Abstract: The author presents a simple proof of a property of the method of least squares variously known as the FWL, the Frisch-Waugh-Lovell, the Frisch-Waugh, or the decomposition theorem.

Keywords: decomposition theorem, FWL theorem, Frisch-Waugh-Lovell theorem, Frisch-Waugh theorem

JEL code: C10

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Ragnar Frisch and E V. Waugh (1933) demonstrated a remarkable property of the method of least squares in a paper published in the first volume of Econometrica. Suppose one is fitting by least squares the variable [Y.sub.t] on a set of k' explanatory variables, plus a linear time trend, t = 1,2, ...

[Y.sub.t] = [b.sub.0] + [b.sub.1][X.sub.1t] + ...