The Econometric SocietyEdited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262
Econometrica: May, 1992, Volume 60, Issue 3
https://doi.org/0012-9682(199205)60:3<505:ASMSEF>2.0.CO;2-M
p. 505-531
Joel L. Horowitz
Manski (1985) has shown that the maximum score estimator of the coefficient vector of a binary response model is consistent under weak distributional assumptions. Cavanagh (1987) and Kim and Pollard (1989) have shown that $N^{1/3}$ times the centered maximum score estimator converges in distribution to the random variable that maximizes a certain Gaussian process. The properties of the limiting distribution are largely unknown, and the result of Cavanagh and Kim and Pollard cannot be used for inference in applications. This paper describes a modified maximum score estimator that is obtained by maximizing a smoothed version of Manski's score function. Under distributional assumptions that are somewhat stronger than Manski's but still very weak, the centered smoothed estimator is asymptotically normal with a convergence rate that is at least $N^{-2/5}$ and can be made arbitrarily close to $N^{-1/2}$, depending on the strength of certain smoothness assumptions. The estimator's rate of convergence is the fastest possible under the assumptions that are made. The parameters of the limiting distribution can be estimated consistently from data, thereby making statistical inference based on the smoothed estimator possible with samples that are sufficiently large.
March 5, 2024
The terms of the Editors of the Econometric Society's three journals end June 30, 2025. We are pleased to announce the incoming Editors and to thank the outgoing Editors for their excellent and continuing service.
Econometrica: Since 2019, Guido Imbens has served as the 14th Editor of Econometrica. On July 1, 2025, Marina Halac will become the Editor.
Quantitative Economics: Stéphane Bonhomme has been the Editor of Quantitative Economics since 2021. His successor will be Bernard Salanié.
Theoretical Economics: The Editor of Theoretical Economics since 2021 has been Simon Board. Taking over for him in July 2025 will be Federico Echenique.
Guido, Stéphane, and Simon have been outstanding Editors. We are grateful to them for the work they have done and will continue to do, and we look forward to further congratulating them next year. We believe Marina, Bernard, and Federico will be outstanding successors and we thank them in advance for their service.
Finally, we are grateful to Larry Samuelson for chairing all three search committees, and we thank the search committee members for their hard and fruitful work:
Econometrica: Christian Dustmann, Lars Hansen, Alessandro Lizzeri, George Mailath, Ariel Pakes, Helene Rey, and Elie Tamer.
QE: Kate Ho, Michael Keane, Felix Kubler, Whitney Newey, and Frank Schorfheide.
TE: Jeff Ely, Johannes Horner, Gilat Levy, Meg Meyer, and Ran Spiegler.
