SINCE the publication of "Capital in the Twenty-First Century", Thomas Piketty has won many plaudits for his work on inequality. The book has so far sold more than 1.5m copies. Its arguments have been praised by Nobel-prize winners and politicians alike. Last year it won the Financial Times's business book of the year award, despite the newspaper's attempts to poke holes in the book's data and arguments. On March 25th Prospect magazine put Mr Piketty atop its World Thinkers list for 2015 (alongside Yanis Varoufakis, Greece's leather-jacket wearing finance minister, Naomi Klein and Russell Brand, it should be noted). But a new challenge to Mr Piketty's book has just appeared, and from an unexpected direction. On March 20th Matthew Rognlie (pictured), a 26-year-old graduate student at the Massachusetts Institute of Technology, presented a new paper at the Brookings Papers on Economic Activity. Although the paper began its life as a 459-word online blog post comment, several reputable economists regard it as the most serious and substantive critique that Mr Piketty's work has yet faced.

Thomas Piketty's In his book, Mr Piketty argues that over the long run the rate on return of wealth exceeds economic growth: a dynamic summed up in the equation r>g. 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 mounts three main criticisms of these arguments. First, he argues that the rate of return from capital probably declines over the long run, rather than remaining high as Mr Piketty suggests, due to the law of diminishing marginal returns. 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 while a new piece of database-management software will be obsolete in a few years at most. This means that although gross returns from wealth may well be rising, they may not necessarily be growing in net terms, since a large share of the gains that flow to owners of capital must be reinvested.

Second, Mr Rognlie’s research suggests that Mr Piketty has overestimated how high the returns on wealth are likely to be in the future. These should also decline over time, he reckons, unless it is very easy for the economy to substitute capital (like robots) for workers. Yet the historical evidence suggests that this is far harder than he suggests.