Nonparametric estimation of private value distributions in first-price auctions: Evaluating quantile density function approaches

Estimating the distribution of private values in first-price auctions is a key challenge in empirical auction analysis due to the strategic bid shading inherent in these environments. We propose nonparametric estimators to recover the distribution function of independent private values by using the quantile density function (QDF) of observed bids. We implement 15 QDF-based estimators, seven core methods combined with two bandwidth selection techniques, alongside a conventional benchmark. We evaluate the performance of these estimators based on three criteria: Mean Integrated Squared Error (MISE), Log Likelihood, and Kolmogorov–Smirnov statistic. Extensive Monte Carlo numerical simulations show that Indirect Poisson and Poisson-based estimators consistently outperform the others. • Develops nonparametric estimators using quantile density functions (QDF). • Recovers private value distributions in first-price auctions under IPV. • Evaluates 7 QDF estimators with BCV and RLCV smoothing parameter selection methods. • MISE, Log-Likelihood, and KS metrics provide a comprehensive performance assessment. • Indirect Poisson and Poisson-based estimators outperform other methods.