The Pew Research group's updated Lower/Middle/Upper Class Calculator will tell you which socio-economic class into which you land based on where you live and how much you make, but home ownership status (rented or owned) doesn't enter into the equation.
Your education, ethnicity, and income are all factors which determine and play into your socio-economic status, but your housing (rented or owned) and an equity you have does not enter into question.
As noted in Rent Your Way to Freedom, "renters" are NOT and should not feel like 2nd class citizens and in fact should potentially pat themselves on the back for avoiding expensive spending as is typically associated with home ownership.