Some of this discussion seems to work from the assumption that the rate of return on government debt and the rate of return on capital are the same thing. For example, Bernanke shows a chart of the 5-year TIPS yield and then, in addressing what this might have to do with secular stagnation, makes this statement:
First, as I pointed out as a participant on the IMF panel at which Larry first raised the secular stagnation argument, at real interest rates persistently as low as minus 2 percent it’s hard to imagine that there would be a permanent dearth of profitable investment projects. As Larry’s uncle Paul Samuelson taught me in graduate school at MIT, if the real interest rate were expected to be negative indefinitely, almost any investment is profitable. For example, at a negative (or even zero) interest rate, it would pay to level the Rocky Mountains to save even the small amount of fuel expended by trains and cars that currently must climb steep grades. It’s therefore questionable that the economy’s equilibrium real rate can really be negative for an extended period.So, Bernanke appears to think that low real Treasury yields are associated with low rates of return on capital. As well, Summers's arguments concerning secular stagnation seem to rely on a loanable funds theory of the real interest rate - the demand for investment (i.e. the demand for loanable funds) is low, which makes the real interest rate low. It seems clear that the real interest rate that Summers has in mind is the real rate of return on capital.
John Cochrane also discusses an idea related to low real bond yields, which he attributes to Summers:
One hypothesis that I learned from Larry Summers is that today's production function needs a lot less physical capital to produce the same productivity. A 1930s steel mill is a lot of accumulated savings. Facebook has nothing but a basketball court sized building full of 20-somethings coding while wearing headphones, and a really cool food court. The company is worth billions but it took comparatively little accumulated savings to start it up. If technology moves so that human, rather than physical capital is the heart of the K in F(K,L), productivity growth may determine interest rates in the long run, but there are lower interest rates on the transition path.Again, this is an explanation for why the real rate of return on capital might be low.
But what if we actually go out and measure rates of return on capital? This work by Paul Gomme, B. Ravikumar, and Peter Rupert, reported in the St. Louis Fed's Economic Synopses, does that exercise. Here's their Figure 2:
In many standard economic models, there is no difference between the real interest rate faced by consumers and the marginal product of capital. But that will not be the case in models in which, for example, government debt plays some special role, for example as collateral, and therefore bears a liquidity premium. There is work by Kiyotaki and Moore that studies this type of effect, and I've worked on models in which government debt can bear liquidity premia, for example in this paper with David Andolfatto, and this paper of mine on QE. The ideas in those papers are related to Caballero's ideas on "safe asset shortages."
I think that the measurements in the work by Gomme/Ravkumar/Rupert are key to thinking about issues related to low real interest rates, so this deserves attention.