Federico Crudu
DEPS, USiena and CRENoS
Giovanni Mellace
University of Southern Denmark
Joeri Smits
Harvard University
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
Jel Codes
C10, C18, C21, C31
