Partitioned Regression and the Frisch-Waugh-Lovell Theorem

Badi Baltagi

Chapter 1 in A Companion to Econometric Analysis of Panel Data, 2026, pp 1-8 from Springer

Abstract: Abstract 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 .

Date: 2026
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DOI: 10.1007/978-3-032-09687-6_1

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