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872. What does OLS identify under the zero conditional mean assumption?

Working Paper n. 872 - Febbraio 2022


Federico Crudu

DEPS, USiena and CRENoS

Giovanni Mellace

University of Southern Denmark

Joeri Smits

Harvard University


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.


OLS, zero conditional mean error, causal inference

Jel Codes

C10, C18, C21, C31