How Many Types are There?

We consider a revealed preference‐based method that will bound the minimal partition of consumer microdata into a set of preference types such that the data are perfectly rationalisable by standard utility theory. This provides a simple, non‐parametric and theory‐driven way of investigating unobserved preference heterogeneity in empirical data, and easily extends to any choice model which has a revealed preference characterisation. We illustrate the approach using survey data and find that the number of types is remarkably few relative to the sample size – only four or five types are necessary to fully rationalise all observed choices in a data set with 500 observations of choice vectors.

[1]  R. Blundell,et al.  Improving Revealed Preference Bounds on Demand Responses , 2007 .

[2]  Hal R. Varian.  Revealed Preference with a Subset of Goods , 1988 .

[3]  Per Hjertstrand,et al.  A Simple Method to Account for Measurement Errors in Revealed Preference Tests , 2013 .

[4]  M. Hill.  Diversity and Evenness: A Unifying Notation and Its Consequences , 1973 .

[5]  H. Theil.  The Information Approach to Demand Analysis , 1965 .

[6]  A. Lewbel,et al.  Tricks With Hicks: The Easi Demand System , 2007 .

[7]  J. Heckman.  Micro Data, Heterogeneity, and the Evaluation of Public Policy: Nobel Lecture , 2001, Journal of Political Economy.

[8]  J. Heckman,et al.  A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data , 1984 .

[9]  Bram De Rock,et al.  Analyzing Cost Efficient Production Behavior Under Economies of Scope: A Nonparametric Methodology , 2006, Oper. Res..

[10]  P. Erd6s.  ON A CLASSICAL PROBLEM OF PROBABILITY THEORY b , 2001 .

[11]  Bram De Rock,et al.  The collective model of household consumption , 2004 .

[12]  James J. Heckman,et al.  Micro Data, Heterogeneity and the Evaluation of Public Policy Part 1 , 2001 .

[13]  Stephen Warshall,et al.  A Theorem on Boolean Matrices , 1962, JACM.

[14]  Hal R. Varian,et al.  Non-parametric analysis of optimizing behavior with measurement error , 1985 .

[15]  B. Efron,et al.  Estimating the number of unseen species: How many words did Shakespeare know? Biometrika 63 , 1976 .

[16]  Rosa L. Matzkin.  Identification in nonparametric limited dependent variable models with simultaneity and unobserved heterogeneity , 2012 .

[17]  M. McElroy.  Additive General Error Models for Production, Cost, and Derived Demand or Share Systems , 1987, Journal of Political Economy.

[18]  K. Lancaster.  A New Approach to Consumer Theory , 1966, Journal of Political Economy.

[19]  Martin Browning,et al.  A Nonparametric Test of the Life-Cycle Rational Expectations Hypothesis , 1989 .

[20]  Debraj Ray,et al.  How Rational are your Choice Data? , 2010 .

[21]  Hal R. Varian,et al.  Nonparametric Tests of Models of Investor Behavior , 1983, Journal of Financial and Quantitative Analysis.

[22]  Aviv Nevo.  Measuring Market Power in the Ready-to-Eat Cereal Industry , 1998 .

[23]  W. M. Gorman.  A Possible Procedure for Analysing Quality Differentials in the Egg Market , 1980 .

[24]  James J. Heckman.  Microdata, Heterogeneity and the Evaluation of Public Policy , 2000 .

[25]  A. Deaton,et al.  Quality, quantity, and spatial variation of price , 1988 .

[26]  Rosa L. Matzkin.  Nonparametric Estimation of Nonadditive Random Functions , 2003 .

[27]  M. Friedman.  Essays in Positive Economics Part I - The Methodology of Positive Economics * , 2004 .

[28]  A. Chao.  Nonparametric estimation of the number of classes in a population , 1984 .

[29]  Martin Browning,et al.  Revealed Preference Analysis of Characteristics Models , 2008 .

[30]  S. Afriat.  THE CONSTRUCTION OF UTILITY FUNCTIONS FROM EXPENDITURE DATA , 1967 .

[31]  John Gross.  Testing Data for Consistency with Revealed Preference , 1995 .

[32]  H. Varian.  The Nonparametric Approach to Production Analysis , 1984 .

[33]  A. Rivlin,et al.  Economic Choices , 2001 .

[34]  J. Bunge,et al.  Estimating the Number of Species: A Review , 1993 .

[35]  Martin Browning,et al.  Nonparametric Engel curves and revealed preference , 2003 .

[36]  George J. Stigler,et al.  De Gustibus Non Est Disputandum , 2010 .

[37]  H. Varian.  Non-parametric Tests of Consumer Behaviour , 1983 .

[38]  A. Lewbel,et al.  Demand Systems with and without Errors , 2001 .

[39]  R. Blundell,et al.  Estimation in Large and Disaggregated Demand Systems: An Estimator for Conditionally Linear Systems , 1999 .

[40]  Berthold R. Haag,et al.  Testing and imposing Slutsky symmetry in nonparametric demand systems , 2009 .

[41]  Rosa L. Matzkin.  Chapter 73 Nonparametric identification , 2007 .

[42]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[43]  Mary Beth Walker,et al.  The Random Utility Hypothesis and Inference in Demand Systems , 1989 .

[44]  J. Raaijmakers,et al.  Statistical analysis of the Michaelis-Menten equation. , 1987, Biometrics.

[45]  Ziv Bar‐Shira.  Nonparametric Test of the Expected Utility Hypothesis , 1992 .

[46]  H. Varian.  The Nonparametric Approach to Demand Analysis , 1982 .

[47]  Robert K. Colwell,et al.  Estimating terrestrial biodiversity through extrapolation. , 1994, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[48]  Market and Plan; Plan and Market: Discussion , 1977 .

[49]  Uskali Mäki.  The Methodology of Positive Economics , 2009 .

[50]  M. Rothschild,et al.  Testing the Assumptions of Production Theory: A Nonparametric Approach , 1972, Journal of Political Economy.

[51]  Walter Diewert,et al.  Afriat and Revealed Preference Theory , 1973 .