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Paul Samuelson pp 193-227 | Cite as

Samuelson’s Approach to Revealed Preference Theory: Some Recent Advances

  • Thomas Demuynck
  • Per HjertstrandEmail author
Chapter
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Part of the Remaking Economics: Eminent Post-War Economists book series (EPWE)

Abstract

Since Paul Samuelson introduced the theory of revealed preference, it has become one of the most important concepts in economics. This chapter surveys some recent contributions in the revealed preference literature. We depart from Afriat’s theorem, which provides the conditions for a data set to be consistent with the utility maximization hypothesis. We provide and motivate a new condition, which we call the Varian inequalities. The advantage of the Varian inequalities is that they can be formulated as a set of mixed integer linear inequalities, which are linear in the quantity and price data. We show how the Varian inequalities can be used to derive revealed preference tests for weak separability and show how they can be used to formulate tests of the collective household model. Finally, we discuss measurement errors in the observed data and measures of goodness-of-fit, power, and predictive success.

Keywords

Afriat’s theorem collective household model GARP mixed integer linear programming revealed preference Varian inequalities weak separability 

Notes

Acknowledgements

Thomas Demuynck acknowledges financial support by the Fonds de la Recherche Scientifique-FNRS under grant nr F.4516.18. Per Hjertstrand acknowledges financial support from Jan Wallander och Tom Hedelius stiftelse, Marcus och Marianne Wallenbergs stiftelse and Johan och Jakob Söderbergs stiftelse.

References

  1. Adams, A., L. Cherchye, B. De Rock and E. Verriest (2014) “Now or Later? Time Inconsistency, Collective Choice and Revealed Preference,” American Economic Review, 104: 4147–4183.CrossRefGoogle Scholar
  2. Afriat, S.N. (1967) “The Construction of Utility Functions from Expenditure Data,” International Economic Review, 8: 67–77.CrossRefGoogle Scholar
  3. Afriat, S.N. (1969) “The Construction of Separable Utility Functions from Expenditure Data,” Tech. rep., University of North Carolina.Google Scholar
  4. Afriat, S.N. (1972) “Efficiency Estimation of Production Functions,” International Economic Review, 13: 568–598.CrossRefGoogle Scholar
  5. Andreoni, J., B.J. Gillen and W.T Harbaugh (2013) “The Power of Revealed Preference Tests: Ex-Post Evaluation of Experimental Design,” Tech. rep., University of California, San Diego.Google Scholar
  6. Apps, P.F. and R. Rees (1988) “Taxation and the Household,” Journal of Public Economics, 35: 355–369.CrossRefGoogle Scholar
  7. Beatty, T.K.M. and I. Crawford (2011) “How Demanding Is the Revealed Preference Approach to Demand,” American Economic Review, 101: 2782–2795.CrossRefGoogle Scholar
  8. Becker, G.S. (1962) “Irrational Behavior and Economic Theory,” Journal of Political Economy, 70: 1–13.CrossRefGoogle Scholar
  9. Belongia, M.T. and K.A. Chrystal (1991) “An Admissible Monetary Aggregate for the United Kingdom,” Review of Economics and Statistics, 73: 497–503.CrossRefGoogle Scholar
  10. Bergstrom, T.C., L. Blume and H.R. Varian (1986) “On the Private Provision of Public Goods,” Journal of Public Economics, 29: 25–49.CrossRefGoogle Scholar
  11. Blundell, R., M. Browning and I. Crawford (2003) “Nonparametric Engel Curves and Revealed Preference,” Econometrica, 71: 205–240.CrossRefGoogle Scholar
  12. Blundell, R., M. Browning and I. Crawford (2008) “Best Nonparametric Bounds on Demand Responses,” Econometrica, 76: 1227–1262.CrossRefGoogle Scholar
  13. Bronars, S.G. (1987) “The Power of Nonparametric Tests of Preference Maximization,” Econometrica, 55: 693–698.CrossRefGoogle Scholar
  14. Brown, D.J. and C. Calsamiglia (2007) “The Nonparametric Approach to Applied Welfare Analysis,” Economic Theory, 31: 183–188.CrossRefGoogle Scholar
  15. Brown, D.J. and R. Kannan (2008) “Two Algorithms for Solving the Walrasian Equilibrium Inequalities,” in D. Brown and F. Kubler (eds.) Computational Aspects of General Equilibrium Theory: Refutable Theories of Value. Lecture Notes in Economics and Mathematical Systems. Berlin, Springer.Google Scholar
  16. Brown, D.J. and R.L. Matzkin (1996) “Testable Restrictions on the Equilibrium Manifold,” Econometrica, 64: 1249–1262.CrossRefGoogle Scholar
  17. Brown, D.J. and C. Shannon (2000) “Uniqueness, Stability, and Comparative Statics in Rationalizable Walrasian Markets,” Econometrica, 68: 1529–1540.CrossRefGoogle Scholar
  18. Browning, M. (1989) “A Nonparametric Test of the Life-Cycle Rational Expectations Hypothesis,” International Economic Review, 30: 979–992.CrossRefGoogle Scholar
  19. Carvajal, A. and N. Gonzáles (2014) “On Refutability of the Nash Bargaining Solution,” Journal of Mathematical Economics, 50: 177–186.CrossRefGoogle Scholar
  20. Carvajal, A. and X. Song (2018) “Testing Pareto Efficiency and Competitive Equilibrium in Economies with Public Goods,” Journal of Mathematical Economics, 75: 19–30.CrossRefGoogle Scholar
  21. Chambers, C.P. and F. Echenique (2014) “On the Consistency of Data with Bargaining Theories,” Theoretical Economics, 9: 137–162.CrossRefGoogle Scholar
  22. Chambers, C.P. and F. Echenique (2016) Revealed Preference Theory. Cambridge, UK, Cambridge University Press.CrossRefGoogle Scholar
  23. Chambers, C.P., F. Echenique and E. Shmaya (2010) “On Behavioural Complementarities and Its Implications,” Journal of Economic Theory, 145: 2332–2355.CrossRefGoogle Scholar
  24. Chambers, C.P., F. Echenique and E. Shmaya (2011) “Testable Implications of Gross Substitutes in Demand for Two Goods,” American Economic Journal: Microeconomics, 3: 129–136.Google Scholar
  25. Cherchye, L., B. De Rock and F. Vermeulen (2007) “The Collective Model of Household Consumption: A Nonparametric Characterization,” Econometrica, 75: 553–574.CrossRefGoogle Scholar
  26. Cherchye, L., I. Crawford, B. De Rock and F. Vermeulen (2009a) “The Revealed Preference Approach to Demand,” in D. Slottje (ed.) Quantifying Consumer Preferences: Estimating Demand Systems. Contributions to Economic Analysis. Bingley, UK, Emerald Press.Google Scholar
  27. Cherchye, L., B. De Rock and F. Vermeulen (2009b) “Opening the Black Box of Intra-Household Decision-Making: Theory and Nonparametric Empirical Tests of General Collective Consumption Models,” Journal of Political Economy, 117: 1074–1104.CrossRefGoogle Scholar
  28. Cherchye, L., B. De Rock and F. Vermeulen (2011a) “The Revealed Preference Approach to Collective Consumption Behavior: Testing and Sharing Rule Recovery,” Review of Economic Studies, 78: 176–198.CrossRefGoogle Scholar
  29. Cherchye, L., T. Demuynck and B. De Rock (2011b) “Revealed Preference Analysis of Noncooperative Household Consumption,” Economic Journal, 121: 1073–1096.CrossRefGoogle Scholar
  30. Cherchye, L., T. Demuynck and B. De Rock (2011c) “Testable Implications of General Equilibrium Models: An Integer Programming Approach,” Journal of Mathematical Economics, 47: 564–575.CrossRefGoogle Scholar
  31. Cherchye, L., T. Demuynck and B. De Rock (2013) “Nash Bargained Consumption Decisions: A Revealed Preference Analysis,” Economic Journal, 123: 195–235.CrossRefGoogle Scholar
  32. Cherchye, L., T. Demuynck and B. De Rock (2014) “Revealed Preference Analysis for Convex Rationalization on Nonlinear Budget Sets,” Journal of Economic Theory, 152: 224–236.CrossRefGoogle Scholar
  33. Cherchye, L., T. Demuynck, B. De Rock and P. Hjertstrand (2015a) “Revealed Preference Tests for Weak Separability: An Integer Programming Approach,” Journal of Econometrics, 186: 129–141.CrossRefGoogle Scholar
  34. Cherchye, L., T. Demuynck and B. De Rock (2015b) “Is Utility Transferable? A Revealed Preference Analysis,” Theoretical Economics, 10: 51–65.CrossRefGoogle Scholar
  35. Cherchye, L., B. De Rock, T. Demuynck and F. Vermeulen (2017) “Household Consumption When the Marriage Is Stable,” American Economic Review, 107: 1507–1534.Google Scholar
  36. Cherchye, L., T. Demuynck and B. De Rock (2018) “Normality of Demand in a Two-goods Setting,” Journal of Economic Theory, 173: 361–382.CrossRefGoogle Scholar
  37. Chiappori, P.-A. (1988) “Rational Household Labor Supply,” Econometrica, 56: 63–89.CrossRefGoogle Scholar
  38. Chiappori, P.-A. (1992) “Collective Labor Supply and Welfare,” Journal of Political Economy, 100: 437–467.CrossRefGoogle Scholar
  39. Chiappori, P.-A. and J.-C. Rochet (1987) “Revealed Preferences and Differentiable Demand,” Econometrica, 55: 687–691.CrossRefGoogle Scholar
  40. Cosaert, S. and T. Demuynck (2015) “Revealed Preference Theory for Finite Choice Sets,” Economic Theory, 59: 169–200.CrossRefGoogle Scholar
  41. Cosaert, S. and T. Demuynck (2018) “Nonparametric Welfare and Demand Analysis with Unobserved Individual Heterogeneity,” Review of Economic and Statistics, 100: 349–361.CrossRefGoogle Scholar
  42. Crawford, I. (2010) “Habits Revealed,” Review of Economic Studies, 77: 1382–1402.CrossRefGoogle Scholar
  43. Crawford, I. and B. De Rock (2014) “Empirical Revealed Preference,” Annual Review of Economics, 6: 503–524.CrossRefGoogle Scholar
  44. Dean, M. and D. Martin (2016) “Measuring Rationality with the Minimum Cost of Revealed Preference Violations,” Review of Economics and Statistics, 98: 524–534.CrossRefGoogle Scholar
  45. Demuynck, T. (2015) “Statistical Inference for Measures of Predictive Success,” Theory and Decision, 79: 689–699.CrossRefGoogle Scholar
  46. Demuynck, T. and C. Seel (2018) “Revealed Preference with Limited Consideration,” American Economic Journal: Microeconomics, 10: 102–131.Google Scholar
  47. Demuynck, T. and E. Verriest (2013) “I’ll Never Forget My First Cigarette: A Revealed Preference Analysis of the Habits as Durables Model,” International Economic Review, 54: 717–738.CrossRefGoogle Scholar
  48. Diewert, W.E. (1973) “Afriat and Revealed Preference Theory,” Review of Economic Studies, 40: 419–425.CrossRefGoogle Scholar
  49. Diewert, W.E. (2012) “Afriat’s Theorem and Some Extensions to Choice Under Uncertainty,” Economic Journal, 122: 305–331.CrossRefGoogle Scholar
  50. Diewert, W.E. and C. Parkan (1985) “Tests for the Consistency of Consumer Data,” Journal of Econometrics, 30: 127–147.CrossRefGoogle Scholar
  51. Echenique, F. (2014) “Testing for Separability Is Hard,” Tech. rep., Caltech.Google Scholar
  52. Echenique, F., S. Lee and M. Shum (2011) “The Money Pump as a Measure of Revealed Preference Violations,” Journal of Political Economy, 119: 1201–1223.CrossRefGoogle Scholar
  53. Echenique, F. and K. Saito (2015) “Savage in the Market,” Econometrica, 83: 1467–1495.CrossRefGoogle Scholar
  54. Elger, C.T., B.E. Jones, D.L. Edgerton and J.M. Binner (2008) “A Note on the Optimal Level of Monetary Aggregation in the United Kingdom,” Macroeconomic Dynamics, 12: 117–131.CrossRefGoogle Scholar
  55. Fisher, D. and A.R. Fleissig (1997) “Monetary Aggregation and the Demand for Assets,” Journal of Money, Credit and Banking, 29: 458–475.CrossRefGoogle Scholar
  56. Fleissig, A.R. and G.A. Whitney (2003) “A New PC-Based Test for Varian’s Weak Separability Condition,” Journal of Business and Economic Statistics, 21: 133–145.CrossRefGoogle Scholar
  57. Fleissig, A.R. and G.A. Whitney (2005) “Testing for the Significance of Violations of Afriat’s Inequalities,” Journal of Business and Economic Statistics, 23: 355–362.CrossRefGoogle Scholar
  58. Forges, F. and V. Iehlé (2013) “Essential Data, Budget Sets and Rationalization,” Economic Theory, 54: 449–461.CrossRefGoogle Scholar
  59. Forges, F. and V. Iehlé (2014) “Afriat’s Theorem for Indivisible Goods,” Journal of Mathematical Economics, 54: 1–6.CrossRefGoogle Scholar
  60. Forges, F. and E. Minelli (2009) “Afriat’s Theorem for General Budget Sets,” Journal of Economic Theory, 144: 135–145.CrossRefGoogle Scholar
  61. Ginsberg, W. (1973) “Concavity and Quasiconcavity in Economics,” Journal of Economic Theory, 6: 596–605.CrossRefGoogle Scholar
  62. Green, E.J. and K. Osband (1991) “A Revealed Preference Theory for Expected Utility,” Review of Economic Studies, 58: 677–695.CrossRefGoogle Scholar
  63. Gross, J. and D. Kaiser (1996) “Two Simple Algorithms for Generating a Subset of Data Consistent with WARP and Other Binary Relations,” Journal of Business and Economic Statistics, 14: 251–255.Google Scholar
  64. Heufer, J. (2014) “Nonparametric Comparative Revealed Risk Aversion,” Journal of Economic Theory, 153: 569–616.CrossRefGoogle Scholar
  65. Heufer, J. and P. Hjertstrand (2015) “Consistent Subsets: Computationally Feasible Methods to Compute the Houtman-Maks-Index,” Economics Letters, 128: 87–89.CrossRefGoogle Scholar
  66. Heufer, J. and P. Hjertstrand (2019) “Homothetic Efficiency: Theory and Applications," forthcoming in Journal of Business and Economic Statistics.Google Scholar
  67. Hjertstrand, P. (2009) “A Monte Carlo Study of the Necessary and Sufficient Conditions for Weak Separability," Advances in Econometrics, 24: 151–182.CrossRefGoogle Scholar
  68. Hjertstrand, P. (2013) “A Simple Method to Account for Measurement Errors in Revealed Preference Tests," IFN Working Paper 990, Research Institute of Industrial Economics, Stockholm.Google Scholar
  69. Hjertstrand, P. and J.L. Swofford (2012) “Revealed Preference Tests for Consistency with Weakly Separable Indirect Utility,” Theory and Decision, 72: 245–256.CrossRefGoogle Scholar
  70. Hjertstrand, P. and J.L. Swofford (2019) “Revealed Preference Tests of Indirect and Homothetic Weak Separability of Financial Assets, Consumption and Leisure," forthcoming in Journal of Financial Stability.Google Scholar
  71. Hjertstrand, P., J.L. Swofford and G.A. Whitney (2016) “Mixed Integer Programming Revealed Preference Tests of Utility Maximization and Weak Separability of Consumption, Leisure and Money,” Journal of Money, Credit and Banking, 48: 1547–1561.CrossRefGoogle Scholar
  72. Hjertstrand, P., J.L. Swofford and G.A. Whitney (2019) “Index Numbers and Revealed Preference Rankings,” forthcoming in Macroeconomic Dynamics.Google Scholar
  73. Hoderlein, S. and J. Stoye (2014) “Revealed Preference in a Heterogeneous Population,” Review of Economics and Statistics, 96: 197–213.CrossRefGoogle Scholar
  74. Houthakker, H.S. (1950) “Revealed Preference and the Utility Function,” Economica, 17: 159–174.CrossRefGoogle Scholar
  75. Houtman, M. and J.A.H. Maks (1985) “Determining All Maximal Data Subsets Consistent with Revealed Preference,” Kwantitatieve Methoden, 89: 89–104.Google Scholar
  76. Jones, B.E., D. Dutkowsky and C.T. Elger (2005) “Sweep Programs and Optimal Money Aggregation,” Journal of Banking and Finance, 29: 483–508.CrossRefGoogle Scholar
  77. Jones, B.E. and D.L. Edgerton (2009) “Testing Utility Maximization with Measurement Errors in the Data,” Advances in Econometrics, 24: 199–236.CrossRefGoogle Scholar
  78. Kawaguchi, K. (2017) “Testing Rationality Without Restricting Heterogeneity,” Journal of Econometrics, 197: 153–171.CrossRefGoogle Scholar
  79. Kitamura, Y. and J. Stoye (2018) “Nonparametric Analysis of Random Utility Models,” Econometrica, 86: 1883–1909.CrossRefGoogle Scholar
  80. Matzkin, R.L. (1991) “Axioms of Revealed Preference for Nonlinear Choice Sets,” Econometrica, 59: 1779–1786.CrossRefGoogle Scholar
  81. Matzkin, R.L. and M.K. Richter (1991) “Testing Strictly Concave Rationality,” Journal of Economic Theory, 53: 287–303.CrossRefGoogle Scholar
  82. McFadden, D.L. and M.K. Richter (1971) “On the Extension of a Set Function on a Set of Events to a Probability on the Generated Boolean \(\sigma \)-Algebra,” Tech. rep., University of California, Berkeley.Google Scholar
  83. McFadden, D.L. (2005) “Revealed Stochastic Preference: A Synthesis,” Economic Theory, 26: 245–264.CrossRefGoogle Scholar
  84. Nishimura, H., E.A. Ok and J.K.H. Quah (2017) “A Comprehensive Approach to Revealed Preference Theory,” American Economic Review, 107: 1239–1263.CrossRefGoogle Scholar
  85. Polisson, M. and J.K.H. Quah (2013) “Revealed Preference in a Discrete Consumption Space,” American Economic Journal: Microeconomics, 5: 28–34.Google Scholar
  86. Polisson, M., J.K.H. Quah and L. Renou (2017) “Revealed Preferences Over Risk and Uncertainty,” School of Economics and Finance Discussion Paper 1706, University of St Andrews.Google Scholar
  87. Samuelson, P.A. (1938) “A Note on the Pure Theory of Consumer’s Behavior,” Economica, 5: 61–71.CrossRefGoogle Scholar
  88. Samuelson, P.A. (1948) “Consumption Theory in Terms of Revealed Preference,” Economica, 15: 243–253.CrossRefGoogle Scholar
  89. Selten, R. (1991) “Properties of a Measure of Predictive Success,” Mathematical Social Sciences, 21: 153–167.CrossRefGoogle Scholar
  90. Smeulders, B., L. Cherchye, B. De Rock and F.C.R. Spieksma (2013) “The Money Pump as a Measure of Revealed Preference Violations: A Comment,” Journal of Political Economy, 121: 1248–1258.CrossRefGoogle Scholar
  91. Swofford, J.L. and G.A. Whitney (1987) “Nonparametric Tests of Utility Maximization and Weak Separability for Consumption, Leisure and Money,” Review of Economics and Statistics, 69: 458–464.CrossRefGoogle Scholar
  92. Swofford, J.L. and G.A. Whitney (1994) “A Revealed Preference Test for Weakly Separable Utility Maximization with Incomplete Adjustment,” Journal of Econometrics, 60: 235–249.CrossRefGoogle Scholar
  93. van Bruggen, P. and J. Heufer (2017) “Afriat in the Lab,” Journal of Economic Theory, 169: 546–550.CrossRefGoogle Scholar
  94. Varian, H.R. (1982) “The Nonparametric Approach to Demand Analysis,” Econometrica, 50: 945–974.CrossRefGoogle Scholar
  95. Varian, H.R. (1983a) “Non-Parametric Tests of Consumer Behavior,” Review of Economic Studies, 50: 99–110.Google Scholar
  96. Varian, H.R. (1983b) “Nonparametric Tests of Models of Investor Behavior,” Journal of Financial and Quantitative Analysis, 18: 269–278.CrossRefGoogle Scholar
  97. Varian, H.R. (1984) “The Nonparametric Approach to Production Analysis,” Econometrica, 52: 579–597.CrossRefGoogle Scholar
  98. Varian, H.R. (1985) “Non-Parametric Analysis of Optimizing Behaviour with Measurement Error,” Journal of Econometrics, 30: 445–458.CrossRefGoogle Scholar
  99. Varian, H.R. (1988) “Estimating Risk Aversion from Arrow-Debreu Portfolio Choice,” Econometrica, 56: 973–979.CrossRefGoogle Scholar
  100. Varian, H.R. (1990) “Goodness-of-Fit in Optimizing Models,” Journal of Econometrics, 46: 125–140.CrossRefGoogle Scholar
  101. Varian, H.R. (2006) “Revealed Preference,” in M. Szenberg, L. Ramrattan and A.A Gottesman (eds.) Samuelson Economics and the Twenty-First Century. Oxford, Oxford University Press.Google Scholar
  102. Warshall, S. (1962) “A Theorem of Boolean Matrices,” Journal of the American Association of Computing Machinery, 9: 11–12.CrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.ECARESUniversité Libre de BruxellesBrusselsBelgium
  2. 2.Research Institute of Industrial EconomicsStockholmSweden

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