probit: marginal effects 
[Jan. 6th, 200811:29 am]

Hi,
I've got already the next question: In a Probit model for whether or not a household has any expenditure on tobacco would the following interpretation for the marginal effect (value = 0.1)of an independent variable "log of total expenditures" be correct? If total expenditures increase 1% the probability of that there are expendiutres on tobacco decreases 10%?
Thanks again!! 


Comments: 
It means that a 10% increase in total expenditures reduces the probability of spending on tobacco by one percentage point.
are you sure? i just found this: "Again, it might be useful to calculate the "elasticities" or effects on the probabilities for a one unit change or a one standard deviation change in each X from the sample mean, holding the other X constant at the sample means. For age, a one year increase reduces the probability of liberalism by .0024, a standard deviation increase in age reduces it by .0340. For education, a one year increase reduces the probability of liberalism by .0049; a one standard deviation unit increase reduces the probability by .0165." http://faculty.ucr.edu/~hanneman/soc203a/logit.html#interpretation
The logit and probit are different models, and they are interpreted differently.
If you have indeed estimated a probit, and if you have indeed calculated the marginal effects of the variables (not the straight coefficients), and the marginal effect of "log x" is 0.1, then the interpretation is that a 1 unit increase in log(x), which represents a 100% increase in x, reduces P[y=1] by 0.1; that is, a 100% increase in x reduces the probability by 10 percentage points.
thanks again!
so is this how I always (e.g. in ols as well) have to interpret a coefficient if the dependet variable is in the logform  a 100% increase of x leads to xxx increase of xxx?
Yes. A change in the (natural) logarithm is always interpreted as (approximately) a percentage change: ∆ln(z) ≈ ∆z/z.
 

