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Pre-Training Estimators for Structural Models: Application to Consumer Search

Yanhao 'Max' Wei, Zhenling Jiang

TL;DR

This work introduces pretrained neural-net estimators (NNE) for structural econometric models, addressing the heavy upfront cost and dataset-specific tuning of traditional estimation by training on simulated data to map data patterns to model parameters. The pretrained NNE for a sequential search model converges to the Bayesian posterior mean $E(\boldsymbol{\theta}|\boldsymbol{m})$ and can be applied across diverse datasets with minimal user effort, yielding speedups of 3–4 orders of magnitude while maintaining accuracy comparable to or better than SMLE/GHK approaches. Empirical tests on 12 real datasets and Monte Carlo simulations demonstrate both substantial computational gains and sensible parameter estimates, highlighting potential for real-time integration in pricing, recommendations, and bandit-style algorithms, as well as privacy advantages from using aggregate data patterns. The paper also outlines limitations and future extensions, including richer heterogeneity, endogeneity/instrumentation, and more flexible priors, to broaden applicability of pretrained estimators in structural econometrics.

Abstract

We develop pre-trained estimators for structural econometric models. The estimator uses a neural net to recognize the structural model's parameter from data patterns. Once trained, the estimator can be shared and applied to different datasets at negligible cost and effort. Under sufficient training, the estimator converges to the Bayesian posterior given the data patterns. As an illustration, we construct a pretrained estimator for a sequential search model (available at pnnehome.github.io). Estimation takes only seconds and achieves high accuracy on 12 real datasets. More broadly, pretrained estimators can make structural models much easier to use and more accessible.

Pre-Training Estimators for Structural Models: Application to Consumer Search

TL;DR

This work introduces pretrained neural-net estimators (NNE) for structural econometric models, addressing the heavy upfront cost and dataset-specific tuning of traditional estimation by training on simulated data to map data patterns to model parameters. The pretrained NNE for a sequential search model converges to the Bayesian posterior mean and can be applied across diverse datasets with minimal user effort, yielding speedups of 3–4 orders of magnitude while maintaining accuracy comparable to or better than SMLE/GHK approaches. Empirical tests on 12 real datasets and Monte Carlo simulations demonstrate both substantial computational gains and sensible parameter estimates, highlighting potential for real-time integration in pricing, recommendations, and bandit-style algorithms, as well as privacy advantages from using aggregate data patterns. The paper also outlines limitations and future extensions, including richer heterogeneity, endogeneity/instrumentation, and more flexible priors, to broaden applicability of pretrained estimators in structural econometrics.

Abstract

We develop pre-trained estimators for structural econometric models. The estimator uses a neural net to recognize the structural model's parameter from data patterns. Once trained, the estimator can be shared and applied to different datasets at negligible cost and effort. Under sufficient training, the estimator converges to the Bayesian posterior given the data patterns. As an illustration, we construct a pretrained estimator for a sequential search model (available at pnnehome.github.io). Estimation takes only seconds and achieves high accuracy on 12 real datasets. More broadly, pretrained estimators can make structural models much easier to use and more accessible.
Paper Structure (29 sections, 1 theorem, 9 equations, 3 figures, 4 tables)

This paper contains 29 sections, 1 theorem, 9 equations, 3 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Literature
  3. Consumer search model
  4. The model
  5. The data
  6. Pretrained NNE
  7. Overview
  8. Connection to Bayesian estimation
  9. Pretraining details
  10. The neural net
  11. The parameter prior
  12. Attributes ($\boldsymbol{x}$)
  13. Applications
  14. Datasets
  15. (4) Expedia: destination 1
  16. ...and 14 more sections

Key Result

Proposition 1

Suppose: (i) $\Theta$ is compact, (ii) $\boldsymbol{m}$ has a compact support, (iii) $\mathbb{E}(\boldsymbol{\theta}|\boldsymbol{m})$ is a continuous function of $\boldsymbol{m}$. We have $\int\lVert\boldsymbol{f}_{L}(\boldsymbol{m})-\mathbb{E}(\boldsymbol{\theta}|\boldsymbol{m})\rVert^{2}dP(\boldsy

Figures (3)

  • Figure 1: An Illustration of NNE
  • Figure 2: Monte Carlo Study with eCommerce: Laptop
  • Figure 3: Real-Data Estimates Across 12 Datasets

Theorems & Definitions (1)

  • Proposition 1