Skip to Main Content
Applied Econometrics Using the SAS® System
book

Applied Econometrics Using the SAS® System

by Vivek B. Ajmani
June 2009
Intermediate to advanced content levelIntermediate to advanced
328 pages
8h 42m
English
Wiley-Interscience
Content preview from Applied Econometrics Using the SAS® System

4

INSTRUMENTAL VARIABLES

4.1 INTRODUCTION

The analysis methods presented in the previous chapters were based on the assumption that the independent variables are exogenous (E(ε|X) = 0). That is, the error terms in the linear regression model are uncorrelated or independent of the explanatory variables. In Chapter 1, we saw that under the exogeneity assumption, the least squares estimator b is an unbiased and consistent estimator of β. This chapter explores the properties of b under departures from the exogenous assumption? Explanatory variables that are not exogenous are called endogenous variables.

Under departures from the exogeneity conditions, b is no longer an unbiased and consistent estimator of β. To see this, in the simple linear regression case, consider the model yi = β0 + β1xi + εi where the disturbances are correlated with the explanatory variable. The least squares estimator of β1 is given by (Chapter 1)

images

which upon simplifying can be written as

images

The second term gives the expression of the least squares estimator of a regression of ε on x. It should be obvious that the second term is not zero unless the disturbances are uncorrelated with the explanatory variable. Therefore, the least squares estimator of β1 is biased. The inconsistency of the least squares estimator can ...

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Applied Econometrics with SAS

Applied Econometrics with SAS

Barry K. Goodwin, A. Ford Ramsey, Jan Chvosta

Publisher Resources

ISBN: 9781118210321Purchase book