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Abstract
One often heard counter to the concern on rising income and wealth inequality is that it is
wrong to focus on inequality of outcomes in a “snapshot.” Intergenerational mobility and “equality
of opportunity”, so the argument goes, is what matters for normative evaluation. In response to this
counter, we ask what pattern of intergenerational mobility leads to lower inequality not between
individuals but between the dynasties to which they belong? And how does this pattern in turn
relate to commonly held views on what constitutes equality of opportunity? We revive and revisit
here our earlier contributions which were in the form of working papers (Kanbur and Stiglitz (1982,
1986) in order to engage with the current debate. Focusing on bistochastic transition matrices in
order to hold constant the steady state snapshot income distribution, we develop an explicit partial
ordering which ranks matrices on the criterion of inequality between infinitely lived dynasties. A
general interpretation of our result is that when comparing two transition matrices, if one matrix is
“further away” from the identity matrix then it will lead to lower dynastic inequality. More
specifically, the result presents a computational procedure to check if one matrix dominates another
on dynastic inequality. We can also assess “equality of opportunity”, defined as identical prospects
irrespective of starting position. We find that this is not necessarily the mobility pattern which
minimizes dynastic inequality.