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Computational Economics

, Volume 53, Issue 2, pp 533–554 | Cite as

What Types are There?

  • Sam CosaertEmail author
Article

Abstract

Preferences differ in the population, and this heterogeneity may not be adequately described by observed characteristics and additive error terms. As a first contribution, this study shows that preference heterogeneity can be represented graphically by means of violations of the Weak Axiom of Revealed Preference (WARP), and that computing the minimum number of partitions necessary to break all WARP violations in the sample is equivalent to computing the chromatic number of this graph. Second, the study builds the bridge between revealed preference theory and cluster analysis to assign individuals to these partitions (i.e. preference types). The practical methods are applied to Dutch labour supply data, to recover reservation wages of individuals who belong to particular preference types.

Keywords

Preference heterogeneity Chromatic number Revealed preference Labour supply Constrained clustering 

JEL Classifications

C14 C38 C44 D12 D13 

Notes

Acknowledgements

I thank Laurens Cherchye, Thomas Demuynck and Ian Crawford, and also Bart Cap éau, John Dagsvik, André Decoster, Bram De Rock, Yuichi Kitamura, Arthur Lewbel, Lars Nesheim, Johannes Spinnewijn and Frederic Vermeulen for valuable suggestions. Furthermore, I am grateful to seminar participants in Kortrijk and Leuven (University of Leuven), Cergy–Pontoise (ADRES conference), Namur (University of Namur) and Esch–sur–Alzette (LISER). The LISS panel data were collected by CentERdata (Tilburg University, The Netherlands) through its MESS project funded by the Netherlands Organization for Scientific Research.

References

  1. Adams, A., Blundell, R., Browning, M., & Crawford, I. (2015). Prices versus preferences: Taste change and revealed preference. Tech. rep., Institute for Fiscal Studies.Google Scholar
  2. Afriat, S. N. (1967). The construction of utility functions from expenditure data. International Economic Review, 8, 67–77.CrossRefGoogle Scholar
  3. Apesteguia, J., & Ballester, M. (2010). The computational complexity of rationalizing behavior. Journal of Mathematical Economics, 46, 356–363.CrossRefGoogle Scholar
  4. Blundell, R., Chiappori, P., Magnac, T., & Meghir, C. (2007). Collective labor supply: Heterogeneity and non-participation. Review of Economic Studies, 74, 417–445.CrossRefGoogle Scholar
  5. Boelaert, J. (2015). Package revealedprefs. Tech. rep.Google Scholar
  6. Cherchye, L., Demuynck, T., & De Rock, B. (2015). Transitivity of preferences: When does it matter? Tech. rep., ECARES working paper 2015-44.Google Scholar
  7. Cherchye, L., De Rock, B., & Vermeulen, F. (2012). Married with children: A collective labor supply model with detailed time use and intrahousehold expenditure information. American Economic Review, 102, 3377–3405.CrossRefGoogle Scholar
  8. Cherchye, L., & Vermeulen, F. (2008). Nonparametric analysis of household labor supply: Goodness-of-fit and power of the unitary and the collective model. Review of Economics and Statistics, 90, 267–274.CrossRefGoogle Scholar
  9. Chiappori, P. (1988). Rational household labor supply. Econometrica, 56, 63–89.CrossRefGoogle Scholar
  10. Chiappori, P. (1992). Collective labor supply and welfare. Journal of Political Economy, 100, 437–467.CrossRefGoogle Scholar
  11. Crawford, I., & Pendakur, K. (2013). How many types are there. Economic Journal, 123, 77–95.CrossRefGoogle Scholar
  12. Dean, M., & Martin, D. (2016). Measuring rationality with the minimum cost of revealed preference violations. Review of Economics and Statistics, 98, 524–534.Google Scholar
  13. Demuynck, T. (2011). The computational complexity of rationalizing boundedly rational choice behavior. Journal of Mathematical Economics, 47, 425–433.CrossRefGoogle Scholar
  14. Diewert, W. E. (1973). Afriat and revealed preference theory. Review of Economic Studies, 40, 419–425.CrossRefGoogle Scholar
  15. Falmagne, J. C. (1978). A representation theorem for finite random scale systems. Journal of Mathematical Psychology, 18, 52–72.CrossRefGoogle Scholar
  16. Houthakker, H. S. (1950). Revealed preference and the utility function. Economica, 17, 159–174.CrossRefGoogle Scholar
  17. Kalai, G., Rubinstein, A., & Spiegler, R. (2002). Rationalizing choice functions by multiple rationales. Econometrica, 70, 2481–2488.CrossRefGoogle Scholar
  18. Karp, R. M. (1972). Reducibility among combinatorial problems. In Complexity of computer computations (pp. 85–103). Berlin: Berlin.Google Scholar
  19. Lewbel, A. (2001). Demand systems with and without errors. American Economic Review, 91, 611–618.CrossRefGoogle Scholar
  20. McFadden, D. L. (2005). Revealed stochastic preference: a synthesis. Economic Theory, 26, 245–264.CrossRefGoogle Scholar
  21. Rose, H. (1958). Consistency of preference: The two-commodity case. Review of Economic Studies, 25, 124–125.CrossRefGoogle Scholar
  22. Samuelson, P. A. (1938). A note on the pure theory of consumer’s behavior. Economica, 5, 61–71.CrossRefGoogle Scholar
  23. Smeulders, B., Cherchye, L., Rock, B. D., Spieksma, F., & Nobibon, F. T. (2015). Complexity results for the weak axiom of revealed preference for collective consumption models. Journal of Mathematical Economics, 58, 82–91.CrossRefGoogle Scholar
  24. Smeulders, B., Spieksma, F., Cherchye, L., & Rock, B. D. (2014). Goodness-of-fit measures for revealed preference tests: Complexity results and algorithms. ACM Transactions on Economics and Computation, 2, 16.CrossRefGoogle Scholar
  25. Talla Nobibon, F., Cherchye, L., De Rock, B., Sabbe, J., & Spieksma, F. C. R. (2011). Heuristics for deciding collectively rational consumption behavior. Computational Economics, 38, 173–204.CrossRefGoogle Scholar
  26. Varian, H. R. (1983). Non-parametric tests of consumer behavior. Review of Economic Studies, 50, 99–110.CrossRefGoogle Scholar
  27. Wagstaff, K. (2001). Constrained kmeans clustering with background knowledge. ICML, 1, 577–584.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Luxembourg Institute of Socio-Economic Research (LISER) and University of Leuven (KU Leuven)Esch-sur-AlzetteLuxembourg

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