[Jeff Wooldridge]

So a 10% increase in income results in a 3.9 percentage point fall in the probability of being above the 75th percentile.

Suggestion: Also try it with the percentile itself, define as a proportion (so 0.75 for the 75th percentile). Then, use fractional probit or fractional logit. You would then be estimating the effect directly on the percentile.

[Lucy Porter]

Thanks so much Jeff! Is this definitely right for the AME interpretation of the log of income? If so, my coefficient has changed after re-running the model and it is -0.085.

If I have effectively understood you... a 10% increase in come results in a 0.85 percentage point reduction in the probability of being above the 75th percentile?

[Lucy Porter]

To clarify, following on from earlier posts... could I also say that a unit increase in log of income (to base e) decreases the probability that y=1 by 0.085 percentage points?
Thanks!

[Jeff Wooldridge]

Lucy: Close, but it's not a probability any more. If your y variable is now the percentile -- measured in decimal form -- than a 10% increase in income reduces the percentile by 0.0085, which means .85 percentage points -- as you calculated. So something like 70.0 to 69.15.

[Lom Newton]

Hello Jeff, I wanted to be clear in my mind regarding the interpretation you provided in #34. Reading your paper with Leslie (Panel data methods for fractional response variables with an application to test pass rates) where you modeled math pass rates with log of (average) expenditure and other variables, the Average Partial Effect (APE) of log(avgrexp) is 0.583. Unless, I am not reading right, you interpreted that as the APE of a 10% increase in spending is 0.583.

I have regression results from completely fractional response model where y is decimals between [0,1] - both lower and upper bounds inclusive. To be specific, y is the ratio

cultivated_acreage/total_acreage_of_cultivable_land_available.

I run the following code:

fracreg probit y log(x1) x2 ..., vce(cluster ID)
margins, dydx(*)

If from the margins result, I have the APE for log(x1) to be 0.036, am I right to interpret this a 10% increase in x1 increases the proportion of land cultivated by 0.036 or by 0.0036 (ie.,0.36 percentage points)?

Also, if the APE of x2 is 0.06, will I be right to say one unit increase in x2 increases the proportion of land cultivated by 0.06 (ie., 6 percentage points)?

Finally, is the percentile suggesting you made in #31 applicable to my situation?

Thank you very much.