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Bounding Sets for Treatment Effects with Proportional Selection

Deepankar Basu ()
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Deepankar Basu: Department of Economics, University of Massachusetts Amherst

UMASS Amherst Economics Working Papers from University of Massachusetts Amherst, Department of Economics

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.

Keywords: treatment effect; omitted variable bias (search for similar items in EconPapers)
JEL-codes: C21 (search for similar items in EconPapers)
Date: 2021
New Economics Papers: this item is included in nep-ecm, nep-isf and nep-ore
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