Hybrid Auctions I: Theory

In this paper we examine the properties of a hybrid auction that combines a sealed bid and an ascending auction. In this auction, each bidder submits a sealed bid. Once the highest bid is known, the bidder who submitted it is declared the winner if her bid is higher than the second highest by more than a predetermined amount or percentage. If at least one more bidder submitted a bid su¢ciently close to the highest bid (that is, if the di¤erence between this bid and the highest bid is smaller than the predetermined amount or percentage) the quali…ed buyers compete in an open ascending auction that has the highest bid of the …rst stage as the reserve price. Quali…ed bidders include not only the highest bidder in the …rst stage but also those who bid close enough to her. We show that this auction generates more revenue than a standard auction. Although this hybrid auction does not generate as much revenue as the optimal auction, it is ex-post e¢cient.

Contributions to the Theory of Optimal Tests

This paper considers tests which maximize the weighted average power (WAP). The focus is on determining WAP tests subject to an uncountable number of equalities and/or inequalities. The unifying theory allows us to obtain tests with correct size, similar tests, and unbiased tests, among others. A WAP test may be randomized and its characterization is not always possible. We show how to approximate the power of the optimal test by sequences of nonrandomized tests. Two alternative approximations are considered. The rst approach considers a sequence of similar tests for an increasing number of boundary conditions. This discretization allows us to implement the WAP tests in practice. The second method nds a sequence of tests which approximate the WAP test uniformly. This approximation allows us to show that WAP similar tests are admissible. The theoretical framework is readily applicable to several econometric models, including the important class of the curved-exponential family. In this paper, we consider the instrumental variable model with heteroskedastic and autocorrelated errors (HAC-IV) and the nearly integrated regressor model. In both models, we nd WAP similar and (locally) unbiased tests which dominate other available tests.