Topic 12: Misspecification

Question 1

What kind of misspecification errors can occur?

Answer 1

• Omitting a relevant variable
• Including an unnecessary or irrelevant variables
• Measurement error
• Other things we don’t care about

Question 2

What is the result of omitting a relevant variable?

Answer 2

• Bias estimators
• Inconsistant
• Incorrect testings

Question 3

What is the expected value of an estimator given a relevant variable has been omitted

Answer 3

E(⍺₂)=B₂+ B₃b₃₂

Question 4

What are the effects of including an irrelevent variable?

Answer 4

σ²still correctly estimated

Higher variance then true model

Still BLUE

Question 5

What can be done to detect misspecification?

Answer 5

• Ramsey’s RESET test
• LM Test

Question 6

Explain the Ramsey’s RESET test

Answer 6

If there is mis-speciication, there may be a apattern between Yi^ and the residuals.
So introducing Yi^ or polynomial forms might improve fit

Run the regression with and without.

Question 7

Give the equation for the RESET test, and state it’s distribution

Answer 7

df = # new regressors, n - # total parameters in new regression

Question 8

Problems with the Ramsey RESET test?

Answer 8

Doesn’t specify the alternate model

Question 9

Explain the LM Test

Answer 9

The Lagrange Multiplier test for adding variables.

1. Run normal regression, get residuals
2. regress residuals on all regressors, normal and with the considered variables
3. nR² _~ chi (number of omitted variables)

H₀is the restricted model, no new variables

Question 10

What is the result of measurement error in the regressant?

Answer 10

More variance in the sample, assumptions all fine, OLS still BLUE/BUE

Question 11

Show mathematically the problem with measurement error in regressors

Answer 11

Yi = B₂X_i*+u_i

Yi=B₂(X_i - ϵ_i) + u_i

Yi=B₂X_i + v_i

v_i = B₂ϵ_i - u_i

E(v_i) = -B₂ϵ_i

Very bad, nonzero expected error and error correlated with regressors

Question 12

What are the implications of measurement error in regressors?

Answer 12

OLS estimators biased and inconsistant

• not valid for testing
• very serious problem with no good solutions, other then get accurate measurements
• some approachs, but we don’t consider them
• Instrumental variables