9. Asymptotic Properties of Estimators

Question 1

When are asymptotic properties important?

Answer 1

When the finite sample properties of estimators can’t be determined or the assumptions of the CLM don’t hold

Question 2

Consistency

Answer 2

A consistent estimator of a regression coefficient has a sampling distribution that converges on the true value as sample size grows

Question 3

Can an estimator be biased and consistent?

Answer 3

Yes

Question 4

Can an estimator be unbiased and incosistent?

Answer 4

No

Question 5

Asymptotic bias

Answer 5

The difference between the estimate of a variable when the sample size is infinite and the true value of the variable

Question 6

How do we decide which estimators to use if they are all biased and inefficient?

Answer 6

We look at their asymptotic sample properties

Question 7

Asymptotically efficient

Answer 7

When the variance of the asymptotic distribution of our estimate is smaller than that of any other consistent estimator

Question 8

Can we still draw inferences from data if the disturbances aren’t normally distributed?

Answer 8

Yes because even when the date are non normal, the sampling distributions of OLS estimators are asymptotically normal

Question 9

Central limit theorem

Answer 9

Irrespective of the distribution of the parent population, the distribution of sample average approaches the normal as sample size grows

Question 10

When can we assume OLS estimators are normally distributed?

Answer 10

If the population is symmetric, then when n>30. If the population isn’t symmetric then when n>200