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1、 Electronic copy available at: http:/ Unobserved Heterogeneity and Reserve Prices in Auctions James W. Roberts Duke University November 6, 2009 ERID Working Paper Number 80 This paper can be downloaded without charge from The Social Science Research Network Electronic Paper Collection: http:/ Electr
2、onic copy available at: http:/ Unobserved Heterogeneity and Reserve Prices in Auctions James W. Roberts November 6, 2009 Abstract This study addresses the need to account for unobserved heterogeneity in auctions to improve our estimates of the distribution of bidder values. The method uses reserve p
3、rices to allow the distribution of bidders private information to depend on the realization of the unobserved het- erogeneity. The identifying assumption is that reserve prices are monotonic in the realization of unobserved heterogeneity and sellers are not required to set reserve prices optimally.
4、The model can be estimated using only transaction prices. The paper proposes an estimation method and derives the asymptotic distribution of the proposed estimator. Working with data on used car auctions, the paper shows that controlling for unobserved heterogeneity affects estimates of the distribu
5、tion of bidder values and impacts predicted outcomes dramatically. JEL CODES: D44, L20, L62 Keywords: Auctions, Unobserved Heterogeneity Department of Economics, Duke University. Contact: j.robertsduke.edu. This paper has benefited from many helpful conversations with and insight from my dissertatio
6、n committee: Robert Porter (chair), Igal Hendel, Ali Hortacsu and Aviv Nevo. I also wish to acknowledge those generous with their time and advice including, but not limited to, John Asker, Matthew Gentzkow, Phil Haile, Ben Handel, Joel Horowitz, Tom Hubbard, Vadim Marmer, Rosa Matzkin, Ryan McDevitt
7、, Kanishka Misra, Pablo Montagnes, Jason OConnor, Mallesh Pai, William Rogerson, Aaron Sojourner, Kane Sweeney, Andrew Sweeting, Elie Tamer, Xun Tang and numerous seminar participants. Financial support from the Center for the Study of Industrial Organization is greatly appreciated. Finally, I am tr
8、uly indebted to Joonsuk Lee for being so gracious in providing the data used in the paper. Any errors are my own. Electronic copy available at: http:/ 1 Introduction Empirical auction work often estimates the underlying model primitives of bidder preferences to answer some counterfactual question. I
9、n this way the field is similar to many other areas of applied economics. However, as it has been recently noted (Einav and Nevo (2007) and Pakes (2008), empirical auction research has not kept pace with other empirical branches of economics in its treatment of unobserved heterogeneity. In much of t
10、he empirical literature analyzing auctions economists make the implicit assumption that their information set about the items to be auctioned is the same as the auction participants information set. This assumption is likely to be violated in many applications. Several papers address the problem, bu
11、t they require rich data sets, potentially unpalatable modeling assumptions and ignore another potential source of information regarding the objects unobserved characteristics: seller behavior. In this paper I loosen these restrictions and incorporate seller behavior in order to demonstrate how to o
12、btain better, in the sense of consistency, estimates of demand in the presence of unobserved heterogeneity. When the auction literature does control for unobserved heterogeneity, it only uses information from bidder behavior. The major insight that this paper brings is that we can also use informati
13、on from seller behavior. If bidders observe and respond to a characteristic about the object that the econometrician cannot observe, it is likely that the seller, who as the objects owner is familiar with its intricacies, also observes this characteristic. While empirical auction work has moved forw
14、ard by utilizing bidder behavior to grapple with unobserved heterogeneity, in this paper I show how to use the behavior of the seller, such as the realizations of one of his choice variables, to recover information about what the econometrician does not observe. One important choice variable of a se
15、ller is his reserve price (the price below which he will not sell the item), and in this paper I propose a general model of reserve price policy and bidding behavior that allows us to control for unobserved item heterogeneity when estimating the distribution of bidder values. I present a general non
16、parametric model of reserve price-setting and bidding behavior, show that the model is identified and present Monte Carlo evidence that using reserve prices improves our estimation of the distribution of bidder values in the presence of unobserved attributes. To reduce dimensionality, I then introdu
17、ce a single index that enters both the reserve pricing and bidding functions and I show that the distribution of bidder values is identified in this model. I then provide justifications for the single index assumption, one of which is that oftentimes the covariates entering the index are quality mea
18、sures. Since I use this single index assumption in my estimation, I derive the asymptotic distribution of my estimator of the distribution of bidder values. I then apply my method in an analysis of Korean used car auctions which present a textbook case for efforts to incorporate unobserved heterogen
19、eity into our analysis. In these auctions owners of used cars employ the services of an auction house to sell their vehicles to used car dealers via a mechanism akin to an English button auction. I make sure to validate my modeling assumptions in the context explored. Among others, I attempt to just
20、ify the single index assumption, that both sellers and bidders observe and respond to what the economist does not observe, that conditional on an automobiles attributes bidders have independent private values and that bidders have unit 2 3 demands. I also show why these used car auctions are an inte
21、resting and appropriate market in which to employ my methods. Aside from these auctions importance to the overall automobile industry (the value of automobiles sold by auctions in the U.S. was almost $89 billion in 2007 and used car dealers filled over 30% of their inventory via auctions), they are
22、likely to be riddled with unobserved heterogeneity. That is, even after controlling for observable differences in cars, like make, model, age and mileage, there are likely to be differences in cars that are observable to auction participants, but are unobservable to the econometrician. I then demons
23、trate that my nonparametric estimates of the distribution of bidder values are dependent on the realization of unobserved heterogeneity. After performing the estimation, I turn to utilizing my estimates to answer policy and counterfac- tual questions of interest and demonstrate the consequences of i
24、gnoring the presence of unobserved heterogeneity in these investigations. First, reserve prices are shown to be particularly useful when attempting to determine within-auction variation in bids when only single bids per auction are avail- able in the data. On average, I show that utilizing reserve p
25、rices allows us to reduce our estimates of the within-auction variation in bids by an average of 75%. Second, I show that the literatures previously held belief that a failure to control for unobserved heterogeneity leads to an overesti- mate of the variation in bidder values, due to attributing too
26、 much variation in bids to variation in values, does indeed hold in my estimation results. More generally, I show that when this is the case, we will tend to overestimate the amount of surplus accruing to the winning bidder. In my data, ignoring unobserved heterogeneity leads to an overestimate of b
27、idder surplus of approximately 30%. Third, I analyze the ramifications of ignoring unobserved heterogeneity when estimating the optimal reserve price. In my data this can lead to a substantial drop in expected revenues and an increased tendency for the item to go unsold. Fourth, I show that if the a
28、uction house faced no cost of price discriminating, it would be optimal for it to charge each seller a fixed fee and no commission. In reality, the auction house charges a $50 fixed fee and collects 4.4% of the winning bid as commission. I claim that this is rational for the auction because of the c
29、osts it faces in de- riving each cars optimal fixed fee based on its characteristics. The auction house faces these costs because of heterogeneity across automobiles, which it cannot observe without further inspection. I then seek to estimate the maximum potential gains from switching to the 0-commi
30、ssion, individual fixed fee form of price discrimination from its current non-price-discriminatory pricing scheme. To do this, I parameterize seller demand for the auction house and use its current pricing scheme to uncover these parameters which can then be used to estimate the optimal fixed fees i
31、n the absence of inspection costs. I show that ignoring unobserved heterogeneity leads us to underestimate the potential gains from price discriminating which may be more than 5% of current revenues per car. As auctions are more frequently used, economists will be increasingly called upon to analyze
32、 their outcomes and advise on their designs. In order to provide sound analysis and recommendations, it is essential to control for the presence of unobserved heterogeneity. This research illustrates how using reserve prices can assist in dealing with unobserved heterogeneity and shows how outcomes
33、of interest depend on our acknowledgment and handling of it. 4 The paper proceeds as follows: Section 2 places this paper in the context of the literature. Section 3 introduces the modeling framework used for estimation and addresses several questions of identification. Section 4 introduces the Kore
34、an automobile auction data. Section 5 discusses estimation, illustrates its results and brings these results to bear on several policy relevant questions. Section 6 concludes. Propositions and their proofs are presented in the appendix and all tables and figures appear at the end. 2 Literature Revie
35、w Accounting for differences in items being auctioned, which are unobservable to the econometrician, is an outstanding issue in empirical auction research and presents serious complications for empirical work. In this section I describe the existing literature on unobserved heterogeneity in auctions
36、 and highlight how this paper advances the current body of work. These contributions are generally a slackening of modeling restrictions and an easing of implementation through the use of seller behavior. While economists have methods for dealing with observable heterogeneity between items, there is
37、 no universal approach for dealing with unobserved heterogeneity. This problem is compounded because auction participants generally have more information about the item for sale than the researcher. The often unstated assumption is that the economists information set about the object coincides perfe
38、ctly with that of the bidders, aside from their private signals, and therefore that any variation in bids across similar objects “on paper” derives solely from variation in bidder values. Recently there have been several attempts to deal with this issue. (Campo, Perrigne, and Vuong (2003), Bajari an
39、d Ye (2003), Hong and Shum (2002), Haile, Hong, and Shum (2006), Krasnokutskaya (2009) and Athey, Levin, and Seira (2004). The first three papers use information provided by the number of bidders. The first in this group assumes that the number of bidders is a sufficient statistic for the unobserved
40、 heterogeneity while the second parametrizes the median of the bid distribution as being normally distributed with a mean dependent on the number of bidders in an auction. In a very different approach to that presented here, Krasnokutskaya (2009) cleverly apples deconvolution techniques, the roots o
41、f which can be found in Li and Vuong (1998), and Li, Perrigne, and Vuong (2000) in the auction literature, to address unobserved heterogeneity. Like this paper, Krasnokutskayas semiparametric method, which has recently been applied by other researchers, such as in Asker (2008), allows the unobserved
42、 heterogeneity to vary within auctions with the same number of bidders. However, there are several differences between our models. First, if she wishes to allow for asymmetric bidders, she requires data on multiple bids from the same auction to identify the distribution of bidder signals, where as m
43、y method, though it requires data on reserve prices (or as will be discussed below, potentially other seller choice variables) only necessitates having data on the winning bid in an auction as well as the identity of the winner and second highest bidder. If symmetry is imposed her method can be adap
44、ted to the case with reserve prices as is done in 5 Decarolis (2009).1 Second, her method assumes that a bidders value (or cost since she is looking at procurement auctions, specifically highway maintenance and paving contracts) is the product of a bidders private cost and a common unobserved compon
45、ent/cost.2 I, on the other hand, do not require specifying the functional relationship between private and common signals. Third, she requires bidders signals to be distributed independently from the common component, where as I allow signals to depend on the unobserved common component. Haile, Hong
46、, and Shum (2006) present a similar idea for handling unobserved heterogeneity. Their paper is focused on developing a test for private vs. common values and in it they address the presence of unobserved heterogeneity in a similar way to this paper by modeling the number of bidders as being strictly
47、 increasing in the unobserved heterogeneity. They address the potential selection problem that participation may signal high unobservable realizations of the unobserved heterogeneity (which would happen if the value of the object needed to pass some threshold in order to be auctioned), something tha
48、t I do not focus on in this paper. However, dealing with this selection problem may prove to be easier in this case since reserve prices are continuous, as opposed to the discreteness of the number of bidders.3 Moreover, they do not employ the single index model used below. In another attempt to add
49、ress the presence of unobserved auction level heterogeneity, Athey, Levin, and Seira (2004), in their study of timber auctions, assume a parametric form for the dis- tribution of bids conditional on the unobserved heterogeneity. They then assume a distribution for this unobserved heterogeneity and form the unconditional likelihood based on their parametric assumptions. They also assume, which I do not, that the unobserved heterog