Heterogeneous coefficients, control variables and identification of multiple treatment effects
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2009.02314.pdf
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Accepted version
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216.37 KB
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12a67b4a15b00747fb4cf91272415852
Author(s)
Newey, WK
Stouli, S
Date Issued
2021
Journal
Biometrika
Publisher
Oxford University Press (OUP)
Citation
Newey, WK and Stouli, S. 2021. "Heterogeneous coefficients, control variables and identification of multiple treatment effects." Biometrika.
Version
Author's final manuscript
Abstract
Summary
Multi-dimensional heterogeneity and endogeneity are important features of models with multiple treatments. We consider a heterogeneous coefficients model where the outcome is a linear combination of dummy treatment variables, with each variable representing a different kind of treatment. We use control variables to give necessary and sufficient conditions for identification of average treatment effects. With mutually exclusive treatments we find that, provided the heterogeneous coefficients are mean independent from treatments given the controls, a simple identification condition is that the generalized propensity scores (Imbens, 2000) be bounded away from zero and that their sum be bounded away from one, with probability one. Our analysis extends to distributional and quantile treatment effects, as well as corresponding treatment effects on the treated. These results generalize the classical identification result of Rosenbaum & Rubin (1983) for binary treatments.
Multi-dimensional heterogeneity and endogeneity are important features of models with multiple treatments. We consider a heterogeneous coefficients model where the outcome is a linear combination of dummy treatment variables, with each variable representing a different kind of treatment. We use control variables to give necessary and sufficient conditions for identification of average treatment effects. With mutually exclusive treatments we find that, provided the heterogeneous coefficients are mean independent from treatments given the controls, a simple identification condition is that the generalized propensity scores (Imbens, 2000) be bounded away from zero and that their sum be bounded away from one, with probability one. Our analysis extends to distributional and quantile treatment effects, as well as corresponding treatment effects on the treated. These results generalize the classical identification result of Rosenbaum & Rubin (1983) for binary treatments.
MIT Department
Massachusetts Institute of Technology. Department of Economics
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DOI of Published Version
https://doi.org/10.1093/BIOMET/ASAB060
