Monotone Treatment Response

Abstract

The standard formalization of the econometric analysis of treatment response assumes that each member of a population of interest receives one of a set of mutually exclusive and exhaustive treatments, and that the outcome under the realized treatment is observable. Outcomes under the nonrealized treatments are necessarily unobservable; hence these outcomes are censored. This paper investigates what may be learned about treatment response when it is assumed that response functions are monotone, semi-monotone, or concave-monotone. The analysis assumes nothing about the process of treatment selection and imposes no cross-individual restrictions on response. The basic idea is to determine, for every member of the population, the set of response functions that pass through that person's realized (treatment, outcome) pair and that are consistent with the functional-form assumption imposed. These person-specific findings are then explicitly aggregated across the population to determine what can be learned about the distribution of response. The findings have application to the econometric analysis of market demand and of production.