In the comments of Askblog, Matt writes:
…the “secular stagnation” hypothesis is in dire need of some cogent back-of-the-envelope estimates, and I don’t think it holds up very well. A long-term fall in the average real interest rate from, say, 2% to -1%, would be absolutely extraordinary. It would imply massive increases in the valuation of long-lived, inelastically supplied assets like land, and massive increases in the quantity of long-lived, elastically supplied capital like structures.
Just to illustrate how extreme the implications can be, consider the following (sloppy) calculation. The BEA’s average depreciation rate for private structures is currently about 2.5%. A decline in the real interest rate from 2% to -1% implies a decline in user cost r+delta from 4.5% to 1.5%, of a factor of three. If the demand for structures is unit elastic (as economists, unjustifiably from an empirical standpoint, tend to assume with Cobb-Douglas functional forms), this would imply a threefold increase in the steady-state quantity. Since structures are already 175% of GDP, this would imply an additional increase of 350% of GDP, more than doubling the overall private capital stock and nearly doubling national net worth. The transition to this level would require such an extraordinary, prolonged investment boom that we would not face slack demand for many, many years.
(There are many things wrong with this calculation, but even an effect a fraction of this size serves my point, especially when you keep in mind that land values would be skyrocketing as well. The bottom line is that proponents of secular stagnation have not yet contended with some of the basic numbers.)
I am still waiting for a model of secular stagnation that rationalizes both a negative real interest rate and positive investment, which indeed we are observing in most countries circa 2014. That means, by the way, I don’t quite agree with Matt’s sentence “The transition to this level would require such an extraordinary, prolonged investment boom that we would not face slack demand for many, many years.” There are some “reasoning from a price change” issues floating around in the background here. Is it the productivity of just new capital that has fallen to bring the natural interest rate to negative one? Or the rate of return on old capital too, in which case the value of the extant capital stock is not given by the calculation in question? Tough stuff, but you know where the burden of proof lies. Can this all fit together with the fact that nominal gdp is now well above its pre-crash peak? And that we are seeing positive net investment? In any case I agree with Matt’s broader point that the implied magnitudes here don’t seem to fit the facts or even to come close.
…here’s what confuses me. Some of the reviews seem to imply that Piketty argues that real rate of return on capital represents the rate at which the wealth of the upper classes grow. Is that right? If so, what is the basis of that argument? I don’t think anyone seriously expects the grandchildren of a Bill Gates or a Warren Buffett to be 10 times as wealthy as they are.