LPM Math Consider the standard linear probability model:
economics
Description
1. LPM Math Consider the standard linear probability model:
Yi = β0 + β1Xi + Ui
In this situation Yi
is 1 or 0, but we know that E(Y |X) = P(Y = 1|X).
1. Using the definition of conditional variance,
V ar(Y |X) = E(Y
2
|X) − E(Y |X)
2
prove that for the LPM model:
V ar(Y |X) = P(Y |X)(1 − P(Y |X)
Hint: How are Y
2 and Y related?
2. Now use the regression equation and the variance rules to conclude that,
V ar(U|X) = P(Y |X)(1 − P(Y |X)
3. Is homoscedasticity a safe assumption for LPMS?
2. Different Levels of Fixed Effects Consider data on trade between countries over time.
There are N countries. Index exporters by i, importers by j, and time by t. Let Sijt be the value
of exports from i to j at time t.
1 Let Xijt be the value of tariffs charged by j on i’s goods at time
t. We are interested in the effect of tariffs on import values.
