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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

5

NONSPHERICAL DISTURBANCES AND HETEROSCEDASTICITY

5.1 INTRODUCTION

The discussion in the previous chapters was based on the assumption that the disturbance vector in the linear model y = Xβ + ε is such that the conditional distribution εi|X is independently and identically distributed with zero mean and constant variance σ2. The implication of this assumption is that the variance of e does not change with changes in the conditional expectation, E(y |X). A plot of ε versus E(y |X) should therefore exhibit a random scatter of data points. The random disturbances under this assumption are referred to as spherical disturbances. This chapter deals with alternative methods of analysis under violations of this assumption. The implication here is that Var(ε |X) = σ2 Ω = Σ, where Ω is a positive definite, symmetric matrix.The random disturbances under this assumption are referred to as nonspherical disturbances. Although the general method presented in this chapter can be extended to instrumental variables regression very easily, we will assume that the explanatory variables that are used in the model are exogenous. We will deal with two cases of nonspherical disturbances.

1. Heteroscedasticity: Here, the disturbances are assumed to have different variances. The variance of the disturbance may, for example, be dependent upon the conditional mean E(y |X). For example, this will happen in the case when the disturbances are assumed to follow the binomial distribution. Recall that if a random ...

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Publisher Resources

ISBN: 9781118210321Purchase book