First, on figuring out the causes of growth

A linear framework rules out the possibility that the effect of a change in the variable of interest may differ according to the initial level of that variable and that the effect of certain variables may depend on the levels of other variables –in short, it rules out the idea that context matters. And when you look at the data we have, it turns out that relationships are almost certainly non-linear or context-dependent. But we don’t have enough data on global economic growth to fully account for all of the context-dependent relationships.

I tried to explain that in layman’s terms in What Causes Prosperity?.

Next, on inequality and convergence.

Buffalo Country in South Dakota has a per capita income of $5,213. Marin County in California has a per capita income of about $44,962. This remaining income gap suggests a great deal about the potential impact of globalization on worldwide income disparities.

…Robert Barro and Xavier Sala-i-Martin estimate the rate of income
convergence between US states at about 2 percent per year between 1880-1998.

…If, tomorrow, we managed to pass a WTO deal that included open borders for goods, services, finance and labor, the intra-country regional results suggest that, optimistically in 100 year’s time, we should still expect the poorest countries to have far less than one tenth the income of the richest –considerably better than now, of course, but less –and less rapid– than one might hope, surely.

Again, thanks to Tyler for the pointer.