Bayesian Inference for a Theory of Random Consumer Demand

• Activity Number: 48
• Type: Contributed
• Date/Time: Sunday, August 11, 2002 : 4:00 PM to 5:50 PM
• Sponsor: Business & Economics Statistics Section*
• Author(s): William McCausland*+
• Affiliation(s): Université de Montréal
• Keywords: consumer demand ; flexible functional forms

Abstract

In a related paper, we describe a new theory of random consumer demand and show that theoretically consistent demand can be represented by a regular "utility" function. Regular utility functions are those satisfying certain monotonicity and concavity restrictions. Here, we describe Bayesian inference for utility functions. We approximate utility functions by elements of a parametric class of functions. Following Geweke and Petrella (2000), we apply a result from Evard and Jafari (1994) to show that any regular utility function can be arbitrarily well approximated on a hyper-rectangle X by a utility function in this class that is regular on X. We can choose X to include all feasible consumer choices. We derive unnormalized data densities from utility functions, but we cannot express normalization factors analytically. This prevents the straightforward use of standard Markov chain Monte Carlo methods for posterior simulation of parameters. We describe a Markov chain on a product space for which the parameter space is a factor space. The chain has an invariant distribution whose marginal distribution on the parameter space is the posterior distribution of the parameters.