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.
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 women 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 pregnancies on workforce participation, twins or a single child,
may be close to randomized, not biased by unmeasured aspirations. In this
comparison, we find in our case study that mothers of twins had more children
but only slightly reduced workforce participation, approximately 5% less time
at work for an additional child.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS770 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
