Fiscal Arithmetic: The Blanchard Rule

When we left off, we'd concluded that the relationship between g, the growth rate of GDP, and i, the after-tax interest rate on government debt, was central to the evolution of public debt. When g > i, any primary deficit is sustainable, in the sense that the debt-GDP ratio converges to a finite value; when i > g, no primary deficit is sustainable, and a primary surplus, while formally sustainable at a certain exact value, occupies a knife-edge. Which invites the natural question, so which is bigger, usually?

There are articles that discuss this (tho not as many as you might think). Here's a good recent article by Jamie Galbraith; I also like this one by Tony Aspromourgos, and "The Intertemporal Budget Constraint and the Sustainability of Budget Deficits" by Arestis and Sawyer. (I'm sorry, I can't find a version of it online). An earlier and more mainstream, but for our current purposes especially interesting, take is this piece by Olivier Blanchard.  Blanchard says:

If i - g were negative, the government would no longer need to generate primary surpluses to achieve sustainability. ... The government could even run permanent primary deficits of any size, and these would eventually lead to a positive but constant level of debt... Theory suggests that this case, which corresponds to what is known as 'dynamic inefficiency', cannot be excluded, and that in such a case, a government should, on welfare grounds, probably issue more debt until the pressure on interest rates made them at least equal to the growth rate.

So much depends on whether the growth rate exceeds the interest rate, or not. Well, so, does it?

The funny thing about this passage in context is that Blanchard acknowledges that over most of the postwar period, the growth rate has exceeded the interest rate. But, he says, the professional consensus is that interest rates ought to equal or exceed growth rates, so he'll stick with that assumption for the rest of the article. (There's almost a genre of economics articles that freely admit a key assumption doesn't seem to be consistently satisfied in practice, but then blithely go on assuming it. The Marshall-Lerner-Robinson condition is a favorite in this vein.) But we're not here to mock; we're here to call the Blanchard rule, the prescription that if i < g, the federal deficit ought to be higher.

Below are graphs of the growth rate and after-tax 10-year government bond rate for 10 OECD countries. Both are deflated by the CPI; the tax rate is the ratio of central government taxes to GDP. This is probably a bit high, but on the other hand the average maturity of government debt is less than 10 years in many OECD countries -- in the US it is currently around 4.7 years -- so these two biases might more or less cancel each other out, leaving the red line close to the economically relevant interest rate. Source is the OECD statistics site. I've excluded 2008-2010 since the Great Recession pulls growth rates sharply down in a (let's hope!) misleading way. The lighter black line is the growth trend.

Click them to make them bigger!

Clearly we can't exclude the relevance of the Blanchard rule; for much of the time, for many rich countries, the growth rate of GDP has exceeded the 10-year interest rate. At other times, interest has exceeded growth. What we see in most cases is a fairly stable growth rate, combined with an interest rate that jumps sharply up around 1980 and then drifts downward from somewhere in the 1990s. At some point soon, I hope, I'll produce decompositions of the change in the fiscal position into the interest rate, the growth rate, changes in taxes and expenditure induced by the growth rate, and autonomous changes in taxes and spending. I suspect the first will be the most important, and the last the least. But in the meantime, we can say just looking at these graphs that changing interest rates are an important component of fiscal dynamics, so it's wrong to think just in terms of the primary balance.

Which suggests -- coming back to the earlier debate with John Quiggin -- that if we are concerned with the long-term fiscal position, we should spend at least as much time worrying about policies that affect the interest rate on government debt relative to the growth rate, as we should about taxes relative to expenditures. And we should not assume a priori that a primary deficit is unsustainable.

Trade: The New Normal Was the Old Normal Too

Matthew Yglesias is puzzled by

the fundamental weirdness of having so much savings flowing uphill from poor, fast-growing countries into the rich, mature economy of the United States. It ought to be the case that people in fast-growing countries are eager to consume more than they produce, knowing that they’ll be much richer in the near future. And it ought to be the case that people in rich countries are eager to invest in poor ones seeking higher returns. But it’s not what was happening pre-crisis and it’s not what’s been happening post-crisis.

He should have added: And it's not what's ever happened.

I'm not sure what "ought" is doing in this passage. If it expresses pious hope, fine. But if it's supposed to be a claim about what's normal or usual, as the contrast with "weirdness" would suggest, then it just ain't so. Sure, in some very artifical textbook models savings flow from rich countries to poor ones. But it has never been the case, since the world economy came into being in the 19th century, that unregulated capital flows have behaved the way they "ought" to.

Albert Fishlow's paper "Lessons from the Past: Capital Markets During the 19th Century and the Interwar Period" includes a series for the net resources transferred from creditor to debtor countries from the mid-19th century up to the second world war. (That is, new investment minus interest and dividends on existing investment.) This series turns negative sometime between 1870 and 1885, and remains so through the end of the 1930s. For 50 years -- the Gold Standard age of stable exchange rates, flexible prices, free trade and unregulated capital flows -- the poor countries were consistently transferring resources to the rich ones. In other words, what Yglesias sees as the "fundamental weirdness" of the current period is the normal historical pattern. Or as Fishlow puts it:

Despite the rapid prewar growth in the stock of foreign capital, at an annual average rate of 4.6 percent between 1870 and 1913, foreign investment did not fully keep up with the reflow of income from interest and dividends. Return income flowed at a rate close to 5 percent a year on outstanding balances, meaning that on average creditors transferred no resources to debtor nations over the period. ... Such an aggregate result casts doubt on the conventional description of the regular debt cycle that capital recipients were supposed to experience. ... most [developing] countries experienced only brief periods of import surplus [i.e. current account deficit]. For most of the time they were compelled to export more than they imported in order to meet their debt payments.

A similar situation existed for much of the post World War II period, especially after the secular increase in world interest rates around 1980.

There is a difference between the old pattern (which still applies to much of the global south) and the new one. Then, net-debtor poor countries  ran current account surpluses to make payments on their high-yielding liabilities to rich countries. Now, net-creditor (relatively-) poor countries run current account surpluses to accumulate low-yielding assets in rich countries. I would argue there are reasons to prefer the new pattern to the old one. But the flow of real resources is unchanged: from the periphery to the center. Meanwhile, those countries that have successfully industrialized, as scholars like Ha-Joon Chang have shown, have done so not by accessing foreign savings by connecting with the world financial system, but by keeping their own savings at home by disconnecting from it.

It seems that an unregulated international finance doesn't benevolently put the world's collective savings to the best use for everyone, but instead channels wealth from the poor to the rich. That may not be the way things ought to be, but historically it's pretty clearly the way things are.

Some Fiscal Arithmetic

If we're going to discuss fiscal policy, we should be clear on the accounting relationships involved. So, here are some basic equations describing how the public debt evolves over time. I should say up front that the relationships I'm describing here, while they suggest an unorthodox skepticism about worries about debt "sustainability," are themselves totally orthodox and noncontroversial. And they don't make any behavioral assumptions -- they're true by definition.

We're interested in the ratio of debt to GDP. What will this be at some time t?

Well, it will be equal to the ratio in the previous period, increased by rate of interest, and decreased by the rate of growth of GDP, (remember, we are talking about the debt-GDP ratio; increasing the denominator makes a fraction smaller), plus the previous period's primary deficit, that is, the difference between spending on everything besides interest, and revenues.

Let b be the government debt and d the primary deficit (i.e. the deficit exclusive of interest payments), both as shares of GDP. Let i be the after-tax interest rate on government borrowing and g the growth rate of GDP (both real or both nominal, it doesn't matter). Then we can rewrite the paragraph above as:

We can rearrange this to see how the debt changes from one period to the next:

Now, what happens if a given primary deficit is maintained for a long time? Does the debt-GDP ratio converge to some stable level? We can answer this question by setting the left-hand side of the above equation to zero. That gives us:

What does this mean? There are three cases to consider. If the rate of GDP growth is equal to the interest on government debt net of taxes, then the only stable primary balance is zero; any level of primary deficit leads to the debt-GDP rate rising without limit as long as its maintained. (And similarly, any level of primary surpluses leads to the government eventually paying off its debt accumulating a positive net asset position that grows without limit.) If g > i, then for any level of primary deficit, there is a corresponding stable level of debt; in this sense, there is no such thing as an "unsustainable" deficit. On the other hand, if g < i, then -- assuming debt is positive -- a constant debt requires a primary surplus.

There is a further difference between the cases. When g > i, the equilibrium is stable; if for whatever reason the debt rises or falls above the level implied by the long-run average primary deficit, it will move back toward that level over time. But when g < i, if the debt is one dollar too high, it will rise without limit; if it is one dollar too low, it will fall without limit, to be eventually replaced by an endlessly growing positive net asset position.

So, which of these three cases is most realistic? Good question! So good, in fact, I'm going to devote a whole nother post to it. The short answer: sometimes one, sometimes another. But in the US, GDP growth has exceeded pre-tax interest on 5-year Treasuries (the average maturity of US debt is around 5 years) in about 50 of the past 60 years.

The discussion up to now has been in terms of the primary balance. But nearly all public discussions of fiscal issues focus on the total deficit, which includes interest along with other categories of spending. We can rewrite the equations above in those terms, adding a superscript T to indicate we're talking about the total deficit. In these equations, g is the nominal growth rate of GDP.

Again, we define equilibrium as a situation in which the debt-GDP ratio is constant. Then we have:

In other words, any total deficit converges to a finite debt-GDP ratio. (And for every debt-GDP ratio, there is a total deficit that holds it stable.) So defining a sustainable total deficit requires picking a target debt-GDP ratio. Let's say we expect nominal GDP growth to average 5% in the future. (That's a bit low by historical standards, but it's what the CBO assumes in its long-run budget forecasts.) Then 2010's deficit of 8.8% of GDP implies a long-run debt-GDP ratio of about 175% -- a number toward the top of the range observed historically in developed countries. 175% too high? Get the long-run average deficit down to 4%, and the debt-GDP ratio converges to 80%. Deficit of 3% of GDP, debt of 60% of GDP. (Yes, the Maastricht criteria apparently assume 5% growth in nominal GDP.) It is not at all clear what the criteria are for determining the best long-run debt-GDP ratio, but that's what you've got to do before you can say whether the total deficit is too high -- or too low.

One last point: An implication of that last equation above is that if the total deficit averages zero over a long period, the debt-GDP ratio will also converge to zero. In other words, "Balance the budget over the business cycle" is another way of saying, "Pay off the whole federal debt." Yet I doubt many of the people who argue for the former, would support the latter. Which only shows how important it is to get the accounting relationships clear.


EDIT: I should stress: There is nothing original here. Any economist who does anything remotely related to public finance would read this and say, yes, yes, so what, of course -- or at least I sure hope they would. But you really do have to be clear on these relationships for terms like "sustainable" to have any meaning.

For instance, let's go back to that Peterson budget summit. As far as I can tell, five of the six organizations that submitted budget proposals used the CBO's assumptions for growth and interest rates. (EPI tweaked them somewhat.) But given those assumptions, only two of the budgets -- EPI  and AEI -- actually stabilize the debt-GDP ratio. (Interestingly, they do so at about the same level -- 70% of GDP for AEI, and 80% of GDP for EPI.) The other four budgets describe a path on which the entire federal debt is retired, and the federal government accumulates a net asset position that grows without limit relative to GDP. Personally, I am all for public ownership of the means of production. But I didn't realize that's what people had in mind when they called a budget "sustainable". Of course, presumably that is, indeed, not what the people at CAP, Heritage, or the Roosevelt Campus Network had in mind; presumably they just didn't think through the long-term implications of their budget numbers. Which is sort of the point of this post.


UPDATE: ... and not 12 hours after I post this, here's John Quiggin at Crooked Timber writing that the US needs "a substantial increase in tax revenue in the long term" and backing it up with the claim,"I assume [the optimal debt-GDP ratio is] finite, which would not be the case under plausible scenarios with no new revenue and maintenance of current discretionary expenditure relative to national income." As we've seen , given the historic pattern where GDP growth is above the interest rate, this statement is simply false.

Of course, John Q. might be assuming this historic relationship will be reversed in the future. But then you could just as logically say that the interest rate is too high, or inflation is too low, as that higher taxes are needed. The view that it must be taxes that adjust implicitly assumes that that longer term interest rates aren't responsive to policy, and that deliberately raising inflation can't even be discussed. In other words, while surpluses later is often presented as part of an argument for deficits now, the case for surpluses in the future rests on premises that also largely rule out more aggressive monetary stimulus in the present.

Help, I'm Stuck in a Fortune Cookie Factory

Remember that old joke?

The Slack Wire was hit by a bunch of spam comments just now, which I promptly deleted. Whatever, it's a blog, happens every day, right? The usual, a bunch of links to sites selling dresses, shoes, thermometers. (Thermometers?)

Except: the text accompanying the links was not the usual spamglish ("Thank You for a Most interesting discution") or - what the cleverer spambots do - quotes from earlier comments. It was: "This is my job. I am so sorry."

I'm sorry too, "Amanda." All the wonderful new forms of creative intellectual work that could be opened up by the Internet, and we've stuck you doing this.

An Ant Not Even Thinking About Pissing on Cotton

Over at Crooked Timber, they're discussing Martha Nussbaum's new book on "Why Democracy Needs the Humanities." Sounds like a real stinker. (Altho the thread has alerted me to the fact that I urgently need to read Randall Jarrell's Pictures from an Institution, so I guess Nussbaum is to thank for that.) Lots of good criticism of the book, there and at the discussion CT is responding to, but most everyone seems to accept at least the premise that there is a crisis in the humanities --  a "silent crisis," says Nussbaum. Or as representative CT commenter puts it, "you won’t be able to get a BA degree from a land-grant university in twenty years."

Really? This must be an extrapolation from the past 20 years, yes? So, ok, what's happened to the humanities since 1990?

Here are the numbers, from the 2010 Digest of Education Statistics:

 

The federal government doesn't designate particular subjects as "liberal arts," as far as I know, so I've presented two possible definitions. The blue line is the narrower one: English, visual & performing arts, foreign languages, philosophy, and area/ethnic/gender studies. The red line includes all those, plus social sciences, psychology, interdisciplinary studies, and architecture.

What do we see? Well, there was a decline in the share of humanities degrees in the 1970s. But there was some recovery in the 1980s, and since 1990, the proportion has been flat: around 20% (for the broad measure) or a bit over 10% (for the narrow -- basically English and its satellites -- measure). Whether these proportions ought to be higher, I couldn't say; but if crisis means a situation that can't persist, then this is clearly not a crisis. Or at least, it's a really, really silent one.

Political Economy 101

When he's right, he's right:

everything we’re seeing makes sense if you think of the Right as representing the interests of rentiers, of creditors who have claims from the past — bonds, loans, cash — as opposed to people actually trying to make a living through producing stuff. Deflation is hell for workers and business owners, but it’s heaven for creditors. ... thinking of what’s happening as the rule of rentiers, who are getting their interests served at the expense of the real economy, helps make sense of the situation.

Or, almost right. Because it isn't just the Right...


EDIT: It's interesting to note how reflexively DeLong shied away from this thought when it occurred to him a while back, with the ludicrous-on-its-face argument that only "coupon-clippers with their portfolios 100% in government bonds" could have an interest in deflation. The existence of rentiers as a distinct social class is an unthought in respectable circles. Which shows how impressively disrespectable Krugman is becoming.

The Beatings Will Continue...

This may be the answer to this.

Shorter DeLong:

It is perfectly obvious that the cause of the Great Recession was an insufficient supply of government debt. And it is perfectly obvious that we need to reduce the supply of government debt.

Let me spoil the joke by explaining it.

The argument that the collapse in demand for currently produced goods and services in 2007-2009 was due to an excess demand for AAA assets, i.e. government debt, is a useful one, as far as it goes. But the strange thing is that the New Keynesians making it don't seem to think it conveys any information about the long-term fiscal position. Presumably, if we'd known about the coming excess demand for government debt, we'd have wanted higher deficits throughout the 2000s, instead of having to ramp them up suddenly at the end of the decade. And presumably, the circumstances that led to higher demand for government debt in 2007-2009 can be expected to recur. So maybe we want to prepare for them going forward? But no, we still need the debt-GDP ratio to be "sustainable" -- a term which is never defined, except it's always lower than where we are now. The fact that the ratio was too low, rather than too high, in the recent past somehow fails to imply that it could be too low, rather than too high, in the future.

Let me come at this another way. Check out the entrants in the Peterson Institute budget beauty contest. All of them are considered by the judges to have rocked the swimsuit competition "put the federal debt on a sustainable trajectory through 2035." But what does this mean? The fiscal positions at the end date range from a surplus of 0.8% of GDP to a deficit of 3.7%. Debt-GDP ratios range from 30% to 81.7%. The highest-deficit entrant (EPI's, for what it's worth) is near the very high end of the historical range, and essentially identical to the CBO's current-policy baseline. If current policy is sustainable, why are we having this conversation? But of course, Peterson gives no indication how "sustainable" is being defined (or for that matter what they're assuming about GDP growth and the interest rate on government debt, quite important for these exercises).

Mainstream discourse on budget deficits (as with inflation) combines an absolute conviction that the current debt-GDP ratio is too high, with a complete lack of principles for telling us what the optimal ratio might be.

Some Should Do One, Others the Other

A friend writes:

In August 1968 I was on an SDS trip to Cuba, one of about 30 student activists from around the US. One day we went to the mission of the Provisional Revolutionary Government of South Vietnam in Havana (it had been called the National Liberation Front but had recently taken on a new name). We decided to see if the NLF, as we called them, could settle some debates in the US antiwar movement. After exchanging pleasantries with the representative of the PRG/NLF, we had the following exchange.

SDS students: We have a debate in the antiwar movement. Some of us think we should organize militant, obstructive demonstrations that are openly in support of victory for the NLF. Others argue we should organize much larger, peaceful, legal demonstrations around the demand of immediate US withdrawal from Vietnam. Which should we do?

PRG/NLF rep: Some of you should do one, and others should do the other.

SDS students: We have another debate in the antiwar movement. When a male antiwar activist gets a draft induction notice, some of us think he should refuse to serve, either going to jail or going to Canada. Others of us argue that he should quietly go into the military to organize among the soldiers for an end to the war. Which should we do?

PRG/NLF rep: Some of you should do one, and others should do the other. And when an antiwar activist goes into the military and ends up in Vietnam, there are ways to arrange contact between the activist and the local NLF fighters.

After that exchange, I began to see why the NLF was so successful in their struggle to force the US out of Vietnam.

Here is a parable for the Left! How many pointless debates about tactics could be avoided if someone just said, "Some of you should do one, and others should do the other." Except in the case of a specific, finite resource, and a decision-making body able to allocate it, the merits of one approach aren't an argument against another.

Peaceful demonstrations, or direct action? Challenge foreclosures in court, or block them in the street? Work within the Democrats, or build a third party? Support organizing and contract fights by AFL-CIO unions, or help build rank-and-file insurgencies? Try to shift the Obama administration from the inside, or pressure it from the outside? Debate the economics mainstream, or build a heterodox alternative? Nationalize the banks, or shoot the bankers? Fight for women's access to male-dominated professions, or for greater social recognition of traditionally female activities? Well-funded public universities, or an end to credentialism? Green capitalism, or cooperatives? Theory, or practice? Recycle, reuse, or reduce? Some of us should do one. And others should do the other.

Anything We Can Do, We Can Afford

John Maynard Keynes, in a 1942 BBC address:

Let us not submit to the vile doctrine of the nineteenth century that every enterprise must justify itself in pounds, shillings and pence of cash income ... Why should we not add in every substantial city the dignity of an ancient university or a European capital ... an ample theater, a concert hall, a dance hall, a gallery, cafes, and so forth. Assuredly we can afford this and so much more. Anything we can actually do, we can afford. ... We are immeasurably richer than our predecessors. Is it not evident that some sophistry, some fallacy, governs our collective action if we are forced to be so much meaner than they in the embellishments of life? ...

Yet these must be only the trimmings on the more solid, urgent and necessary outgoings on housing the people, on reconstructing industry and transport and on replanning the environment of our daily life. Not only shall we come to possess these excellent things. With a big programme carried out at a regulated pace we can hope to keep employment good for many years to come. We shall, in fact, have built our New Jerusalem out of the labour which in our former vain folly we were keeping unused and unhappy in enforced idleness.

 (Collected Works XXVII)

Relevant today, obviously: Thirteen million people unemployed, 25 percent of industrial capacity idle, and capital, if the interest rate is any guide, more abundant than it's been in decades. If our masters were only interested in what's best for everyone, as they always claim, now would be the moment for new bridges, hospitals, subways, colleges, and public housing, and for parks, theaters, museums, and cafes. Not to mention wind farms. A recession isn't the time to trim sails and take short views, it's the time to go long. So let's build that New Jerusalem.