Estimating Discrete Choice Demand Models with Sparse Market-Product Shocks

We propose a new approach to estimating the random coefficient logit demand model for differentiated products when the vector of market-product-level shocks is sparse. Assuming sparsity, we establish nonparametric identification of the distribution of random coefficients and demand shocks under mild conditions. Then we develop a Bayesian estimation procedure, which exploits the sparsity structure using shrinkage priors, to conduct inference about the model parameters and counterfactual quantities. Compared with the standard BLP (Berry, Levinsohn, and Pakes 1995) method, our approach does not require demand inversion or instrumental variables (IVs), and thus provides a compelling alternative when IVs are not available or their validity is questionable. Monte Carlo simulations validate our theoretical findings and demonstrate the effectiveness of our approach, while empirical applications reveal evidence of sparse demand shocks in well-known datasets.