L3

Question 1

What is omitted variable bias?

Answer 1

When a variable that affects the independent variable is not included in the model specification, and therefore resides in the error term. This causes the error term to become correlated with one/more of the x variables, causing bias (eg. ‘unobserved ability’ in a wage estimation model?)

Question 2

2 conditions which the omitted variable ‘Z’ must satisfy to create OVB?

Answer 2

1) Z is a determinant of Y (ie. a part of u)

2) Z is correlated with the regressor X (Corr(Z,X) nto equal to 0)

Question 3

see

Answer 3

slides 5, 6, and 7 for example of OVB

Question 4

Which direction will an omitted variable bias go when there is a positive correlation between X and u? and for negative?

Answer 4

Upwards

If negative correlation, bias will go in a downward direction

Question 5

Explain what an ideal randomised controlled experiment is by defining each term?

Answer 5

Ideal = subjects follow the treatment protocol-perfect compliance (ie. no reporting errors etc.)
Randomised = subjects from pop. of interest are randomly assigned to a treatment/control group
Controlled = having a control group allows for measuring differential effect of treatment
Experiment = treatment is assigned as part of an experiment, tf subjects have no 'choice' tf no reverse causality

Question 6

Define a causal effect?

Answer 6

The effect measured in an ideal randomised controlled experiment

Question 7

Will there ever be OVB in an IRCE? Why?

Answer 7

Bc E(ui|X)=0 (ie. LSA1 holds) tf no OVB

Question 8

3 ways to overcome OVB?

Answer 8

1) Run a randomised experiment where the treatment is assigned - this works because although part of the error still determines Y, it is now uncorrelated with the regressor X (rarely feasible)
2) Use ‘cross-tabulation’ approach
3) Use a regression in which the OV is no longer omitted! (see notes for examples)

Question 9

Explain what the ‘cross-tabulation’ approach is, and how it controls for OVB? What is a problem with it?

Answer 9

Within each group, control for the OVB by having each subgroup have the same level of the OVB (see notes) (may run out of data!)

Question 10

MRM: What is beta(i)?

Answer 10

The effect on Y of a change in beta(i) holding all beta(j) constant (where i not equal to j)

Question 11

What is beta(0) in the MRM?

Answer 11

Predicted value of Y when all Xi=0

Question 12

MRM: What is R^2 and what is R(bar)^2? What is the difference between them?

Answer 12

R^2 = fraction of variability in Y explained by X
R(bar)^2 = adjusted R^2; R^2 with a DofF correction that adjusts for estimation uncertainty

Normally, R(bar)^2 will be smaller, but if n is very large they will be roughly the same

Question 13

Explain why the adjusted R^2 is more appropriate for a MRM?

Answer 13

The normal R^2 will always increase when you all in another regressor; this is a problem for measuring ‘fit’ because almost all data will have some kind of correlation with Y, and the R^2 normal sees this as increased explanatory power of the model.
The adjusted R(bar)^2 corrects this problem by ‘penalising’ you for adding another regressor tf it won’t necessarily increase as you add more Xs

Question 14

State the 4 LSAs for Multiple regression?

Answer 14

See notes; side 2 at the bottom

Question 15

MRM: what happens if the LSA 1 fails?

Answer 15

This implies there is an OVB (tf either include OV in regression or a variable that controls for the OVB)

Question 16

How should one check if LSA 3 holds?

Answer 16

Check scatterplots for outliers/typos

Question 17

Define perfect multicollinearity?

Answer 17

When one of the regressors is an exact linear function of one of the other regressors

Question 18

What happens if you include k binary regressors for k discrete options?

Answer 18

Perfect multicollinearity - should use k-1 regressors

Question 19

What is the Dummy Variable Trap?

Answer 19

Given a set of multiple dummy variables that are mutually exclusive and exhaustive, if you include ALL these dummys and a constant beta(0), there will be perfect multicollinearity

Question 20

2 solutions to the DVT?

Answer 20

1) Omit one of the groups

2) Omit the constant (intercept)

Question 21

What is imperfect multicollinearity?

Answer 21

When 2/more of the regressors are very highly correlated

Question 22

What is the implication of imperfect multicollinearity? Explain why.

Answer 22

One or more of the regressors will be imprecisely estimated

Why? β(1) is the effect of X1 on Y holding X2 constant. BUT if X1 and X2 are highly correlated, then there is very little variation in X1 ONCE X2 is held constant tf the data lacks information about the change in X1 when X2 is held constant which leads to large variance of OLS estimator on X1 and large SEs