The paper proposes a parsimonious and flexible semiparametric quantile regression specification for asymmetric bidders within the independent private value framework. Asymmetry is parameterized using powers of a parent private value distribution, which is generated by a quantile regression specification. As noted in Cantillon (2008), this covers and extends models used for efficient collusion, joint bidding and mergers among homogeneous bidders. The specification can be estimated for ascending auctions using the winning bids and the winner’s identity. The estimation is in two stage. The asymmetry parameters are estimated from the winner’s identity using a simple maximum likelihood procedure. The parent quantile regression specification can be estimated using simple modifications of Gimenes (2017). Specification testing procedures are also considered. A timber application reveals that weaker bidders have 30\% less chances to win the auction than stronger ones. It is also found that increasing participation in an asymmetric ascending auction may not be as beneficial as using an optimal reserve price as would have been expected from a result of Bulow and Klemperer (1996) valid under symmetry.
The Key Class in Networks (with Nizar Allouch, University of Kent ) (European Economic Review (2025))
This paper examines optimal targeting of multiple network players from a new perspective, focusing on classes of players holding similar network positions - and thus fulfilling similar network roles - as captured by the graph theoretic notion of equitable partition. Unlike existing centrality measures, we show that analysing the network game with local payoff complementarities under symmetry brings out new insights about the relative influence of classes of similarly positioned network players on the Nash equilibrium activity. Our analysis introduces two novel class-based centrality measures with broad theoretical and empirical applicability that geometrically characterize the key class whose removal results in the maximal reduction of aggregate and per-capita network activity, respectively.
We study a general class of linear quantile regression models in which the regressors, the dependent variable, or both are not directly observed but estimated in a preliminary first step. We develop the asymptotic theory for the resulting generated quantile regression (GQR) estimator, uniformly over quantile levels. First, we establish a uniform Bahadur expansion with a precise stochastic order for the remainder term, extending classical one-step expansions to settings with generated variables. Building on this linearization, we establish a functional central limit theorem for the GQR process over a compact set of quantile levels, which yields both pointwise confidence intervals and uniform confidence bands for the conditional quantile process. Finally, we show that a multiplier bootstrap procedure consistently approximates the associated supremum distribution for practical implementation. We illustrate the performance of the GQR estimator through simulations and an empirical application based on auctions.