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Re: st: Not Quite Quadratic Regression


From   Christopher Baum <kit.baum@bc.edu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Not Quite Quadratic Regression
Date   Sun, 5 Aug 2012 13:11:34 +0000

<>
On Aug 5, 2012, at 2:33 AM, A. wrote:

> Theory predict an u-shaped relation between two variables, y and x.
> When I perform a quadratic linear regression with a model like
> 
>     y = ax + bx^2 + constant + error,
> 
> the coefficients a and b are not significant. However, if I change the
> exponent to something less than 2, e.g. 1.5, I obtain significance. In
> other words a model like
> 
>     y = ax + bx^1.5 + constant + error,
> 
> yields significant estimates of a and b. The curvature is still quite
> marked using the exponent of 1.5. I can even use an exponent of 1.1
> and obtain significance and a nice shape. But I don't think I can
> simply choose the exponent based on whatever yields significance. Or
> can I? This is my question.
> 
> I have tried to run a non-linear regression where the exponent was a
> free parameter. Although it tend to yield an exponent around 1 to 2,
> everything turns out highly insignificant. If I plug the estimated
> exponent into an OLS model, like the ones above, I get significance. I
> have also tried to use splines as well as a piecewise constant
> formulation. Again the results are less than ideal (although I get the
> same overall picture).
> 
> The non-linearity is rather apparant in a scatterplot (although
> extremely noisy), and the problem shows up when controlling for other
> covariates where a simple graphical/nonparametric approach is
> unfeasible.


Sounds like a job for Box & Cox... help boxcox

Kit

Kit Baum   |   Boston College Economics & DIW Berlin   |   http://ideas.repec.org/e/pba1.html
                             An Introduction to Stata Programming  |   http://www.stata-press.com/books/isp.html
  An Introduction to Modern Econometrics Using Stata  |   http://www.stata-press.com/books/imeus.html


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