Identification and Estimation of Seller Risk Aversion in Ascending Auctions

TL;DR

This paper identifies and estimates seller risk aversion in ascending auctions within a semiparametric framework: the seller’s utility is parametric (e.g., CRRA or CARA) while bidder valuations follow a flexible, linear-quantile specification. It develops a two-step estimator that uses augmented quantile regression (AQR) to recover bidder valuation quantiles and their derivatives, which enter a first-order condition for the optimal reserve price, enabling identification of the risk-aversion parameter. The authors prove consistency and asymptotic normality under standard regularity conditions, validate the approach via Monte Carlo simulations, and apply it to foreclosure real estate auctions in São Paulo, finding evidence of seller risk aversion and better data fit than risk-neutral benchmarks. Counterfactuals show that assuming risk neutrality would raise reserve prices and alter bidder participation and welfare, underscoring the practical importance of correctly accounting for seller risk preferences in auction design and policy analysis.

Abstract

This paper shows how to identify and estimate the seller's risk parameter in an ascending auction. We consider a semiparametric model where the seller has a parametric utility function (such as CARA or CRRA) and the distribution of bidder valuations is modeled flexibly. We provide primitive conditions under which the risk parameter is identified and show that it can be consistently estimated with an asymptotically normal limiting distribution under standard regularity conditions. A Monte Carlo study demonstrates good finite-sample performance of the proposed estimator. We apply our approach to foreclosure real estate auction data from São Paulo. We find evidence that sellers are risk-averse, which leads to a much better fit to the data than a model with risk-neutral sellers, which would substantially underpredict the reserve price relative to what is observed.

Figures (6)

• Figure 1: Simulation results for $\widehat{V}$ and $\widehat{V}^{(1)}$.
• Figure 2: Scatter figures of $X$, $B$, and $R$.
• Figure 3: Plots of $\widehat{V}(\cdot|X)$.
• Figure 4: Model fit of winning bid distribution.
• Figure 5: Model fit of reserve price distribution.