In this study we introduce a new stochastic choice rule that categorizes objects in order to simplify the choice procedure. At any given trial, the decision maker deliberately randomizes over mental categories and chooses the best item according to her utility function within the realized consideration set formed by the intersection of the mental category and the menu of alternatives. If no alternative is present both within the considered mental category and within the menu the decision maker picks the default option. We provide the necessary and sufficient conditions that characterize this model in a complete stochastic choice dataset in the form of an acyclicicity restriction on a stochastic choice revealed preference and other regularity conditions. We recover the utility function uniquely up to a monotone transformation and the probability distribution over mental categories uniquely.
A long-standing question about consumer behavior is whether individuals’ observed purchase decisions satisfy the revealed preference (RP) axioms of the utility maximization theory (UMT). Researchers using survey or experimental panel data sets on prices and consumption to answer this question face the well-known problem of measurement error. We show that ignoring measurement error in the RP approach may lead to overrejection of the UMT. To solve this problem, we propose a new statistical RP framework for consumption panel data sets that allows for testing the UMT in the presence of measurement error. Our test is applicable to all consumer models that can be characterized by their first-order conditions. Our approach is nonparametric, allows for unrestricted heterogeneity in preferences, and requires only a centering condition on measurement error. We develop two applications that provide new evidence about the UMT. First, we find support in a survey data set for the dynamic and time-consistent UMT in single-individual households, in the presence of nonclassical measurement error in consumption. In the second application, we cannot reject the static UMT in a widely used experimental data set in which measurement error in prices is assumed to be the result of price misperception due to the experimental design. The first finding stands in contrast to the conclusions drawn from the deterministic RP test of Browning (1989). The second finding reverses the conclusions drawn from the deterministic RP test of Afriat (1967) and Varian (1982).
Satiscing is a hugely inuential model of boundedly rational choice, yet it cannot be easily tested using standard choice data. We develop necessary and sucient conditions for stochastic choice data to be consistent with satiscing, assuming that preferences are xed, but search order may change randomly. The model predicts that stochastic choice can only occur amongst elements that are always chosen, while all other choices must be consistent with standard utility maximization. Adding the assumption that the probability distribution over search orders is the same for all choice sets makes the satiscing model a subset of the class of random utility models.
Given any observed demand behavior by means of a demand function, we quantify by how much it departs from rationality. Using a recent elaboration of the "almost implies near" principle, the measure of the gap is the smallest norm of the correcting matrix that would yield a Slutsky matrix with its standard rationality properties (symmetry, singularity, and negative semidefiniteness). A useful classification of departures from rationality is suggested as a result. Variants, examples, and applications are discussed, and illustrations are provided using several bounded rationality models.
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