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Re: st: Re: dprobit coefficients greater than 1

From   May Boggess <>
Subject   Re: st: Re: dprobit coefficients greater than 1
Date   Fri, 07 Oct 2005 14:13:34 -0500

On thursday afternoon Friedrich commented on a Stata FAQ on marginal effects:

The FAQ states in the second to last paragraph "At gear_ratio=4, the
line has [a] y value much greater than 1." Is it not true that
0<=y<=1 at any gear ratio?
The sentence is refering to the tangent line rather than the curve. I will make some changes to that sentence so it is more clear. The following graph also helps:

sysuse auto
probit foreign gear_ratio
mfx, at(3.3)
predict pgear, p
sort gear_ratio
gen a =2.9 in 1
replace a =3.3 in 2
replace a =4 in 3
gen b =1.37969*a-4.062977
twoway scatter pgear gear
|| line b a , lcolor(red)
legend(label(2 "tangent at gear=3.3"));
#d cr

-mfx- calculates the marginal effect to be 1.38 at gear=3.3. This is the
slope of the tangent line at gear=3.3. If we draw the line (in red on the graph) we see that, since the slope of the curve is changing rapidly in that region, the slope is not a good approximation to the change in y between gear=3 and gear=4. The tangent line is far away from the curve at gear=4. Indeed, the curve is near 1 at gear=4 but the tangent line is much greater than 1 at gear=4.

Radu makes a good point in his previous mail to the list: one would not
expect the marginal effect of a dummy variable to be greater than 1
since it is calculated as the difference between two probabilities.
If Radu would like to send his dataset and code to me off the list, I will take a look at it.


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