Zusammenfassung der Ressource
Linear Regression
with Multiple
Regressors
- Omitted
Variable Bias
- Omitted factor
W must be:
- Determinant of Y
- Correlated with
the regressor x
- OLS estimator is biased
and inconsistent
- Formula to get bias
- Solutions
- Run a randomized
controlled experiment
- Adopt "cross
tabulation" approach
- Include omitted variable:
multiple regression
- Multiple Regression Model
- Interpretation of coefficients
- Get BAD
- OLS estimator
- Beta1Small vs. Beta1Large
- Measures of Fit
- R
- SER
- R adjusted
- LSA for Multiple
Regression
- Conditional
Mean Zero
- Omitted variable
- Belongs in equation
(is in U)
- Correlated with an
included X
- i.i.d.
- X and Y have finite 4th
moments
- No perfect
multicolinearity
- One of the regressors is an exact
linear function of the other
regressors
- Control variable vs.
Variable of Interest
- Conditional Mean
Independence
- Implications
- OLS estimator
beta1hatlarge is unbiased
and consistent
- betawhat is not
consistent and
not meaningful
- Usual inference methods
apply to beta1hatlarge
- Sampling Distribution of
the OLS estimator
- Multicollinearity and
Dummy Variable Trap
- Perfect Multicollinearity
- One of the regressors is an exact
linear function of the other
regressors
- Dummy Variable
Trap
- When happens?
- Full set of binary variables and an
intercept are included
- Solutions?
- Omit one of the groups
- Omit the intercept
- Imperfect Multicollinearity
- 2 or more regressors
are highly correlated