Automatically Differentiable Random Coefficient Logistic Demand Estimation

TL;DR

This paper introduces a differentiable formulation of the random coefficient logistic demand model, enabling gradient-based estimation methods like CUE, and compares their performance with traditional approaches through Monte Carlo experiments.

Contribution

It presents an automatically differentiable moment function for the BLP model, integrating machine learning best practices into demand estimation.

Findings

CUE with LTE and frequentist optimization shows lower bias than 2S-GMM.

Using MCMC credible intervals improves empirical coverage for non-linear parameters.

The admest Python package facilitates replication and further research.

Abstract

We show how the random coefficient logistic demand (BLP) model can be phrased as an automatically differentiable moment function, including the incorporation of numerical safeguards proposed in the literature. This allows gradient-based frequentist and quasi-Bayesian estimation using the Continuously Updating Estimator (CUE). Drawing from the machine learning literature, we outline hitherto under-utilized best practices in both frequentist and Bayesian estimation techniques. Our Monte Carlo experiments compare the performance of CUE, 2S-GMM, and LTE estimation. Preliminary findings indicate that the CUE estimated using LTE and frequentist optimization has a lower bias but higher MAE compared to the traditional 2-Stage GMM (2S-GMM) approach. We also find that using credible intervals from MCMC sampling for the non-linear parameters together with frequentist analytical standard errors for the concentrated out linear parameters provides empirical coverage closest to the nominal level. The accompanying admest Python package provides a platform for replication and extensibility.