It is with some trepidation that I offer my review of Thomas Piketty’s Capital in the 21st Century, as so much has been written, almost all of it verging on the adulatory. Of course it’s an important book – who could disagree with that when almost everybody in my world is talking about it, and it has cemented the question of inequality of income and wealth on the economic policy agenda? The book has obviously plugged into the zeitgeist. It has some flaws too.

Piketty’s construction of a long-run multi-country World Top Incomes Database for income and wealth, along with Emmanuel Saez and Anthony Atkinson,’ is a magnificent achievement. As the book notes several times, the data – constructed from a range of sources including tax records – are likely to understate the very highest fortunes and incomes because of the failure to declare everything. The assembly of these statistics has helped put inequality at the centre of economic debate.

Capital in the 21st Century concentrates on wealth and on the share of capital’s income in total national income. ‘Capital’ is defined as marketable assets, at their market price, including land, houses, shares and other financial instruments (but not for example bridges or factories). James Galbraith’s review of the book was critical of the definition. I think Galbraith is right to pick away at the data used and what the definitions actually mean.

Setting this aside, Piketty shows that the income share of (marketed financial) capital (at market values) declined substantially in the second half of the 20th century but is now climbing again. His argument is that this increase is a near-inexorable trend. The mid-20th century decline was essentially the result of Depression and war, or in other words, the massive destruction of assets and social dislocation; and the capital share stayed low for some decades because economic growth was unusually high, which – he argues – will no longer be the case. Specifically, population growth has slowed or turned negative, and Piketty is clearly gloomy about the prospect of productivity growth.

It’s clear that many readers have taken this argument as a given without concerning themselves about how it adds up. It is based on two equations (the only two in the book), which are asserted rather than given a clear rationale. I couldn’t work out the reasoning until I found Piketty’s lecture notes. So this is my explanation of the lecture notes.

One equation says that the share of capital in national income (α) is defined as the rate of return on capital (r) times the ratio of the capital stock to income (β). This is an accounting identity – it is how the concepts are defined and the figures calculated. If the capital stock is six times a year’s national income, and the rate of return on capital is 5%, the capital share is 30%. Historically, the rate of return on capital has been in the range 3-6%, which for that size of capital stock implies a capital share of 18% to 36% a year of national income, roughly one fifth to one third. Again, in the historical figures, the capital income ratio has typically been 5 or 6.

The second equation, which drives his argument about the upward trend in capital’s share, is a ‘steady state’ condition: when the economy settles down in a stable way in the very long run, at its long-term potential growth rate, the ratio of capital stock to income equals the savings rate (s) divided by the growth rate (g) – in other words, in the unchanging steady state, the ratio of the annual changes in capital growth (saving) and in income growth is the same as the ratio of the capital stock to the level of income.

This is not made all that clear in the book, but putting the two together, the capital share will tend to rise when the rate of return on capital is greater than the growth rate, assuming the saving rate does not decline to offset the impact of r > g. Piketty notes that in the long term data set, this inequality happens to have held: “The inequality r > g is a contingent historical proposition, which is true in some periods and political contexts and not in others.” The exception was the latter part of the 20th century.

This simple algebra based on an accounting identity and a balanced growth rule are the basis of the book’s argument – which has been pounced on by commentators – of an almost inexorable upward trend in the capital share. I am sceptical about the economy ever reaching the balanced growth state, although perhaps this is a useful tool for thinking about direction of travel, and I’m also doubtful that the saving rate would not adjust should the capital share in national grow ever-bigger. I also wish Piketty had spent more time discussing the rate of return on capital – both how it is constructed in the data set and what determines it – as the book treats it as a given at 4-5%. As Barry Eichengreen pointed out in a recent Project Syndicate article, there are some puzzles in saving and interest rate data, and real interest rates have been declining for 30 years. They are only one element of the rate of return series Piketty considers, but at 2-3%, this real interest rate is not too far above the potential growth rate of the major OECD economies. This takes us back to James Galbraith’s point about the definitions: is marketable capital consisting mainly of financial assets the right definition to plug into a balanced growth model?

I would like to have had more practical explanation of the data used in the book in general, as some of the charts are surprising. For instance, the charts suggest the housing stock in France is a bigger share of national income, and has grown faster, than in the UK. (As an aside, the charts are terrible – very hard to decipher, a decade on the x-axis given the same space as a half century or 60 years, multiple lines of equal weight with clashing symbols, much chart junk, Australia classed as ‘Anglo-Saxon’ when it looks like Germany in the data – I hope they all get redrawn for future editions.)

Of course I’m nit-picking by complaining about the impression of an inexorable trend towards an ever-greater capital share created by Piketty’s reliance on a growth model, because there is a deeper truth – as he puts it: “The inequality r > g in one sense implies that the past tends to devour the future: wealth originating in the past automatically grows more rapidly, even without labour, than wealth stemming from work, which can be saved.” In order for an economy to grow at all, the future must win the struggle against the past. But of course there have been several episodes when that has been the case – not just the aftermath of World War 2, highlighted in the book, but also much of the Victorian era, and the early Industrail Revolution (even though the charts here show r well in excess of g during those years too).

Still, the sense of inevitability or otherwise does matter. Piketty’s policy proposal is a global wealth tax. He’s acknowledged how unrealistic this is, but says it’s important to change the intellectual climate. True, but how about also debating the rigged markets in finance and the corporate legal framework that have contributed so significantly to the growth in very high incomes, which are quickly turned into new wealth? What about income and inheritance taxes? And rather than treating savings, the return on capital and the growth rate as givens, isn’t it worth thinking about what determines them, and what actually determines causality in the book’s simple algebra.

I’m glad Capital in the 21st Century has succeeded in drawing such attention to inequality of wealth as well as incomes, and to our new era of patrimonial capitalism. (Another sobering illustration of this is Greg Clark’s recent book, The Son Also Rises.) It’s just a bit of a shame it does so in such a deterministic – and therefore disempowering – way.

Nevertheless, pretty much every review I’ve read has raved about the book! Here are Paul Krugman, Branko Milanovic, John Cassidy, The Economist. No doubt there will be many more positive reviews to come.