Saturday, November 12, 2016

Monte Carlo Simulation Basics, II: Estimator Properties

In the early part of my recent post on this series of posts about Monte Carlo (MC) simulation, I made the following comments regarding its postential usefulness in econometrics:
".....we usually avoid using estimators that are are "inconsistent". This implies that our estimators are (among other things) asymptotically unbiased. ......however, this is no guarantee that they are unbiased, or even have acceptably small bias, if we're working with a relatively small sample of data. If we want to determine the bias (or variance) of an estimator for a particular finite sample size (n), then once again we need to know about the estimator's sampling distribution. Specifically, we need to determine the mean and the variance of that sampling distribution. 
If we can't figure the details of the sampling distribution for an estimator or a test statistic by analytical means - and sometimes that can be very, very, difficult - then one way to go forward is to conduct some sort of MC simulation experiment."
Before proceeding further, let's recall just what we mean by a "sampling distribution". It's a very specific concept, and not all statisticians agree that it's even an interesting one.