Zhentong Lu | Searcharxiv

arXiv2026

A Stochastic Nested Fixed Point Algorithm for Large-Scale BLP Estimation

We develop a stochastic nested fixed point (SNFP) estimator for random coefficients logit demand models that updates model parameters using stochastic gradients and performs demand inversion one market at a time. Relative to the conventional nested fixed point (NFP) estimator, SNFP substantially reduces memory requirements and computational cost, making estimation feasible in very large datasets. We establish the large-$T$ (number of markets) asymptotic properties of the estimator under regularity conditions. We also characterize the effect of sharing one block of simulation draws across markets and show how to correct for it. Monte Carlo simulations show that the SNFP estimator achieves statistical accuracy comparable to the NFP estimator, and in our benchmark a single online pass estimates a model with 100 million markets in about 5.5 hours. An empirical application using scanner data further demonstrates the practical advantages of SNFP for large-scale demand estimation.

econ.EM↗

arXiv2026

Estimating Discrete Choice Demand Models with Sparse Market-Product Shocks

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.

econ.EM↗