Identification and Estimation of Consumers' Preferences from Repeated Observations under Nonlinear Pricing

TL;DR

This paper introduces a nonparametric method to identify and estimate consumer preferences and heterogeneity using data from multiple nonlinear pricing schedules, with robust estimation and inference procedures.

Contribution

It develops a novel nonparametric identification and estimation framework leveraging variation across price schedules, including an iterative estimation approach with near-parametric convergence.

Findings

Successfully identifies utility functions and preference distributions in simulations.

Provides a bootstrap inference procedure for finite samples.

Demonstrates the method with real data from a European mail carrier.

Abstract

We develop a nonparametric approach to identify and estimate consumer preferences and unobserved heterogeneity under nonlinear price schedules. Leveraging variation across multiple price schedules, we show that both the utility function and the distribution of preference types can be nonparametrically identified. The quantile function of unobserved types becomes solution of a functional equation, and we derive conditions ensuring identification. We propose an iterative approach for estimation, in which the regularization bias decays exponentially in the number of iterations while the variance grows only polynomially, yielding a near-parametric convergence rate. We propose a valid bootstrap procedure for finite-sample inference and extend the framework to accommodate potential endogeneity of prices and additional observed heterogeneity. Monte Carlo simulations and an empirical application to data from a European mail carrier demonstrate how we can recover the utility functions and preference distributions in finite samples.