Re: st: Re: dprobit coefficients greater than 1

[May Boggess <mboggess@stata.com>]

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:

 clear
 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
 #d;
 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.

 --May
 mmb@stata.com



*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/