National open university of nigeria introduction to econometrics I eco 355

 
 
 
 
 
UNIT TWO: OLS ESTIMATORS UNDER THE NORMALITY ASSUMPTION 
 
CONTENTS 
 
1.0
Introduction 
2.0 Objectives 
3.0 Main content 
3.1. Properties of OLS Estimators under the Normality Assumption 
4.0 
Conclusion 
5.0 
Summary 
2.0
Tutor-Marked Assignment 
7.0. 
References/Further Readings 
 
 
1.0.
 
INTRODUCTION 
The OLS estimators that we create through linear regression give us a relationship 
between the variables. However, performing a regression does not automatically give us a 
reliable relationship between the variables. In order to create reliable relationships, we 

---

77 
must know the properties of the estimators and show that some basic assumptions about 
the data are true under the normality assumption. One must understand that having a 
good dataset is of enormous importance for applied economic research. Therefore, in this 
unit we will vividly discuss the OLS estimators under the normality assumption. 
 
2.0.
 
OBJECTIVES 
At the end of this unit, you should be able to: 

identify the properties of OLS estimators under the normality assumption 

understand what is probability distribution 
3.0.
 
MAIN CONTENT 
3.1. PROPERTIES OF OLS ESTIMATORS UNDER THE NORMALITY 
ASSUMPTION 
With the assumption that u, follow the normal distribution as in (4.2.5), the OLS 
estimators have the following properties; Appendix A provides a general discussion of 
the desirable statistical properties of estimators. 
1.
They are unbiased. 
2.
They have minimum variance. Combined with 1, this means that they are 
minimum-variance unbiased, or efficient estimators. 
3. 
They have consistency; that is, as the sample size increases indefinitely, the 
estimators converge to their true population values. 
4 
̂
(being a linear function of u,) is 
normally distributed 
with 
Mean:
̂