THERE are lots of critics of “Capital in the Twenty-First Century”, Thomas Piketty’s study of increasing inequality in the rich world. Few have been as effective, however, as Matthew Rognlie, a 26-year-old graduate student at the Massachusetts Institute of Technology, who first took Mr Piketty to task in a 459-word blog post last year. On March 20th he presented a paper that expanded on the flaws he sees in Mr Piketty’s book.

Mr Piketty argues that over the long run the rate of return on wealth exceeds economic growth. Over time, this relationship increases inequality as the share of national income going to those who own capital (the rich) rises, while the portion going to labour (everyone else) falls. He also argues that the return on capital in recent history has been remarkably stable, even as economic growth has fallen, and that this trend will continue in the future.

Mr Rognlie has three main criticisms of all this. Several commentators have pointed out that the rate of return from capital should decline in the long run, rather than remaining high as Mr Piketty maintains, owing to the law of diminishing returns. Mr Rognlie expands on this, arguing that Mr Piketty has an inflated idea of the current return. Modern forms of capital, such as software, depreciate faster in value than equipment did in the past: a giant metal press might have a working life of decades whereas a new piece of database-management software will be obsolete in a few years at most. This means that returns from wealth may not necessarily be growing in net terms, since a rising share of the gains that flow to the owners of capital must be reinvested.

Second, Mr Rognlie finds that higher returns to wealth have not been distributed equally across all investments. The return on assets other than housing has been remarkably stable since 1970. In fact, surging house prices are almost entirely responsible for growing returns on capital.

Third, the idea that workers’ share of wealth can continue to decline rests on the assumption that it is easy to substitute capital (ie, robots) for workers. But if lots of the capital in question is tied up in houses, then this switch would be far harder than Mr Piketty suggests.

Mr Rognlie has critics of his own. He appears to underestimate the role that changing technology plays in widening inequality (by making it simpler to substitute capital for labour, for instance, or by concentrating jobs in expensive cities). But his observation that it is homeowners in particular, rather than rentiers generally, who are grabbing a larger share of the pie is important. For one thing, homeowners are a much bigger and more lovable group than hedge-fund managers. Moreover, if housing is the biggest source of rising inequality, then the wealth tax Mr Piketty advocates is the wrong response. Policymakers should instead try to reduce the planning restrictions which, by inhibiting new construction, allow homeowners to earn such big returns on their assets.

Just how inconvenient Mr Rognlie’s argument is for Mr Piketty’s overarching narrative is a matter of perspective. The celebrated French economist certainly did not make housing wealth the central theme of his bestselling book. But a story in which a privileged elite uses its political clout to create economic rents for the few (albeit through the planning system) fits Mr Piketty’s argument to a tee.