Estimating Discrete Choice Demand Models with Sparse Market-Product Shocks

Abstract

When credible instruments are scarce or estimates hinge on instrument choice, an alternative to the leading Berry--Levinsohn--Pakes (BLP) approach to demand estimation with aggregate data can be useful. We propose a Bayesian random-coefficients discrete-choice demand estimator that jointly recovers preference parameters and market--product demand shocks under a sparsity restriction, without requiring instrumental variables. Shrinkage priors select a sparse set of active shocks, and the posterior supports inference on elasticities, forecasts, and other counterfactuals. Applications to supermarket scanner and automobile data find substantial sparsity and interpretable latent demand variation. We establish identification under sparsity and corroborate the approach with Monte Carlo experiments.