Midterm Flashcards
LSA 1
- (E(u|x=x) = 0
i.e. Linearity and expectation of errors = 0
Error term expected value of 0 given any values of independent variables
LSA 2
I.I.D.
Observations in sample independent of each other
Each observation follows same probability distribution
Main place non IID is when data recorded over time
LSA 3
Large outliers are in X and/or Y are rare
Sampling distribution for B1(hat)
approx normal
Homoskedastic
Var(u|X=x) is constant
If don’t use robust S.E. when required
Standard errors (and test statistics and confidence intervals) will be wrong. Typically, homoskedasticity only SEs are too small
LSA 4
u is homoskedastic
LSA 5
u is distributed N(0,sigma^2)
LSA 4 guarantees
OLS estimator has smallest variance among all linear estimators
LSA 5 guarantees
OLS estimator has smallest variance of all consistent estimators
If all 5 assumptions hold, B0 hat and B1 hat
B0 hat and B1 hat are normally distributed for all n, The t-statistic has Student t distribution with n-2 degrees of freedom (holds exactly for all n)
OVB
Bias in estimator that occurs as a result of omitted factor (Z). Z must be determinant of Y, and be correlated to regressor X.
SER formula
RMSE formula
r squared formula
Adjusted r square
Three ways to overcome OVB
Include the OV as an additional regressor
Dummy variable trap
F test (restricted r2 vs non restricted)
Effective control variable
- When included in regression, makes error term uncorrelated with variable of interest
- Holding constant control variable(s), variable of interest is “as if” randomly assigned
- Among individuals with same value of control variable(s), variable of interest is uncorrelated with omitted determinants of Y
Unbiased estimator
E(Y hat) = miuY
Consistent estimator
Lin-Log
1% increase in X is associated with B1/100
Log-lin
1 unit change in X is associated with 100B1% change in Y
