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"For a more mathematical/numerical reason....
the standard error of the marginal effect is obtained by the delta
method, which means that the standard error for the marginal effect of
one independent variable involves the whole variance-covariance matrix
from the estimation together with the appropriate entries from the
Jacobian. In other words, there is a lot of stuff that goes into the
calculation beyond just the standard error of the coefficient of that
variable, and these other things can cause it to be greater than 0.05,
even when the coefficient standard error is less than 0.05."


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