Patrick Marsh (Nottingham)

"Small(ish) Sample Econometrics"

Abstract:

All applied work ultimately relies upon theoretical econometrics constructing inferential procedures which are accurate and reliable. For the most part that accuracy and reliability is justified via two almost ubiquitous steps: 1) Detail the limiting distribution of some proposed estimator or test. 2) Monte Carlo it. (To assess the accuracy of the implied approximate critical or probability values).

This approach does beg a couple of questions: A) If the implied approximate critical values are not accurate how can we improve them? B) If two competing statistics have identical limiting properties how do we choose between them? Is Monte Carlo enough?

The answers lie in field of econometrics which concerns the properties of statistics in small(ish) samples. We can `correct’ critical values and we can also directly compare the theoretical properties of competing statistics. In this talk I’ll discuss the main ways of doing this and will actually do so for the world’s second simplest regression model – the AR(1) (there are a myriad of other applications, of course, but this is a Granger Centre seminar). The focus will be on what does and does not work and also demonstrating that one statistic (the t-statistic) is unequivocally better than another (the normalized estimator), admittedly via a somewhat circuitous route.