A copula-quantile density approach to affiliated private value auctions

We develop a tractable semiparametric framework for estimating affiliated private value (APV) models in first-price sealed-bid auctions by combining copula-based dependence modeling with quantile density function (QDF) methods. Building on the identification results of Li, Perrigne, and Vuong (2002), we propose a two-stage estimator that (i) uses nonparametric QDF methods (Doosti et al., 2025) to estimate marginal distributions, achieving superior boundary performance, and (ii) employs parametric Archimedean copulas to model affiliation, ensuring computational tractability while respecting the equilibrium structure. Our approach decomposes the inverse bid function into an affiliation component (copula multiplier ψ(u)) and a marginal component (quantile density q(u)), providing both theoretical insights and practical advantages. We extend this framework by developing a fully nonparametric estimator of the copula multiplier, enabling specification tests for parametric copula assumptions. Monte Carlo simulations demonstrate that our estimators substantially outperform existing methods.