9. Misspecification and data issues Flashcards
When MLR.4 holds, what do we say about the explanatory variables?
When MLR.4 holds we sat that we have exogenous explanatory variables
When do we call our explanatory variables endogenous?
If xj is correlated with u for any reason then xj is said to be endogenous explanatory variable
Why is MLR.4 (Zero conditional mean) not holding important?
Because we no longer have unbiased estimators
What are the three reasons why an explanatory variable could be exogenous?
- Omitting a key variable
- Functional form misspecification
- Measurement error
What is excluding a relevant variable called?
Underspecification of the model
What is the impact of overspecifying the model?
It lowers precision
What does under specifying the model cause?
It will cause all the OLS estimators to be biased an inconsistent
If we assume that two of our explanatory variables may be correlated what do we assume about them?
If x1 and x2 are correlated, assume a linear regression relationship between them
What is functional form misspecificiation?
When a model does not properly account for the relationship between the dependent and the observed explanatory variables
How can we test for functional form misspecification?
Using F-tests for joint exclusion restrictions (L4)
How does an F-test for joint exclusion restrictions work?
- Add quadratic terms of any significant variables to a model
- Perform a joint test of significance on all quadratic terms
- If they are significant they can be added to the model
What is the full name of a RESET test?
Regression specification error test
What is the idea of a RESET test?
The idea is to include squares and possibly higher order fitted values in the regression
What does a rejection of the null hypothesis under the RESET test tell us?
That there is evidence of joint significance and therefore evidence of misspecification
What should we do if we reject the null in our model?
Try something else, log them for example
What does the Davidson-MacKinnon test do?
Tests whether you should take the log form or not
What are lagged variables?
The same value as your dependent variable but from an earlier time period
Define measurement error
Difference between the observed value y and the actual value y*
What is an indicator variable?
A binary variable
What should you do if you are missing data?
Use the missing indicator method
What should you do if you have large outliers in your model but you don’t want to take them out?
Use the least absolute deviation estimation
Why can large outliers cause problems for OLS?
Because OLS works by taking the deviation from the average and squaring it which skews the results of OLS
If you are struggling to find a proxy variable, what could you use?
A general possibility is to use the lag of the dependent variable
How can we try and solve the omitted variables problem?
Using a proxy variable
What are the advantages of a RESET test?
It is easy to apply because it does not require one to specify what the alternative model is
What are the disadvantages of a RESET test?
We only know whether the model is misspecified or not, but it does not help us necessarily in choosing a better alternative
