IDEAS home Printed from https://ideas.repec.org/a/oup/qjecon/v129y2014i4p1661-1710.html
   My bibliography  Save this article

A Sparsity-Based Model of Bounded Rationality

Author

Listed:
  • Xavier Gabaix

Abstract

This article defines and analyzes a “sparse max” operator, which is a less than fully attentive and rational version of the traditional max operator. The agent builds (as economists do) a simplified model of the world which is sparse, considering only the variables of first-order importance. His stylized model and his resulting choices both derive from constrained optimization. Still, the sparse max remains tractable to compute. Moreover, the induced outcomes reflect basic psychological forces governing limited attention. The sparse max yields a behavioral version of basic chapters of the microeconomics textbook: consumer demand and competitive equilibrium. I obtain a behavioral version of Marshallian and Hicksian demand, Arrow-Debreu competitive equilibrium, the Slutsky matrix, the Edgeworth box, Roy’s identity, and so on. The Slutsky matrix is no longer symmetric: nonsalient prices are associated with anomalously small demand elasticities. Because the consumer exhibits nominal illusion, in the Edgeworth box, the offer curve is a two-dimensional surface rather than a one-dimensional curve. As a result, different aggregate price levels correspond to materially distinct competitive equilibria, in a similar spirit to a Phillips curve. The Arrow-Debreu welfare theorems typically do not hold. This framework provides a way to assess which parts of basic microeconomics are robust, and which are not, to the assumption of perfect maximization. JEL Codes: D01, D03, D11, D51.

Suggested Citation

  • Xavier Gabaix, 2014. "A Sparsity-Based Model of Bounded Rationality," The Quarterly Journal of Economics, Oxford University Press, vol. 129(4), pages 1661-1710.
  • Handle: RePEc:oup:qjecon:v:129:y:2014:i:4:p:1661-1710
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/qje/qju024
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    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. Ricardo J. Caballero & Arvind Krishnamurthy, 2008. "Collective Risk Management in a Flight to Quality Episode," Journal of Finance, American Finance Association, vol. 63(5), pages 2195-2230, October.
    2. David K. Levine & Drew Fudenberg, 2006. "A Dual-Self Model of Impulse Control," American Economic Review, American Economic Association, vol. 96(5), pages 1449-1476, December.
    3. Kehoe, Patrick & Midrigan, Virgiliu, 2015. "Prices are sticky after all," Journal of Monetary Economics, Elsevier, vol. 75(C), pages 35-53.
    4. Isabelle Brocas & Juan D. Carrillo, 2008. "The Brain as a Hierarchical Organization," American Economic Review, American Economic Association, vol. 98(4), pages 1312-1346, September.
    5. Botond Kőszegi & Matthew Rabin, 2006. "A Model of Reference-Dependent Preferences," The Quarterly Journal of Economics, Oxford University Press, vol. 121(4), pages 1133-1165.
    6. Xavier Gabaix & David Laibson & Guillermo Moloche & Stephen Weinberg, 2006. "Costly Information Acquisition: Experimental Analysis of a Boundedly Rational Model," American Economic Review, American Economic Association, vol. 96(4), pages 1043-1068, September.
    7. Madarász, Kristóf & Prat, Andrea, 2010. "Screening with an Approximate Type Space," CEPR Discussion Papers 7900, C.E.P.R. Discussion Papers.
    8. Raj Chetty, 2012. "Bounds on Elasticities With Optimization Frictions: A Synthesis of Micro and Macro Evidence on Labor Supply," Econometrica, Econometric Society, vol. 80(3), pages 969-1018, May.
    9. Richard H. Thaler, 2008. "Mental Accounting and Consumer Choice," Marketing Science, INFORMS, vol. 27(1), pages 15-25, 01-02.
    10. Heidhues, Paul & Koszegi, Botond, 2014. "Regular prices and sales," Theoretical Economics, Econometric Society, vol. 9(1), January.
    11. Matthew Rabin & Georg Weizsacker, 2009. "Narrow Bracketing and Dominated Choices," American Economic Review, American Economic Association, vol. 99(4), pages 1508-1543, September.
    12. Brigitte C. Madrian & Dennis F. Shea, 2001. "The Power of Suggestion: Inertia in 401(k) Participation and Savings Behavior," The Quarterly Journal of Economics, Oxford University Press, vol. 116(4), pages 1149-1187.
    13. Raj Chetty & Adam Looney & Kory Kroft, 2009. "Salience and Taxation: Theory and Evidence," American Economic Review, American Economic Association, vol. 99(4), pages 1145-1177, September.
    14. Reis, Ricardo, 2006. "Inattentive consumers," Journal of Monetary Economics, Elsevier, vol. 53(8), pages 1761-1800, November.
    15. Klenow, Peter J. & Malin, Benjamin A., 2010. "Microeconomic Evidence on Price-Setting," Handbook of Monetary Economics, in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 6, pages 231-284, Elsevier.
    16. Akerlof, George A & Yellen, Janet L, 1985. "Can Small Deviations from Rationality Make Significant Differences to Economic Equilibria?," American Economic Review, American Economic Association, vol. 75(4), pages 708-720, September.
    17. Enriqueta Aragones & Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2005. "Fact-Free Learning," American Economic Review, American Economic Association, vol. 95(5), pages 1355-1368, December.
    18. Vincent P. Crawford & Nagore Iriberri, 2007. "Level-k Auctions: Can a Nonequilibrium Model of Strategic Thinking Explain the Winner's Curse and Overbidding in Private-Value Auctions?," Econometrica, Econometric Society, vol. 75(6), pages 1721-1770, November.
    19. Andrew B. Abel & Janice C. Eberly & Stavros Panageas, 2013. "Optimal Inattention to the Stock Market With Information Costs and Transactions Costs," Econometrica, Econometric Society, vol. 81(4), pages 1455-1481, July.
    20. Drew Fudenberg & David K. Levine, 2009. "Learning and Equilibrium," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 385-420, May.
    21. Andreas Fuster & David Laibson & Brock Mendel, 2010. "Natural Expectations and Macroeconomic Fluctuations," Journal of Economic Perspectives, American Economic Association, vol. 24(4), pages 67-84, Fall.
    22. Matějka, Filip, 2015. "Rigid pricing and rationally inattentive consumer," Journal of Economic Theory, Elsevier, vol. 158(PB), pages 656-678.
    23. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, Oxford University Press, vol. 112(2), pages 443-478.
    24. Nicola Gennaioli & Andrei Shleifer & Robert Vishny, 2010. "Financial Innovation and Financial Fragility," Working Papers 2010.114, Fondazione Eni Enrico Mattei.
    25. MacLeod W. Bentley, 2002. "Complexity, Bounded Rationality and Heuristic Search," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 1(1), pages 1-52, September.
    26. David Hirshleifer & Sonya Seongyeon Lim & Siew Hong Teoh, 2009. "Driven to Distraction: Extraneous Events and Underreaction to Earnings News," Journal of Finance, American Finance Association, vol. 64(5), pages 2289-2325, October.
    27. Martin Eichenbaum & Nir Jaimovich & Sergio Rebelo, 2008. "Reference Prices and Nominal Rigidities," NBER Working Papers 13829, National Bureau of Economic Research, Inc.
    28. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2010. "Strategic Thinking," Levine's Working Paper Archive 661465000000001148, David K. Levine.
    29. Stefano DellaVigna & Ulrike Malmendier, 2004. "Contract Design and Self-Control: Theory and Evidence," The Quarterly Journal of Economics, Oxford University Press, vol. 119(2), pages 353-402.
    30. Nicola Gennaioli & Andrei Shleifer, 2010. "What Comes to Mind," The Quarterly Journal of Economics, Oxford University Press, vol. 125(4), pages 1399-1433.
    31. Gabriel D. Carroll & James J. Choi & David Laibson & Brigitte C. Madrian & Andrew Metrick, 2009. "Optimal Defaults and Active Decisions," The Quarterly Journal of Economics, Oxford University Press, vol. 124(4), pages 1639-1674.
    32. Abhijit Banerjee & Sendhil Mullainathan, 2010. "The Shape of Temptation: Implications for the Economic Lives of the Poor," NBER Working Papers 15973, National Bureau of Economic Research, Inc.
    33. John A. List, 2003. "Does Market Experience Eliminate Market Anomalies?," The Quarterly Journal of Economics, Oxford University Press, vol. 118(1), pages 41-71.
    34. Pinelopi Koujianou Goldberg & Rebecca Hellerstein, 2013. "A Structural Approach to Identifying the Sources of Local Currency Price Stability," Review of Economic Studies, Oxford University Press, vol. 80(1), pages 175-210.
    35. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August.
    36. Malcolm Baker & Stefan Nagel & Jeffrey Wurgler, 2007. "The Effect of Dividends on Consumption," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 38(1), pages 231-292.
    37. Judith A. Chevalier & Anil K. Kashyap, 2011. "Best Prices," NBER Working Papers 16680, National Bureau of Economic Research, Inc.
    38. Laura L. Veldkamp, 2011. "Information Choice in Macroeconomics and Finance," Economics Books, Princeton University Press, edition 1, number 9621.
    39. Patrick Bolton & Antoine Faure-Grimaud, 2009. "Thinking Ahead: The Decision Problem," Review of Economic Studies, Oxford University Press, vol. 76(4), pages 1205-1238.
    40. Gur Huberman & Wei Jiang, 2006. "Offering versus Choice in 401(k) Plans: Equity Exposure and Number of Funds," Journal of Finance, American Finance Association, vol. 61(2), pages 763-801, April.
    41. Samuelson, William & Zeckhauser, Richard, 1988. "Status Quo Bias in Decision Making," Journal of Risk and Uncertainty, Springer, vol. 1(1), pages 7-59, March.
    42. John Conlisk, 1996. "Why Bounded Rationality?," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 669-700, June.
    43. Janet Currie, 2009. "Healthy, Wealthy, and Wise: Socioeconomic Status, Poor Health in Childhood, and Human Capital Development," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 87-122, March.
    44. Daniel Kahneman, 2003. "Maps of Bounded Rationality: Psychology for Behavioral Economics," American Economic Review, American Economic Association, vol. 93(5), pages 1449-1475, December.
    45. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
    46. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    47. Xavier Gabaix & David Laibson & Guillermo Moloche & Stephen Weinberg, 2005. "Information Acquisition: Experimental Analysis of a Boundedly Rational Model," Levine's Bibliography 666156000000000480, UCLA Department of Economics.
    48. Ignacio Esponda, 2008. "Behavioral Equilibrium in Economies with Adverse Selection," American Economic Review, American Economic Association, vol. 98(4), pages 1269-1291, September.
    49. Fryer Roland & Jackson Matthew O., 2008. "A Categorical Model of Cognition and Biased Decision Making," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 8(1), pages 1-44, February.
    50. Xavier Gabaix & David Laibson, 2002. "The 6D Bias and the Equity-Premium Puzzle," NBER Chapters, in: NBER Macroeconomics Annual 2001, Volume 16, pages 257-330, National Bureau of Economic Research, Inc.
    51. Duffie, Darrell & Sun, Tong-sheng, 1990. "Transactions costs and portfolio choice in a discrete-continuous-time setting," Journal of Economic Dynamics and Control, Elsevier, vol. 14(1), pages 35-51, February.
    52. Timothy Van Zandt & Roy Radner, 1998. "Real-Time Decentralized Information Processing and Returns to Scale," Discussion Papers 1233, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    53. Colin F. Camerer & Teck-Hua Ho & Juin-Kuan Chong, 2004. "A Cognitive Hierarchy Model of Games," The Quarterly Journal of Economics, Oxford University Press, vol. 119(3), pages 861-898.
    54. Sendhil Mullainathan, 2002. "A Memory-Based Model of Bounded Rationality," The Quarterly Journal of Economics, Oxford University Press, vol. 117(3), pages 735-774.
    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. Xavier Gabaix, 2017. "Behavioral Inattention," NBER Working Papers 24096, National Bureau of Economic Research, Inc.
    2. S. Dellavigna., 2011. "Psychology and Economics: Evidence from the Field," VOPROSY ECONOMIKI, N.P. Redaktsiya zhurnala "Voprosy Economiki", vol. 5.
    3. Francisco Gomes & Michael Haliassos & Tarun Ramadorai, 2021. "Household Finance," Journal of Economic Literature, American Economic Association, vol. 59(3), pages 919-1000, September.
    4. Gabaix, Xavier, 2015. "Behavioral Macroeconomics Via Sparse Dynamic Programming," CEPR Discussion Papers 11026, C.E.P.R. Discussion Papers.
    5. Choi, James J. & Haisley, Emily & Kurkoski, Jennifer & Massey, Cade, 2017. "Small cues change savings choices," Journal of Economic Behavior & Organization, Elsevier, vol. 142(C), pages 378-395.
    6. Committee, Nobel Prize, 2017. "Richard H. Thaler: Integrating Economics with Psychology," Nobel Prize in Economics documents 2017-1, Nobel Prize Committee.
    7. Dean Karlan & Margaret McConnell & Sendhil Mullainathan & Jonathan Zinman, 2016. "Getting to the Top of Mind: How Reminders Increase Saving," Management Science, INFORMS, vol. 62(12), pages 3393-3411, December.
    8. Raj Chetty & Adam Looney & Kory Kroft, 2009. "Salience and Taxation: Theory and Evidence," American Economic Review, American Economic Association, vol. 99(4), pages 1145-1177, September.
    9. Guiso, Luigi & Sodini, Paolo, 2013. "Household Finance: An Emerging Field," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1397-1532, Elsevier.
    10. Johannes Abeler & Simon Jäger, 2013. "Complex Tax Incentives - An Experimental Investigation," CESifo Working Paper Series 4231, CESifo.
    11. Eduard Marinov, 2017. "The 2017 Nobel Prize in Economics," Economic Thought journal, Bulgarian Academy of Sciences - Economic Research Institute, issue 6, pages 117-159.
    12. Emmanuel Farhi & Xavier Gabaix, 2020. "Optimal Taxation with Behavioral Agents," American Economic Review, American Economic Association, vol. 110(1), pages 298-336, January.
    13. Erwin Bulte & John A. List & Daan Van Soest, 2019. "Toward an Understanding of the Welfare Effects of Nudges: Evidence from a Field Experiment in Uganda," NBER Working Papers 26286, National Bureau of Economic Research, Inc.
    14. Raj Chetty, 2015. "Behavioral Economics and Public Policy: A Pragmatic Perspective," American Economic Review, American Economic Association, vol. 105(5), pages 1-33, May.
    15. Dolan, P. & Hallsworth, M. & Halpern, D. & King, D. & Metcalfe, R. & Vlaev, I., 2012. "Influencing behaviour: The mindspace way," Journal of Economic Psychology, Elsevier, vol. 33(1), pages 264-277.
    16. McConnell, Margaret, 2013. "Behavioral economics and aging," The Journal of the Economics of Ageing, Elsevier, vol. 1, pages 83-89.
    17. Malmendier, Ulrike M. & Della Vigna, Stefano, 2002. "Overestimating Self-Control: Evidence from the Health Club Industry," Research Papers 1880, Stanford University, Graduate School of Business.
    18. Pedro Bordalo & Nicola Gennaioli & Andrei Shleifer, 2013. "Salience and Consumer Choice," Journal of Political Economy, University of Chicago Press, vol. 121(5), pages 803-843.
    19. Heutel, Garth, 2019. "Prospect theory and energy efficiency," Journal of Environmental Economics and Management, Elsevier, vol. 96(C), pages 236-254.
    20. Drew Fudenberg, 2006. "Advancing Beyond Advances in Behavioral Economics," Journal of Economic Literature, American Economic Association, vol. 44(3), pages 694-711, September.

    More about this item

    JEL classification:

    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • G1 - Financial Economics - - General Financial Markets

    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:oup:qjecon:v:129:y:2014:i:4:p:1661-1710. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: .

    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: Oxford University Press (email available below). General contact details of provider: .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.