Capital is Back — But Not As We Know It: Comment on Piketty
Writing about web page http://www2.warwick.ac.uk/fac/arts/history/research/seminars_readinggroups/historyseminar/
Recently Warwick’s History Department held a roundtable on Thomas Piketty’s important and bestselling blockbuster, Capital in the Twenty-first Century (Piketty 2014). I was on the panel, which was ably organized and chaired by Maxine Berg, whom I thank for the invitation. Here I’ll summarize my remarks, which have benefited from listening to the other panelists and the discussion. For better or worse my words seem to have been modified by the passage of time; I sense that their tone has sharpened since that evening.
Piketty’s book has been reviewed thousands of times; we have already seen reviews of the reviews. I have little to say that can be original. I prefer not to comment on Piketty’s conclusions, because most readers seem to have made up their minds on those before reading the book. Instead, I’ll focus on the early chapters, where Piketty sets out his contention that “capital is back”; nearly everything else in the book follows from that foundational claim.
Here’s the short version of my assessment: The problem? Hugely topical. I won’t spend any time on that. The model?Unobjectionable in principle, flaky in use. I’ll explain briefly. The historical data? A wonderful contribution, yet they do not show what many suppose, and that would seem to include Piketty himself. My conclusion? Capital is back -- but not as corporate capital. If capital is back, it is not, apparently, because of financial deregulation or capital account liberalization. And, if capital is back, there are clear candidates for countervailing forces that will tend to restrict its further rise in the twenty-first century.
Now for the detail, some of it unavoidably technical. Let’s start with the model. Piketty writes (2014, p. 32):
The discipline of economics has yet to get over its childish passion for mathematics and for purely theoretical and highly ideological speculation …
(So of course we don’t expect to find anything like that in the pages that follow.) What we do find is this:
- A first fundamental law (p. 52): the profit share in income rises with the profit rate on capital and with the capital/income ratio.
α = rβ
- A second fundamental law (p. 166): the capital/income ratio rises with the saving rate out of income (which governs the rate at which income adds to capital), and it also rises as the income growth rate falls.
β → s/g
- A fundamental force (p. 35): profit rate on capital tends to exceed income growth rate.
r > g
The generality of the model is notable. In fact there is almost nothing in it, so far, that could be considered novel. It is also simple to an extreme. Of course, all models are just simplified representations of reality. Is it oversimplified? The question calls to mind the maxim of Box and Draper (1987, p. 74):
All models are wrong; the practical question is how wrong do they have to be to not be useful.
Our question for Piketty, correctly formulated, is not whether his model is “wrong,” as it surely is, but whether his model is “not-wrong” enough to be useful. Considered in these terms, the maths is not the problem. The problem is in the application of the maths to a necessarily complex reality.
How does this simple model lend support to the claim that capital is back? Piketty puts his two laws and the fundamental force to work in the following way.
- Start with the fundamental force: r > g. Here is a gap, made up by the excess of the rate of return on capital over the growth rate of the economy. According to Piketty the gap has widened because g has fallen (pp. 99-102), but r is fairly stable and we do not expect it to fall (pp. 220-223).
- Now the second law comes into play: β → s/g. Piketty appears to argue that the saving rate is stable, or at least is not falling (pp. 173-178), but the growth rate has fallen, so β, the ratio of capital to income, must be rising towards a new, higher steady state.
- Finally the first law swings into action: α = rβ. Given that the capital/income ratio is rising and the rate of return on capital is not falling, the profit share in income must be rising too, with all that might imply for social inequality.
- (The maths is neat too: the three expressions collapse easily into α → s × r/g, meaning that the steady-state profit share equals the saving rate times the rate of return over the growth rate. So far, the logic is unassailable.)
The question that comes naturally to mind is whether Piketty might have neglected some countervailing force that would eventually nullify or attenuate the tendency that he has identified. (In thinking about this I’ve been influenced by the insights of many, but I ought to mention especially Krusell and Smith 2014).
Picketty concludes that capital is back because, he maintains, the growth rate of the economy has fallen, the rate of return on capital is relatively stable, and so is the saving rate out of income. How robust is this chain? Consider each link in turn.
- First, Piketty asserts that the long-term growth rate of the economy has fallen: Maybe, but also maybe not. Secular stagnation is possible but the concept is also speculative and contentious (for discussion see Teulings and Baldwin 2014). It is even a little unhistorical – the last time secular stagnation was predicted was at the end of the 1930s, since when global output has multiplied by at least 10 times (Maddison 2010). If the prediction of secular stagnation turns out wrong, then Piketty’s prediction is largely sunk by a countervailing factor: the return to faster growth will hold down the capital/income ratio and the profit share in income.
- Second, Piketty asserts that the rate of return on capital will not decline as capital is accumulated. This outcome is possible, of course, in the general sense that we really don’t know about the future of technology, but this one too is speculative and contentious. A long term conjunction of low growth, high capital accumulation, and high profits is (in my opinion) highly improbable. If we are doomed to secular stagnation, and capital accumulation continues unchecked, the return on new investments will surely fall relative to the past. If the return on capital declines significantly as capital is accumulated faster than income, then here is a factor that would automatically hold down the profit share in income. Thus, a fall in the rate of return cannot be ruled out and would be another countervailing factor.
- Third, Piketty appears to rely on maintenance of the saving rate out of income. Others have noted that Piketty should have distinguished between gross and net saving. Here net saving = gross saving – depreciation, and depreciation means the annual deterioration of the capital stock through wear and tear and obsolescence. Piketty gets the definition, of course (p. 178), but on my reading he misapplies it. The point is that depreciation is a function of the capital stock: the more capital we hold, the greater must be our provision for its depreciation. Depreciation is not a function of income. If the capital/income ratio rises, then the depreciation/income ratio must rise too. Piketty doesn’t appear to get this (p. 178 again), because he presents depreciation as a proportion of income, not of capital. If the capital/income ratio rises, the depreciation/income ratio must rise. If the depreciation/income ratio rises, and if gross saving is stable, then net saving out of income must fall. If the result of capital accumulation is a fall in the net saving rate, then this must slow net capital accumulation, making a third countervailing factor.
The three countervailing factors are reasons why I concluded that Piketty's basic insight is flaky, in the sense that it might be a good description of what is going on but equally it might not. Still, this does not settle the bigger question: do its predictions fit the known facts? If so, it must surely still merit serious consideration; perhaps the countervailing factors are simply unimportant?
The test here is: what’s been happening to the capital/income ratio? And Piketty’s data do show that the capital/income ratio is rising, don't they? Well, let’s check the data (and here I need to acknowledge a debt to Bonnet, Bono, Chapelle, and Wasmer 2014).
Piketty has five countries in his sample: Britain, France, Germany, Canada, and the US. These data show, as is now well known, a U-shaped pattern in the ratio of capital to income over the twentieth century: high at the beginning, slumping in mid-century, and rising again: hence, “capital is back.”
Piketty’s explanation, by the way, is that in the era of the two world wars the asset markets of these five countries underwent a common pattern of regulation that depressed relative asset prices, and neoliberal deregulation has now released them.
But there are strange things in the data. They are not immediately apparent from Piketty’s stacked-area charts, mostly because of the vertical ordering of the series. (To a smaller extent they are affected because Piketty does not understand how Excel processes the data for stacked charts when one of the series has negative values, as is the case for net foreign capital order in several countries, although only Canada is seriously affected.)
- First strange thing: If we accept that capital is back, it is not all elements of capital that are back, and it is specifically not corporate capital. It is residential capital. Residential capital is certainly part of the capital stock, but it is probably not what most people think of when they think about the return of (or on) “capital.” More likely they think about Goldman Sachs or Amazon. But capital is not back because of Goldman Sachs or Amazon.
A simple calculation makes the point. For each country, take the increase in the capital/income ratio from 1950 to 2010. Then calculate how much of that increase is due to rising values of residential capital. The result is the proportion of the increase in capital/income from 1950 to 2010 that is explained by the increase in housing wealth:
- United Kingdom 72%
- France 103%
- Germany 102%
- Canada 63%
- United States 72%
The figures show that in every country housing wealth accounts for at least three fifths of the increase in the capital/income ratio since the middle of the twentieth century, and in two countries (France and Germany) it accounts for all of the increase in the ratio.
- Second strange thing. If housing wealth is so important to the claim that “capital is back,” what can we say about the return on housing wealth? Go back to the basic model to recall that the stability of the return on capital is crucial to Piketty’s prediction that the capital share of income is rising. Is the return on housing capital stable? No, it’s not. Bonnet et al. (2014) show clearly that in four out of five countries the return on housing wealth, measured by the ratio of housing rents to housing prices, has fallen over forty years from 1970 to 2010: in the US by nearly 20 percent, and in Britain, France, and Canada by around 40 percent. Only in Germany has it risen.
- Third strange thing: Asset prices are formed in markets. Sometimes, these markets are regulated, and this affects prices. There are variations across markets and across countries in how regulated these markets are, and I am not expert in measuring this variation. But I venture to claim that in every wealthy country the housing market is one of the most regulated asset markets. Indeed bad regulation of the US housing market was arguably a prime cause of the asset price crash and financial crisis of 2008 (Rajan 2010). And if housing wealth is increasingly a factor in inequality in the UK, policy interventions that have pumped up the demand and restricted the supply must shoulder much of the blame.
To conclude: Capital is back -- but not as corporate capital. If capital is back, it is not, apparently, because of financial deregulation or capital account liberalization. And, if capital is back, there are clear candidates for countervailing forces that will tend to restrict its further rise in the twenty-first century.
if I had been Piketty’s editor I would have been excited and honoured to publish his book. But I might not have allowed him to call it Capital in the Twenty-first Century. More accurately, it would have been called Housing in the Twenty-first Century. But then there would be a marketing problem, because Marx never wrote three volumes on Die Behausung, and Piketty's publisher would have lost a lot of sales. Well, that’s business.
- Bonnet, Odran, Pierre-Henri Bono, Guillaume Chapelle, and Etienne Wasmer. 2014. Does Housing Capital Contribute to Inequality? A Comment on Thomas Piketty’s Capital in the 21st Century. Working Paper. Sciences-Po.
- Box, George E. P., and Draper, Norman R. 1987. Empirical Model Building and Response Surfaces. New York: Wiley.
- Krusell, Per, and Tony Smith. 2014. Is Piketty's Second Law of Capitalism Fundamental? Working Paper. Stockholm and Yale.
- Maddison, Angus. 2010. Statistics on World Population, GDP and Per Capita GDP, 1-2008AD. Available at http://www.ggdc.net/maddison/oriindex.htm.
- Piketty, Thomas. 2014. Capital in the Twenty-first Century. Cambridge, Mass.: Belknap.
- Rajan, Raghuram. 2010. Fault Lines: How Hidden Fractures Still Threaten the World Economy. Princeton: Princeton University Press.
- Teulings, Coen, and Richard Baldwin, eds. 2014. Secular Stagnation: Facts, Causes, and Cures (VOXeu.org and CEPR)