Hurdle Rates for Public Infrastructure and Private Investment: How Low Should We Go? Under 2% Real in Normal Times, and Still Lower Now

Matthew Yglesias tweeted:

1. @tylercowen questions the idea that low interest rates raise the optimal level of infrastructure spending https://t.co/f3QxvBzmwh

— Matthew Yglesias (@mattyglesias) August 12, 2016

I responded:

.@mattyglesias I think @tylercowen is simply confused about the relationship between the equity premium and societal hurdle rates..,

— J. Bradford DeLong (@delong) August 12, 2016

Then Matt challenged:

@delong @tylercowen Write it up and change my mind back again.

— Matthew Yglesias (@mattyglesias) August 12, 2016

And I think: Gee, if I rise to this, like a moth to the flame, then Chris Shea of http://vox.com–to whom I owe 3000 overdue words on trade, manufacturing, politics, NAFTA, China’s accession to the WTO, and TPP–will be really annoyed that I am letting Matt Yglesias be a higher priority assignment editor than him.

I need to lie down until the desire to respond to Matt goes away, and then get up on things that have, you know, deadlines in the past…

Didn’t work…

We have a pretty good theory of how we ought to make decisions under uncertainty. It is, in fact, the same as our pretty good theory of how we ought to make decisions for society as a whole…

Let’s take the individual-uncertainty version first:

We exist behind a veil of ignorance: We do not know what the future will bring. We can, say, slice the future into 10,000 different 0.01% probability chunks, in each of which we would be different. Maybe only one of those 10,000 will actually happen, and the rest are unreal shadows produced only by our ignorance. Maybe (this is version I prefer) all 10,000 of them “exist” and will “occur”, as they are different branches of the quantum wave function of the multiverse, with each having wave-function amplitude that is the appropriate complex square root of 0.0001. (But the answer to the question of which appears to be unknowable. And which is “true” makes no difference.)

In deciding to take action X today, we are, given the uncertainties, doing something to benefit some of our 10,000 future selves and penalize others. We have some sort of obligation to our future selves, either because it makes us happy to sacrifice some of our present comfort for the sake of our future selves or because we wish to be people who are not total a–holes. (Again, it makes no difference.)

Do we take action X?

The economists’ theory tells us that if the effects on our 10,000 future selves generated by action X are unsystematic–if the variance of the effects over our 10,000 future selves is of the kind that can be diversified away–we should just care about the average effect. Thus we should take action X if the average effect is such that we would judge it worthwhile if we knew that the average effect would occur with certainty.

The economists’ theory further tells us that if the variability of the effects on our 10,000 future selves is systematic–that it tends to make those of our future selves who are relatively poor even poorer, and those who are relatively rich even richer–then we should aggregate the effects on our 10,000 future selves with an egalitarian bias: It makes little difference to our aggregation calculation if action X takes an extra dollar away from a future self with a lifetime income 90% and gives one to one with 110% of the future-self average. But by the time the consequences of our actions are taking wealth away from future selves with 30% and giving them to future selves with 170% of the average–then we need to incorporate a risk premium into our calculations.

And here comes punchline one: The effects of government interventions in infrastructure are about as systematic as are corporate business investments. The two, after all, are very strong complements. If the value of private sector goods produced is lower, the value of the infrastructure that enables the efficient production of those private sector goods is lower as well. If the value of infrastructure is high, that can only be because it is greatly assisting in the production and distribution of high-value goods. Tyler is right in asserting that the hurdle rate for government infrastructure and private sector investments should be roughly the same.

But–and here comes punchline two–Tyler goes wrong in asserting that the price charged by savers to fund private sector corporate investments is the right price from society’s point of view, and the price charged the government for borrowing is the wrong price to use to calculate the common hurdle rate for public infrastructure and private investments

Think of it: Neither government investments in infrastructure nor private sector investments in physical capital are that systematic as far as their risk his concert. And, at least on the scale at which we are currently investing, we are much closer to the 90% – 110% case than to the 30%-170% case. The average return required should therefore be governed by:

• pure time preference,
• the speed with which are wealth is increasing, and
• the degree to which increasing wealth satiates us.

I see few signs that we are at the stage where increasing wealth satiates us to any strong degree. The speed with which our wealth is increasing is a per capita rate of about 1.5% per year. And as for pure time preference–well, from a social choice point of view, such a thing can only be irrational myopia. Your future self has the same philosophical and moral standing that your present self does: there is no compelling reason to prefer the interests of the one over the interests of the other. There is force majeur–your present self is here and now and has its mits on the stuff and controls what happens–but that is not a principal of moral but rather of immoral philosophy. In fact, there is an evolutionary-morality point working in the other direction, if you believe in any form of evolutionary morality. (You don’t have to.) Just because your present self happens to come first and time does not produce a moral principle that the interests of later-comers should be sacrificed to its selfish hedonistic pleasures.

Thus I, at least, find there to be a very strong and not yet refuted by anyone case that the presumption should be for a very low hurdle rate, from a social choice point of view at least. That low hurdle rate should apply to both government infrastructure and to private corporate investments. Claims that a higher hurdle rate is in some sense optimal or appropriate seem to me implausible, and to require very hard argumentative work for plausibility that has not yet been done.

What is this hurdle rate? I think you have to start from the rate of growth of per capita income, and make adjustments up and down from there: 1.5% per year in real terms. That is punchline two.

Why, then, does the financial system of a modern capitalist market economy grind out not a 1.5% per year real interest rate for risky private corporate investments? Why does it grind out a 5% per year rate for β=1 investments? Good question!

In my view, the answer is threefold. The market grinds out a wrong 5%/year rather than the right 1.5%/year because:

1. Modern capitalist financial markets do a horrible job at mobilizing the potential systematic risk-bearing capacity of society as a whole.
2. Modern capitalist financial markets singularly fail to solve the enormous moral-hazard and adverse-selection asymmetric-information problems involved in trusting your money to Steve Ballmer or Jamie Dimon–let alone Dick Fuld. (Cf.: Noah Smith.)
3. We have brains design by evolution to do three things: calculate (a) whether the fruit is ripe; (b) whether it is safe to leap to the next branch, and (c) whether we should and how best to amuse men (women) so that they might mate with us. We do not have ranged can reliably make complicated and appropriate moral-philosophical calculations under conditions of great uncertainty and ignorance.

But that modern private capitalist financial markets are ridden by market failures of human psychological myopia, institutional map-design, and asymmetric information–and thus use the wrong hurdle rate–provides no reason at all for using the wrong hurdle rate when solving the public-sector part of the societal-welfare optimization problem.

Moreover, I have a punchline three: The argument as I have made it so far is a very general argument. It creates, in my mind at least a very strong and so far unrebutted (but possibly, with sufficient very hard intellectual work, rebuttable) presumption that the appropriate real hurdle rate is an expected return of less than 2% per year.

But ever since 2005 or so we have been in a very unusual time. For a large number of poorly understood reasons, the world has been awash in savings and yet short of investment. The appropriate hurdle rate has thus been less than the one established by the general argument. We are still in an unusual time. The U.S. labor market no longer has large obvious amounts of slack, but as the Paul Krugman with his Krell-like brain points out, considerations of asymmetric policy risks and global rather than local macroeconomic balance strongly suggest that the right policy is to still act as though the U.S. still has large obvious amounts of slack, and so needs to penalize saving and encourage investment at the margin by more than it is currently doing.