  Many econometrics textbooks imply that under mean independence of the
regressors and the error term, the OLS parameters have a causal interpretation.
We show that even when this assumption is satisfied, OLS might identify a
pseudo-parameter that does not have a causal interpretation. Even assuming that
the linear model is "structural" creates some ambiguity in what the regression
error represents and whether the OLS estimand is causal. This issue applies
equally to linear IV and panel data models. To give these estimands a causal
interpretation, one needs to impose assumptions on a "causal" model, e.g.,
using the potential outcome framework. This highlights that causal inference
requires causal, and not just stochastic, assumptions.
