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Regression as Best Linear Prediction: The Case of Discrete Regressors

Rainer Winkelmann

Journal of Econometric Methods2025https://doi.org/10.1515/jem-2025-0016article
AJG 1ABDC B
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0.50

Abstract

This paper examines the properties of the ordinary least squares (OLS) estimator when applied to a model with a non-linear relationship between outcome and a discrete regressor. I investigate what parameters OLS estimates in such a case, focusing on both level and incremental effects. The analysis reveals that the OLS estimand is a convex average of incremental effects, but weights can be negative for level effects and in the presence of neglected heterogeneity. An empirical application to a wage equation demonstrates these issues, highlighting the importance of using unrestricted models or carefully considering the limitations of OLS estimates in similar situations.

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https://doi.org/https://doi.org/10.1515/jem-2025-0016

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@article{rainer2025,
  title        = {{Regression as Best Linear Prediction: The Case of Discrete Regressors}},
  author       = {Rainer Winkelmann},
  journal      = {Journal of Econometric Methods},
  year         = {2025},
  doi          = {https://doi.org/https://doi.org/10.1515/jem-2025-0016},
}

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Regression as Best Linear Prediction: The Case of Discrete Regressors

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