Properties of Estimators

Once we have invented an estimator, a natural question arises: is it any good?

There are several different ways to answer this. An estimator might be correct on average, giving us the idea of unbiasedness. It might vary relatively little from sample to sample, leading to efficiency. Or it might become increasingly unlikely to go wrong as the sample grows, which is the idea of consistency.

These properties are related, but importantly they are not the same thing. We also introduce mean squared error (MSE), which provides another useful way of comparing our estimation methods.

This material becomes especially important later in econometrics. This subject will require us to develop many different estimators, and we then use the ideas in this section to assess whether these methods should actually be trusted.