Summary Unobserved confounding presents a major threat to causal inference in observational studies. Recently, several authors have suggested that this problem could be overcome in a shared confounding setting where multiple treatments are independent given a common latent confounder. It has been shown that under a linear Gaussian model for the treatments, the causal effect is not identifiable without parametric assumptions on the outcome model. In this note, we show that the causal effect is indeed identifiable if we assume a general binary choice model for the outcome with a non-probit link. Our identification approach is based on the incongruence between Gaussianity of the treatments and latent confounder and non-Gaussianity of a latent outcome variable. We further develop a two-step likelihood-based estimation procedure.
This content will become publicly available on August 1, 2023
The Future Strikes Back: Using Future Treatments to Detect and Reduce Hidden Bias
Conventional advice discourages controlling for postoutcome variables in regression analysis. By contrast, we show that controlling for commonly available postoutcome (i.e., future) values of the treatment variable can help detect, reduce, and even remove omitted variable bias (unobserved confounding). The premise is that the same unobserved confounder that affects treatment also affects the future value of the treatment. Future treatments thus proxy for the unmeasured confounder, and researchers can exploit these proxy measures productively. We establish several new results: Regarding a commonly assumed data-generating process involving future treatments, we (1) introduce a simple new approach and show that it strictly reduces bias, (2) elaborate on existing approaches and show that they can increase bias, (3) assess the relative merits of alternative approaches, and (4) analyze true state dependence and selection as key challenges. (5) Importantly, we also introduce a new nonparametric test that uses future treatments to detect hidden bias even when future-treatment estimation fails to reduce bias. We illustrate these results empirically with an analysis of the effect of parental income on children’s educational attainment.
- Award ID(s):
- 2042875
- Publication Date:
- NSF-PAR ID:
- 10348443
- Journal Name:
- Sociological Methods & Research
- Volume:
- 51
- Issue:
- 3
- Page Range or eLocation-ID:
- 1014 to 1051
- ISSN:
- 0049-1241
- Sponsoring Org:
- National Science Foundation
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