Toward Choice-Theoretic Foundations for Behavioral Welfare Economics

Interest in behavioral economics has grown in recent years, stimulated largely by accumulating evidence that the standard model of consumer decision making provides an inadequate, positive description of human behavior. Behavioral models are increasingly finding their way into policy evaluation, which inevitably involves welfare analysis. No consensus concerning the appropriate standards and criteria for behavioral welfare analysis has emerged yet. This paper summarizes our effort to develop a unified framework for behavioral welfare economics (for a detailed discussion see Bernheim and Rangel 2007) — one that can be viewed as a natural extension of standard welfare economics. Standard welfare analysis is based on choice, not on utility or preferences. In its simplest form, it instructs the planner to respect the choices an individual would make for himself. The guiding normative principle is an extension of the libertarian deference to freedom of choice, which takes the view that it is better to give a person the thing he would choose for himself rather than something that someone else would choose for him. We show that it is possible to extend the standard choice-theoretic approach to welfare analysis to situations where individuals make inconsistent choices, which are prevalent in behavioral economics

Beyond revealed preference: choice-theoretic foundations for behavioral welfare economics

We propose a broad generalization of standard choice-theoretic welfare economics that encompasses a wide variety of nonstandard behavioral models. Our approach exploits the coherent aspects of choice that those positive models typically attempt to capture. It replaces the standard revealed preference relation with an unambiguous choice relation: roughly, x is (strictly) unambiguously chosen over y (written xP*y) iff y is never chosen when x is available. Under weak assumptions, P* is acyclic and therefore suitable for welfare analysis; it is also the most discerning welfare criterion that never overrules choice. The resulting framework generates natural counterparts for the standard tools of applied welfare economics and is easily applied in the context of specific behavioral theories, with novel implications. Though not universally discerning, it lends itself to principled refinements

Bayesian multivariate mixed-scale density estimation

Although continuous density estimation has received abundant attention in the Bayesian nonparametrics literature, there is limited theory on multivariate mixed scale density estimation. In this note, we consider a general framework to jointly model continuous, count and categorical variables under a nonparametric prior, which is induced through rounding latent variables having an unknown density with respect to Lebesgue measure. For the proposed class of priors, we provide sufficient conditions for large support, strong consistency and rates of posterior contraction. These conditions allow one to convert sufficient conditions obtained in the setting of multivariate continuous density estimation to the mixed scale case. To illustrate the procedure a rounded multivariate nonparametric mixture of Gaussians is introduced and applied to a crime and communities dataset

Suicidal altruism under random assortment

Questions: Can there be a selective explanation for suicide? Or are all suicides evolutionary mistakes, ever pruned by natural selection to the extent that the tendency to perform them is heritable? Model: A simple variant of trait group selection (where a population is divided into mutually exclusive groups, with the direct effects of behaviour limited to group-mates), employing predators as the mechanism underlying group selection. Predators evaluate groups to avoid potentially suicidal defenders (which, when present, limit a predator’s net return), thus acting as a group selection mechanism favouring groups with potentially suicidal altruists. Conclusion: The model supports contingent strong altruism (depressing one’s direct reproduction – absolute fitness – to aid others) without kin assortment. Even an extreme contingent suicidal type (destroying self for the sake of others) may either saturate a population or be polymorphic with a type avoiding such altruism. The model does not, however, support a sterile worker caste, where sterility occurs before life-history events associated with effective altruism; under random assortment, reproductive suicide must remain contingent or facultative.Publicad

Nonparametric Bayes modeling of count processes

Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from hierarchical Poisson components. The Poisson assumption is not warranted in many applications, and hierarchical Poisson models make restrictive assumptions about over-dispersion in marginal distributions. This article proposes a class of nonparametric Bayes count process models, which are constructed through rounding real-valued underlying processes. The proposed class of models accommodates applications in which one observes separate count-valued functional data for each subject under study. Theoretical results on large support and posterior consistency are established, and computational algorithms are developed using Markov chain Monte Carlo. The methods are evaluated via simulation studies and illustrated through application to longitudinal tumor counts and asthma inhaler usage

Multiscale Bernstein polynomials for densities

Our focus is on constructing a multiscale nonparametric prior for densities. The Bayes density estimation literature is dominated by single scale methods, with the exception of Polya trees, which favor overly-spiky densities even when the truth is smooth. We propose a multiscale Bernstein polynomial family of priors, which produce smooth realizations that do not rely on hard partitioning of the support. At each level in an infinitely-deep binary tree, we place a beta dictionary density; within a scale the densities are equivalent to Bernstein polynomials. Using a stick-breaking characterization, stochastically decreasing weights are allocated to the finer scale dictionary elements. A slice sampler is used for posterior computation, and properties are described. The method characterizes densities with locally-varying smoothness, and can produce a sequence of coarse to fine density estimates. An extension for Bayesian testing of group differences is introduced and applied to DNA methylation array data

Bohmian Trajectories of Airy Packets

The discovery of Berry and Balazs in 1979 that the free-particle Schr\"odinger equation allows a non-dispersive and accelerating Airy-packet solution has taken the folklore of quantum mechanics by surprise. Over the years, this intriguing class of wave packets has sparked enormous theoretical and experimental activities in related areas of optics and atom physics. Within the Bohmian mechanics framework, we present new features of Airy wave packet solutions to Schr\"odinger equation with time-dependent quadratic potentials. In particular, we provide some insights to the problem by calculating the corresponding Bohmian trajectories. It is shown that by using general space-time transformations, these trajectories can display a unique variety of cases depending upon the initial position of the individual particle in the Airy wave packet. Further, we report here a myriad of nontrivial Bohmian trajectories associated to the Airy wave packet. These new features are worth introducing to the subject's theoretical folklore in light of the fact that the evolution of a quantum mechanical Airy wave packet governed by the Schr\"odinger equation is analogous to the propagation of a finite energy Airy beam satisfying the paraxial equation. Numerous experimental configurations of optics and atom physics have shown that the dynamics of Airy beams depends significantly on initial parameters and configurations of the experimental set-up.Comment: 8 page