Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/283963 
Authors: 
Year of Publication: 
2023
Series/Report no.: 
Working Paper No. 2023-8
Publisher: 
University of Massachusetts, Department of Economics, Amherst, MA
Abstract: 
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 of the residual vectors and does not use any information about the covariate matrix other than its dimensions. While estimation of the full model uses the full set of instrumental variables, estimation of the partial model uses the residualized version of the same set of instrumental variables, with residualization carried out, with respect to the set of exogenous variables. Second, I show why the theorem applies in large samples to the limited information maximum likelihood (LIML) estimator but not to linear GMM estimators. Third, I trace the historical and analytical development of the theorem and suggest that it be renamed as the Yule-Frisch-Waugh-Lovell (YFWL) theorem to recognize the pioneering contribution of the statistician G. Udny Yule in its development.
Subjects: 
multiple regression
partial regression
Frisch-Waugh-Lovell theorem
instrumental variables estimation
JEL: 
C26
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Working Paper

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