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What does OLS identify under the zero conditional mean assumption?

Author

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  • Federico Crudu
  • Giovanni Mellace
  • Joeri Smits

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.

Suggested Citation

  • Federico Crudu & Giovanni Mellace & Joeri Smits, 2022. "What does OLS identify under the zero conditional mean assumption?," Department of Economics University of Siena 872, Department of Economics, University of Siena.
    • Handle: RePEc:usi:wpaper:872
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    Keywords

    OLS; zero conditional mean error; causal inference;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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