Ma, J., Marmer, V., Shneyerov, A., & Xu, P. (2021). “Monotonicity-constrained nonparametric estimation and inference for first-price auctions.” Econometric Reviews, 40, 944-982.
In the independent private values framework for first-price auctions, we propose a new nonparametric estimator of the probability density of latent valuations 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 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.