Sunday, May 22, 2016

A Quick Illustration of Pre-Testing Bias

The statistical and econometric literature on the properties of "preliminary-test" (or "pre-test") estimation strategies is large and well established. These strategies arise when we proceed in a sequential manner when drawing inferences about parameters. 

A simple example would be where we fit a regression model; test if a regressor is significant or not; and then either retain the model, or else remove the (insignificant) regressor and re-estimate the (simplified) model.

The theoretical literature associated with pre-testing is pretty complex. However, some of the basic messages arising from that literature can be illustrated quite simply. Let's look at the effect of "pre-testing" on the bias of the OLS regression estimator.