Working Papers

Scalable Estimation of Multinomial Response Models with Uncertain Consideration Sets (with Siddhartha Chib, Aug 2023)

Keywords: Quantitative Marketing, Random Choice Sets, Curse of Dimensionality, Panel Data

A standard assumption in the fitting of unordered multinomial response models for J mutually exclusive nominal categories, on cross-sectional or longitudinal data, is that the responses arise from the same set of J categories between subjects. However, when responses measure a choice made by the subject, it is more appropriate to assume that the distribution of multinomial responses is conditioned on a subject-specific consideration set, where this consideration set is drawn from the power set of {1,2,...,J}. Because the cardinality of this power set is exponential in J, estimation is infeasible in general. In this paper, we provide an approach to overcoming this problem. A key step in the approach is a probability model over consideration sets, based on a general representation of probability distributions on contingency tables. Although the support of this distribution is exponentially large, the posterior distribution over consideration sets given parameters is typically sparse, and is easily sampled as part of an MCMC scheme that iterates sampling of subject-specific consideration sets given parameters, followed by parameters given consideration sets. The effectiveness of the procedure is documented in simulated longitudinal data sets with J=100 categories and real data from the cereal market with J=73 brands.

Semiparametric Bayesian Estimation of Dynamic Discrete Choice Models (with Andriy Norets, Revise & Resubmit, Journal of Econometrics) [Replication code]

Keywords: Industrial Organization, Partial Identification, Mixture Model, Hamiltonian Monte Carlo

We propose a tractable semiparametric estimation method for structural dynamic discrete choice models. The distribution of additive utility shocks in the proposed framework is modeled by location-scale mixtures of extreme value distributions with varying numbers of mixture components. Our approach exploits the analytical tractability of extreme value distributions in the multinomial choice settings and the flexibility of the location-scale mixtures. We implement the Bayesian approach to inference using Hamiltonian Monte Carlo and an approximately optimal reversible jump algorithm. In our simulation experiments, we show that the standard dynamic logit model can deliver misleading results, especially about counterfactuals, when the shocks are not extreme value distributed. Our semiparametric approach delivers reliable inference in these settings. We develop theoretical results on approximations by location-scale mixtures in an appropriate distance and posterior concentration of the set identified utility parameters and the distribution of shocks in the model.

International Association for Applied Econometrics (IAAE) at King’s Business School in London, 2022

Australasia Meeting of the Econometric Society at University of Queensland (Virtual), 2022

12th World Congress of the Econometric Society at Bocconi University, 2020

NSF-NBER Seminar on Bayesian Inference in Econometrics and Statistics at Brown University, 2019

European Seminar on Bayesian Econometrics at the New Orleans Fed, 2018

A Bayesian Approach to Demand Estimation for Differentiated Products (with Zhentong Lu, Aug 2023)

Keywords: Industrial Organization, BLP

Published Papers

Asymptotic Properties of Bayesian Inference in Linear Regression with a Structural Break (July 2023, Journal of Econometrics) [Published Version]

Keywords: Robust Inference

In this paper, I study large sample properties of a Bayesian approach to inference about slope parameters in linear regression models with a structural break. In contrast to the conventional approach to inference about the slope parameters that does not take into account the uncertainty of the unknown break location, the Bayesian approach that I consider incorporates such uncertainty. My main theoretical contribution is a Bernstein-von Mises type theorem (Bayesian asymptotic normality) for the slope parameters under a wide class of priors, which essentially indicates an asymptotic equivalence between the conventional frequentist and Bayesian inference. Consequently, a frequentist researcher could look at credible intervals of the slope parameters to check robustness with respect to the uncertainty of the break location. Simulation studies show that the conventional confidence intervals of the slope parameters tend to undercover in finite samples whereas the credible intervals offer more reasonable coverages in general. As the sample size increases, the two methods coincide, as predicted from my theoretical conclusion. Using data from Paye and Timmermann (2006) on stock return prediction, I illustrate that the traditional confidence intervals on the slope parameters might underrepresent the true sampling uncertainty.

NSF-NBER Seminar on Bayesian Inference in Econometrics and Statistics at Washington University in St. Louis, 2020

14th RCEA Bayesian Econometrics Workshop at Wilfrid Laurier University, 2020 (postponed)

Bayesian Approaches to Shrinkage and Sparse Estimation (with Dimitris Korobilis, 2022, Foundations and Trends in Econometrics) [Published Version, Matlab code]

Keywords: Bayesian LASSO, Bayesian Ridge

In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference is the norm in several fields of applied econometric work. The purpose of this paper is to introduce the reader to the world of Bayesian model determination, by surveying modern shrinkage and variable selection algorithms and methodologies. Bayesian inference is a natural probabilistic framework for quantifying uncertainty and learning about model parameters, and this feature is particularly important for inference in modern models of high dimensions and increased complexity. We begin with a linear regression setting in order to introduce various classes of priors that lead to shrinkage/sparse estimators of comparable value to popular penalized likelihood estimators (e.g. ridge, lasso). We explore various methods of exact and approximate inference, and discuss their pros and cons. Finally, we explore how priors developed for the simple regression setting can be extended in a straightforward way to various classes of interesting econometric models. In particular, the following case-studies are considered, that demonstrate application of Bayesian shrinkage and variable selection strategies to popular econometric contexts: i) vector autoregressive models; ii) factor models; iii) time-varying parameter regressions; iv) confounder selection in treatment effects models; and v) quantile regression models. A MATLAB package and an accompanying technical manual allow the reader to replicate many of the algorithms described in this review.

Works in progress

A Comparative Review of Bayesian Shrinkage and Variable Selection in Econometrics (with Dimitris Korobilis and Duong Trinh, Dec 2022)

Keywords: Covid-19, Time-varying parameters, Forecasting, Vector Autoregression