How Many Types Are There?

We consider an revealed preference based method which will partition consumer microdata into an approximate minimal number of preference types such that the data are perfectly rationalisable by standard utility theory. This provides a simple, nonparametric 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 …nd that the number of types is remarkably few relative to the sample size only 4 or 5 types are necessary to fully characterise all observed choices in a dataset with 500 observations of choice vectors. Key Words: applied econometrics, unobserved heterogeneity, revealed preference, salamanders. JEL Classi…cation: C43, D11. Acknowledgements: Pendakur acknowledges the …nancial support of the Social Sciences and Humanities Research Council of Canada. We are very grateful to Soren Arnberg, Richard Blundell, Martin Browning, Andrew Chesher, Simon Sokbae Lee, Arthur Lewbel and J. Peter Neary for helpful comments. 1 Unobserved Heterogeneity in Microdata One of the most striking features of consumer microdata is the great heterogeneity in choice behaviour which is evident, even amongst economic agents which are otherwise similar in observable respects. This presents researchers with a di¢ cult problem how to model behaviour in a way which accommodates this heterogeneity and yet preserves theoretical consistency and tractability. One rather robust response is to demand that everything should be explainable by the theory in terms of observables alone. This view is typi…ed by Becker and Stigler (1977): “Tastes neither change capriciously nor di¤er importantly between people.”G. Becker and G. Stigler De Gustibus Non Est Disputandum, AER, 1977 The research agenda which follows from this view is one which tries to explain di¤erences in observed behaviour without recourse to unobserved heterogeneity in tastes, but instead purely in terms of the theory and observable di¤erences in constraints, characteristics of market goods and characteristics of agents. From this point of view, resorting to unobserved preference heterogeneity in order to rationalise behaviour is a cop-out; it is an admission of failure on the part of the theory.