Isolation in the Construction of Natural Experiments

A natural experiment is a type of observational study in which treatment assignment, though not randomized by the investigator, is plausibly close to random. A process that assigns treatments in a highly nonrandom, inequitable manner may, in rare and brief moments, assign aspects of treatments at random or nearly so. Isolating those moments and aspects may extract a natural experiment from a setting in which treatment assignment is otherwise quite biased, far from random. Isolation is a tool that focuses on those rare, brief instances, extracting a small natural experiment from otherwise useless data. More precisely, isolation uses risk set matching to focus on a moment and differential effects to focus on an aspect, so the random aspect of a specific moment is separated from all else. We discuss the theory behind isolation and illustrate its use in a reanalysis of a well-known study of the effects of fertility on workforce participation. Whether a woman becomes pregnant at a certain moment in her life and whether she brings that pregnancy to term may reflect her aspirations for family, education and career, the degree of control she exerts over her fertility, and the quality of her relationship with the father; moreover, these aspirations and relationships are unlikely to be recorded with precision in surveys and censuses, and they may confound studies of workforce participation. However, given that a woman is pregnant and will bring the pregnancy to term, whether she will have twins or a single child is, to a large extent, simply luck. Given that a woman is pregnant at a certain moment, the differential comparison of two types of pregnancy, twins or a single child, may be close to randomized, not biased by unmeasured aspirations. Risk set matching for differential effects (i.e., isolation) compares two ostensibly similar women at similar moments in their lives: it conditions on the fact that both are pregnant at that moment (the risk set) and it conditions on the additional fact that one had twins and the other had a single child (the differential effect). Isolation removes certain types of unmeasured biases, called generic biases, that promote pregnancies but do not promote twins rather than single children conditionally given a pregnancy. Each mother of twins was compared to five mothers of single children, all with similar histories of fertility and education prior to the given pregnancy. In this comparison, mothers of twins had more children but only slightly reduced workforce participation, approximately 5% less time at work for an additional child.