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<p>The Frisch-Waugh-Lovell (FWL) theorem is one of the most widely used results in linear regression analysis. In this paper, I trace the historical and analytical development of this theorem to highlight two points. First, I show how the scope of the theorem has expanded over the decades from least squares estimators to a much larger class of estimators that now include the whole k-class of estimators and generalized method of moments estimators. Second, I highlight the pioneering contribution of the statistician G. Udny Yule in the development of the theorem at its very inception and suggest that the theorem be renamed as the Yule-Frisch-Waugh-Lovell (YFWL) theorem.</p>

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An Analytical History of the Yule-Frisch-Waugh-Lovell Theorem

  • 期刊论文

  • 发表日期：

    2026年3月26日

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  • Deepankar Basu

摘要

The Frisch-Waugh-Lovell (FWL) theorem is one of the most widely used results in linear regression analysis. In this paper, I trace the historical and analytical development of this theorem to highlight two points. First, I show how the scope of the theorem has expanded over the decades from least squares estimators to a much larger class of estimators that now include the whole k-class of estimators and generalized method of moments estimators. Second, I highlight the pioneering contribution of the statistician G. Udny Yule in the development of the theorem at its very inception and suggest that the theorem be renamed as the Yule-Frisch-Waugh-Lovell (YFWL) theorem.