Nonparametric Tests for Common Values at First-Price Sealed-Bid Auctions

Abstract

We develop tests for common values at first-price sealed-bid auctions. Our tests are nonparametric, require observation only of the bids submitted at each auction, and are based on the fact that the "winner's curse" arises only in common values auctions. The tests build on recently developed methods for using observed bids to estimate each bidder's conditional expectation of the value of winning the auction. Equilibrium behavior implies that in a private values auction these expectations are invariant to the number of opponents each bidder faces, while with common values they are decreasing in the number of opponents. This distinction forms the basis of our tests. We consider both exogenous and endogenous variation in the number of bidders. Monte Carlo experiments show that our tests can perform well in samples of moderate sizes. We apply our tests to two different types of U.S. Forest Service timber auctions. For unit-price ("scaled") sales often argued to fit a private values model, our tests consistently fail to find evidence of common values. For "lumpsum" sales, where a priori arguments for common values appear stronger, our tests yield mixed evidence against the private values hypothesis.

Semi‐nonparametric Estimation of Consumer Search Costs

“…The estimates of the model using residuals are similar to the estimates using prices (see footnote 15 and Figure 4 …”

“…These graphs also show how the estimated search cost cutoffs (red dots) cover the support of the search cost distribution. The dashed curves are the estimated search cost CDF and PDF if we use the residuals of the regression model specified in equation (15). The graph illustrates that both are very similar.…”

“…14 Table 3 shows that all parameter estimates are significant at a 1% level, except for θ 1 and θ 2 , which are significant at a 5% level. 15 The standard errors reported in the table are meaningful in the case when the presented model is the true parametric model. The solid curves in Figures 4(a) and 4(b) denote the estimated search cost CDF and PDF respectively.…”

“…The gain in computing time is huge and the results for our data are very similar. 15 When we use the residuals of the regression model specified in equation (15) to estimate the model, the estimates obtained are the following: γ = 0.697, σ = 0.778, θ0 = 1.000, θ1 = 0.264, θ2 = −0.382, and θ3 = −1.668. The fact that a significant proportion of consumers does not compare prices gives substantial market power to the firms.…”

Structural Econometric Methods in Auctions: A Guide to the Literature

“…Under assumptions of bidder symmetry, affiliation and equilibrium bidding, Haile, Hong, and Shum (2003) develop a testing strategy for comparing hypotheses of common versus private values without the use of parametric assumptions. This method differs from other methods in that it doesn't test any particular PV or CV models (e.g., Paarsch (1992); Campo et al (2003)); but rather, it enables testing of a null hypothesis including all PV models within the standard AV framework against an alternative including all CV models within that framework.…”