Bayesian estimation of bidding process and bidder’s preference under shape restrictions

Abstract

This paper applies a novel nonparametric estimator to the modeling of auctions subject to shape restrictions. In particular, we employ a Bayesian estimator with a Gaussian process prior parameterized by a spectral representation. We use squared Gaussian processes to model the functional derivatives and therefore are able to impose global shape restrictions. Our first application is the estimation of a monotonically increasing bidding process of online auctions. The second application concerns the estimation of bidders’ risk-averse latent preferences in sealed-bid timber auctions. The results show that the shape-constrained estimator not only ensures the conformity with economic theories but also improves estimation precision.