Quantitative Economics: Nov, 2013, Volume 4, Issue 3

Bounds in auctions with unobserved heterogeneity

Timothy B. Armstrong

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 restric-
tive 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 con-
ditions. The results apply to certain quantities related to expectations of valua-
tions, 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 num-
ber of auctions observed and depends on the number of bidders. These results ap-
ply more generally to estimation of functionals of a distribution from repeated ob-
servations 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 auc-
tions for highway construction in Michigan with random assignment.
Keywords. Auctions, unobserved heterogeneity, L-statistics, nonstandard asymp-
totics.
JEL classification. C14, C44.

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