How should I regress income inequality on economic growth?
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 &quot;Banerjee, A. V., &amp; Duflo, E. (2003). Inequality and growth: What can the data say?. Journal of economic growth, 8(3), 267-299.&quot;