Bundle Choice Model with Endogenous Regressors: An Application to Soda Tax

TL;DR

This paper introduces a Bayesian factor-augmented bundle choice model that accounts for endogenous regressors and heterogeneity, applied to soda tax analysis, revealing broader health benefits through joint consumption effects.

Contribution

It develops a novel Bayesian sparse factor model for endogenous regressors in bundle choice, capturing high-dimensional error correlations and heterogeneity, applied to soda tax effects.

Findings

Soda tax reduces sugary drink consumption.

Tax also decreases salty snack intake, indicating broader health benefits.

Model captures complex substitution and complementarity effects.

Abstract

This paper proposes a Bayesian factor-augmented bundle choice model to estimate joint consumption as well as the substitutability and complementarity of multiple goods in the presence of endogenous regressors. The model extends the two primary treatments of endogeneity in existing bundle choice models: (1) endogenous market-level prices and (2) time-invariant unobserved individual heterogeneity. A Bayesian sparse factor approach is employed to capture high-dimensional error correlations that induce taste correlation and endogeneity. Time-varying factor loadings allow for more general individual-level and time-varying heterogeneity and endogeneity, while the sparsity induced by the shrinkage prior on loadings balances flexibility with parsimony. Applied to a soda tax in the context of complementarities, the new approach captures broader effects of the tax that were previously overlooked. Results suggest that a soda tax could yield additional health benefits by marginally decreasing the consumption of salty snacks along with sugary drinks, extending the health benefits beyond the reduction in sugar consumption alone.