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# st: Comparaison of turning points (Inverted U curve) for the same model on different samples

 From "L.M.A. Mulotte" To "statalist@hsphsun2.harvard.edu" Subject st: Comparaison of turning points (Inverted U curve) for the same model on different samples Date Sun, 3 Jul 2011 20:06:42 +0000

```Dear readers,

I have an OLS model that includes both a linear effect and the quadratic term.

I would like to do a test that compares whether the turning points obtained with two different samples are significantly different.
I would welcome any help for this test.

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

------------------------------------------------------------------------------
ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
age |   .0676212   .0043444    15.56   0.000     .0591057    .0761368
age2 |  -.0008728   .0000723   -12.07   0.000    -.0010145    -.000731
birth_yr |  -.0017474   .0011531    -1.52   0.130    -.0040075    .0005128
grade |      .0758   .0015348    49.39   0.000     .0727917    .0788083
_cons |  -.3189213   .0826224    -3.86   0.000    -.4808699   -.1569727
------------------------------------------------------------------------------

-- Turning point is 38.74 --

regress ln_wage age age2 birth_yr grade if south==1

------------------------------------------------------------------------------
ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
age |   .0485752   .0049546     9.80   0.000     .0388635     .058287
age2 |  -.0005538   .0000819    -6.76   0.000    -.0007144   -.0003932
birth_yr |    .004853    .001272     3.82   0.000     .0023597    .0073463
grade |    .077252   .0015179    50.90   0.000     .0742767    .0802273
_cons |   -.531555   .0939837    -5.66   0.000    -.7157788   -.3473311
------------------------------------------------------------------------------

-- Turning point is 43.85 --

Now I want to know whether the turning point of the "south" sample (i.e. 43.85) is statistically different from the turning point of the "North" sample (i.e. 38.74)

I would be very grateful for any advice. Thanks for your consideration!

Best regards,

Louis

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```