HANDOUT 11 Flashcards
Perfect multicollinearity =
one of the variables is a perfect linear function of another
Why can’t we use OLS?
OLS does partial derivatives to see effect of X1 on Y holding X2 constant. But if X1 and X2 perfectly related, we cannot extract the effect of X1 on Y holding X2 constant.
example of perfect multicollinearity for continuous variables
real IR = nominal IR - inflation
Cannot include all 3
Include 2/3
example of perfect multicollinearity for categorical variables
Male = 1 - female
Therefore cannot include both a male and female dummy
Why should perfect multicollinearity never arise?
It reflects a mistake on the part of the researcher
Imperfect multicollinearity =
Very high correlation between 2 variables, but not +-1
Can we estimate coefficients for imperfect multicollinearity?
YES - they are UNBIASED still
What’s the problem with OLS and imperfect multicollinearity?
v(b1) = sigma^2 / sum(x1i tilda - x1 tilda bar)^2
Denominator = RSS from regression of X1 on X2
If X1 and X2 highly correlated, RSS –> 0
So v(b1) –> infinity
Very large SE = t-stats very small = can never rly reject H0
What is X1 tilda bar = ?
It is 0 (but analysis is the same)
How do we detect imperfect multicollinearity? (2 ways)
- correlation coefficient > 0.85 = concerning
2. Even if corre<0.85, we may have very large SE. Small individual t-ratios but large F-stats = indicator.
Multicollinearity is mainly an issue for…
TIME-SERIES DATA
name 4 solutions to imperfect multicollinearity
- do nothing - we don’t care if both controls
- drop one of collinear - the control
- increase sample size
- Transform the collinear variables
2 examples of transforming collinear variables
a) principle component analysis - form 1 big variable from several collinear ones
b) take first differences with time series
Corr between GDPt and GDPt-1, then for first differences of both
Corr(GDPt, GDPt-1) = 0.999
Corr(change GDPt, change GDPt-1) = 0.420
