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.

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