Frisch–Waugh–Lovell theorem

In econometrics, the Frisch–Waugh–Lovell (FWL) theorem is named after the econometricians Ragnar Frisch, Frederick V. Waugh, and Michael C. Lovell.

The Frisch–Waugh–Lovell theorem states that if the regression we are concerned with is:

where ${\displaystyle X_{1}}$ and ${\displaystyle X_{2}}$ are ${\displaystyle n\times k_{1}}$ and ${\displaystyle n\times k_{2}}$ matrices respectively and where ${\displaystyle \beta _{1}}$ and ${\displaystyle \beta _{2}}$ are conformable, then the estimate of ${\displaystyle \beta _{2}}$ will be the same as the estimate of it from a modified regression of the form:

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