Monday, October 27, 2014

Daisy Chain Time Travel Macro

For some reason, my comments never show up on Simon Wren-Lewis’ blog, Mainly Macro.  Maybe they were not meant to be.  But today I will use this site as a soapbox to reply to his (and Nick Rowe’s) argument that public borrowing can impose a burden on future generations.

You can read the original, but the basic idea is that lending money is a form of deferred consumption that wends its way through time like a daisy chain.  People live for two periods, with overlapping generations.  They buy bonds during the first period and sell them during the second.  Thus in each period the debt is neatly handed off to the following generation.  But there is an end time, when public debt must be retired.  At that point, instead of allowing the final generation, in the bloom of period 1, to purchase and thereby rollover the debt of their ancestors, the government taxes them to retire it.  So behold, the borrowing of government from generation the first is a delayed charge against generation the last.  And that is why paygo pension systems are an intergenerational crime.

The logic is impeccable, in the sense that if you accept the premises you must accept the conclusion.  The question is whether the premises correspond in any meaningful way to the world we inhabit.

One obvious problem is the assertion of an end time.  The Greatest Generation, as we know, ran up what was at that point the Greatest Debt; in fact, gross federal debt (including the portion held by the Fed) topped out in 1946 at just under 120% of GDP.  Those living today are heirs to that borrowing “binge”.  But we haven’t suffered for it, since (1) that specific chunk of debt has become much smaller in relation to our incomes today due to inflation and real growth, and (2) we continue to roll over principle and interest, since the end time is not nigh.  As long as we don’t go crazy, and keep our current and future borrowing on a sustainable basis, the end time need never come.  (And I’m abstracting, as Simon and others do, from the benefits financed by borrowing—like saving the world from Hitler or, more mundanely, all those nice CCC-built parks—that are also legacies for the future.)

The second is less recognized.  The consumption-smoothing life plan at the heart of the standard OLG model, simply does not reflect the facts.  Here, for instance, is the 2011 average household net worth (not including home equity) by age of household head, as estimated by the Census Bureau:

Except for those over 75, older people have more net income-generating assets than younger people, and even the geeziest geezers hold more assets than those under 45.  They die with their financial boots on, making the daisy chain of deferred consumption a false depiction.

The bottom line is that the generation is not a meaningful unit of accounting when it comes to the distributive effects of public deficits.  How about shifting attention to the decision to sell bonds to the rich instead of taxing them?


Nick Rowe said...

Peter: a couple of times my comment didn't show up there either. But it did the next time. Just a glitch, I think.

"And that is why paygo pension systems are an intergenerational crime."

Whoa! No! Just there may be costs, as well as benefits. Are PAYGO pension systems good or bad? It depends. Especially on whether r <> g.

"One obvious problem is the assertion of an end time."

Agreed. If r < g always, there never need be an end time. All generations can be made better off. If r > g always, then the debt/GDP ratio will rise without limit unless taxes are raised at some future time, which makes some future generations worse off. If r < g sometimes, and r < g other depends (my math isn't good enough to work that case out).

"Except for those over 75, older people have more net income-generating assets than younger people, and even the geeziest geezers hold more assets than those under 45. They die with their financial boots on, making the daisy chain of deferred consumption a false depiction."

You lost me there. Sure, people save for their retirement. I don't see why this invalidates the burden on future generations argument. If anything, it supports it.

(What does invalidate the burden argument is Barro-Ricardian Equivalence -- we make bequests to our kids to offset the burden of the debt. But "keynesians" don't want to go there, presumably!)

Peter Dorman said...

Thanks for the reassurance about Simon's website, Nick. Naturally I thought it was something about me!

Agreed that, net of changes in the Fed's balance sheet, g-r determines the long run sustainability of rolling over debt plus interest -- but those two caveats matter. First, the Fed can be assumed to expand its holdings of public debt over time, and some such increase is sustainable in the long run. (You don't have to sign on to MMT and say any such increase is sustainable.) Second, governments can run a primary balance so that only the principle is rolled over. In that case each generation from day 1 is paying and receiving the same interest, the debt is sustainable indefinitely (unless g is long run negative in which case we'll have lots of other things to worry about), and there is no end time.

The point about household asset accumulation is that households continue accumulating until a very ripe age and only partially decumulate thereafter. In fact, the official statistics don't tell us how much of the decumulation is actually granted to heirs before death. Thus the portrayal of asset accumulation as consumption smoothing literally doesn't add up.

In terms of a simple OLG model, you need the two periods to represent about a 90-10 split, with deferred consumption attributable to earlier saving being a small fraction of that saving.

Incidentally, I'm curious about how much of the non-consumption-smoothing portion of accumulation (i.e. most of it) is properly attributable to bequest motive. This is an empirical question. For instance, one could compare the behavior of HH's in which there is, say, a sole surviving heir to those in which such an heir died before a bequest could take place. Did HH's in category 2 change their behavior post-heir-death compared to HH's in category 1 at similar ages?

My hypothesis going in would be that pure bequest is a small part of motivation, and that, for lack of a better term, what we see is simply an accumulation motive: wealth is addictive. But this is all off-topic.

Nick Rowe said...

Peter: this is my rough and ready way of handling the issues that you raise in your second paragraph:

1. The Bank of Canada's annual seigniorage profit, from issuing 0% interest currency while holding a portfolio of assets with r > 0%, are around 0.25% of NGDP, on average. That gets included in government revenue anyway ("profits from Crown Corporations") so we don't need to adjust the deficit for that.

2. I assume 2% inflation, plus 2% real growth, = 4% NGDP growth. I take 4% of the debt, and subtract it from the reported deficit, to get the adjusted deficit. If that adjusted deficit is zero, it's sustainable, because the debt/NGDP ratio stays constant over time. It makes quite a big difference.

Peter Dorman said...

Good point about seigniorage. All the same, in any modeling of the future growth of debt, this factor has to be taken into consideration.

As for your second point, this is a condition for debt/GDP stationarity at the existing ratio. But if there is fiscal space (which there is), that is not the same as sustainability per se. Sustainability means achieving stationarity at some viable ratio, but not necessarily this one. The reason I mention this is that the size of your deduction from the published deficit depends on the level of the debt. You could have a positive deficit post deduction and still be sustainable if a larger sustainable debt would give you a sufficient deduction. Not elegantly expressed, but I hope it's clear.

Nick Rowe said...

Peter: yes, clear enough to be understood.