Econometrics: L3
OLS Asymptotics
Sung Y. Park
Chung-Ang Univ.
Motivation
We considered small sample, finite sample or exact properties
of the OLS estimator so far.
Gauss-Markov theorem is a finite sample property: it holds for
any sample size n
It is also very useful to see the asymptotic properties or large
sample properties.
For example, we know that t-stat does not follow Student’s t
distribution when A6 (normality of error term) is violated.
However, we can show t and F statistics have approximately t
and F distribution in large sample sizes
Consistency
Consistency is minimal requirement for an estimator
Consider OLS estimator β n
For each n (sample size), β n has a probability distribution
β n is a consistent estimator as sample size (n) increases,
β n becomes more and more tightly distributed around β. As
n→∞, the distribution of β n is degenerated to the single
point β
