I am trying to calculate the standard error for the discrete change in probability associated with a dummy variable in a logit model by hand. The effect itself is given by the difference in predicted probability with and without the dummy variable equal to 1:
E[P|d=1]-E[P|d=0],
where E[P] is the predicted probability and d is the dummy variable.
The variance of the difference should be given by
Var(E[P|d=1]) + Var(E[P|d=0]) - 2*Cov(E[P|d=1],E[P|d=0]).
Greene (2000, p.824) has a nice little formula for the variance of the individual predicted probabilities (i.e., the first two terms). Does anybody know the formula for the covariance of two predicted probabilities (i.e., the last term)?
Soren Anderson
Resources for the Future
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