Does r - g cause inequality?

In his bestseller Capital in the Twenty-First Century, Thomas Piketty argues that a key driving force behind income and wealth inequality is r - g, the difference between the rate of return on capital and the growth rate of the economy. Because the rich hold a disproportionate share of the capital, when r is greater than g, income should accrue to the rich at a faster rate than it accrues to the middle-class and the poor, leading to ever greater concentration of income and wealth. 

Yet in a recent working paper, Daron Acemoglu and James Robinson document essentially zero empirical support for the claim that r - g is an important cause of income inequality. They examine the effect of r - g on the top 1% income share using data on a panel of up to 28 countries from 1870-2012. Across a variety of different specifications, encompassing three alternative definitions of r - g (details of which can be found on pages 13-14), they generally observe non-significant estimates of r - g; among those that are significant, the majority are negative rather than positive. Their main table is shown below. 

Acemoglu and Robinson do not deny that r - g could in principle give rise to greater inequality; they simply argue that it pales in comparison to various institutional factors, such as government corruption, labour-market regulations, and welfare arrangements. In their own words:

Though this evidence is tentative and we are not pretending to estimate any sort of causal relationship between r - g and the top 1% share, it is quite striking that such basic conditional correlations provide no support for the central thesis of Capital. This is not to say that higher r is not a force towards greater inequality in society--it very probably is. It is just that there are many other forces promoting inequality and our regressions suggest that, at least in a correlational sense, these are quantitatively more important than r - g.