Monotonicity-Constrained Nonparametric Estimation and Inference for First-Price Auctions

TL;DR

This paper introduces a new nonparametric estimator for first-price auctions that enforces monotonicity, resulting in lower variance and enabling reliable inference through bootstrap confidence bands.

Contribution

It proposes a monotonicity-constrained estimator for auction models, improving variance properties and providing a bootstrap method for uniform confidence band construction.

Findings

Estimator has smaller asymptotic variance than previous methods.

Provides asymptotic normality and bootstrap confidence bands.

Enhances inference accuracy for auction valuation densities.

Abstract

We propose a new nonparametric estimator for first-price auctions with independent private values that imposes the monotonicity constraint on the estimated inverse bidding strategy. We show that our estimator has a smaller asymptotic variance than that of Guerre, Perrigne and Vuong's (2000) estimator. In addition to establishing pointwise asymptotic normality of our estimator, we provide a bootstrap-based approach to constructing uniform confidence bands for the density function of latent valuations.