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On the Role of the Zero Conditional Mean Assumption for Causal Inference in Linear Models

Federico Crudu, Michael C. Knaus, Giovanni Mellace, Joeri Smits

arXiv 17 Nov 2022 · Econometrics · publishedCanadian Journal of Economics/Revue canadienne d économique (2025) · 2 citations (OpenAlex)

arXiv:2211.09502 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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.

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8
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1G. W. Imbens and J. M. Wooldridge (2009) Recent developments in the econometrics of program evaluation0.40511100%
2J. D. Angrist and J.-S. Pischke (2017) Undergraduate econometrics instruction: through our classes, darkly0.40511100%
3A. C. Cameron and P. K. Trivedi (2005) Microeconometrics: methods and applications0.40511100%
4J. Hahn and G. Ridder (2011) Conditional moment restrictions and triangular simultaneous equations0.40511100%
5F. Hayashi (2000) Econometrics0.40511100%
6J. H. Stock and M. W. Watson (2019) Introduction to econometrics0.40511100%
7J. M. Wooldridge (2010) Econometric analysis of cross section and panel data0.40511100%
8J. M. Wooldridge (2019) Introductory econometrics: A modern approach0.40511100%

Showing the top 8 of 8 scored citations.