March.
    5. Lakdawalla, Darius & Malani, Anup & Reif, Julian, 2017. "The insurance value of medical innovation," Journal of Public Economics, Elsevier, vol. 145(C), pages 94-102.
    6. Tomas J. Philipson & Gary S. Becker, 1998. "Old-Age Longevity and Mortality-Contingent Claims," Journal of Political Economy, University of Chicago Press, vol. 106(3), pages 551-573, June.
    7. Wojciech Kopczuk & Joseph P. Lupton, 2007. "To Leave or Not to Leave: The Distribution of Bequest Motives," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(1), pages 207-235.
    8. Jeffrey R. Brown & Jeffrey R. Kling & Sendhil Mullainathan & Marian V. Wrobel, 2008. "Why Don’t People Insure Late-Life Consumption? A Framing Explanation of the Under-Annuitization Puzzle," American Economic Review, American Economic Association, vol. 98(2), pages 304-309, May.
    9. Chen, Brian K. & Jalal, Hawre & Hashimoto, Hideki & Suen, Sze-chuan & Eggleston, Karen & Hurley, Michael & Schoemaker, Lena & Bhattacharya, Jay, 2016. "Forecasting trends in disability in a super-aging society: Adapting the Future Elderly Model to Japan," The Journal of the Economics of Ageing, Elsevier, vol. 8(C), pages 42-51.
    10. Isaac Ehrlich & Yong Yin, 2005. "Explaining Diversities in Age-Specific Life Expectancies and Values of Life Saving: A Numerical Analysis," Journal of Risk and Uncertainty, Springer, vol. 31(2), pages 129-162, September.
    11. Leung, Siu Fai, 1994. "Uncertain Lifetime, the Theory of the Consumer, and the Life Cycle Hypothesis," Econometrica, Econometric Society, vol. 62(5), pages 1233-1239, September.
    12. Olivia S. Mitchell, 1999. "New Evidence on the Money's Worth of Individual Annuities," American Economic Review, American Economic Association, vol. 89(5), pages 1299-1318, December.
    13. Thomas Davidoff & Jeffrey R. Brown & Peter A. Diamond, 2005. "Annuities and Individual Welfare," American Economic Review, American Economic Association, vol. 95(5), pages 1573-1590, December.
    14. Adler, Matthew D. & Hammitt, James K. & Treich, Nicolas, 2014. "The social value of mortality risk reduction: VSL versus the social welfare function approach," Journal of Health Economics, Elsevier, vol. 35(C), pages 82-93.
    15. Rosen, Sherwin, 1988. "The Value of Changes in Life Expectancy," Journal of Risk and Uncertainty, Springer, vol. 1(3), pages 285-304, September.
    16. Charles N. Noussair & Stefan T. Trautmann & Gijs van de Kuilen, 2014. "Higher Order Risk Attitudes, Demographics, and Financial Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(1), pages 325-355.
    17. Marc Fleurbaey, 2010. "Assessing Risky Social Situations," Journal of Political Economy, University of Chicago Press, vol. 118(4), pages 649-680, August.
    18. Lydia Lawless & Andreas Drichoutis & Rodolfo Nayga, 2013. "Time preferences and health behaviour: a review," Agricultural and Food Economics, Springer;Italian Society of Agricultural Economics (SIDEA), vol. 1(1), pages 1-19, December.
    19. Evans, William N & Viscusi, W Kip, 1991. "Estimation of State-Dependent Utility Functions Using Survey Data," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 94-104, February.
    20. Mariacristina De Nardi & Eric French & John B. Jones, 2010. "Why Do the Elderly Save? The Role of Medical Expenses," Journal of Political Economy, University of Chicago Press, vol. 118(1), pages 39-75, February.
    21. Liran Einav & Amy Finkelstein & Mark R. Cullen, 2010. "Estimating Welfare in Insurance Markets Using Variation in Prices," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(3), pages 877-921.
    22. Viscusi, W Kip & Aldy, Joseph E, 2003. "The Value of a Statistical Life: A Critical Review of Market Estimates throughout the World," Journal of Risk and Uncertainty, Springer, vol. 27(1), pages 5-76, August.
    23. Amy Finkelstein & Erzo F. P. Luttmer & Matthew J. Notowidigdo, 2013. "What Good Is Wealth Without Health? The Effect Of Health On The Marginal Utility Of Consumption," Journal of the European Economic Association, European Economic Association, vol. 11, pages 221-258, January.
    24. Viscusi, W Kip & Evans, William N, 1990. "Utility Functions That Depend on Health Status: Estimates and Economic Implications," American Economic Review, American Economic Association, vol. 80(3), pages 353-374, June.
    25. Dana P. Goldman & Peter R. Orszag, 2014. "The Growing Gap in Life Expectancy: Using the Future Elderly Model to Estimate Implications for Social Security and Medicare," American Economic Review, American Economic Association, vol. 104(5), pages 230-233, May.
    26. Michaud, Pierre-Carl & Goldman, Dana P. & Lakdawalla, Darius N. & Zheng, Yuhui & Gailey, Adam H., 2012. "The value of medical and pharmaceutical interventions for reducing obesity," Journal of Health Economics, Elsevier, vol. 31(4), pages 630-643.
    27. Dranove, David, 1998. "Is there underinvestment in R & D about prevention?," Journal of Health Economics, Elsevier, vol. 17(1), pages 117-127, January.
    28. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    29. Nord, Erik & Richardson, Jeff & Street, Andrew & Kuhse, Helga & Singer, Peter, 1995. "Maximizing health benefits vs egalitarianism: An Australian survey of health issues," Social Science & Medicine, Elsevier, vol. 41(10), pages 1429-1437, November.
    30. An, Mark Y. & Roberto Ayala, 1995. "A Mixture Model of Willingness to Pay Distributions," Working Papers 95-21, Duke University, Department of Economics.
    31. Stephen Martin, 2019. "The Potential Compensation Principle and Constant Marginal Utility of Income," The Japanese Economic Review, Springer, vol. 70(3), pages 383-393, September.
    32. Fischer, Stanley, 1973. "A Life Cycle Model of Life Insurance Purchases," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(1), pages 132-152, February.
    33. Michael Hurd & James P. Smith, 2002. "Expected Bequests and Their Distribution," NBER Working Papers 9142, National Bureau of Economic Research, Inc.
    34. Robert E. Hall & Charles I. Jones, 2007. "The Value of Life and the Rise in Health Spending," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(1), pages 39-72.
    35. Johansson, Per-Olov, 2002. "On the Definition and Age-Dependency of the Value of a Statistical Life," Journal of Risk and Uncertainty, Springer, vol. 25(3), pages 251-263, November.
    36. Edwards, Ryan D, 2008. "Health Risk and Portfolio Choice," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 472-485.
    37. Johansson, Per-Olov, 2002. "On the Definition and Age-Dependency of the Value of a Statistical Life. A Review and Extension," SSE/EFI Working Paper Series in Economics and Finance 490, Stockholm School of Economics, revised 29 Jan 2002.
    38. Shah, Koonal K. & Tsuchiya, Aki & Wailoo, Allan J., 2018. "Valuing health at the end of life: A review of stated preference studies in the social sciences literature," Social Science & Medicine, Elsevier, vol. 204(C), pages 39-50.
    39. Rheinberger, Christoph M. & Herrera-Araujo, Daniel & Hammitt, James K., 2016. "The value of disease prevention vs treatment," Journal of Health Economics, Elsevier, vol. 50(C), pages 247-255.
    40. Robin Boadway, 1974. "A Note on the Welfare Foundations of Cost-Benefit Analysis," Working Paper 149, Economics Department, Queen's University.
    41. Lillard, Lee A & Weiss, Yoram, 1997. "Uncertain Health and Survival: Effects on End-of-Life Consumption," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(2), pages 254-268, April.
    42. Stephen Martin, 2019. "The Kaldor–Hicks Potential Compensation Principle and the Constant Marginal Utility of Income," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 55(3), pages 493-513, November.
    43. Kevin M. Murphy & Robert H. Topel, 2006. "The Value of Health and Longevity," Journal of Political Economy, University of Chicago Press, vol. 114(5), pages 871-904, October.
    44. Michael Kremer & Christopher M. Snyder, 2015. "Preventives Versus Treatments," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 130(3), pages 1167-1239.
    45. An, Mark Yuying, 1996. "Semiparametric Estimation of Willingness to Pay Distributions," Working Papers 96-20, Duke University, Department of Economics.
    46. Drummond, Michael F. & Sculpher, Mark J. & Claxton, Karl & Stoddart, Greg L. & Torrance, George W., 2015. "Methods for the Economic Evaluation of Health Care Programmes," OUP Catalogue, Oxford University Press, edition 4, number 9780199665884.
    47. David B Agus & Étienne Gaudette & Dana P Goldman & Andrew Messali, 2016. "The Long-Term Benefits of Increased Aspirin Use by At-Risk Americans Aged 50 and Older," PLOS ONE, Public Library of Science, vol. 11(11), pages 1-12, November.
    48. Boadway, Robin W, 1974. "The Welfare Foundations of Cost-Benefit Analysis," Economic Journal, Royal Economic Society, vol. 84(336), pages 926-939, December.
    49. Shah, Koonal K., 2009. "Severity of illness and priority setting in healthcare: A review of the literature," Health Policy, Elsevier, vol. 93(2-3), pages 77-84, December.
    50. Sloan, Frank A. & Kip Viscusi, W. & Chesson, Harrell W. & Conover, Christopher J. & Whetten-Goldstein, Kathryn, 1998. "Alternative approaches to valuing intangible health losses: the evidence for multiple sclerosis1," Journal of Health Economics, Elsevier, vol. 17(4), pages 475-497, August.
    51. Janusz R. Mrozek & Laura O. Taylor, 2002. "What determines the value of life? a meta-analysis," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 21(2), pages 253-270.
    52. Peter A. Diamond, 1967. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparison of Utility: Comment," Journal of Political Economy, University of Chicago Press, vol. 75(5), pages 765-765.
    53. Cameron, Trudy Ann & DeShazo, J.R., 2013. "Demand for health risk reductions," Journal of Environmental Economics and Management, Elsevier, vol. 65(1), pages 87-109.
    54. Damon Jones & David Molitor & Julian Reif, 2019. "What do Workplace Wellness Programs do? Evidence from the Illinois Workplace Wellness Study," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 134(4), pages 1747-1791.
    55. Seierstad, Atle & Sydsaeter, Knut, 1977. "Sufficient Conditions in Optimal Control Theory," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 367-391, June.
    56. James O’Brien, 2018. "Age, autos, and the value of a statistical life," Journal of Risk and Uncertainty, Springer, vol. 57(1), pages 51-79, August.
    57. Garber, Alan M. & Phelps, Charles E., 1997. "Economic foundations of cost-effectiveness analysis," Journal of Health Economics, Elsevier, vol. 16(1), pages 1-31, February.
    58. Michaud, Pierre-Carl & Goldman, Dana & Lakdawalla, Darius & Gailey, Adam & Zheng, Yuhui, 2011. "Differences in health between Americans and Western Europeans: Effects on longevity and public finance," Social Science & Medicine, Elsevier, vol. 73(2), pages 254-263, July.
    59. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
    60. Richard A. Hirth & Michael E. Chernew & Edward Miller & A. Mark Fendrick & William G. Weissert, 2000. "Willingness to Pay for a Quality-adjusted Life Year," Medical Decision Making, , vol. 20(3), pages 332-342, July.
    61. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63(4), pages 309-309.
    62. Moore, Michael J & Viscusi, W Kip, 1990. "Models for Estimating Discount Rates for Long-term Health Risks Using Labor Market Data," Journal of Risk and Uncertainty, Springer, vol. 3(4), pages 381-401, December.
    63. Felix Reichling & Kent Smetters, 2015. "Optimal Annuitization with Stochastic Mortality and Correlated Medical Costs," American Economic Review, American Economic Association, vol. 105(11), pages 3273-3320, November.
    64. Milton C. Weinstein & Donald S. Shepard & Joseph S. Pliskin, 1980. "The Economic Value of Changing Mortality Probabilities: A Decision-Theoretic Approach," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 94(2), pages 373-396.
    65. Goldman, Dana & Michaud, Pierre-Carl & Lakdawalla, Darius & Zheng, Yuhui & Gailey, Adam & Vaynman, Igor, 2010. "The Fiscal Consequences of Trends in Population Health," National Tax Journal, National Tax Association;National Tax Journal, vol. 63(2), pages 307-330, June.
    66. Michael G. Palumbo, 1999. "Uncertain Medical Expenses and Precautionary Saving Near the End of the Life Cycle," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(2), pages 395-421.
    67. Siegel, Jeremy J., 1992. "The real rate of interest from 1800-1990 : A study of the U.S. and the U.K," Journal of Monetary Economics, Elsevier, vol. 29(2), pages 227-252, April.
    68. repec:reg:rpubli:282 is not listed on IDEAS
    69. Goldman, D.P. & Zheng, Y. & Girosi, F. & Michaud, P.-C. & Olshansky, S.J. & Cutler, D. & Rowe, J.W., 2009. "The benefits of risk factor prevention in Americans aged 51 years and older," American Journal of Public Health, American Public Health Association, vol. 99(11), pages 2096-2101.
    70. Christopher D. Carroll & Lawrence H. Summers, 1991. "Consumption Growth Parallels Income Growth: Some New Evidence," NBER Chapters, in: National Saving and Economic Performance, pages 305-348, National Bureau of Economic Research, Inc.
    71. Ehrlich, Isaac, 2000. "Uncertain lifetime, life protection, and the value of life saving," Journal of Health Economics, Elsevier, vol. 19(3), pages 341-367, May.
    72. Charles Blackorby & David Donaldson, 1990. "A Review Article: The Case against the Use of the Sum of Compensating Variations in Cost-Benefit Analysis," Canadian Journal of Economics, Canadian Economics Association, vol. 23(3), pages 471-494, August.
    73. Donald S. Shepard & Richard J. Zeckhauser, 1984. "Survival versus Consumption," Management Science, INFORMS, vol. 30(4), pages 423-439, April.
    74. Pratt, John W & Zeckhauser, Richard J, 1996. "Willingness to Pay and the Distribution of Risk and Wealth," Journal of Political Economy, University of Chicago Press, vol. 104(4), pages 747-763, August.
    75. Weisbrod, Burton A, 1991. "The Health Care Quadrilemma: An Essay on Technological Change, Insurance, Quality of Care, and Cost Containment," Journal of Economic Literature, American Economic Association, vol. 29(2), pages 523-552, 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. Ning Wang, 2019. "The demand for life insurance in a heterogeneous-agent life cycle economy with joint decisions," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 44(2), pages 176-206, September.
    2. Shaun Da Costa, 2019. "The Impact of the Ebola Crisis on Mortality and Welfare in Liberia," Working Papers 1911, Herman Deleeck Centre for Social Policy, University of Antwerp.
    3. Shaun M. Da Costa, 2020. "The impact of the Ebola crisis on mortality and welfare in Liberia," Health Economics, John Wiley & Sons, Ltd., vol. 29(12), pages 1517-1532, December.
    4. Ketcham, Jonathan & Kuminoff, Nicolai & Saha, Nirman, 2023. "Valuing Statistical Life Using Seniors' Medical Spending," RFF Working Paper Series 23-16, Resources for the Future.

    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. Antoine Bommier & Bertrand Villeneuve, 2012. "Risk Aversion and the Value of Risk to Life," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(1), pages 77-104, March.
    2. Henrik Andersson & Nicolas Treich, 2011. "The Value of a Statistical Life," Chapters, in: André de Palma & Robin Lindsey & Emile Quinet & Roger Vickerman (ed.), A Handbook of Transport Economics, chapter 17, Edward Elgar Publishing.
    3. Antoine Bommier & François Grand, 2014. "Too risk averse to purchase insurance?," Journal of Risk and Uncertainty, Springer, vol. 48(2), pages 135-166, April.
    4. James K. Hammitt, 2017. "Valuing Non-Fatal Health Risks: Monetary and Health-Utility Measures," Revue économique, Presses de Sciences-Po, vol. 68(3), pages 335-356.
    5. James Hammitt, 2013. "Admissible utility functions for health, longevity, and wealth: integrating monetary and life-year measures," Journal of Risk and Uncertainty, Springer, vol. 47(3), pages 311-325, December.
    6. Kuhn, Michael & Wrzaczek, Stefan & Prskawetz, Alexia & Feichtinger, Gustav, 2015. "Optimal choice of health and retirement in a life-cycle model," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 186-212.
    7. Kuhn, Michael & Frankovic, Ivan & Wrzaczek, Stefan, 2017. "Medical Progress, Demand for Health Care, and Economic Performance," VfS Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168249, Verein für Socialpolitik / German Economic Association.
    8. Jiakun Zheng, 2021. "Willingness to pay for reductions in health risks under anticipated regret," Post-Print hal-04227414, HAL.
    9. repec:dau:papers:123456789/4812 is not listed on IDEAS
    10. Andersson, Henrik, 2006. "Willingness to Pay for Road Safety and Estimates of the Risk of Death: Evidence from a Swedish Contingent Valuation Study," Working Papers 2006:5, Swedish National Road & Transport Research Institute (VTI).
    11. Herrera-Araujo, Daniel & Rochaix, Lise, 2020. "Does the Value per Statistical Life vary with age or baseline health? Evidence from a compensating wage study in France," Journal of Environmental Economics and Management, Elsevier, vol. 103(C).
    12. Herrera-Araujo, Daniel & Hammitt, James K. & Rheinberger, Christoph M., 2020. "Theoretical bounds on the value of improved health," Journal of Health Economics, Elsevier, vol. 72(C).
    13. James K. Hammitt, 2002. "QALYs Versus WTP," Risk Analysis, John Wiley & Sons, vol. 22(5), pages 985-1001, October.
    14. Henrik Andersson, 2008. "Willingness to Pay for Car Safety: Evidence from Sweden," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 41(4), pages 579-594, December.
    15. Aldy, Joseph Edgar & Smyth, Seamus J, 2014. "Heterogeneity in the Value of Life," Scholarly Articles 23017248, Harvard Kennedy School of Government.
    16. Shelby Gerking & Wiktor Adamowicz & Mark Dickie & Marcella Veronesi, 2017. "Baseline risk and marginal willingness to pay for health risk reduction," Journal of Risk and Uncertainty, Springer, vol. 55(2), pages 177-202, December.
    17. Ryan Edwards, 2013. "The cost of uncertain life span," Journal of Population Economics, Springer;European Society for Population Economics, vol. 26(4), pages 1485-1522, October.
    18. James K. Hammitt, 2020. "Valuing mortality risk in the time of COVID-19," Journal of Risk and Uncertainty, Springer, vol. 61(2), pages 129-154, October.
    19. Rheinberger, Christoph M. & Hammitt, James K., 2014. "The welfare value of FDA's mercury-in-fish advisory: A dynamic reanalysis," Journal of Health Economics, Elsevier, vol. 37(C), pages 113-122.
    20. Hammitt, James K., 2022. "Prevention, Treatment, and Palliative Care: The Relative Value of Health Improvements under Alternative Evaluation Frameworks," TSE Working Papers 22-1339, Toulouse School of Economics (TSE).
    21. Kevin Haninger & James K. Hammitt, 2011. "Diminishing Willingness to Pay per Quality‐Adjusted Life Year: Valuing Acute Foodborne Illness," Risk Analysis, John Wiley & Sons, vol. 31(9), pages 1363-1380, September.

    More about this item

    JEL classification:

    • H51 - Public Economics - - National Government Expenditures and Related Policies - - - Government Expenditures and Health
    • H55 - Public Economics - - National Government Expenditures and Related Policies - - - Social Security and Public Pensions
    • I10 - Health, Education, and Welfare - - Health - - - 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:nbr:nberwo:25055. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.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.