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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


What is the implication of imperfect multicollinearity? Explain why.

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