Topic 12: Misspecification Flashcards Preview

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Flashcards in Topic 12: Misspecification Deck (12)
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1
Q

What kind of misspecification errors can occur?

A
  • Omitting a relevant variable
  • Including an unnecessary or irrelevant variables
  • Measurement error
  • Other things we don’t care about
2
Q

What is the result of omitting a relevant variable?

A
  • Bias estimators
  • Inconsistant
  • Incorrect testings
3
Q

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

A

E(⍺2)=B2+ B3b32

4
Q

What are the effects of including an irrelevent variable?

A

σ2still correctly estimated

Higher variance then true model

Still BLUE

5
Q

What can be done to detect misspecification?

A
  • Ramsey’s RESET test
  • LM Test
6
Q

Explain the Ramsey’s RESET test

A

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.

7
Q

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

A

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

8
Q

Problems with the Ramsey RESET test?

A

Doesn’t specify the alternate model

9
Q

Explain the LM Test

A

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

10
Q

What is the result of measurement error in the regressant?

A

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

11
Q

Show mathematically the problem with measurement error in regressors

A

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

12
Q

What are the implications of measurement error in regressors?

A

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