A geometric representation of the Frisch-Waugh-Lovell theorem
Even though the result recently referred to as the "Frisch-Waugh-Lovell theorem" (FWL theorem, henceforth) has been around for a long time, it is relatively recently that it has been widely used by econometricians as a powerful pedagogical tool to express in a simple and intuitive way many...
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| Formato: | Articulo Documento de trabajo |
| Lenguaje: | Inglés |
| Publicado: |
2001
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| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/3500 http://www.depeco.econo.unlp.edu.ar/doctrab/doc29.pdf |
| Aporte de: |
| Sumario: | Even though the result recently referred to as the "Frisch-Waugh-Lovell theorem" (FWL theorem, henceforth) has been around for a long time, it is relatively recently that it has been widely used by econometricians as a powerful pedagogical tool to express in a simple and intuitive way many results that often rely on tedious and seldom intuitive algebraic steps, which are also notationally cumbersome. Even though a proof of the FWL theorem can be based entirely on standard algebraic results, the main reason of its increasing popularity is its strong geometric appeal. Recent texts and articles provide a mix between algebraic proofs and geometrical illustrations of the theorem, but none of them presents a fully geometrical proof of the result. The goal of this note is very modest: it extends the standard geometrical representations of the theorem to actually prove it based on geometrical arguments, which should, hopefully, provide a richer understanding of the scope of the theorem. |
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