Instrumental Variables Regression (2)

Question 1

A parameter is said to be identified:

Answer 1

IF changes in parameter values leads to changes in distributions of observed variables.

Question 2

In general IV regression

Answer 2

It essentially depends on the relation between

• the number of instruments (m)
• the number of endogenous regressors (k)

Question 3

the coefficients b1, …, bk are said to be:

Answer 3

Exactly identified if m=k
(there are just enough instruments to estimate

over-identified if m>k
(there are more than enough instruments to estimate b’s)

under-identified if m < k
there are too few instruments to estimate b’s

Question 4

The IV regression assumptions

Answer 4

1. E(u/W1, … , Wr) = 0, “ the exogenous regressors are exogenous”
2. (Y, X1 , … , X k , W1 , .. , W, Z1, .. , Zm) are i.i.d
3. The X’s, W’s , Z’s , and Y have nonzero, finite 4th moments
4. The instrumetns (Z1, .. , Zm) are valid

Question 5

what happens if instrumetns are weak?

Answer 5

If the instruments are weak, the sampling distribution of TSLS and its t-statistic are not well approximated by normal distribution with n large

Question 6

what the First-stage F-statistic measure?

Answer 6

I measure the instrumetns