National open university of nigeria introduction to econometrics I eco 355

6.0 
TUTOR MARKED ASSESSMENT EXERCISE 
 
List and explain the properties of OLS estimators under the normality assumption. 
 
7.0 
REFERENCES/FURTHER READINGS 
Gujarat, D. N. (2007) Basic Econometrics, 4
th
Edition, tata Mcgraw – Hill publishing 
company limited, New Delhi. 
Faraday, M.N., (2014) Applied Econometrics, 1
st
Edition, Pentagon Publication limited.
 
 
 
 
 
 

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UNIT 3 
THE METHOD OF MAXIMUM LIKELIHOOD (ML)
 
CONTENTS 
 
1.0 Introduction 
2.0 Objectives 
3.0
Main content 
3.1. Maximum Likelihood Estimation of two variable regression Model. 
4.0 
Conclusion 
5.0 
Summary 
4.0
Tutor-Marked Assignment 
7.0. 
References/Further Readings 
 
 
 
1.0.
 
INTRODUCTION 
 
A method of point estimation with some stronger theoretical properties than the method 
of OLS is the method of maximum likelihood (ML). Since this method is slightly 

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involved, it is discussed in the appendix to this chapter. For the general reader, it will 
suffice to note that if 
 
are assumed to be normally distributed, as we have done for 
reasons already discussed, the ML and OLS estimators of the regression coefficients, the 
, are identical, and this is true of simple as well as multiple regressions. The ML 
estimator of 
is 
∑ ̂
. This estimator is biased, whereas the OLS estimator of 
∑ ̂
), as we have seen, is unbiased. But comparing these two estimators of 
, we see that as the sample size n gets larger the two estimators of 
 
tend to be equal. 
Thus, asymptotically (i.e., as 
n 
increases indefinitely), the ML estimator of 
is also 
unbiased. 
Since the method of least squares with the added assumption of normality of u, provides 
us with all the tools necessary for both estimation and hypothesis testing of the linear 
regression models, there is no loss for readers who may not want to pursue the maximum 
likelihood method because of its slight mathematical complexity.