Stability in the Absence of Treatment

When subjects are measured twice, once at each of two symmetrical locations or times, stability of responses in the absence of treatment within subjects, together with comparability of untreated responses between subjects, is often viewed as supporting a conclusion that differences between treated and control responses reflect effects actually caused by the treatment. The degree to which this intuitive argument is formally correct is explored in several related models: a multivariate Normal model, a nonparametric model defined by symmetries, an analogous randomized experiment, and a sensitivity analysis model for observational studies in which treatments are not randomly assigned to subjects, nor to locations within subjects. Card and Kreuger's study of the employment effects of the minimum wage is used to illustrate the methods.