Econ B L6

Question 1

Can we test for omitted variables?

Answer 1

Only when they are non linear functions of x

Question 2

Give an example where there may be an omitted, non-linear variable?

Answer 2

In wage example, having just exper implies that going from 2-3yrs experience is same as going from 20-21yrs; this is wrong, it is likely that exper^2 has been omitted

Question 3

What is a RESET test for and what does it stand for?

Answer 3

For detecting omitted non-linear variables REgression Specification Error Test

Question 4

How do you implement a RESET test?

Answer 4

You must decide how many function of the fitted values to include in the expanded regression, no right answer but squared and cubed terms normally suffice (see notes page 6 of mine)
Then RESET is the F-statistic for testing:
H0: γ1= γ2=…= γk=0
in the expanded model, ~F2,(n-k-3)

Question 5

What does a significant F in the RESET test imply?

Answer 5

Some sort of functional form problem

Question 6

Explain how we can learn something from a model with omitted variable bias?

Answer 6

If the estimates are coupled in the direction of the biases for key parameters (see and understand example page 6 of my notes)

Question 7

What is a solution for endogeneity problem and explain idea behind it?

Answer 7

Leave a variable in the error term, but don’t estimate model by least squares (now biased and inconsistent), use an Instrumental Variable instead

Question 8

See example

Answer 8

bottom of my notes page 6

Question 9

Explain steps of using instrumental variables to solve the endogeneity problem?

Answer 9

1) Add in a variable z that satisfies the 2 assumptions

Question 10

What are the 2 assumptions that z must satisfy? Which one can’t be statistically tested?

Answer 10

1) z is uncorrelated with u: E(u|z)=0 (cant be stat. checked)
2) z is correlated with x: Cov(z,x) not equal to 0

Question 11

How can you check if z is correlated with x?

Answer 11

Run the regression: x=π0+π1z+v

Since π1=Cov(x,z)/V(x) it only holds if π1=/0 tf should be able to reject null: H0:π1=0

Question 12

Explain the intuition behind the instrumental variable estimator?

Answer 12

Suppose that
y = β0 + β1x +u
and that
Corr(x,u) = 0.6
-Then, the variation in x can be split in two parts
60% “commovent” with u 40% independent
-We want z uncorrelated with u but correlated with x : Thus z must explain the 40% independent variation from u.
-Using z is like keeping only the good part of the variation in x!