st: Shapes of two Inverted U curves (same model on two different samples)

["L.M.A. Mulotte" <L.Mulotte@uvt.nl>]

Dear Readers

I have an OLS model that includes both a linear effect and the quadratic term. I run this model on two samples, one with a treatment (sample X) and one without treatment (Sample Y). I find that the turning point of Curve Y is significantly smaller than the turning point of Curve X. 

Is there any means to test whether the "legs" of Curve Y are steeper than the "legs" of Curve X? 

Put differently, I would like to do a test to know whether Curve Y is closer to Curve Y1 or closer to Curve Y2, as described hereafter:


[
[                     # #
[                   #     #
[  curve Y1       #         #
[       +       #             #
[      + +    #                 #
[     +   + #      @ @            #
[    +    #+    @       @           #
[   +   #   +@             @          #
[  +  #   @  +                @         # curve X
[ + #  @      +         curve Y2  @        #
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 


Here is an example showing my problem 

use http://www.stata-press.com/data/r11/nlswork
gen age2=age*age
regress ln_wage age age2 birth_yr grade if south==0
regress ln_wage age age2 birth_yr grade if south==1

Which of the two Inverted-U curves exhibits the "steepest" legs ? And, can I do a statistical test for that?

Thanks for your consideration

Best, 
Louis

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