Re: st: ok to include the denominator of ratio dep var as an independentvar too?

[Richard Goldstein <richgold@ix.netcom.com>]

Use of a ratio in this way is problematic.  I suggest

1. Kronmal, RA (1993), "Spurious Correlation and the Fallacy
of the Ratio Standard Revisited," _Journal of the Royal
Statistical Society, Series A_, 156: 379-392 as a good
summary of a large literature

2. If you want a much briefer and less technical summary,
I put one on statalist a number of years ago; I assume it
can be found in the archives.

Rich Goldstein

Jason Yackee wrote:
> Dear all,
>
> I just received this question at a presentation of a paper and I wasn’t sure how to answer it.
>
> I have a panel data set, and a model that is of the general form: (y/x) = a + b + c+…+ x.  My dependent variable (y/x) is a ratio of the total dollar amount of foreign capital inflows that a host country receives in a given year as a ratio of the host country’s GDP in that same year (annual capital inflows = y, gdp = x in the model above).  
> This ratio is called the “penetration ratio” in the literature.  I also included GDP on the right-hand side of the equation as a control for each country’s overall economic size.  The GDP variable was a significant, negative predictor of the penetration ratio.  Larger GDP → Less Penetration.  
> The questioner said that it was improper to have “GDP” on “both sides of the equation”, and that it was sufficient to have a model of the form y = a + b + c +…+ x, where “x” is GDP is “y” is simply the dollar value of foreign capital inflows in absolute, not ratio, form. He couldn't explain why.  I couldn't explain why not.
>
> I re-ran the model in the form the questioner suggested, and the results are overall quite different for the theoretically interesting independent variables.  But my own sense is still that the questioner is wrong, and that my original model was not necessarily improperly specified.  But I don’t have the mastery of statistics to justify my “sense”.  
> Would some kind soul be able to weigh in before my next presentation?
>
> Jason Webb Yackee, J.D.
> Fellow, Gould School of Law
> University of Southern California
> jyackee@law.usc.edu
> Cell: 919-358-3040
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