Treatment Under Ambiguity

Economics have long associated decision making with optimization. The decision maker chooses an action from a known choice set C. The chosen action maximizes a known real-valued objective function $F(\cdot) : C --> R$. Optimization assumes enough knowledge of $C$ and $f(\cdot)$ to determine an optimal action. Suppose the decision maker knows $C$ but not $f(\cdot)$. He knows only that $f(\cdot) \in F$, where $F$ is a specified set of functions mapping $C$ into $R$. Then the decision maker may not have enough information to determine an optimal action. This is a problem of decision under “ambiguity.” After introducing basic themes about decision under ambiguity, I examine the problem of treatment choice. A social planner must choose a “treatment rule” assigning a treatment to each member of a population. Each person has some observed covariates and a “response function” mapping treatments into real-valued outcomes. The planner wants to choose treatments that maximize the population mean value of the outcome. It has been conventional to assume that the planner knows (or at least can estimate) the population distribution of response functions conditional on covariates. With this knowledge, the planner faces a problem of decision under uncertainty and can choose an optimal treatment rule. There are, however, fundamental and practical limits to the knowledge of response functions that planners commonly possess. Thus planners choosing treatment rules ordinarily face problems of decision under ambiguity. This paper gives the key theoretical findings and considers the implications for treatment choice.