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Relaxed Optimization: e-Rationalizability and the FOC-Departure Index in Consumer Theory

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  • Geoffroy de Clippel
  • Kareen Rozen

Abstract

We propose relaxing the first-order conditions in optimization to approximate rational consumer choice. Departures from the FOCs are assessed using an axiomatically founded measure that is also interpretable in terms of a money-pump multiplier. The framework encompasses measurement errors, information unobservable to the modeler, and consumer misperception. We develop testable implications for demand data, including for subclasses of regular utility functions, and develop the FOC-Departure Index (FDI), which is applicable in all contexts where the first-order approach is meaningful. We extend these ideas to convex budget sets. Our analysis extends to non-convex preferences under a narrower interpretation of price misperception.

Suggested Citation

  • Geoffroy de Clippel & Kareen Rozen, 2020. "Relaxed Optimization: e-Rationalizability and the FOC-Departure Index in Consumer Theory," Working Papers 2020-07, Brown University, Department of Economics.
    • Handle: RePEc:bro:econwp:2020-07
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    1. Syngjoo Choi & Shachar Kariv & Wieland M?ller & Dan Silverman, 2014. "Who Is (More) Rational?," American Economic Review, American Economic Association, vol. 104(6), pages 1518-1550, June.
    2. Ignacio Esponda & Demian Pouzo, 2016. "Berk–Nash Equilibrium: A Framework for Modeling Agents With Misspecified Models," Econometrica, Econometric Society, vol. 84, pages 1093-1130, May.
    3. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    4. Emmanuel Saez & Joel Slemrod & Seth H. Giertz, 2012. "The Elasticity of Taxable Income with Respect to Marginal Tax Rates: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 50(1), pages 3-50, March.
    5. Matthew Polisson & John K.-H. Quah & Ludovic Renou, 2020. "Revealed Preferences over Risk and Uncertainty," American Economic Review, American Economic Association, vol. 110(6), pages 1782-1820, June.
    6. Donald J. Brown & Caterina Calsamiglia, 2008. "The Nonparametric Approach to Applied Welfare Analysis," Lecture Notes in Economics and Mathematical Systems, in: Computational Aspects of General Equilibrium Theory, pages 41-46, Springer.
    7. Ariel Rubinstein & Yuval Salant, 2012. "Eliciting Welfare Preferences from Behavioural Data Sets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(1), pages 375-387.
    8. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, vol. 144(1), pages 135-145, January.
    9. Green, Richard C. & Srivastava, Sanjay, 1986. "Expected utility maximization and demand behavior," Journal of Economic Theory, Elsevier, vol. 38(2), pages 313-323, April.
    10. Xavier Gabaix, 2014. "A Sparsity-Based Model of Bounded Rationality," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(4), pages 1661-1710.
    11. Hugh Rose, 1958. "Consistency of Preference: The Two-Commodity Case," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 124-125.
    12. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-686, May.
    13. Chiappori, Pierre-Andre & Rochet, Jean-Charles, 1987. "Revealed Preferences and Differentiable Demand: Notes and Comments," Econometrica, Econometric Society, vol. 55(3), pages 687-691, May.
    14. Matzkin, Rosa L. & Richter, Marcel K., 1991. "Testing strictly concave rationality," Journal of Economic Theory, Elsevier, vol. 53(2), pages 287-303, April.
    15. Yoram Halevy & Dotan Persitz & Lanny Zrill, 2018. "Parametric Recoverability of Preferences," Journal of Political Economy, University of Chicago Press, vol. 126(4), pages 1558-1593.
    16. Federico Echenique & Sangmok Lee & Matthew Shum, 2011. "The Money Pump as a Measure of Revealed Preference Violations," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1201-1223.
    17. Varian, Hal R., 1990. "Goodness-of-fit in optimizing models," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 125-140.
    18. Afriat, S N, 1973. "On a System of Inequalities in Demand Analysis: An Extension of the Classical Method," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(2), pages 460-472, June.
    19. Jose Apesteguia & Miguel A. Ballester, 2015. "A Measure of Rationality and Welfare," Journal of Political Economy, University of Chicago Press, vol. 123(6), pages 1278-1310.
    20. Jakub Steiner & Colin Stewart, 2016. "Perceiving Prospects Properly," American Economic Review, American Economic Association, vol. 106(7), pages 1601-1631, July.
    21. W. Erwin Diewert, 2012. "Afriat's Theorem and some Extensions to Choice under Uncertainty," Economic Journal, Royal Economic Society, vol. 122(560), pages 305-331, May.
    22. Mark Dean & Daniel Martin, 2016. "Measuring Rationality with the Minimum Cost of Revealed Preference Violations," The Review of Economics and Statistics, MIT Press, vol. 98(3), pages 524-534, July.
    23. repec:ecj:econjl:v:122:y:2012:i::p:305-331 is not listed on IDEAS
    24. Koichiro Ito, 2014. "Do Consumers Respond to Marginal or Average Price? Evidence from Nonlinear Electricity Pricing," American Economic Review, American Economic Association, vol. 104(2), pages 537-563, February.
    25. repec:dau:papers:123456789/4099 is not listed on IDEAS
    26. Matthew Polisson & John K.-H. Quah & Ludovic Renou, 2020. "Revealed Preferences over Risk and Uncertainty," American Economic Review, American Economic Association, vol. 110(6), pages 1782-1820, June.
    27. Peter Lee & Kam-Chau Wong, 2005. "Revealed preference and differentiable demand," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(4), pages 855-870, June.
    28. Francoise Forges & Enrico Minelli, 2009. "Afriat's theorem for generalized budget sets," Post-Print hal-00360726, HAL.
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