Different variables Flashcards
Dummy variables
A variable used in the regression analysis to represent sub groups of the sample
Dummy variable trap
Where there is perfect collinearity. E.g - when female and male are both added. Need of one of them omitted to be the base category
What do dummy variables do to the regression
They are an intercept shift so doesn’t affect the slope
Multiple dummies rule
g groups, then g - 1 dummies
Interacting dummy variables with continuous variables
Changes delta 0 into a slope shifter
Omitted variable
When a variable is left out of the model which has significance
Omitted variable bias
Causes the regression coefficients to be biased and the standard errors to be invalid
Omitted variable bias example
Class size and test score. If you omit ability, B1 turns out to be positive. This obviously should be a negative correlation ut it’s because the clever students are put in larger classes
The strength of the proxy effect when X1 is acting for missing X2. Calculating the bias:
Strength of the effect of X2 on Y - given by B2
The strength of the correlation between X1 and X2. Shown by the slope coefficient obtained when X2 is regressed on X1
Both of these multiplied by each other
Which direction is the bias
Upward - If going in the same direction as model
Downward - If going in opposite direction as model
Inclusion of irrelevant variables
In this case the coefficients aren’t biased but they are inefficient. The standard errors remain valid but they are needlessly large.
What can we do about omitting an important variable
Either add it back in if forgotten.
Use a proxy variable
What is a proxy variable
One that is linearly related to the omitted variable.
Which variables does the proxy variable enable to be found
Coefficient of X1
SE + T statistic of X1
R^2
T statistic for Z
Which coefficients does the proxy variable not help find
Coefficient of Z
Intercept Bo
