Imposing Monotonicity Nonparametrically in First-Price Auctions

Monotonicity of the equilibrium bidding strategy is a key property of structural auction models. Traditional nonparametric estimators provide a flexible means of uncovering salient features of auction data, but do not formally impose the monotonicity assumption that is inherent in the models during estimation. Here, we develop a nonparametric estimator which imposes the monotonicity assumption. We accomplish this by employing the constraint weighted bootstrapping theory developed in the statistics literature. The finite sample performance of our estimator is examined using simulated data, experimental data, as well as a naturally occurring data set composed of thousands of bids from Canadian timber auctions.