Interpreting the marginal effect in Probit with a logged transformed covariate

[Pythagore Donfouet]

Hi everyone,


I have a challenge with interpreting the marginal effect in Probit model with a logged transformed covariate. Please, let us assumed that the dependent variable is no schooling (a binary variable which takes 1 if the child was not enrolled in school and 0 if enrolled). The variable of interest is the welfare variable which is logX (measured by the logged of the total household consumption) and the coefficient of the logX is -0.335. Other covariates are included in the model.


In my humble opinion, this means that if the total household consumption increased by 10%, the proportion of children who did not go to school will be reduced by 3 percentage points (0.335*10/100).

Please, is it by 3 percentage points or 3 percent? This is where I am confused.


In the Probit model, I know that for the continuous covariate (age), the marginal effect is interpreted as a percent (increased or decreased depending on the sign of the coefficient). For the binary covariate (gender), it is interpreted as a percentage point (increased or decreased depending on the sign of the coefficient). But, with the logged covariate, it is not straightforward. I am confused.

I would appreciate your value inputs.

Thanks

[Fei Wang]

I assume the -0.335 has already been the marginal effect from -margins-. Then, it should be 3 percentage points.

[Pythagore Donfouet]

Dear Fei,

Yes the -0.335 is the marginal effect from -margins- command. Thanks a lot for your quick reply. Much appreciated.