I would like to know which variables to use to regress income inequality on economic growth. For income inequality, I am thinking of using the Gini index, but don't know what measurement exactly. For the growth should I use GDP per capita, GDP per capita growth, real GDP per capita, or just annual GDP values?
If your are interested in the statistic relationship between income inequality and economic growth, you should use GDP per capita growth since the others indicate level rather than growth.
More generally, the choice of the variable in your (and any other) regression depends on your economics model, otherwise you are just doing some linear projections.
A good reference you may start with this topic is "Banerjee, A. V., & Duflo, E. (2003). Inequality and growth: What can the data say?. Journal of economic growth, 8(3), 267-299."
At first, you should pay much more attention to your Model's structure. It means we must be careful about our economy environment. By doing that, you will become more aware about;
- What regressors could/should be piked?
- What kind of those must be introduced in regression? If you go through these steps you will be able to pick the most appropriate variables. My suggestions about this case :
- search in Google Scholar with some relative keywords like; inequality & Growth
- set a good time filter if you want to find recent tested models.
- carefully compare that article's economy with yours.
- If some significant relativity found, you can choose that model as your benchmark.
- Do not stop here. Keep this search steps on and find more models. These will help you to do after regression robust testings.