Estimating risk aversion from ascending and sealed-bid auctions: the case of timber auction data

Estimating bidders’ risk aversion in auctions is a challeging problem because of identification issues. This paper takes advantage of bidding data from two auction designs to identify nonparametrically the bidders’ utility function within a private value framework. In particular, ascending auction data allow us to recover the latent distribution of private values, while first-price sealed-bid auction data allow us to recover the bidders’ utility function. This leads to a nonparametric estimator. An application to the US Forest Service timber auctions is proposed. Estimated utility functions display concavity, which can be partly captured by constant relative risk aversion.Risk Aversion; Nonparametric Identi.cation; Nonparametric and Semipara-metric Estimation; Timber Auctions

DO AUCTION BIDS BETRAY EXPECTATIONS-BASED REFERENCE DEPENDENT PREFERENCES? A TEST, EXPERIMENTAL EVIDENCE, AND ESTIMATES OF LOSS AVERSION

In this paper, we provide a novel experimental auction design that exploits an exogenous variation in the probability of winning to test for the presence of expectations-based reference dependent preferences. We prove that (i) in this design, (which is a one parameter modification of a Becker-de Groote-Marschak (BDM) auction), a lower probability of winning will cause a loss averse agent to bid lower, for a large range of intrinsic values for the object. Data from an experiment demonstrate the existence of this effect. The effect would be absent if preferences were 'standard', or if the status quo was the reference point. Thus we contribute to the nascent literature that empirically documents the importance of expectations as a source of reference points. (ii) We further prove that the experimental design enables unique identification of participants' value distribution and loss averse than men. Finally, as a contribution to experimental methodology, we prove that the BDM mechanism will underestimate loss averse participants' values, we quantify the underestimation, and we suggest methods to bound this bias.Auctions, Expectations, Loss Aversion, Reference dependence

Identification of Insurance Models with Multidimensional Screening

We study the identification of an insurance model with multidimensional screening, where insurees are characterized by risk and risk aversion. The model is solved using the concept of certainty equivalence under constant absolute risk aversion and an unspecified joint distribution of risk and risk aversion. The paper then analyzes how data availability constraints identification under four data scenarios from the ideal situation to a more realistic one. The observed number of accidents for each insuree plays a key role to identify the model. In a first part, we consider the case of a continuum of coverages offered to each insuree whether the damage distribution is fully observed or truncated. Truncation arises from that an insuree files a claim only when the accident involves a damage above the deductible. Despite bunching due to multidimensional screening, we show that the joint distribution of risk and risk aversion is identified. In a second part, we consider the case of a finite number of coverages offered to each insuree. When the full damage distribution is observed, we show that despite additional pooling due to the finite number of contracts, the joint distribution of risk and risk aversion is identified under a full support assumption and a conditional independence assumption involving the car characteristics. When the damage distribution is truncated, the joint distribution is identified up to the probability that the damage is above the deductible. In a third part, we derive the restrictions imposed by the model on observables for the fourth scenario. We also propose several identification strategies for the damage probability at the deductible. These identification results are further exploited in a companion paper developing an estimation method with an application to insurance data

Quantile-Based Nonparametric Inference for First-Price Auctions

We propose a quantile-based nonparametric approach to inference on the probability density function (PDF) of the private values in first-price sealed-bid auctions with independent private values. Our method of inference is based on a fully nonparametric kernel-based estimator of the quantiles and PDF of observable bids. Our estimator attains the optimal rate of Guerre, Perrigne, and Vuong (2000), and is also asymptotically normal with the appropriate choice of the bandwidth.First-price auctions; independent private values; nonparametric estimation; kernel estimation; quantiles; optimal reserve price

Structural Econometric Methods in Auctions: A Guide to the Literature

Auction models have proved to be attractive to structural econometricians who, since the late 1980s, have made substantial progress in identifying and estimating these rich game-theoretic models of bidder behavior. We provide a guide to the literature in which we contrast the various informational structures (paradigms) commonly assumed by researchers and uncover the evolution of the eld. We highlight major contributions within each paradigm and benchmark modi cations and extensions to these core models. Lastly, we discuss special topics that have received substantial attention among auction researchers in recent years, including auctions formultiple objects, auctions with risk averse bidders, testing between common and private value paradigms, unobserved auction-speci c heterogeneity, and accounting for an unobserved number of bidders as well as endogenous entry

Quantile Analysis of "Hazard-Rate" Game Models

This paper consists of an econometric analysis of a broad class of games of incomplete information. In these games, a player’s action depends both on her unobservable characteristic (the private information), as well as on the ratio of the distribution of the unobservable characteristic and its density function (which we call the "hazard-rate"). The goal is to use data on players’actions to recover the distribution of private information. We show that the structural parameter (the distribution of the unobservable characteristic) can be related to the reduced form parameter (the distribution of the data) through a quantile relation that avoids the inversion of the players’ strategy function. We estimate non-parametrically the density of the unobserved variables and we show that this is the solution of a well-posed inverse problem. Moreover, we prove that the density of the private information is estimated at a Vpn speed of convergence. Our results have several policy applications, including better design of auctions and public good contracts

Comparing Open and Sealed Bid Auctions: Theory and Evidence from Timber Auctions

We study entry and bidding patterns in sealed bid and open auctions with heterogeneous bidders. Using data from U.S. Forest Service timber auctions, we document a set of systematic effects of auction format: sealed bid auctions attract more small bidders, shift the allocation towards these bidders, and can also generate higher revenue. We propose a model, which extends the theory of private value auctions with heterogeneous bidders to capture participation decisions, that can account for these qualitative effects of auction format. We then calibrate the model using parameters estimated from the data and show that the model can explain the quantitative effects as well. Finally, we use the model to provide an assessment of bidder competitiveness, which has important consequences for auction choice.Auctions, Timber

Local Identification in Empirical Games of Incomplete Information

This paper studies identification for a broad class of empirical games in a general functional setting. Global identification results are known for some specific models, for instance in some standard auction models. We use functional formulations to obtain general criteria for local identification. These criteria can be applied to both parametric and nonparametric models, as well as models with asymmetry among players and affiliated private information. A benchmark model is developed where the structural parameters of interest are the distribution of private information and an additional dissociated parameter, such as a parameter of risk aversion. Criteria are derived for some standard auction models, games with exogenous variables, games with randomized strategies, such as mixed strategies, and games with strategic functions that cannot be derived analytically