Correct interpretation of elasticities from fractional response models

[Tarjei W. Havneraas]

I am interested in the relationship between two fractions. I have a cross-section data set with a fraction of the population with a diagnosis and a fraction of the population with symptom levels above a certain threshold.

As the outcome is a fraction and there are some 0 and 1 observations, the fractional response model -fracreg- seems suitable. I have followed the approach outlined on Stata's site for fractional response models.

My approach is

fracreg probit a b
margins, dyex(_all)

I obtain this elasticity:

I want to interpret this as the percent change in a with a 1 % increase in b. (I assume we obtain the relative percent - not the absolute percent point - increase in a.).

What confuses me on the Stata "walkthrough" linked to above is that they write this after the elasticities are obtained:

A truly careful reader will have noticed that we typed dyex(), not eyex(). The dependent variable is already a proportion and so is already on a percentage scale. We just need its change, not its percentage change.

When interpreting the elasticity, I wonder if I either interpret it as:

1. When b increase 1 %, a increases by .0022 percent?
2. Or do I need to multiply .0021 by 100 to interpret this as: When b increase 1 %, a increases by .22 percent?

Finally, can the reasoning be extended to, say, if b increases by 10% then a increases by .22 * 10 = 2.2 percent?

[Tarjei W. Havneraas]

Any takers? To correct myself, the calculation of the 10% increase is probably more like this:

The unit of analyses are regions. Say a region has a = 2 then a 10% increase in b would correspond to a increasing to 2*1.022 = 2.044.