Job Market Paper: The Behavioral Implications of Statistical Decision Theory
Statistical decision theory (SDT), pioneered by Abraham Wald, models how decision makers use data for decisions under uncertainty. Despite its prominence in information economics and econometrics, SDT has not been given formal choice-theoretic or behavioral foundations. This paper axiomatizes preferences over decision rules and experiments for a broad class of SDT models. The axioms show how certain seemingly-natural decision rules are incompatible with this broad class of SDT models. Using my representation result, I develop a methodology to translate axioms from classical decision-theory, a la Anscombe and Aumann (1963), to the SDT framework. I illustrate its usefulness by translating various classical axioms to refine my baseline SDT framework into more specific SDT models, some of which are novel to SDT. I also discuss foundations for SDT under other kinds of choice data.
“Statistical Mechanism Design: Robust Pricing and Reliable Projections” with Duarte Gonçalves
This paper studies the robustness of pricing strategies when a firm is uncertain about the distribution of consumers’ willingness-to-pay. When the firm has access to data to estimate this distribution, a simple strategy is to implement the mechanism that is optimal for the estimated distribution. We find that such empirically optimal mechanism boasts strong profit and regret guarantees. Moreover, we provide a toolkit to evaluate the robustness properties of different mechanisms, showing how to consistently estimate and conduct valid inference on the profit generated by any one mechanism, which enables one to evaluate and compare their probabilistic revenue guarantees.
“Rational Choice with Full-Comparability Domains’‘ with Leandro Nascimento and Gil Riella
We propose a new model of choice in the presence of incomplete preferences. Instead of simply choosing an element which is maximal according to her preferences, the decision maker divides the space of alternatives into subdomains inside which her preferences are complete. She then acts fully rationally and maximizes her preferences inside these domains of full comparability. Representation theorems are given in which the decision maker always satisfies a weaker form of the Weak Axiom of Revealed Preference and different postulates are imposed on a general notion of revealed preference. They identify a class of choice functions that is nested between choice functions represented by multiple rationales and the standard model of rational choice.
Work in Progress
“Identifiability of Finite Mixture Models via Non-negative Matrix Factorization”
High-dimensional latent parameter models, such as finite mixtures and topic models, are notoriously only set identifiable, in general. By establishing directly verifiable conditions under which a matrix has a unique exact non-negative factorization (up to permutations), I provide sufficient conditions for point identifiability of mixture models. Since these conditions are imposed on the data matrix before factorization, they can be checked prior to estimation. I also show that, when the model is identifiable, approximate non-negative matrix factorization provides a consistent, likelihood-free estimator of mixture weights. Applications include identifiability and point estimation of topic models.
“The Ex-Post Value of Information under Ambiguity”
Information economics often hinges on balancing the benefits and costs of obtaining or transmitting a piece of information. Bayesian agents are the workhorse of such models not only due to tractability concerns, but also because there are substantial challenges in defining the value of information (VoI) for non-Bayesian agents. Recently, there has been growing interest in models involving agents that deviate from the Bayesian paradigm. This paper aims to develop a suitable notion the VoI for such decision makers. I define the VoI as the willingness-to-pay for a given signal realization from a known experiment, and characterize its functional form for different preference update rules for a general class of non-Bayesian objective functions. I then connect the properties of the VoI to different axioms that may characterize the agent’s updated preferences.