Imposing and Testing for 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 they are trying to estimate. 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. We further develop a bandwidth test for monotonicity of the bid function. The finite sample performance of our estimator and test are examined by using simulated data, experimental data, as well as a real world data set.