Working Paper: NBER ID: w25671
Authors: Amanda E. Kowalski
Abstract: The LATE monotonicity assumption of Imbens and Angrist (1994) precludes “defiers,” individuals whose treatment always runs counter to the instrument, in the terminology of Balke and Pearl (1993) and Angrist et al. (1996). I allow for defiers in a model with a binary instrument and a binary treatment. The model is explicit about the randomization process that gives rise to the instrument. I use the model to develop estimators of the counts of defiers, always takers, compliers, and never takers. I propose separate versions of the estimators for contexts in which the parameter of the randomization process is unspecified, which I intend for use with natural experiments with virtual random assignment. I present an empirical application that revisits Angrist and Evans (1998), which examines the impact of virtual random assignment of the sex of the first two children on subsequent fertility. I find that subsequent fertility is much more responsive to the sex mix of the first two children when defiers are allowed. [This paper has been combined with “A Model of a Randomized Experiment with an Application to the PROWESS Clinical Trial” (www.nber.org/papers/w25670) and superseded by “Counting Defiers: Examples from Health Care” (https://arxiv.org/abs/1912.06739) as of July 17, 2020.]
Keywords: No keywords provided
JEL Codes: C1; C9; H10; J01
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Instrument assignment to intervention group (C90) | Having a third child (J13) |
| Sex mix of first two children (J12) | Having a third child (J13) |
| Including defiers (Y60) | Compliers constitute approximately 25% of the sample (C88) |
| Including defiers (Y60) | Defiers constitute approximately 19% of the sample (D91) |