Zhentong Lu, Myung Hwan Seo, Youngki Shin, Qichen Zhang
arXiv 21 Sep 2026 · Econometrics
arXiv:2609.23998 · PDF · Extracted main text
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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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Chen, Kim, Lee, Seo and Song (2025) SLIM: Stochastic Learning and Inference in Overidentified Models | 1.000 | 8 | 3 | 100% |
| 2 | Dubé, Fox and Su (2012) Improving the Numerical Performance of Static and Dynamic Aggregate Discrete Choice Random Coefficients Demand Estimation | 1.000 | 5 | 3 | 100% |
| 3 | Freyberger (2015) Asymptotic Theory for Differentiated Products Demand Models with Many Markets | 0.928 | 10 | 4 | 80% |
| 4 | Conlon and Gortmaker (2020) Best Practices for Differentiated Products Demand Estimation with PyBLP | 0.928 | 5 | 4 | 80% |
| 5 | Polyak and Juditsky (1992) Acceleration of Stochastic Approximation by Averaging | 0.874 | 6 | 3 | 67% |
| 6 | Chen, Lee, Liao, Seo, Shin and Song (2025) SGMM: Stochastic Approximation to Generalized Method of Moments | 0.874 | 6 | 2 | 100% |
| 7 | Hong, Li and Li (2021) BLP Estimation Using Laplace Transformation and Overlapping Simulation Draws | 0.811 | 4 | 2 | 100% |
| 8 | Robbins and Monro (1951) A Stochastic Approximation Method | 0.737 | 3 | 2 | 100% |
| 9 | Ruppert (1988) Efficient Estimations from a Slowly Convergent Robbins–Monro Process | 0.737 | 3 | 2 | 100% |
| 10 | Berry, Linton and Pakes (2004) Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems | 0.644 | 4 | 2 | 50% |
Showing the top 10 of 45 scored citations.