Does Regression Produce Representative Estimates of Causal Effects?

41 Pages Posted: 8 Jul 2013 Last revised: 11 Feb 2015

Peter M. Aronow

Yale University - Department of Political Science

Cyrus Samii

New York University (NYU) - Wilf Family Department of Politics

Date Written: February 2, 2015

Abstract

With an unrepresentative sample, the estimate of a causal effect may fail to characterize how effects operate in the population of interest. What is less well understood is that conventional estimation practices for observational studies may produce the same problem even with a representative sample. Causal effects estimated via multiple regression differentially weight each unit's contribution. The "effective sample'' that regression uses to generate the estimate may bear little resemblance to the population of interest, and the results may be nonrepresentative in a manner similar to what quasi-experimental methods or experiments with convenience samples produce. There is no general external validity basis for preferring multiple regression on representative samples over quasi-experimental or experimental methods. We show how to estimate the "multiple regression weights'' that allow one to study the effective sample. We discuss alternative approaches that, under certain conditions, recover representative average causal effects. The requisite conditions cannot always be met.

Keywords: causal inference; external validity; multiple regression; observational studies; randomized experiments

Suggested Citation

Aronow, Peter M. and Samii, Cyrus, Does Regression Produce Representative Estimates of Causal Effects? (February 2, 2015). EPSA 2013 Annual General Conference Paper 585. Available at SSRN: https://ssrn.com/abstract=2224964

Peter Michael Aronow

Yale University - Department of Political Science ( email )

P.O. Box 208301
New Haven, CT 06520-8269
United States

Cyrus Samii (Contact Author)

New York University (NYU) - Wilf Family Department of Politics ( email )

715 Broadway
New York, NY 10003
United States

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