Chile is a terrible example of this; it has one of the higher levels of income inequality on that side of the continent and privatized education and health care. Private education in Chile is appalling; wealthy Chileans send their kids to study to the US or EU and the middle class that can't afford education sends them to Argentina or Brazil. Capital is concentrated on a few hands with a strong dependency on basic commodities exports with low added value. It's better than many places, but the GDP figures don't reflect the realities of a substantial amount of its population.