Optimal Decision Rules when Payoffs are Partially Identified
We derive optimal statistical decision rules for discrete choice problems when payoffs depend on a partially-identified parameter θ and the decision maker can use a pointidentified parameter P to deduce restrictions on θ. Leading examples include optimal treatment choice under partial identification and optimal pricing with rich unobserved heterogeneity. Our optimal decision rules minimize the maximum risk or regret over the identified set of payoffs conditional on P and use the data efficiently to learn about P. We discuss implementation of optimal decision rules via the bootstrap and Bayesian methods, in both parametric and semiparametric models. We provide detailed applications to treatment choice and optimal pricing. Using a limits of experiments framework, we show that our optimal decision rules can dominate seemingly natural alternatives. Our asymptotic approach is well suited for realistic empirical settings in which the derivation of finite-sample optimal rules is intractable.
Date: 3 November 2023, 14:15 (Friday, 4th week, Michaelmas 2023)
Venue: Manor Road Building, Manor Road OX1 3UQ
Venue Details: Seminar Room A or https://zoom.us/j/93054414699?pwd=NEFiL2ZNc0t5N3ZIUTE2VEh5OXhZUT09
Speaker: Timothy Christensen (University College London)
Organising department: Department of Economics
Part of: Nuffield Econometrics Seminar
Booking required?: Not required
Audience: Members of the University only
Editors: Emma Heritage, Shreyasi Banerjee