Regression with Many Generated Controls
Abstract
We consider linear regression when some covariates are endogenous, a variable sufficient to control for endogeneity exists but is latent, and the practitioner can generate many proxies for the latent control. For instance, one could cheaply but imperfectly impute the latent control using different AI/ML methods, each generating a different proxy. There are several options the practitioner might consider in this scenario: including all proxies or factors computed from the proxies as controls, instrumental variables estimation, and some nonlinear variants thereof. We use a transparent model to derive the implicit estimand each approach targets, determine when these estimands recover the parameter of interest, and provide some practical recommendations. We show that with a sufficiently rich set of generated controls, practitioners can consistently estimate the parameter of interest without relying on validation data.
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BibTeX
@misc{christensen2026regression,
title = {{Regression with Many Generated Controls}},
author = {Timothy Christensen and Daniel Vebman},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06855},
eprint = {2611.06855},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06855},
}
RIS
TY - UNPB
TI - Regression with Many Generated Controls
AU - Timothy Christensen
AU - Daniel Vebman
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06855
UR - https://arxiv.org/abs/2611.06855
AB - We consider linear regression when some covariates are endogenous, a variable sufficient to control for endogeneity exists but is latent, and the practitioner can generate many proxies for the latent control. For instance, one could cheaply but imperfectly impute the latent control using different AI/ML methods, each generating a different proxy. There are several options the practitioner might consider in this scenario: including all proxies or factors computed from the proxies as controls, instrumental variables estimation, and some nonlinear variants thereof. We use a transparent model to derive the implicit estimand each approach targets, determine when these estimands recover the parameter of interest, and provide some practical recommendations. We show that with a sufficiently rich set of generated controls, practitioners can consistently estimate the parameter of interest without relying on validation data.
ER -