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Economics Department Working Paper Series
Multiple regression; partial regression; Frisch-Waugh-Lovell theorem; instrumental variables estimation.
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The Yule-Frisch-Waugh-Lovell Theorem For Linear Instrumental Variables Estimation, Deepankar Basu
The Yule-Frisch-Waugh-Lovell Theorem For Linear Instrumental Variables Estimation, Deepankar Basu
Economics Department Working Paper Series
In this paper, I discuss three aspects of the Frisch-Waugh-Lovell theorem. First, I show that the theorem holds for linear instrumental variables estimation of a multiple regression model that is either exactly or overidentified. I show that with linear instrumental variables estimation: (a) coefficients on endogenous variables are identical in full and partial (or residualized) regressions; (b) residual vectors are identical for full and partial regressions; and (c) estimated covariance matrices of the coefficient vectors from full and partial regressions are equal (up to a degree of freedom correction) if the estimator of the error vector is a function only …