Market-Price Learning under Endogenous Bid Censoring: Limits, Identification, and Correction

In real-time bidding, a bidder's shading and pacing decisions depend on the distribution of the market price it must beat. The bidder learns this distribution from its own auction logs, which record every bid but reveal the price only when the bid wins. Statistically, this is estimation under dependent censoring in which the censoring variable, the bid, is always observed. Standard censored estimation relies on bid–price independence, but bids respond to the signals that drive prices, making the censoring endogenous. Without any assumption on this dependence, the logs identify the price margin only up to a sharp band whose width is the share of auctions lost with lower bids. This ambiguity yields an assumption-free minimax error floor. Under affiliation between the bid and the price, the band narrows to a closed-form interval, and standard censored estimation understates the price CDF. To correct this bias, we assume a concordance-ordered copula family. Given this family, the observed bids and win-region cells identify the dependence parameter and the price distribution through the largest bid. The sharp band then collapses to a point and the minimax floor vanishes over the same range. We fit neural bid and price distributions in two stages, first from the fully observed bids, then through a Gaussian-copula observed-data likelihood. For the finite model under standard regularity conditions, the two-stage estimator is consistent and asymptotically normal at the root-$n$ rate. On AuctionNet the correction cuts the largest gap of the censored network's CDF from 0.14 to 0.04 and closes about three quarters of its CRPS gap to the oracle. The gain persists when the bidding rule uses a market signal withheld from every estimator and when the coupling is planted outside the fitted family. It also reaches the decision layer, where the corrected bids cut the overshoot of a 10% target win rate on AuctionNet from 17.8 to 7.9pp.