Regression with percentage changes

[Clemens Oberhuemer]

Hello,

I run a regression where the dependent variable is the fraction of individuals in a certain category that voted for a party (the fractions are between 0 and 1). My explanatory variable is the change in the gender wage ratio (women/men; the ratios are larger than 0 and most of them time smaller than 1) between the year in which the outcome variable is observed and some previous year. Thus, for a certain category, this could for example be 0.87-0.83=0.04. Since my variables are already in percent and percentage point changes, respectively, does it make sense to apply a log transformation to the outcome variable or both the outcome and the dependent variable for ease of interpretation? How would the coefficients be interpreted in those two cases? How do i interpret the coefficients without applying log transformations?
Thank you.

[Clyde Schechter]

It sounds like you would probably create confusion by applying log transformations here.

If you compare two observation units whose values of the change in gender wage ratio is 1 percentage point (i.e. differ by 0.01), then if you do a straight linear-linear regression and you get a coefficient of b for that gender wage ratio change variable, the expected value of the dependent variable will go up by an amount = 0.01*b. This would correspond to a percentage point difference of b. So the interpretation is straightforward.

That said, while it is certainly common for researchers to decide whether to log transform variables based on whether they want to be able to phrase their results in terms of relative or absolute differences in variables. But it is scientifically wrong to do that. The logarithm function is very non-linear when applied over wide ranges of numbers. Consequently if the relationship y = b0 + b1*x is reasonable, then the relationships between y and log x, or x and log y, or log x and log y must be non-linear, so that these alternative regressions are inherently mis-specified. And if one of those other relationships is a good specification of the relationship, then the linear relationship between y and x is mis-specified. At most one of the four possibilities can be a good specification. On the other hand, if the range of values of x and y are narrow, the degree of non-linearity of logarithm doesn't matter so much. But when the range of either variable is large enough, then the non-linearity of log will lead to the specification problem of the preceding paragraph.

Really the decisions about log transformations should be made based on proper model specification. Exploring scatter plots of the data, with and without transformations, before modeling can be very helpful in this regard.

[Clemens Oberhuemer]

Thank you a lot, Clyde, that's very helpful!

[Tiago Pereira]

Beta-regression followed by -margins- seems the way to go.

help betareg

[George Ford]

or fracreg.

Common practice is not to log a ratio/fraction, though doing so does not affect the general interpretation (but might make it more confusing). Theoretically, the share might be 0, so the natural log is not a conceptually-sound transformation in general. The X variable could be zero or negative, even if it isn't.

[Maarten Buis]

fracreg is in many cases more robust than betareg, so unless you need an estimate for the entire conditional distribution, I would prefer fracreg.

[Tiago Pereira]

Hi, Maarten. What does it mean more robust?

[Romano Piras]

Dear All,

I'm working with a dependent variable (the share of self-employed workers over total employment), which is a proportion strictly bounded between 0 and 1. My model looks like:

y_it = a0 + a1 * x1_it + a2 * x2_it + a3 * (x1_it * x2_it) + other covariates + year_dummies + country_dummies + error_it.

where x1 is the unemployment rate, and x2 is an index (0<index<100) of migrants' ethnic concentration.

My dataset is an unbalanced panel of data covering a variable number of EU countries over a span of approximately 15 years, with gaps in some years. I'm planning to use fracreg or betareg.

1) Is it correct to include year_dummies and country_dummies when using fracreg or betareg? I mean, can I simply add these dummies into a regression using fracreg or betareg?
2) Since I have an interaction between x1 and x2, is it possible to use fracreg or betareg?

Best,
Romano

[Clyde Schechter]

This post has nothing to do with the topic of this thread. By posting it on a thread that is unrelated to the content of your post, you decrease the chances that people who would be capable of, and interested in, answering you will even see it: they will pass it by because the thread title is about something completely different. And on the chance that somebody did see it and respond here, the chances that others who come and search for answers to a similar problem in the future will find it and learn from it are also decreased.

Your chances of getting a timely and helpful response would be greatly improved by starting a new thread with a title that clearly reveals what it is about. Please do that.

[Clyde Schechter]

When I responded to #9, I had not yet seen that the same question is duplicate-posted at https://www.statalist.org/forums/for...-data-in-stata. However, there, it is on topic for the thread. Those who are interested should view it there.

[Romano Piras]

Dear Clyde Schechter,

I apologise for the inconvenience. After I posted my question here, I realised there was another thread on the topic regarding my question.

Sorry for my error.