Victor H. Aguiar

Slutsky matrix norms: The size, classification, and comparative statics of bounded rationality

Abstract Given any observed demand behavior —by means of a demand function—, we quantify by how much it departs from rationality. The measure of the gap is the smallest Frobenius norm of the correcting matrix function that would yield a Slutsky matrix with its standard rationality properties (symmetry, singularity, and negative semidefiniteness). As a result, we are able to suggest a useful classification of departures from rationality, corresponding to three anomalies: inattentiveness to changes in purchasing power, money illusion, and violations of the compensated law of demand. Errors in comparative-statics predictions from assuming rationality are decomposed as the sum of a behavioral error (due to the agent) and a specification error (due to the modeller). Illustrations are provided using several bounded rationality models.

Satisficing and stochastic choice

Satisficing is a hugely influential model of boundedly rational choice, yet it cannot be easily tested using standard choice data. We develop necessary and sufficient conditions for stochastic choice data to be consistent with satisficing, assuming that preferences are fixed, 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 satisficing model a subset of the class of random utility models.

Random Categorization and Bounded Rationality

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 acyclicity 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. This model is able to accommodate violations of IIA (independence of irrelevant alternatives), of stochastic transitivity, and of the Manzini–Mariotti menu independence notion (i-Independence).

Stochastic Choice and Attention Capacities: Inferring Preferences from Psychological Biases

This paper shows that frequently observed violations of IIA (Independence of Irrelevant Alternatives), namely the similarity and attraction effect can be compatible with the maximization of rational preferences and the violations themselves can be used to infer the underlying rational preference relation. In order to do this, I introduce a new choice rule that is based on the evidence that decision makers do not pay attention to all items in a menu. Nevertheless they have an underlying rational preference. The Fuzzy Attention Model (FAM) is characterized by an axiom based on revealed stochastic choice akin to the Strong Axiom of Revealed Preference (SARP). The model explains both effects by introducing the idea of an attention capacity that allows for complementarity and substitutability in attention. The similarity effect is related to substitutability while the attraction effect has to do with complementarity. The FAM nests the literature on random consideration sets proposed by Manzini and Mariotti (2014) and the standard rational model, but is not nested in the random utility framework.

Measuring and decomposing the distance to the Shapley wage function with limited data

We study the Shapley wage function, a wage scheme in which a workers pay depends both on the number of hours worked and on the output of the firm. We then provide a way to measure the distance of an arbitrary wage scheme to this function in limited datasets. In particular, for a fixed technology and a given supply of labor, this distance is additively decomposable into violations of the classical axioms of efficiency, equal treatment of identical workers, and marginality. The findings have testable implications for the different ways in which popular wage schemes violate basic properties of distributive justice in market organizations. Applications to the linear contract and to other well-known compensation schemes are shown.

Slutsky Matrix Norms and Revealed Preference Tests of Consumer Behaviour

Given any observed finite sequence of prices, wealth and demand choices, we characterize the relation between its underlying Slutsky matrix norm (SMN) and some popular discrete revealed preference (RP) measures of departures from rationality, such as the Afriat index. We show that testing rationality in the SMN aproach with finite data is equivalent to testing it under the RP approach. We propose a way to “summarize” the departures from rationality in a systematic fashion in finite datasets. Finally, these ideas are extended to an observed demand with noise due to measurement error; we formulate an appropriate modification of the SMN approach in this case and derive closed-form asymptotic results under standard regularity conditions.

A non-parametric approach to testing the axioms of the Shapley value with limited data

The unique properties of the Shapley value–efficiency, equal treatment of identical input factors, and marginality–have made it an appealing solution concept in various classes of problems. It is however recognized that the pay schemes utilized in many real-life situations generally depart from this value. We propose a nonparametric approach to testing the empirical content of this concept with limited datasets. We introduce the Shapley distance, which, for a fixed monotone transferable-utility game, measures the distance of an arbitrary pay profile to the Shapley pay profile, and show that it is additively decomposable into the violations of the classical Shapley axioms. The analysis has several applications. In particular, it can be used to assess the extent to which an income distribution or a cost allocation can be considered fair or unfair, and whether any particular case of unfairness is due to the violation of one or a combination of the Shapley axioms.