In the comments on this post, he suggests a possible way to reconcile secular stagnation with a high return on capital.
One way to reconcile the two is to say that Piketty’s return on capital includes the equity premium (and other premia for privately held businesses, etc.), whereas the secular stagnation idea of a perpetual ZLB deals with only the riskfree rate.
Some remarks:
1. Fischer Black said that finance is about time and risk. The risk-free rate is the price of time. The equity premium might be a proxy for the price of risk.
2. In Keynesian terms, perhaps one can think of a low risk-free rate as reflecting the desire to hoard and a high risk premium as reflecting low animal spirits.
3. As Matt notes, this approach to reconciling secular stagnation with a high return on capital implies that those earning the high returns are being rewarded for taking risks in an economy in which such risk-taking is scarce. Picketty seems to be pretty confident that high earners will not change their behavior much in response to higher taxes. Perhaps this might be true of labor supply. But can one rule out a significant dampening effect on risk-taking?
Read Matt’s entire comment. As he points out, the secular stagnation story is difficult to reconcile with some fairly basic calculations concerning capital and investment.
“As Matt notes, this approach to reconciling secular stagnation with a high return on capital implies that those earning the high returns are being rewarded for taking risks in an economy in which such risk-taking is scarce.”
High risky returns, available mostly because opportunities or risk appetite is scarce can not reconcile much because it implies that the capitalist’s portoflio will/is increasingly converging to a low risk benchmark. This would have to result in low overall returns on capital.
Arnold,
I like Matt and I really miss his blog, but he really strikes out on this comment. After he correctly points out that the difference between Piketty’s “r” and the risk free rate is risk premium, he proceeds to illustrate the absurdity of valuations under secular stagnation by discounting long term assets at the risk free rate! That’s the whole point! The economy has become *more* risk averse and that includes the future value of land and structures, neither of which are technologies capable of riskless transportation of consumption into the future. The only agent capable of risk-free intertemporal consumption transportation is the government via commitment to future expropriation (which is what backs the 2% inflation commitment and thus the real return of government debt). Matt should read Abel, Mankiw, Summers (89) on dynamic efficiency who make the point about the riskiness of land.
A high risk premium is *exactly* what you need to 1) get the return on capital above the rate of growth and 2) get the nominal natural rate below zero. There is no tension here. These are part of the same problem.
MG,
You’ve misunderstood. Capital is no compounded in aggregate at its rate of return. Some of the return (part of dividends) is consumed and not reinvested. That’s what permits the return to exceed the growth rate of the economy. Richer agents, however, consume a smaller fraction than the representative agent and therefore wealth compounds for them faster than the economy and they accumulate an increasing fraction of all wealth.
One shouldn’t rule out significant amplifying of risk taking though as high taxes encourage reinvestment and consumption deferral.
Piketty does not define “capital” to mean equity or ownership in publicly traded corporations. He defines it as all valuable assets besides income from labor. This includes real estate, patents, oil wells, etc.
K,
I agree that discounting structures at the risk free rate is probably too extreme. My justification was that since the relative price of structures is actually quite stable, there is not that much risk in the valuation of the structure component of real estate (as opposed to the land component), for which I was doing the calculation.
But this is admittedly somewhat sloppy, since the “structure” and “land” components of real estate inherently cannot be traded and valued separately, and there is some difficult-to-value idiosyncratic risk arising from indivisibility and lack of intermediation (you can’t put everything into an REIT) in most real estate investments. (Then again, owning a home is effectively a way to insure yourself against housing cost risk, which can be a big deal as a renter – so in principle it’s not even clear that the risk premium here is positive.)
The more fundamental point is that the numbers involved are so huge that even much more conservative calculations give the same qualitative result (that secular stagnation is very difficult). Let’s say that the average real rate at which structure rents were discounted was 5% before, including a healthy risk premium, and in a secular stagnation regime would go down to 2%. Excluding mining structures (which are much more short-lived than other structures) and broker’s commissions (which the BEA formally capitalizes as part of the “residential structures” stock, but also don’t really belong), the depreciation rate for private structures is 2%.
So in this thought experiment we’d see the user cost go down from 7% to 4%. With unit elastic demand, this would mean a 75% increase in the target structures stock as a share of GDP. Since private structures (excluding mining and transfer costs as mentioned above) are currently 165% of GDP, this would imply an increase to 289% of GDP. The construction boom accompanying this transition path would be immense, far greater than any in US history, surely purging the economy of any kind of slack.
Of course, you could argue that the elasticity of capital demand with respect to user cost is not really 1, and I might agree with you. (Honestly, I don’t know what to think – the short run elasticity is definitely far below 1, but we don’t have much solid evidence about the medium to long run elasticity.)
But this is where the clash between Piketty and secular stagnation becomes clearest. Piketty’s argument is basically that as growth falls, the capital-to-GDP ratio will converge to a new, much higher level. (He makes a lot of the steady-state relation beta = s/g, where beta is the ratio of capital to GDP, s is net savings, and g is the growth rate. He likes to think of s as exogenous.) But this would hardly be much of a problem from a welfare and inequality perspective if all this capital accumulation was balanced by a decline in the rent to capital, leaving the capital income share constant.
So if he wants to make the case that a higher capital income share (arising from his chosen mechanism) is a threat, he has to argue that the elasticity of capital demand with respect to ‘r’ is greater than 1. This is two steps beyond the usual parameterization – not only is he assuming an elasticity greater than 1, but he’s describing an elasticity *with respect to the r rather than the user cost r+delta*. The latter assumption is extremely important for him, because otherwise – under any finite elasticity – sufficient accumulation of capital K will eventually push down the net income r*K.
Let’s think about what this means quantitatively. Suppose that we even use an elasticity . Then Piketty is saying that if ‘r’ falls by some small x%, demand for the overall capital stock (including parts with high depreciation rate) will rise by 1.5*x%. The full private capital stock is currently about 220% of GDP. Piketty does many of his calculations with r=5%, which is roughly what you get from the national accounts data. Assuming that the shift to a secular stagnation regime did not increase or decrease the risk premia that drive a wedge between the return on T-bills and the relevant discount rate for capital, this would decline to something like r=2% under secular stagnation. Given an elasticity of 1.5, this would imply a (5/2)^(1.5) = 4-fold increase in capital demand, or an increase from 220% of GDP to 880% of GDP. That transition path would take a long time, to say the least, and easily give us full demand in the process.
I think that an elasticity of 1.5 of capital demand with respect to ‘r’ is somewhat outlandish – and these calculations are a good proof of that – but an elasticity substantially greater than 1 is necessary for Piketty’s argument, and he tries to make the case for it. Even with an elasticity of exactly 1 – at which point Piketty no longer has any argument, because net capital income will remain constant even in the face of accumulation – the low ‘r’ scenario implies an increase in private capital demand from 220% to 550% of GDP, which is more than enough.
The bottom line is that Piketty and secular stagnation are essentially impossible to reconcile (even more than I initially realized). Secular stagnation implicitly assumes a very low capital demand elasticity, while Piketty explicitly assumes a very high one.
(sorry, above I meant to say “suppose that we use an elasticity of 1.5”, not “Suppose that we even use an elasticity “)