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st: RE: Inflection point

From   "Nick Cox" <>
To   <>
Subject   st: RE: Inflection point
Date   Wed, 14 Apr 2010 12:47:41 +0100

The turning point [not inflection point] of a quadratic is a property of
the curve.  Variability around the curve is immaterial, except for
influencing how seriously we take the curve. 

However, although the quadratic you fitted will have a turning point
somewhere; it need not be within the range of the data. If it is, your
model seems a little implausible, at least on the information here. 

And a cubic polynomial with two turning points within the range of your
data sounds even more implausible. 

Alternatively, it may that quadratic (and cubic) terms just capture
nonlinearity in what is monotonic in the range of your data. 


Francesco Burchi

I have run the following IV estimates:

ivreg2 wage EDU EDUSquared X1 X2 (X3=Instrument1) X4 X5 X6 X7, robust 

I would like to calculate the inflection point of EDU (=years of
schooling). Therefore, I have used the following formula:
Is this the right way to calculate the inflection point? I am surprised
that I don't use the standard deviation in the formula. Moreover, is
there a way to show graphically the effect of EDU controlling for all
the other covariates (including the squared form and the endogenous
variable X3) and visualizing the inflection point?
Finally, should I use also the cubic form to see whether eventually
there is more than one inflection point?

I am using Stata 10.

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