Mankiw has an interesting post in his blog where he says that: “In light of the heritability of talent, it would be shocking if we did not find some significant heritability of income”. This is logical, but it ignores other important determinants of the nature vs. nurture debate, most importantly the opposite effects of nepotism and indolence. While rich kids benefit from nepotism they are also victims of laziness. The better policy to eliminate the bias introduced by these two factors is to increase the share of market capitalism in the economy. In end, the rise of government and managerial capitalism benefits more the incumbents than the newcomers.
His other point that “moving up and down a short ladder is a lot easier than moving up and down a tall one” is a fallacy. Economic mobility must be measured between all steps of the ladder, not just between the first and last steps (that is why economists prefer the Atkinson measure of inequality). We (I) may wish to claim that a more egalitarian society creates greater economic mobility. However, this only applies in relation to share of capital of the super-rich. If for tax reasons, like in the USA, it rises disproportionally they will obviously capture a top-heavy share of investment opportunities.
Arguments based on the observation that countries with the greatest income inequality (USA and UK) are the ones with lesser intergenerational mobility are not solid. For instance Canada and Sweden, two of the countries with greater mobility (see data here), have substantially different levels of income inequality (find data here).