OVER the last few days a couple of interesting critiques of Thomas Piketty's "Capital in the Twenty-First Century" have been published, by Matt Rognlie and Justin Wolfers. Both touch on the importance of housing wealth to Mr Piketty's story, and suggest that the role housing plays in the data weakens the book's argument. I expressed some disagreement with this view on Twitter, and Mr Rognlie wrote me to explain his view in a bit more detail. I've responded to him, and I thought I would publish the response here.

First, I certainly don't think that criticism of Mr Piketty's book, on the issue of housing or anything else, is unreasonable. On the contrary, the discussion the book has attracted has for the most part been really interesting and illuminating. And challenging, which is good. What occasionally strikes me as odd is the tendency for criticisms of the book to reach inexorably for the conclusion that "Piketty is wrong", whether or not that is the most obvious upshot of the particular critique. He surely is about some things. On others he isn't, on others we are unable to say for now, and on others he is useful whether or not the details turn out to be right.

In my view, for example, one of the main contributions of the book is a mental framework, scrutable to the layman, for assessing how particular economic changes might influence the distribution of wealth. Economists may feel that they already had perfectly good frameworks for doing that. I don't know that they did; plenty of academic economists seem to have found Mr Piketty's framework useful. At any rate, those that already had models they liked made very little effort to make them accessible to the public.

Part of the attraction of Mr Piketty's framework is that it leaves one free to make up one's own mind about what is likely to happen. The structure he provides allows us to work through the distributional effect of a falling growth rate or a rising savings rate. Maybe he is incorrect to think that g can decline over the long run without triggering a one-for-one decline in r. If so, the framework he has provided allows us to think through the implications of that outcome. And others as well: worlds in which technology makes it much easier to substitute capital for labour, for instance, which is one in which I've developed a particular interest.

On to housing. The question I have raised is whether the importance of housing to Mr Piketty's story is a strength or, as some critics suggest, a weakness, possibly fatal. The housing critique, if I've understood it correctly, is as follows. Quite a lot of the recent rise in the ratio of national capital to national income can be attributed to growth in housing wealth; in some economies, like France, housing is basically the whole story. What's more, quite a lot of the rise in housing wealth is down to growth in housing values, and quite a lot of the growth in housing values can be attributed to restrictions on housing supply growth. What we're left with, then, is a mechanism for rising wealth inequality that does not seem to have much to do with the rate of return on capital r holding steady as the economic growth rate g falls.

I have two broad thoughts about this critique. One is that it misses the forest for the trees. That is, a story in which Palo Alto millionaires use their political influence to protect the value of a major capital investment, with generally negative distributional consequences, is not exactly antithetical to the general argument made in "Capital". Now as Mr Rognlie notes, this dynamic certainly points us toward a much broader set of policy recommendations than Mr Piketty gives us. A global wealth tax might not be nearly as effective as reforms that boost housing construction, for instance. But the rent-seeking rich capturing a larger share of national income seems pretty compatible to me with Mr Piketty's overall argument. Mr Piketty pretty closely aligns himself with David Ricardo's land-scarcity analysis and says it applies in the case of urban housing, so we certainly can't say he is unaware of what is happening.

The second is that the economics of the housing story are more complicated than the critique lets on.

I have written quite a lot about housing supply restrictions and the macroeconomy, and here is the general argument that I make. Over the last few decades technological changes have greatly increased the return to locating in large cities filled with skilled people. Being in such places makes workers more productive and raises the income they are able to earn. But skilled cities have not allowed housing supply to expand to meet rising demand. Housing has therefore been rationed by price, pushing less productive workers toward cities where housing supply growth is higher and housing cost growth is lower. As a result, fewer people live in the most productive places, and quite a lot of the gain from employment in productive places is captured by landowners earning rents thanks to artificial housing scarcity. This may mean lower overall productivity, more income inequality, and more income flowing to capital rather than labour.

How do I reconcile that story with the mechanics in "Capital"? I think the place to begin is to note that this is not just a supply-side question; there are lots of places in the world where it is difficult to build but where prices remain low because no one wants to live there. So we need to recognise that part of what is going on is a rising contribution to production from scarce land in big, rich metropolitan areas. The contribution is entirely due to the crowds of people sitting on top of the land (rather than any natural productivity) but that doesn't matter. The scarcity of productive land is a natural, inevitable thing, because if people are going to crowd together they can only do it in a few places at once (for now, at least, though technology may eventually solve that problem).

What would happen if we got rid of all restrictions on the construction of new housing? We should see lots of new investment in places where the gap between housing costs and construction costs is largest: in central London, New York, San Francisco, and so on. Housing cost growth in those cities would slow relative to income growth, real wage growth would soar, and many more people would move in. Over time, prices would converge toward construction costs. More people would be working at higher wages and productivity levels, which suggests that inequality in labour income should fall and the labour share should rise.

But there are other things that need to be considered. A much larger share of a nation's housing stock would be located in more expensive cities (the cost to build the marginal unit in New York is substantially higher than the cost to build the marginal unit in Houston), so it's possible the total value of housing wealth might not fall that much. Housing unit values in expensive cities might drop but would land values? I suspect the total value of land in San Francisco would rise, possibly by quite a lot—and land ownership is more concentrated than housing ownership. Housing ownership might also become more concentrated, given greater property-management efficiencies in dense housing. Managing congestion would require huge capital investment, and workers might pay some of their real wage gains from cheaper housing to owners of infrastructure capital.

The point is that artificial housing scarcity greatly exacerbates the problem, but it is not the origin of the problem and eliminating it does not eliminate the problem. The problem is the return of land as a critical input to production.

Taking a step back, I think a fair read of the book actually identifies four mechanisms through which capital is increasing in importance. The first is the continued rebound in wealth from the interwar euthanasia of the rentiers and postwar suppression of inequality. The second is increased substitutability of capital for labour, which is generating employment polarisation and contributing to a falling labour share. The third is a return on invested capital that is generally higher than income growth—with returns tending to rise as one goes up the wealth distribution—that pushes an economy toward greater concentration of wealth. And the fourth is the return of land. These trends are unfolding in tandem and often reinforce each other. Technological change raises demand for expensive cities. And real estate investment in expensive cities requires an ever larger initial pool of capital: among the reasons the rich may wring better returns from their investments. Tight housing supply may have supercharged property-price rises, leading land's contribution to the puzzle to dominate. But that doesn't mean that the stories Mr Piketty tells about the component trends aren't persuasive.

So there you go. As I have mentioned on Twitter, I think economists want to read the book, and particularly its analytical framework, much more narrowly than is appropriate. They want the mechanics to be pinned down by a particular set of equations that can be understood to contain the entirety of the book's argument. But the book is a sweeping narrative about the relationship between wealth and labour over very long periods of time! There is a reason he didn't just scratch out a few equations and submit it to a journal for publication. I understand some economists may interpret that choice as an attempt to dodge academia's demands for a particular level of rigor. I've always seen it as simply a way to tell a big story effectively, using a number of different approaches.