L2

Question 1

What assumptions are used to show that beta(hat1) is approximately distributed by a normal distribution?

Answer 1

3 LSAs and the assumption that n is large!

Question 2

Diagramatically, what is the p-value?

Answer 2

The probability in tails outside of the +-t(actual) of a normal distribution. If p-value is less than 5%, then can reject at the 5% significance level

Question 3

n is large, n=(maybe)…?

Answer 3

50+

Question 4

A 95% confidence level is…? (2, just need one of them!)

Answer 4

1) the set of points that cannot be rejected at the 5% SL.

2) a set-valued function of the data that contains the TRUE PARAMETER VALUE 95% of the time in repeated samples

Question 5

What regression error does Stata report in parentheses?

Answer 5

Room MSE

Question 6

In Stata, what is: a) _cons, b) p>|t|, and c) ‘t’ column?

Answer 6

a) constant (ie. beta0)
b) p-value
c) t-statistic for β(i)=0

Question 7

How do we interpret the coefficient of a binary variable? Equation showing this?

Answer 7

If β=1, it is the effect on Y that the variable has (ie. the effect of ‘being a man’ on ‘wage rate’)
Can be described by the equation:

β(1) = E(Yi|Xi=1) - E(Yi|Xi=0)
tf is the population difference in group means

Question 8

What are homoskedastic errors?

Answer 8

The errors when the error term is uncorrelated with the X variable(s)

ie. var(u|X=x) = σ^2 (ie. constant) (if not then HTSK)

Question 9

Check

Answer 9

Check that I can tell from data is errors are homo or hetero

Question 10

Advantage and disadvantage of the homo-only SE formula?

Answer 10

Pro: simple
Con: only works for homo errors

Question 11

What are Robust SEs?

Answer 11

Usual standard errors, valid whether homo or heteroskedastic errors

Question 12

Why is better to always use robust SEs?

Answer 12

Since the two different formulas coincide when n is large anyway!

Question 13

What are the extended LSAs?

Answer 13

Original 3 plus two more:

4) u is homoskedastic
5) u is distributed N(0,σ^2)

Question 14

Why do we need to be careful with LSAs 4 and 5?

Answer 14

They are more restrictive than LSAs 1-3, tf apply to less cases (but give opportunity to prove strong results)

Question 15

What is the Gauss-Markov Theorem?

Answer 15

Under LSAs 1-4 (ie. originals plus homoskedasticity), β(hat1) has the smallest variance among all linear estimators (ie. efficient) (don’t think I need proof of this, page 36 if I do need it)

Question 16

Efficiency of OLS under all 5 LSAs? Explain.

Answer 16

β(hat1) has the smallest variance of all consistent estimators (ie. linear or non-linear combinations of Yi) as n->infinity

This means that OLS is the best you can do among consistent estimators, and since non-consistent ones aren’t really an option, OLS is really the best you can do!

Question 17

3 problems with OLS estimation? (2 efficiency assumption points + one other)

Answer 17

1) GM Theorem isn’t that compelling (result is only for linear estimators, homo often doesn’t hold)
2) 5LSA efficiency requires homo and normal errors, which is often not plausible!
3) OLS is more sensitive to outliers than some other estimators

Question 18

Possible estimator to use if there are large outliers in OLS?

Answer 18

Least Absolute Deviations (LAD) estimator (see notes)

Question 19

What can we conclude if all 5 assumptions hold?

Answer 19

1) Beta(hat0) and beta(hat1) are normally distributed

2) The t-statistic has a student t-distribution with n-2 degrees of freedom

Question 20

When can you use t(n-2) CVs instead of N(0,1) for hypothesis tests and CIs?

Answer 20

When u is definitely homoskedastic and normally distributed, and n is LESS THAN 50