Ratio as a Dependent Variable (Regressing Y/Zit on Zit-1)

[Tate Kihara]

Hi, Statalisters,

I am analyzing a cross sectional time series dataset by running a fixed effects and random effects model. My unit of analysis is country-year and my dependent variable is naturalization rate(='number of naturalized people'/'number of stock of foreigners'*100). For one of my control variables, I have one-year lagged 'number of stock of foreigners'. Basically, what I am doing is trying to estimate the following model.

Y/Zit=α+β1Zit-1+β2Xit+ui+eit

(In the above model, i is country, t is time, Y/Z is naturalization rate, Z is number of stock of foreigners, X is another independent variable, α is intercept, βs are coefficients, ui is country specific residual, and eit is the remaining residual.)

I am wondering whether including a lagged denominator of the dependent variable in my model causes any bias.
If anyone has any information, I would be glad to know.

Thank you very much.

Best,

[Rich Goldstein]

ratio variables always cause problems; this has been discussed several times on Statalist and in the stat lit going back to at least 1897; I think a good summary article is: Kronmal, RA (1993), "Spurious correlation and the fallacy of the ratio standard revisited," Journal of the Royal Statistical Society, Series A, 156 (3), 379-392; if you feel the need to use ratios, I suggest Rosenbaum, PR and Rubin, DB (1984), "Difficulties with regression analyses of age-adjusted rates," Biometrics, 40(2): 437-443

[Carlo Lazzaro]

Rich deserves credits for having covered this topic at http://biostat.mc.vanderbilt.edu/wik...ein.ratios.pdf

[Tate Kihara]

Dear Dr.Goldstein and Dr.Lazzaro,

Thank you very much your comments!

Best,

Tate