Thursday, June 20, 2019
12:00pm-1:00pm
Room 128, Mining Building
170 College Street
This event is open to the public and registration is not required. Part of the Operations Research Seminar Series coordinated by Merve Bodur.
Abstract
Principal-agent models are widely used to identify optimal incentive contracts. In comparison, the inference of agent models from historical contract data has received relatively less attention. In this paper, we propose an estimator for a general class of principal-agent models where agent actions are hidden — a central feature of many agency problems. We show the estimator to be statistically consistent under mild conditions. In contrast to the case where agent actions are observable, the estimation problem with hidden actions is NP-hard. Although the estimator can be expressed exactly as a mixed-integer linear program, the resulting formulation scales poorly in the size of the data due to weak linear programming relaxations. We bypass this deficiency in the exact formulation by proposing a restricted estimator that minimizes the loss function over a subset of the parameter space, and takes the form of a 0-1 integer program. We present a data-driven approach for constructing the restricted parameter space, show that the resulting formulation is asymptotically optimal with respect to the exact estimator, and characterize the error of the restricted estimator under additional conditions. To solve the 0-1 integer program, we propose a statistical column generation algorithm that employs a series of two-sample, non-parametric hypothesis tests to identify columns to introduce into the formulation. We show that the proposed algorithm preserves the statistical consistency of the exact estimator, and present a bound on the expected number of iterations as a function of the Type I error rate. Finally, we demonstrate the efficacy of the estimator and solution algorithm in a numerical study, using both synthetic data and empirical data related to a class of widely implemented Medicare contracts.
Speaker Bio
Auyon Siddiq is an Assistant Professor of Decisions, Operations and Technology Management at the UCLA Anderson School of Management. He received a PhD in Operations Research from UC Berkeley, an MASc in Industrial Engineering from University of Toronto, and a BEng in Electrical Engineering from Dalhousie University. His research interests include analytics, optimization, and incentive problems.
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The Operations Research (OR) seminar series brings together graduate students, faculty and researchers from the University of Toronto community to interact with prominent scholars in the field of OR. Seminars feature visiting scholars from around the world as well as professors and post-docs. Topics include all variants of OR theory and their applications. Questions? Contact Merve Bodur at bodur@mie.utoronto.ca
