What auction prices hide when nobody bids

Suppose an auction has two potential bidders, but neither values the item above the seller’s minimum acceptable price. Nobody bids, nothing sells, and no transaction price enters the database. Looking only at completed sales therefore means looking at a selected sample.

In the preprint Identification in Auctions with Truncated Transaction Prices, Tonghui Qi of Renmin University of China asks when economists can nevertheless recover the distribution of bidders’ private valuations. The paper develops mathematical identification results, not an empirical analysis of auction records.

Missing sales, missing competitors

A binding reserve price screens out bidders whose valuations fall below the seller’s minimum. An entry cost can also discourage participation: bidders may know their valuations but decide that entering is not worthwhile. If everyone stays out, the auction produces no observed sale price.

These mechanisms create two information gaps. Economists may not know how many auctions ended without a sale. They may also see only active bidders—those who submitted bids—rather than all potential bidders who could have participated.

Qi compares settings with a fixed or varying number of potential bidders, and with records revealing either potential or active bidder counts. The analysis assumes transaction prices are available, rather than the complete collection of bids.

The central question is identification: could different underlying valuation distributions produce exactly the same observable data? Point identification means the model and observable distributions select one answer. Finite set identification leaves finitely many possibilities. Non-identification here means infinitely many possibilities remain compatible with the observations. These are distinctions about what data can reveal in principle, not measures of statistical precision in a finite sample.

A participation threshold holds the key

The paper expresses screening through a percentile of the valuation distribution: the fraction of potential bidders whose values are too low for participation. Knowing the monetary reserve price is not the same as knowing that fraction.

Recovering it matters because the valuations of participants alone do not reveal how much of the original population stayed out. Under a binding reserve, even successful identification recovers the valuation distribution only at and above the reserve. The shape below it remains hidden.

Auction rules determine which clues survive. In a first-price auction, the winner pays their own bid. In a second-price auction, the winner pays the higher of the second-highest bid and the reserve.

With a fixed, known number of at least two potential bidders, Qi finds that second-price transaction prices identify the screening fraction and the valuation distribution above the reserve. The clue is a concentration of sales exactly at the reserve: this occurs when only one bidder clears it. The frequency of these sales reveals participation information under the model.

First-price sales lack that same concentration. In this setting, transaction prices alone leave multiple valuation distributions compatible with the evidence. Recording the frequency of no-sale auctions restores point identification, because those failures reveal how often every potential bidder was screened out.

Competition can supply—or obscure—the missing clue

When the observed number of potential bidders takes at least two values greater than one, both formats become point identified under a binding reserve, provided the valuation distribution stays unchanged across those competition levels. A constant reserve then creates a common screening fraction linking the auctions.

The ranking changes when potential bidder counts are unobserved and only active counts are available. With a finite potential-bidder population independent of valuations, the paper establishes point identification for first-price auctions, but generally not second-price auctions. Strategic first-price bids carry information about potential competition that truthful second-price bids do not. For second-price auctions, adding no-sale frequencies narrows the possibilities to a finite set.

Entry costs produce related, but not identical, results. Even a constant entry cost generates participation thresholds that change with potential competition. Consequently, varying observed potential-bidder counts guarantees only a finite identified set in first-price auctions, rather than always the unique answer obtained with a binding reserve. Rich enough variation may still identify a unique answer. With a fixed, known bidder count, observing the positive entry cost restores first-price point identification; second-price prices already identify the cost and upper valuation distribution under the model.

What the results do not establish

The preprint studies symmetric independent private-value auctions, with continuous, strictly positive valuation densities on bounded supports and specified equilibrium behavior. Its entry model assumes bidders learn their valuations before deciding whether to pay to participate. Results need not extend to asymmetric bidders, correlated values or unobserved differences between auctions.

Nor does identification guarantee reliable estimation from limited records. Developing estimation methods is left for future work. The practical implication is narrower: whether auction prices reveal underlying demand depends critically on what participation and failed-sale information accompanies them.