This thesis consists of three papers on a new theory
of random consumer demand.
The first paper develops the theory from an axiomatic
foundation. There are n consumer goods, and a consumption set X whose elements
are bundles of these goods. A consumer faces various choice sets contained in X
, and must choose a single bundle from each choice set. The primitive concept is
that of a random demand function. It assigns to each choice set that a consumer
might face a probability distribution on that choice set, characterizing the
consumer's random choice of a bundle. Assumptions analogous to those of standard
consumer theory constrain the set of random demand functions. Every random
demand function satisfying the assumptions can be represented by a function on X
with certain monotonicity and concavity properties.
The second paper describes Bayesian econometric
techniques allowing one to use the theory and consumer demand data to learn
about the behavior of real consumers. The functions representing theoretically
consistent consumer behavior are approximated by elements of a flexible
parametric class of functions. Prior and posterior uncertainty about a function
is expressed by probability distributions on the parameter space.
The subject of the third paper is the application of
the theory and econometric techniques. It describes a parametric family of
proper prior distributions on the parameter space. Each prior distribution is
derived from a distribution over economically relevant quantities, which makes
it possible to elicit a prior from a consumer economist who knows nothing about
the parameterization of the representation. A prior predictive analysis for one
of the priors in our parametric family illustrates the implications of that
prior on observable quantities. The paper includes an analysis of artificial
data experiments, and individual choice data from a consumer demand experiment
described in Harbaugh et al. (2001).
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