Econometrics Midterm

LSA #1 (OLS)

E(u | X) = 0; X and u are not correlated; necessary for OLS estimates to be unbiased

LSA #2 (OLS)

(X,Y) are independent and identically distributed; any pair of X and Y, any pair of Xs, and any pair of Y’s are all independent of each other; X and Y have the same joint distribution, all X’s have the same distribution, and all Y’s have the same distribution 

LSA #3 (OLS)

large outliers are unlikely

Law of Iterated Expectations

E(E(Y|A)|A) = E(Y|A)

heteroskedasticity

when the variance of the error term (residual) is not constant; means the spread of residuals changes systematically across the range of an independent variable

omitted variable bias

error in u arises because factors that influence Y are not included in the regression function

conditions for omitted variable

1) a determinant of Y 2) correlated with the regressor X

(imperfect) multicollinearity

occurs when any two or more regressors have high correlation; causes under rejection of the null hypothesis; results in large standard errors for one or more coefficients

perfect multicollinearity

two or more independent variables are perfectly linearly related; coefficients cannot be uniquely determined, as there are infinite solutions

Root Mean Square Error

measures the differences between predicted and actual values

R²

measures fraction of variance of Y that is explained by X; unitless; ranges between 0 (no fit) and 1 (perfect fit)

endogeneity

occurs when an independent variable is correlated with the error term, violating LSA #1

control variable (W)

variable that is correlated with and controls for an omitted causal factor in the regression of Y on X, but which itself does not necessarily have a causal effect on Y; makes the error term uncorrelated with the variable of interest

linear-log

a 1% increase in X is associated with a 0.01B change in Y

log-linear

a change in X by one unit is associated with a 100B% change in Y

log-log

a 1% change in X is associated with a B% change in Y