What is the Frisch-Waugh-Lovell (FWL) Theorem? | 【Five Minute Econometrics】Topic 15
00:00 Frisch-Waugh-Lovell Theorom and the partialing out interpretation of the OLS estimator in multiple regression
05:26 Prove the two versions of the FWL Theorem
07:43 Verify the FWL Theorem in Stata with real data and simulated data
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【Five Minute Econometrics】 Topic 15: What is the Frisch-Waugh-Lovell (FWL) Theorem?
Hi, I am Bob. Welcome to the Five Minute Econometrics, a tutorial for basic econometric concepts and estimation methods. Today, I want to introduce the Frisch-Waugh-Lovell Theorem. When we interpret the estimated coefficient of an explanatory variable we are interested in, we usually say that the outcome variable changes by beta hat units as that explanatory variable increases by one unit, holding other variables in the model fixed. What does it mean when we say holding other variables fixed or other factors are held constant? This means we have partialled out the effects of the other variables in the model. In other words, we have removed the influences from other variables on the outcome variable and the explanatory variable we are interested in. That is why we use multiple regression and add more explanatory variables to the model to control for the influences of these variables on the outcome.
The Frisch-Waugh-Lovell Theorom helps us better understand this mechanism. According to the FWL Theorem, when we say ``we hold the other variables in the model fixed or the other factors are held constant", we mean the effects of the other variables in the model on the outcome variable and the explanatory variable we are interested in have been partialled out or removed.
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