An Introduction to Econometric Theory

11Partitioning and Specification

11.1 The Partitioned Regression

In nearly every modelling exercise, explanatory variables fall into two groups. There are the focus variables, the significance, sign, or magnitude of whose coefficients are the object of the analysis. And there are also what are often called nuisance variables, which are included because they help to explain , although there is no particular interest in their coefficients. Focus and nuisance parameters may be spoken of in the same vein. The intercept term is perhaps the most frequently encountered of the latter type. This is a natural motivation for partitioning the regressor matrix by columns and the coefficient vector to match. Choosing and such that , write

where is and is , partition conformably, and hence write

(11.1)