MLR issues

Question 1

What is the Ommitted Variable Problem? How can this problem be dealt with?

Answer 1

• The regression fails to consider pertenant variables that should have been included
• Implying that β1 = 0 means that α and β2 don’t equal, αhat and β2hat
• This can be detected using the Regression Specification Error Term

Question 2

What is included in Specification Error?

Answer 2

• Specification Error includes missing variables and incorrect functional form
• If γ1 = 0, then the explanatory variable does not explain variation in Yt, meaning that the model is misspecified

Question 3

What is the Irrelevant Variable Problem?

Answer 3

• Irrelevant variables are variables that should not be included within the model
• These variables don’t affect the overall regression
• You will be unable to reject H0 of the variable being insignificant

Question 4

What is Multicollinearity? Why is this an issue?

Answer 4

• Multicollinerarity: Variables are highly correlated (not perfect [otherwise OLS isn’t used])
• ISSUES: Marginal Product is tough to find, Cannot ensure ‘ceteris paribus’, interpreting Marginal impact is difficult
• High Collinearity gives a volatile OLS, leading to false H1 rejections

Question 5

How can Multicollinearity be found?

Answer 5

• High ρX1X2 means high multicollinearity
• Auxiliary Regression: Regress one variable that is correlated, then consult R²

Question 6

How can Multicollinearity be solved?

Answer 6

• No real solution, due to a lack of information
• The solution would be from non-sample information, which would surprise more information
• This trades precision with Bias
• If non-sample information is good, this reduces the cost

Question 7

What are Dummy Variables?

Answer 7

• Qualitative Binary Values [males Vs females, White Vs other]
• There is no definition of dummy variables
• If variable is one, δ = 1, if not δ = 0
• If δ=1, we can say that it has an effect

Question 8

What happens when R² increases?

Answer 8

• SST stays fixed
• SSR decreases
• (T-K) falls as K increases

Question 9

What are non-linear relations? How can these be tested?

Answer 9

• In MLR, we assume linear relations, which are unrealistic
• DMR is likely to occur
• Therefore, we can add a ‘²’ term
• This can be tested by theory and examining data

Question 10

What is Non-Sample information?

Answer 10

• Non-data information can be accounted for in estimation
• Non-data restrictions (i.e. 24 hours in a day) can also be utilised within the constraint
• Principally: transform the regression using exogenous data

Question 11

What is the concerns of Non-Sample Information [relationship between bias and precision]?

Answer 11

• BIAS
• PRECISION
• When non-sample information is used, it is biased unless the restrictions are exactly true [GMT =/=]
• When non-sample information is used, it is less volatile