I study the problem of choice between two treatments for a population of observationally identical individuals based on statistical evidence about average treatment effects that does not reveal the best treatment with certainty. I approach the problem from the perspective of statistical decision theory, derive treatment rules that minimize maximum regret and contrast them with inference and decision making methods of classical statistics. In Chapter 1, the choice is between a status quo treatment with a known outcome distribution and an innovation whose outcomes are observed only in a randomized experiment. I introduce criteria that asymmetrically treat Type I regret (from adopting an inferior innovation) and Type II regret (from rejecting a superior innovation). I derive exact finite sample solutions for experiments with normal, Bernoulli, or bounded distributions of individual outcomes and discuss approaches for other sampling distributions. For normal outcomes, asymmetric minimax regret rules coincide with classical hypothesis testing rules, but conventional test levels imply unrealistic degrees of asymmetry. In Chapter 2, written with Charles Manski, the treatments have binary outcomes and the objective is to maximize a concave-monotone function of the success rate. We show that admissibility of statistical treatment rules depends on that function's curvature. We establish a general complete class for concave and strictly monotone functions and a more specific result for functions with weak curvature, including the logarithmic function often used to model risk aversion. We compute minimax regret rules for specific welfare functions to demonstrate how they depend on the functions' curvature. Chapter 3 studies the measurement of the precision of inference on partially identified parameters. Planners of surveys and experiments that partially identify parameters of interest can choose between using resources to reduce sampling error or to reduce the extent of partial identification. Previous research unanimously measured precision of inference by the length of 95% confidence intervals for the identification region. In a problem with normally distributed data, I show that other measures of precision (maximum mean squared error and maximum regret for treatment choice) yield qualitatively different conclusions about the relative value of reducing sampling error and the extent of partial identification.

Last modified

• 09/08/2018

Creator

• Aleksey Tetenov

DOI

• https://doi.org/10.21985/N2W14F

Subject

• Economics

Keyword

• statistical decision theory
• treatment choice
• minimax regret
• partial identification
• ambiguity

Date created

• 2008-05-08

Resource type

• Dissertation

Rights statement

• In Copyright