log of regressor - interpretation

[Marry Lee]

Dear all,

I am interested in interpreting the average marginal effect of the log of income, after a probit regression.

Outcome: Y = 1/0.

AME = 0.052

Interpretation: a 1% increase in the income increases the probability of Y = 1 by 0.05 percentage points, right?

My question: can I also say: individuals with Y=1 are 0.05 percentage points more likely to have higher incomes? is this correct?

Thank you!

[Clyde Schechter]

Interpretation: a 1% increase in the income increases the probability of Y = 1 by 0.05 percentage points, right?

Not quite. Unless you have somehow done an experiment where you actually randomly assigned income, you should not describe your results in causal terms. Say, rather, that the 1% difference in income is associated with a certain difference in the probability of Y.

[George Ford]

That is not the correct interpretation. First, the effect is from income to Y, not from Y to income. Second, probit coefficients are tricky to interpret. They represent a change in the z-score, not Y specifically.

This may help.

https://stats.oarc.ucla.edu/stata/output/probit-regression/
https://stats.stackexchange.com/questions/42956/how-do-i-interpret-a-probit-model-in-stata

You can run a Linear Probability Model to get a sense of the size of the effect in probabilistic terms.

I think margins will give you the predicted probabilities and not the z-score after probit.

[Clyde Schechter]

In #1, O.P. refers to the number 0.052 as the AME. If that is the coefficient from the -probit- regression, then, #3 is correct and she has misinterpreted it, because coefficients in non-linear models are not AME's.

In my response in #2, I assumed that she obtained this AME from the -margins- command. If so, then her interpretation is correct.

[George Ford]

Oh, I was thinking AME was the income variable.

If it came from margins, then it would be a change (not sure whether linear or log form for income) in prob Y for a change in income (dollars or percent change). How big the change in Y is depends on the change in income. I suppose if income was dichotomous (high/low), then the interpretation may be correct.

[Marry Lee]

In my response in #2, I assumed that she obtained this AME from the -margins- command. If so, then her interpretation is correct.

Clyde Schechter, thank you for your answer, and you were right in understanding that the AME is the average marginal effect for the variable income after margins.

[George Ford]

how is income defined?

[Marry Lee]

George Ford, it is the logarithm of income (a continous variable).

[George Ford]

So you get a 0.005 point increase in outcome for a 10% increase in income. Divide 0.005 by mean of outcome to get elasticity at the mean.