Maximum Likelihood Estimation Basics

Maximum likelihood estimation is one of the most widely used methods for estimating unknown quantities in statistics, and is used within econometrics too.

The key idea is surprisingly simple. Once we have observed some data, we ask which possible value of an unknown parameter would have made those same data most likely to occur.

We begin by carefully distinguishing likelihood from probability, before using a simple example to introduce the maximum likelihood estimation (MLE) method. We then extend the method to full random samples, where the likelihood combines information from many observations.

Finally, we look at how the same idea works with continuous data, where density functions take the place of probabilities.

Maximum likelihood will reappear later in econometrics, so this section provides the basic machinery and intuition we will need.