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Pseudo Maximum Likelihood Methods: Theory

Econometrica 1984 52(3), 681 open access
Estimators obtained by maximizing a likelihood function are studied in the case where the true p.d.f. does not necessarily belong to the family chosen for the likelihood function. When such a procedure is applied to the estimation of the parameters of the first order moments, it is possible to prove a necessary and sufficient condition for its consistency. Asymptotic normality is shown as well as the existence of a lower bound for the asymptotic covariance matrix. It is also seen that this bound can be reached if consistent estimates are available for the parameters of the second order moments. Finally, a necessary and sufficient condition for the consistency if the pseudo maximum likelihood estimation of the first and second moments is given.

Theory and Behavior of Multiple Unit Discriminative Auctions

Journal of Finance 1984 39(4), 983-1010
ABSTRACT This paper reports the results of controlled experiments designed to test the Harris‐Raviv generalization of the Vickrey theory of bidding in multiple unit discriminative auctions. The paper also discusses further development of the theory—in a way suggested by the experimental results—to include bidders with distinct risk preferences.