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

 From "Samuel R. Lucas" To statalist@hsphsun2.harvard.edu Subject Re: st: Comparaison of turning points (Inverted U curve) for the same model on different samples Date Sun, 3 Jul 2011 23:35:16 -0700

This is not my area, but I wonder why you don't run one regression for
both groups, using interactions to produce group-specific
coefficients.  Then, you can calculate the predicted value of the
turning points, and, using the standard errors (and covariance of the
two estimates) to test whether the estimates are discernibly
different.

I hope this helps.
Sam

On Sun, Jul 3, 2011 at 1:06 PM, L.M.A. Mulotte <L.Mulotte@uvt.nl> wrote:
>
> 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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