st: Interpreting marginal effects with a transformed independent variable in a logit using margins

[Paul GERRANS <p.gerrans@ecu.edu.au>]

Hello Statalisters,
I have a logit regression with wealth as an independent variable, which enters the regression in natural log form.  I then estimate the marginal effect at means after the logit
<margins, dydx(*) atmeans>
My question relates to the interpretation of the marginal effect. In the output it indicates the mean value of wealth is 8.9814 (in its natural log form) whereas the mean of wealth is $24873 in its original form. I appreciate that by taking the log I have changed the distribution and hence the mean values won’t directly translate. But my question is how best to report the marginal effect?  If the marginal effect is 0.03 for the transformed variable can I talk in terms of the original level terms? Can I say the probability increases by 0.03 if the wealth increases from $7954 to $21622 which is a unit change in the transformed variable (8.9814 to 9.9814) .
Equivalently would it be okay to estimate the marginal effect at 10.1215 (which is the mean level of the untransformed variable) and report the marginal effect as the change in probability for a unit change in the log of wealth, which would be 10.1215 to 11.1215 or $42738 change in untransformed terms?
Appreciate any advice, thanks
Paul

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