• Open Access

Bounds in auctions with unobserved heterogeneity


  • Timothy B. Armstrong

    1. Yale University; timothy.armstrong@yale.edu
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    • Thanks to Han Hong and Liran Einav for support and helpful discussions, and to Jon Levin, Jakub Kastl, a co-editor, and three anonymous referees, and participants at the Stanford IO Seminar and Third Year Seminar for comments. I also thank Liran Einav and Ignacio Esponda for sharing the data from the Michigan Department of Transportation. All remaining errors are my own. This paper was written with generous support from a fellowship from the endowment in memory of B. F. Haley and E. S. Shaw through the Stanford Institute for Economic Policy Research.


Many empirical studies of auctions rely on the assumption that the researcher observes all variables that make auctions differ ex ante. When there is unobserved heterogeneity, the direction of the bias this causes is known only in a few restrictive examples. In this paper, I show that ignoring unobserved heterogeneity in a first price sealed bid auction with symmetric independent private values gives bounds on several quantities of economic interest under surprisingly general conditions. The results apply to certain quantities related to expectations of valuations, including bidder profits (which can be used to recover bid preparation costs in entry models) and the efficiency loss of assigning the object randomly. I then turn to estimation of these bounds, and show that, when only the winning bid is available, the rate of convergence can be slower than the square root of the number of auctions observed and depends on the number of bidders. These results apply more generally to estimation of functionals of a distribution from repeated observations of an order statistic and may be of independent interest. I apply these methods to bound the efficiency loss from replacing a set of procurement auctions for highway construction in Michigan with random assignment.