This paper is an exposition of an experiment on revealed preferences, where we posite a novel discrete binary choice model. To estimate this model, we use general estimating equations or GEE. This is a methodology originating in biostatistics for estimating regression models with correlated data. In this paper, we focus on the motivation for our approach, the logic and intuition underlying our analysis and a summary of our findings. The missing technical details are in the working paper by Bunn, et al. (2013).
The experimental data is available from the corresponding author: donald.brown@yale.edu. The recruiting poster and informed consent form are attached as appendices.
We conduct two experiments where subjects make a sequence of binary choices between risky and ambiguous binary lotteries. Risky lotteries are defined as lotteries where the relative frequencies of outcomes are known. Ambiguous lotteries are lotteries where the relative frequencies of outcomes are not known or may not exist. The trials in each experiment are divided into three phases: pre-treatment, treatment and post-treatment.
The trials in the pre-treatment and post-treatment phases are the same. As such, the trials before and after the treatment phase are dependent, clustered matched-pairs, that we analyze with the alternating logistic regression (ALR) package in SAS. In both experiments, we reveal to each subject the outcomes of her actual and counterfactual choices in the treatment phase. The treatments differ in the complexity of the random process used to generate the relative frequencies of the payoffs of the ambiguous lotteries. In the first experiment, the probabilities can be inferred from the converging sample averages of the observed actual and counterfactual outcomes of the ambiguous lotteries. In the second experiment the sample averages do not converge.
If we define fictive learning in an experiment as statistically significant changes in the responses of subjects before and after the treatment phase of an experiment, then we expect fictive learning in the first experiment, but no fictive learning in the second experiment. The surprising finding in this paper is the presence of fictive learning in the second experiment. We attribute this counterintuitive result to apophenia: “seeing meaningful patterns in meaningless or random data.” A refinement of this result is the inference from a subsequent Chi-squared test, that the effects of fictive learning in the first experiment are significantly different from the effects of fictive learning in the second experiment.
Changes in total surplus and deadweight loss are traditional measures of economic welfare. We propose necessary and sufficient conditions for rationalizing consumer demand data with a quasilinear utility function. Under these conditions, consumer surplus is a valid measure of consumer welfare. For nonmarketed goods, we propose necessary and sufficient conditions on market data for efficient production , i.e., production at minimum cost. Under these conditions we derive a cost function for the nonmarketed good, where producer surplus is the area above the marginal cost curve.
We show that a demand function is derived from maximizing a quasilinear utility function subject to a budget constraint if and only if the demand function is cyclically monotone. On finite data sets consisting of pairs of market prices and consumption vectors, this result is equivalent to a solution of the Afriat inequalities where all the marginal utilities of income are equal.
We explore the implications of these results for maximization of a random quasilinear utility function subject to a budget constraint and for representative agent general equilibrium models.
The duality theory for cyclically monotone demand is developed using the Legendre-Fenchel transform. In this setting, a consumer’s surplus is measured by the conjugate of her utility function.
Keywords: Permanent income hypothesis, Afriat’s theorem, Law of demand, Consumer’s surplus, Testable restrictions
In the empirical and theoretical literature a consumer’s utility function is often assumed to be quasilinear. In this paper we provide necessary and sufficient conditions for testing if the consumer acts as if she is maximizing a quasilinear utility function over her budget set. If the consumer’s choices are inconsistent with maximizing a quasilinear utility function over her budget set, then we compute the “best” quasilinear rationalization of her choices.