A Stochastic Nested Fixed Point Algorithm for Large-Scale BLP Estimation
Abstract
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.
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BibTeX
@misc{lu2026stochastic,
title = {{A Stochastic Nested Fixed Point Algorithm for Large-Scale BLP Estimation}},
author = {Zhentong Lu and Myung Hwan Seo and Youngki Shin and Qichen Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23998},
eprint = {2609.23998},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23998},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - A Stochastic Nested Fixed Point Algorithm for Large-Scale BLP Estimation
AU - Zhentong Lu
AU - Myung Hwan Seo
AU - Youngki Shin
AU - Qichen Zhang
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.23998
UR - https://arxiv.org/abs/2609.23998
AB - 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.
ER -