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This research explores the performance of ordinary least squares with discrete regressors in a non-linear model.

December 11, 2025Journal of Econometric Methods0 citations

Regression as Best Linear Prediction: The Case of Discrete Regressors

Key Points

This research explores the performance of ordinary least squares with discrete regressors in a non-linear model.
Investigated properties of OLS estimator
Analyzed level and incremental effects
Conducted empirical application on a wage equation
OLS estimand is a convex average of incremental effects
Weights for level effects can be negative
Emphasizes importance of unrestricted models in regression analysis

Abstract

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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