IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v148y2013i3p1255-1267.html
   My bibliography  Save this article

On multivariate prudence

Author

Listed:
  • Jouini, Elyès
  • Napp, Clotilde
  • Nocetti, Diego

Abstract

In this note we extend the theory of precautionary saving to the case of multivariate risk. We introduce a notion of multivariate prudence, related to a precautionary premium, and we propose a matrix-measure to capture the strength of the precautionary saving motive. We discuss the usefulness of this measure, in particular for comparing precautionary behavior among individuals. We also characterize the notion of multivariate downside risk aversion as a preference for disaggregating harms across outcomes of multivariate lotteries. We show the link between this notion and the notion of multivariate prudence, we propose a matrix-measure of its intensity, and we illustrate the usefulness of our results in a problem of social discounting.

Suggested Citation

  • Jouini, Elyès & Napp, Clotilde & Nocetti, Diego, 2013. "On multivariate prudence," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1255-1267.
    • Handle: RePEc:eee:jetheo:v:148:y:2013:i:3:p:1255-1267
    DOI: 10.1016/j.jet.2012.10.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S002205311300029X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2012.10.007?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. L. Eeckhoudt & B. Phuong & D. Crainich, 2005. "Priorities in health care : risk aversion and prudence matter," Post-Print hal-00326114, HAL.
    2. Becker, Gary S, 1974. "A Theory of Social Interactions," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1063-1093, Nov.-Dec..
    3. Carroll, Christopher D., 2009. "Precautionary saving and the marginal propensity to consume out of permanent income," Journal of Monetary Economics, Elsevier, vol. 56(6), pages 780-790, September.
    4. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    5. Abel, Andrew B, 1990. "Asset Prices under Habit Formation and Catching Up with the Joneses," American Economic Review, American Economic Association, vol. 80(2), pages 38-42, May.
    6. Paroush, Jacob, 1975. "Risk premium with many commodities," Journal of Economic Theory, Elsevier, vol. 11(2), pages 283-286, October.
    7. Modica, Salvatore & Scarsini, Marco, 2005. "A note on comparative downside risk aversion," Journal of Economic Theory, Elsevier, vol. 122(2), pages 267-271, June.
    8. Michael Hoel, 2003. "Allocating health care resources when people are risk averse with respect to life time," Health Economics, John Wiley & Sons, Ltd., vol. 12(7), pages 601-608, July.
    9. Denuit, Michel & Eeckhoudt, Louis, 2010. "Stronger measures of higher-order risk attitudes," LIDAM Discussion Papers ISBA 2010010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Phuong Bui & David Crainich & Louis Eeckhoudt, 2005. "Allocating health care resources under risk: risk aversion and prudence matter," Health Economics, John Wiley & Sons, Ltd., vol. 14(10), pages 1073-1077, October.
    11. Denuit, Michel M. & Eeckhoudt, Louis, 2010. "Stronger measures of higher-order risk attitudes," Journal of Economic Theory, Elsevier, vol. 145(5), pages 2027-2036, September.
    12. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
    13. David Crainich & Louis Eeckhoudt, 2008. "On the intensity of downside risk aversion," Journal of Risk and Uncertainty, Springer, vol. 36(3), pages 267-276, June.
    14. Hayne E. Leland, 1968. "Saving and Uncertainty: The Precautionary Demand for Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 82(3), pages 465-473.
    15. Dreze, Jacques H. & Modigliani, Franco, 1972. "Consumption decisions under uncertainty," Journal of Economic Theory, Elsevier, vol. 5(3), pages 308-335, December.
    16. Gollier, Christian, 2010. "Ecological discounting," Journal of Economic Theory, Elsevier, vol. 145(2), pages 812-829, March.
    17. Kihlstrom, Richard E. & Mirman, Leonard J., 1974. "Risk aversion with many commodities," Journal of Economic Theory, Elsevier, vol. 8(3), pages 361-388, July.
    18. Eeckhoudt, Louis & Schlesinger, Harris, 2008. "Changes in risk and the demand for saving," Journal of Monetary Economics, Elsevier, vol. 55(7), pages 1329-1336, October.
    19. Carroll, Christopher D & Kimball, Miles S, 1996. "On the Concavity of the Consumption Function," Econometrica, Econometric Society, vol. 64(4), pages 981-992, July.
    20. Diego Nocetti & William T. Smith, 2011. "Precautionary Saving and Endogenous Labor Supply with and without Intertemporal Expected Utility," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43(7), pages 1475-1504, October.
    21. 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.
    22. Louis Eeckhoudt & Harris Schlesinger, 2006. "Putting Risk in Its Proper Place," American Economic Review, American Economic Association, vol. 96(1), pages 280-289, March.
    23. Keenan, Donald C. & Snow, Arthur, 2009. "Greater downside risk aversion in the large," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1092-1101, May.
    24. Christophe Courbage & Béatrice Rey, 2007. "Precautionary saving in the presence of other risks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(2), pages 417-424, August.
    25. Michel Denuit & Louis Eeckhoudt & Mario Menegatti, 2011. "Correlated risks, bivariate utility and optimal choices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(1), pages 39-54, January.
    26. Hardle, Wolfgang & Hildenbrand, Werner & Jerison, Michael, 1991. "Empirical Evidence on the Law of Demand," Econometrica, Econometric Society, vol. 59(6), pages 1525-1549, November.
    27. Miles S. Kimball, 1990. "Precautionary Saving and the Marginal Propensity to Consume," NBER Working Papers 3403, National Bureau of Economic Research, Inc.
    28. Louis Eeckhoudt & Béatrice Rey & Harris Schlesinger, 2007. "A Good Sign for Multivariate Risk Taking," Management Science, INFORMS, vol. 53(1), pages 117-124, January.
    29. Miles Kimball & Philippe Weil, 2009. "Precautionary Saving and Consumption Smoothing across Time and Possibilities," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(2‐3), pages 245-284, March.
    30. repec:cor:louvrp:-2431 is not listed on IDEAS
    31. Christophe Courbage & Béatrice Rey, 2007. "Precautionary saving in the presence of other risks," Post-Print halshs-03353387, HAL.
    32. Duncan, George T, 1977. "A Matrix Measure of Multivariate Local Risk Aversion," Econometrica, Econometric Society, vol. 45(4), pages 895-903, May.
    33. A. Sandmo, 1970. "The Effect of Uncertainty on Saving Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(3), pages 353-360.
    34. Nocetti, Diego & Smith, William T., 2011. "Price uncertainty, saving, and welfare," Journal of Economic Dynamics and Control, Elsevier, vol. 35(7), pages 1139-1149, July.
    35. Karni, Edi, 1979. "On Multivariate Risk Aversion," Econometrica, Econometric Society, vol. 47(6), pages 1391-1401, November.
    36. Gali, Jordi, 1994. "Keeping Up with the Joneses: Consumption Externalities, Portfolio Choice, and Asset Prices," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 26(1), pages 1-8, February.
    37. Menezes, C & Geiss, C & Tressler, J, 1980. "Increasing Downside Risk," American Economic Review, American Economic Association, vol. 70(5), pages 921-932, December.
    38. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
    39. Mario Menegatti, 2009. "Precautionary saving in the presence of other risks: a comment," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(3), pages 473-476, June.
    40. Jindapon, Paan & Neilson, William S., 2007. "Higher-order generalizations of Arrow-Pratt and Ross risk aversion: A comparative statics approach," Journal of Economic Theory, Elsevier, vol. 136(1), pages 719-728, September.
    41. Stiglitz, Joseph E, 1969. "Behavior Towards Risk with Many Commodities," Econometrica, Econometric Society, vol. 37(4), pages 660-667, October.
    42. Joseph E. Stiglitz, 1969. "A Note on Behavior towards Risk with Many Commodities," Cowles Foundation Discussion Papers 262, Cowles Foundation for Research in Economics, Yale University.
    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. Jouini, Elyès & Napp, Clotilde & Nocetti, Diego, 2013. "The marginal propensity to consume and multidimensional risk," Economics Letters, Elsevier, vol. 119(2), pages 124-127.
    2. Christoph Heinzel, 2014. "Term structure of discount rates under multivariate s-ordered consumption growth," Working Papers SMART 14-01, INRAE UMR SMART.
    3. Eric André & Antoine Bommier & François Le Grand, 2022. "The impact of risk aversion and ambiguity aversion on annuity and saving choices," Journal of Risk and Uncertainty, Springer, vol. 65(1), pages 33-56, August.
    4. Crainich, David & Eeckhoudt, Louis & Courtois, Olivier Le, 2020. "Intensity of preferences for bivariate risk apportionment," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 153-160.
    5. Antoine Bommier & François Le Grand, 2019. "Risk Aversion and Precautionary Savings in Dynamic Settings," Management Science, INFORMS, vol. 65(3), pages 1386-1397, March.
    6. Crainich, David & Eeckhoudt, Louis & Le Courtois, Olivier, 2017. "Health and portfolio choices: A diffidence approach," European Journal of Operational Research, Elsevier, vol. 259(1), pages 273-279.

    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. Donatella Baiardi & Marco Magnani & Mario Menegatti, 2020. "The theory of precautionary saving: an overview of recent developments," Review of Economics of the Household, Springer, vol. 18(2), pages 513-542, June.
    2. Christoph Heinzel, 2014. "Term structure of discount rates under multivariate s-ordered consumption growth," Working Papers SMART 14-01, INRAE UMR SMART.
    3. Antoine Bommier & François Le Grand, 2019. "Risk Aversion and Precautionary Savings in Dynamic Settings," Management Science, INFORMS, vol. 65(3), pages 1386-1397, March.
    4. Liqun Liu & William S. Neilson, 2019. "Alternative Approaches to Comparative n th-Degree Risk Aversion," Management Science, INFORMS, vol. 65(8), pages 3824-3834, August.
    5. Crainich, David & Eeckhoudt, Louis & Le Courtois, Olivier, 2017. "Health and portfolio choices: A diffidence approach," European Journal of Operational Research, Elsevier, vol. 259(1), pages 273-279.
    6. Donatella Baiardi & Marco Magnani & Mario Menegatti, 2014. "Precautionary saving under many risks," Journal of Economics, Springer, vol. 113(3), pages 211-228, November.
    7. Heinzel Christoph & Richard Peter, 2021. "Precautionary motives with multiple instruments," Working Papers SMART 21-09, INRAE UMR SMART.
    8. Baiardi, Donatella & Manera, Matteo & Menegatti, Mario, 2013. "Consumption and precautionary saving: An empirical analysis under both financial and environmental risks," Economic Modelling, Elsevier, vol. 30(C), pages 157-166.
    9. Donatella Baiardi & Mario Menegatti, 2011. "Pigouvian tax, abatement policies and uncertainty on the environment," Journal of Economics, Springer, vol. 103(3), pages 221-251, July.
    10. AJ A. Bostian & Christoph Heinzel, 2016. "Consumption Smoothing and Precautionary Saving under Recursive Preferences," FOODSECURE Working papers 44, LEI Wageningen UR.
    11. Christoph Heinzel & Richard Peter, 2021. "Precautionary motives with multiple instruments [Motifs de précaution en cas de multiples instruments]," Working Papers hal-03484875, HAL.
    12. Heinzel, Christoph & Peter, Richard, 2021. "Precautionary motives with multiple instruments," Working Papers 316521, Institut National de la recherche Agronomique (INRA), Departement Sciences Sociales, Agriculture et Alimentation, Espace et Environnement (SAE2).
    13. Christophe Courbage & Richard Peter & Béatrice Rey, 2022. "Incentive and welfare effects of correlated returns," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(1), pages 5-34, March.
    14. Jingyuan Li, 2012. "Precautionary saving in the presence of labor income and interest rate risks," Journal of Economics, Springer, vol. 106(3), pages 251-266, July.
    15. Christian Gollier & James Hammitt & Nicolas Treich, 2013. "Risk and choice: A research saga," Journal of Risk and Uncertainty, Springer, vol. 47(2), pages 129-145, October.
    16. Michel Denuit & Louis Eeckhoudt & Mario Menegatti, 2011. "Correlated risks, bivariate utility and optimal choices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(1), pages 39-54, January.
    17. James Huang & Richard Stapleton, 2017. "Higher-order risk vulnerability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 387-406, February.
    18. Liu, Liqun, 2014. "Precautionary saving in the large: nth degree deteriorations in future income," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 169-172.
    19. Heinzel, Christoph, 2023. "Comparing utility derivative premia under additive and multiplicative risks," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 23-40.
    20. Dionne, Georges & Li, Jingyuan, 2014. "Comparative Ross risk aversion in the presence of mean dependent risks," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 128-135.

    More about this item

    Keywords

    Precautionary saving; Multivariate risk; Prudence; Multivariate risk aversion; Downside risk aversion;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

    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:eee:jetheo:v:148:y:2013:i:3:p:1255-1267. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    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.