Flashcards in L3 Deck (22)
What is omitted variable bias?
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?)
2 conditions which the omitted variable 'Z' must satisfy to create OVB?
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)
slides 5, 6, and 7 for example of OVB
Which direction will an omitted variable bias go when there is a positive correlation between X and u? and for negative?
If negative correlation, bias will go in a downward direction
Explain what an ideal randomised controlled experiment is by defining each term?
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
Define a causal effect?
The effect measured in an ideal randomised controlled experiment
Will there ever be OVB in an IRCE? Why?
Bc E(ui|X)=0 (ie. LSA1 holds) tf no OVB
3 ways to overcome OVB?
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)
Explain what the 'cross-tabulation' approach is, and how it controls for OVB? What is a problem with it?
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!)
MRM: What is beta(i)?
The effect on Y of a change in beta(i) holding all beta(j) constant (where i not equal to j)
What is beta(0) in the MRM?
Predicted value of Y when all Xi=0
MRM: What is R^2 and what is R(bar)^2? What is the difference between them?
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
Explain why the adjusted R^2 is more appropriate for a MRM?
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
State the 4 LSAs for Multiple regression?
See notes; side 2 at the bottom
MRM: what happens if the LSA 1 fails?
This implies there is an OVB (tf either include OV in regression or a variable that controls for the OVB)
How should one check if LSA 3 holds?
Check scatterplots for outliers/typos
Define perfect multicollinearity?
When one of the regressors is an exact linear function of one of the other regressors
What happens if you include k binary regressors for k discrete options?
Perfect multicollinearity - should use k-1 regressors
What is the Dummy Variable Trap?
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
2 solutions to the DVT?
1) Omit one of the groups
2) Omit the constant (intercept)
What is imperfect multicollinearity?
When 2/more of the regressors are very highly correlated