I am running a probit model with several continous and one log-transformed predictor (firm size as total assets). I am unsure how to interpret the coefficient of -0.341 on that variable. I used the natural logarithm to transform the data. Thankful for any help.
1 Answers
Probit coefficients don't have a straightforward interpretation like the ones in logit (see this question). Use marginal effects (if in Stata, the margins command) to obtain the change in $Pr(y)$ for a one-unit increase in $x$ for interpreting the coefficients of a probit.
If your predictor would not be log transformed, you could stop by here, as you would have the change in $Pr(y)$ by a one-unit increase in $x$. Log transformed variables require one more step, because for them a one-unit increase in $x$ means multiplying $x$ by the base (in this case $e$).
In this case, the marginal effects that you would obtain for your log transformed predictor would show the change in $Pr(y)$ for a 2.7182818285-fold change in $x$. Not very pretty. Your best bet is to use a logarithm with base 2 or base 10, so that you can interpret this as the marginal effects as the change in $Pr(y)$ for a two-fold or a ten-fold change in $x$. See this discussion on Statalist for another example.

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