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This chapter introduces important background material on the partitioned regression model. It serves as a refresher on matrix algebra results related to the partitioned regression model as well as the associated Frisch-Waugh-Lovell (FWL) theorem due to Frisch and Waugh (Econometrica 1:387–401, 1933) and Lovell ( J Am Stat Assoc 58:993–1010, 1963) (see Davidson and MacKinnon, Estimation and inference in econometrics. New York: Oxford University Press, 1993). The Frisch-Waugh-Lovell (FWL) theorem is shown to be a useful tool for proving key results in the fixed effects model in Chap. 2 as well as the artificial regressions used to test panel data models such as the Hausman test in Chap. 4 .

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Partitioned Regression and the Frisch-Waugh-Lovell Theorem

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  • 发表日期：

    2026年

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  • Badi H. Baltagi

摘要

This chapter introduces important background material on the partitioned regression model. It serves as a refresher on matrix algebra results related to the partitioned regression model as well as the associated Frisch-Waugh-Lovell (FWL) theorem due to Frisch and Waugh (Econometrica 1:387–401, 1933) and Lovell ( J Am Stat Assoc 58:993–1010, 1963) (see Davidson and MacKinnon, Estimation and inference in econometrics. New York: Oxford University Press, 1993). The Frisch-Waugh-Lovell (FWL) theorem is shown to be a useful tool for proving key results in the fixed effects model in Chap. 2 as well as the artificial regressions used to test panel data models such as the Hausman test in Chap. 4 .