Some 30 years ago the issue of how to deal with ratio variables arose in criminological research concerning crime deterrence. The question arose of whether it was legitimate to regress a crime rate for a city or state (crime counts divided by population) against the probability of being arrested (arrest counts divided by crime counts). The worry was that the common prison of crime counts on both sides of the equation would create an artifactual negative correlation, giving the appearance of deterrence. The consensus that emerged was that if the equation was properly specified theoretically, and all variables were measured with perfect accuracy, then it was legitimate to use ratios. However, measurement error in the crime rate (which everyone knows to exist) would potentially create problems. David Greenberg, Sociology Department, New York University
----- Original Message -----
From: Austin Nichols <[email protected]>
Date: Tuesday, June 26, 2007 10:14 am
Subject: Re: st: RE: dependent as denominator on the RHS
To: [email protected]
> VU HOANG NAM:
> I disagree with Dirk's characterization--regressing R on E/R is not
> the same as regressing R2 (=R*R) on XR and E, which is not the same as
> regressing R on sqrt(E) and sqrt(XR), where X is all other RHS
> ("independent") variables, even if only a constant term. Unless you
> replace R and E/R in your specification with their logs, so that you
> can add or subtract rather than multiply and divide the equation, you
> cannot easily convert between functional forms.
>
> sysuse auto, clear
> g pm=pr/mpg
> reg mpg pm
> g mpg2=mpg^2
> reg mpg2 pr
> gen rootpr=sqrt(pr)
> reg mpg rootpr
>
> There are conceptual issues in regressing R on E/R that depend on your
> specific application (what is your theoretical model justifying the
> regression?) but there is also endogeneity induced by measurement
> error in R. Normally, measurement error in the dependent variable is
> of no consequence to the estimated coef, but here it is quite
> problematic. Classical measurement error in E presumably has the
> usual effect (bias toward zero), and can be addressed through -ivreg-
> or -ivreg2- with appropriate instruments, but measurement error in R
> introduces nonclassical measurement error. The problem is usually
> known by the name "division bias" and frequently occurs when
> regressing H (hours) on Y/H (wage rate) in labor economics, see e.g.
>
> George J. Borjas
> The Relationship between Wages and Weekly Hours of Work: The Role of
> Division Bias
> The Journal of Human Resources, Vol. 15, No. 3 (Summer, 1980), pp. 409-423
>
> Eric French
> The Labor Supply Response to (Mismeasured but) Predictable Wage Changes
> The Review of Economics and Statistics
> May 2004, Vol. 86, No. 2, Pages 602-613
>
>
> On 6/26/07, Nachbar, Dirk <[email protected]> wrote:
> > Vu
> >
> > It seems you want to regress R on E/R. Rearranging you actually regress
> > R on sqrt(E). So I would test which of these regressions gives you a
> > better fit.
> >
> > Gen roote=sqrt(e)
> > reg r roote
> > reg r e
> >
> > Dirk
> >
> >
> > -----Original Message-----
> > From: [email protected]
> > [mailto:[email protected]] On Behalf Of VU HOANG
> NAM
> > Sent: 26 June 2007 02:50
> > To: [email protected]
> > Subject: st: dependent as denominator on the RHS
> >
> > Dear statalisters,
> >
> > May I have a question regarding using dependent variable as a
> > denominator of one independent variable? I have searched your site but
> > could not find a clear answer. To be specific, this is my model:
> >
> > Revenue: dependent variable
> > Export ratio= Export / Revenue: independent variable
> >
> > I treat "export ratio" as an endogenous variable and expect it to
> have a
> > positive effect on "revenue".
> >
> > Could you please tell me if I will be criticized to make my model like
> > this?
> >
> > I have cross-section data. Can I just use normal endogenous model to
> run
> > or is there any better model?
> *
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