Interpreting rescaled variables in PPML

[Anne Wanyonyi]

I rescaled my dependent variable and main covariate by dividing both by 1 million while carrying out my analysis using PPML. The dependent variable is in levels but the covariate is logged as its a continuous variable. How can I interpret the estimated co-efficient?

Also, I get an R-squared which is less than 5, does that invalidate the results?

[Joao Santos Silva]

Dear Anne Wanyonyi,

The coefficient of a logged regressors in a Poisson regression can be interpreted as an elasticity and therefore the estimate and the interpretation do not change if you rescale your dependent variable.

Your question about the R-squared is not clear but the R-square tells us very little about model validity..

Best wishes,

Joao

[Noemi Seng]

Dear Joao Santos Silva

what if I rescale not my dependent variable but my independent variable? I divided real GDP by 1 million before taking the logarithm (regressor is log of GDP) but the coefficient doesn't change. The only thing that changes is the intercept.

Best
Noemi

[Joao Santos Silva]

That is because ln(ax) = ln(a) + ln(x). Also, because the coefficient is an elasticity, the scale does not matter.