What question did this study set out to answer?

The research examines the implications of the zero conditional mean assumption for causal inference in linear models.

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January 22, 2026

On the role of the zero conditional mean assumption for causal inference in linear models

Key Points

The research examines the implications of the zero conditional mean assumption for causal inference in linear models.
Analyzed the relationship between mean independence and OLS parameters.
Investigated the interpretation of OLS estimands under structural models.
Explored the implications for instrumental variable and panel data models.
Identified that OLS may estimate pseudoparameters lacking causal meaning.
Confirmed that structural models can lead to ambiguous representations of regression errors.
Highlighted the necessity of causal assumptions for valid causal inference.

Abstract

Abstract Many econometrics textbooks imply that under mean independence of the regressors and the error term, the ordinary least squares (OLS) parameters have a causal interpretation. We show that even when this assumption is satisfied, OLS might identify a pseudoparameter 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 instrumental variable and panel data models. To give these estimands a causal interpretation, one needs to impose assumptions on a “causal” model, for example, using the potential outcome framework. This highlights that causal inference requires causal and not just stochastic assumptions.

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