Treatment choice under ambiguity induced by inferential problems |
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| Institution: | 1. Department of Data Analysis and Mathematical Modelling, Ghent University, Coupure links 653, B-9000 Gent, Belgium;2. Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Krijgslaan 281 S9, B-9000 Gent, Belgium;1. School of Mathematics and Statistics, Nanjing University of Information Science & Technology, China;2. School of Economics and the Wang Yanan Institute for Studies in Economics, Xiamen University, China;3. School of Mathematics and Statistics, University of New South Wales, Australia;4. Academy of Mathematics and Systems Science, Chinese Academy of Science, China;1. Department of Economics, University of Colorado Boulder, Boulder, CO 80309, USA;2. Department of Economics, University of Maryland, College Park, MD 20742, USA;1. Department of Mathematics, University of York, United Kingdom;2. Department of Statistics and Applied Probability, National University of Singapore, Singapore;3. School of Mathematical Sciences, University of Electronic Science and Technology of China, China |
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| Abstract: | This paper describes the author's research connecting the empirical analysis of treatment response with the normative analysis of treatment choice under ambiguity. Imagine a planner who must choose a treatment rule assigning a treatment to each member of a heterogeneous population of interest. The planner observes certain covariates for each person. Each member of the population has a response function mapping treatments into a real-valued outcome of interest. Suppose that the planner wants to choose a treatment rule that maximizes the population mean outcome. An optimal rule assigns to each member of the population a treatment that maximizes mean outcome conditional on the person's observed covariates. However, identification problems in the empirical analysis of treatment response commonly prevent planners from knowing the conditional mean outcomes associated with alternative treatments; hence planners commonly face problems of treatment choice under ambiguity. The research surveyed here characterizes this ambiguity in practical settings where the planner may be able to bound but not identify the relevant conditional mean outcomes. The statistical problem of treatment choice using finite-sample data is discussed as well. |
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