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Bounding Sets for Treatment Effects with Proportional Selection

Author

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  • Deepankar Basu

    (Department of Economics, University of Massachusetts Amherst)

Abstract

In linear econometric models with proportional selection on unobservables, omitted variable bias in estimated treatment effects are roots of a cubic equation involving estimated parameters from a short and intermediate regression, the former excluding and the latter including all observable controls. The roots of the cubic are functions of delta, the degree of proportional selection on unobservables, and R_max, the R-squared in a hypothetical long regression that includes the unobservable confounder and all observable controls. In this paper a simple method is proposed to compute roots of the cubic over meaningful regions of the delta-R_max plane and use the roots to construct bounding sets for the true treatment effect. The proposed method is illustrated with both a simulated and an observational data set.

Suggested Citation

  • Deepankar Basu, 2021. "Bounding Sets for Treatment Effects with Proportional Selection," UMASS Amherst Economics Working Papers 2021-10, University of Massachusetts Amherst, Department of Economics.
    • Handle: RePEc:ums:papers:2021-10
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    File URL: https://scholarworks.umass.edu/econ_workingpaper/307/
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    Keywords

    treatment effect; omitted variable bias;

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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