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On Recoding Ordered Treatments as Binary Indicators

2021/11/24 by Evan K. Rose, Yotam Shem-Tov, Rose, Evan K. +1
Mathematics · #Advanced Causal Inference Techniques #Econometrics (econ.EM) #FOS: Computer and information sciences #FOS: Economics and business #Methodology (stat.ME)

paper · pdf · doi:10.48550/arxiv.2111.12258

openalex publication_date 2021/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Researchers using instrumental variables to investigate ordered treatments often recode treatment into an indicator for any exposure. We investigate this estimand under the assumption that the instruments shift compliers from no treatment to some but not from some treatment to more. We show that when there are extensive margin compliers only (EMCO) this estimand captures a weighted average of treatment effects that can be partially unbundled into each complier group's potential outcome means. We also establish an equivalence between EMCO and a two-factor selection model and apply our results to study treatment heterogeneity in the Oregon Health Insurance Experiment.

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