Scandinavian Working Papers in Economics
Discussion Papers on Economics,
University of Southern Denmark, Department of Economics
No 3/2022: What does OLS identify under the zero conditional mean assumption?
Federico Crudu (), Giovanni Mellace (), Joeri Smits () and Michael Knaus ()
Additional contact information
Federico Crudu: University of Siena and CRENoS, Postal: P.zza S.Francesco, 7-8, 53100 Siena, Italy
Giovanni Mellace: Department of Economics, Postal: University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
Joeri Smits: Harvard University
Michael Knaus: School of Business and Economics, Postal: School of Business and Economics, University of Tübingen
Abstract: Many econometrics textbooks imply that under mean independence of the regressors and the error term, the OLS estimand has a causal interpretation. We provide counterexamples of data-generating processes (DGPs) where the standard assumption of zero conditional mean error is satisfied, but where OLS identifies a pseudo-parameter that does not have a causal interpretation. No such counterexamples can be constructed when the assumption needed is stated in the potential outcome framework, highlighting the fact that causal inference requires causal, and not just stochastic, assumptions.
Keywords: OLS; zero conditional mean error; causal inference
Language: English
12 pages, First version: February 23, 2022. Revised: November 15, 2022. Earlier revisions: November 15, 2022.
Full text files
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