An Introduction to Econometric Theory

7The Classical Regression Model

7.1 The Classical Assumptions

Chapters 1to 4 of this book have developed the mathematics of the linear regression model, but were careful to avoid any statistical context. Deliberately, the issue was treated wholly as a line‐fitting exercise. In particular, the residual was treated simply as the unexplained part of the dependent variable, with the property, implicit in the least squares fit, of orthogonality with the regressors, but otherwise simply expected to be small in a well‐fitting regression.

Now that the key concepts of distribution theory have been introduced in Chapters 5 and 6, it is possible to return to these procedures and view them in a new light. The classical model defines what has been taught to students, at least at an elementary level, ever since econometrics became a regular component of the economics syllabus. It has some features that are not very appropriate in an economics context, but it has the benefit of delivering interesting results using quite elementary techniques.

Begin with the full‐sample matrix representation of the regression model in (4.12). Section 4.2 should be consulted for the relevant definitions and notation. The new ingredient is the treatment of the vector , and by extension the observed vector , as random in ...