In the decade of the 1970s there was a flurry of articles on the ratio
variable problem, with contributions by Glenn Firebaugh and others. The
general consensus that emerged from these discussions was that if theory
says that the dependent variable is a ratio, then one should use the
ratio in the regression. In the regression of
y/x against x (and perhaps other predictors as well), one may use x as a
predictor if x is expected to predict the ratio outcome. However, if
there is measurement error in x, then an artificial negative correlation
is created between the observed ratio dependent variable and the
observed independent variable. This will lead to biased parameter
estimation. David Greenberg, Sociology Department, New York University
----- Original Message -----
From: Jason Yackee <[email protected]>
Date: Wednesday, January 24, 2007 11:02 pm
Subject: st: ok to include the denominator of ratio dep var as an
independent var too?
> 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+�K+ 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 +�K+ 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
> [email protected]
> Cell: 919-358-3040
>
>
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