What kind of misspecification errors can occur?
-Omitting a relevant variable
-Including an unnecessary or irrelevant variables
-Other things we don't care about
What is the result of omitting a relevant variable?
- Bias estimators
- Incorrect testings
What is the expected value of an estimator given a relevant variable has been omitted
What are the effects of including an irrelevent variable?
σ2 still correctly estimated
Higher variance then true model
What can be done to detect misspecification?
-Ramsey's RESET test
Explain the Ramsey's RESET test
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.
Give the equation for the RESET test, and state it's distribution
df = # new regressors, n - # total parameters in new regression
Problems with the Ramsey RESET test?
Doesn't specify the alternate model
Explain the LM Test
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)
H0 is the restricted model, no new variables
What is the result of measurement error in the regressant?
More variance in the sample, assumptions all fine, OLS still BLUE/BUE
Show mathematically the problem with measurement error in regressors
Yi = B2Xi*+ui
Yi=B2(Xi - ϵi) + ui
Yi=B2Xi + vi
vi = B2ϵi - ui
E(vi) = -B2ϵi
Very bad, nonzero expected error and error correlated with regressors
What are the implications of measurement error in regressors?
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