A capital offence

Reading Thomas Piketty’s Capital in the Twenty-First Century from front to back was a mistake.

Better to read the last hundred pages first, with their recommendations for the confiscation of wealth and marginal income tax rates nearing 100 per cent, and then read the preceding 470 pages to decide whether the flimsy evidence, conjecture and questionable theories the author offers justify such draconian measures.

Mr Piketty’s thesis rests on a simple insight. If the rate of return r is higher than the growth rate of wages of the economy as a whole g, the incomes of those who own more capital will grow faster than the incomes of those who own less. Indeed, his oft-cited inequality r>g has many virtues. Like E=mc2 it is short enough to fit on a t-shirt, yet seems oddly profound. It is even true. The consequent theory that, absent revolution or government intervention, the rich inevitably keep pulling ever further ahead sounds plausible too. It is, however, on closer inspection, complete nonsense.

Karl

To see why, suppose Karl is a worker who earns £1 a year. His wage grows at a rate of g=0.01, or 1 per cent a year.

By contrast, his friend Friedrich is heir to a fortune worth £100 that earns a return of r=0.04, or 4 per cent a year. Assume as well that both save at a rate of s=0.05, or 5 per cent of their income each year.

In year one, nasty rentier Friedrich enjoys an income four times larger than Karl without having to work. How much income does each receive in year two? Karl gets £1.01 in wages, and collects an additional 2/10th of one penny in interest on his savings. Friedrich’s capital has grown to £100.2 and that pays him the same income of £4 plus an additional 8/10ths of one penny. Carry this forward and it will become apparent that Karl’s income grows faster than Friedrich’s, and eventually overtakes it. It will take 155 years, but the direction of travel is what matters here.

Of course it is still possible for Mr Piketty’s mechanism of inequality to work, if Karl chooses not to save. If people differ in their savings behaviour, perhaps because they discount future consumption with different rates of time preference, the most thrifty or the most patient individual will eventually accumulate everything. Robert A. Becker described this possibility in a paper in 1980, but it is an idea Mr Piketty only introduces rather sheepishly on page 359 (and without attribution). It is easy to understand his reticence – acknowledging this channel for the propagation of inequality sounds too much like blaming the poor for their circumstances. Yet as is often the case, concern for the downtrodden coexists happily with snobbery aimed at those in the middle. Once, only the children of the very rich could expect to inherit assets from predecessors. But the average size of estates has fallen as inheritance has become more commonplace. This democratisation of family inheritance might be welcomed by someone so inimical to inequality, but no, all the machinery of the state must be deployed to prevent the rise of a class of ‘petits rentiers’.