The Wrong Side of Cobb-Douglas: Matt Rognlie’s Smackdown of Thomas Piketty Gains Traction

I have been impressed with Matt Rognlie ever since our discussion in “Sticky Prices vs. Sticky Wages: A Debate Between Miles Kimball and Matthew Rognlie.” Matt also had a guest post here: “Matt Rognlie on Misdiagnosis of Difficulties and the Fear of Looking Foolish as Barriers to Learning.” 

I posted a link to Matt’s paper “A note on Piketty and diminishing returns to capital” when I say Tyler Cowen’s post on it. Now I am glad to see it making its way into the consciousness of journalists with “Wealth inequalityNIMBYs in the twenty-first century” in The Economist, and Greg Ferenstein’s piece “A 26-year-old MIT graduate is turning heads over his theory that income inequality is actually about housing (in 1 graph).”

The key graph is shown above: there is no upward trend in capital’s share once housing rents are accounted for. The production of housing services is, of course, mostly provided by the house itself, which is counted as capital. So housing services have a capital’s share close to 1. So if the weight of housing goes up, it will drive up the overall share of capital, including the production of housing services. But there is no reason from the graph above to believe that the production function for goods and services other than housing services is on the side of Cobb-Douglas that Thomas Piketty needs–a direction in which a much higher amount of capital would be associated with only a slightly lower rate of return. (See my post “The Shape of Production: Charles Cobb’s and Paul Douglas’s Boon to Economics” for my effort at an intuitive treatment of the logic for why Cobb-Douglas leads to a constant share for capital and for labor.) Matt cites a large body of micro-empirical work suggesting that the elasticity of capital-labor substitution is quite a bit below the Cobb-Douglas level of 1, so that things are on the wrong side of Cobb-Douglas for what Thomas Piketty wants. There are some subtle arguments involving other adjustments that mimic a higher elasticity of capital-labor substitution that could make things look closer to Cobb-Douglas in the aggregate. But it still looks as if in the aggregate, when the real interest rate goes down, it goes down fast enough that the overall gross rental rate of capital goes down proportionally faster than the amount of capital relative to output goes up.   

The title of Greg Ferenstein’s piece is a bit misleading. Capital’s share is an important issue and capital overall is certainly central to Thomas Piketty’s story, but as for inequality, as Matt says in his conclusion, “Inequality of labor income, for instance, is a very different issue–one that remains valid and important.”    

It is good news if a lot of wealth and inequality is about housing, because we have known for a long time how to deal with wealth inequality from at least the land component of the value of housing: Henry George’s idea of a tax on land values that Noah Smith talks about, for example, in his Quartz column “This 100-year-old idea could end San Francisco’s class war.” Land taxes are typically much less distortionary than taxes on any other form of capital. So to the extent that inequality is about high land values, it doesn’t run into the issues I talked about in my post “Is Taxing Capital OK?” 

It does make sense, however, to have provisions in land tax policies to give to developers some of the increase in the value of land engendered by their activities when others want to be near some new development–just as we would want to make sure that developers pay some of the costs of the reductions in the quality of life nearby when others don’t want to be near some new development. The post “Charles Lane on Thomas Piketty and Henry George” discusses some of these issues. “Henry George and the Carbon Tax: A Quick Response to Noah Smith” discusses how some of the logic of a land tax extends to natural resources.

Land-price-based inequality can also be addressed by loosening restrictions on building. C.R. in the Economist writes in the article about Matt: “Policy-makers should deal with the planning regulations and NIMBYism that inhibit housebuilding and which allow homeowners to capture super-normal returns on their investments.” Let me explore the logic behind this. Land prices are pushed up when regulations require that land be used in a high ratio to construction in creating housing. That is zoning and other regulations that limit housing density enrich landowners. 

Above, I wrote that developers should have to pay some of the costs of reductions in the quality of life nearby when higher density is unpleasant to live nearby–say by blocking out the sun. In an earlier version of this post, I actually made the serious mistake of saying they should pay for the reduction in “land values” from development nearby. But that is wrong by a cost-benefit test. Suppose a particular housing development is neutral for the quality of life nearby. Then it would still reduce the values of land nearby by providing more housing competition. This is not a social loss but rather a shift in wealth from landowners renters and future buyers of land, which reduces inequality. So a key conceptual issue for appropriate land policy is to not think of everything that reduces neighboring land values as a bad thing, but to distinguish when (and how much) it brings down land prices by reducing the quality of life nearby from when (and how much) it brings down land prices by providing additional housing competition.