Estimating linear regression with OLS vs. ML

Assume that I’m going to estimate a linear regression where I assume uN(0,σ2). What is the benefit of OLS against ML estimation? I know that we need to know a distribution of u when we use ML Methods, but since I assume uN(0,σ2) whether I use ML or OLS this point seems to be irrelevant. Thus the only advantage of OLS should be in the asymptotic features of the β estimators. Or do we have other advantages of the OLS method?


Using the usual notations, the log-likelihood of the ML method is


It has to be maximised with respect to β0 and β1.

But, it is easy to see that this is equivalent to minimising


Hence, both ML and OLS lead to the same solution.

More details are provided in these nice lecture notes.

Source : Link , Question Author : MarkDollar , Answer Author : ocram

Leave a Comment