Lost in Fiscal Space

Arjun and Jayadev and I have a working paper up at the Washington Center for Equitable Growth on the conflict between conventional macroeconomic policy and Lerner-style functional finance. Here’s the accompanying blogpost, cross-posted from the WCEG blog.


One pole of current debates about U.S. fiscal policy is occupied by the “functional finance” position—the view usually traced back to the late economist Abba Lerner—that a government’s budget balance can be set at whatever level is needed to stabilize aggregate demand, without worrying about the level of government debt. At the other pole is the conventional view that a government’s budget balance must be set to keep debt on a sustainable trajectory while leaving the management of aggregate demand to the central bank. Both sides tend to assume that these different policy views come from fundamentally different ideas about how the economy works.

A new working paper, “Lost in Fiscal Space,” coauthored by myself and Arjun Jayadev, suggests that, on the contrary, the functional finance and the conventional approaches can be understood in terms of the same analytic framework. The claim that fiscal policy can be used to stabilize the economy without ever worrying about debt sustainability sounds radical. But we argue that it follows directly from the standard macroeconomic models that are taught to undergraduates and used by policymakers.

Here’s the idea. There are two instruments: first, the interest rate set by the central bank; and second, the fiscal balance—the budget surplus or deficit. And there are two targets: the level of aggregate demand consistent with acceptable levels of inflation and unemployment; and a stable debt-to-GDP ratio. Each instrument affects both targets—output depends on both the interest rate set by monetary authorities and on the fiscal balance (as well as a host of other factors) while the change in the debt depends on both new borrowing and the interest paid on existing debt. Conventional policy and functional finance represent two different choices about which instrument to assign to which target. The former says the interest rate instrument should focus on demand and the fiscal-balance instrument should focus on the debt-ratio target, the latter has them the other way around.

Does it matter? Not necessarily. There is always one unique combination of interest rate and budget balance that delivers both stable debt and price stability. If policy is carried out perfectly then that’s where you will end up, regardless of which instrument is assigned to which target. In this sense, the functional finance position is less radical than either its supporters or its opponents believe.

In reality, of course, policies are not followed perfectly. One common source of problems is when decisions about each instrument are made looking only at the effects on its assigned target, ignoring the effects on the other one. A government, for example, may adopt fiscal austerity to bring down the debt ratio, ignoring the effects this will have on aggregate demand. Or a central bank may raise the interest rate to curb inflation, ignoring the effects this will have on the sustainability of the public debt. (The rise in the U.S. debt-to-GDP ratio in the 1980s owes more to Federal Reserve chairman Paul Volcker’s interest rate hikes than to President Reagan’s budget deficits.) One natural approach, then, is to assign each target to the instrument that affects it more powerfully, so that these cross-effects are minimized.

So far this is just common sense; but when you apply it more systematically, as we do in our working paper, it has some surprising implications. In particular, it means that the metaphor of “fiscal space” is backward. When government debt is large, it makes more sense, not less, to use active fiscal policy to stabilize demand—and leave the management of the public debt ratio to the central bank. The reason is simple: The larger the debt-to-GDP ratio, the more that changes in the ratio depend on the difference in between the interest rate and the growth rate of GDP, and the less those changes depend on current spending and revenue (a point that has been forcefully made by Council of Economic Advisers Chair Jason Furman). This is what we see historically: When the public debt is very large, as in the United States during and immediately after the Second World War, the central bank focused on stabilizing the public debt rather than on stabilizing demand, which means responsibility for aggregate demand fell to the budget authorities.

We hope this paper will help clarify what’s at stake in current debates about U.S. fiscal policy. The question is not whether it’s economically feasible to use fiscal policy as our primary instrument to manage aggregate demand. Any central bank that is able to achieve its price stability and full employment mandates is equally able to keep the debt-to-GDP ratio constant while the budget authorities manage demand. The latter task may even be easier, especially when debt is already high. The real question is who we, as a democratic society, trust to make decisions about the direction of the economy as a whole.

UPDATE: Nick Rowe has an interesting response here. (And an older one here, with a great comments thread following it.)

Are US Households Done Deleveraging?

This Tuesday, I’ll be  at Joseph Stiglitz’s event at Columbia University on finance and inequality, presenting my work with Arjun Jayadev on household debt. You can find the latest version of our paper here.

In preparation, I’ve been updating the numbers and the results are interesting. As folks at the Fed have noted, the post-2007 period of household deleveraging seems to have reached its end. Here’s what the household debt picture looks like, in the accounting framework that Arjun and I prefer.

The units are percent of adjusted household income. (We can ignore the adjustments here.) The heavy black line shows the year-over-year change in household debt-income ratios. The bars then disaggregate that change into new borrowing by households — the primary deficit — and the respective contributions of interest payments, inflation, income growth, and defaults. A negative bar indicates a factor that reduces leverage; in most years, this includes both (real) income and inflation, since by raising the denominator they reduce the debt-income ratio. A positive bar indicates a factor that increases leverage; this includes interest payments (which are always positive), and the primary deficit in years in which households are on net receiving funds from credit markets.

Here’s what we are seeing:

In 2006 and 2007, debt-income ratios rose by about 3 percent each year; this is well below the six-point annual increases earlier in the 2000s, but still substantial. In 2008, the first year of the recession, the household debt-income ratio rises by another 3 points, despite the fact that households are now paying down debt, with repayments exceeding new borrowing by nearly 8 percent of household income. This is an astonishing rate of net repayment, the greatest since at least 1931. But despite this desperate effort to deleveraging, household debt-income ratios actually rose in 2008, thanks to the sharp fall in income and to near-zero inflation — in most years, the rise in prices automatically erodes the debt-income ratio. The combination of negative net borrowing and a rising debt burden is eerily reminiscent of the early Depression — it’s a clear sign of how, absent Big Government, the US at the start of the last recession was on track for a reprise of the Depression.

Interest payments make a stable positive contribution to the debt-incoem ratio throughout this period. Debt-service payments do fall somewhat, from around 7 percent of household income in 2006 to around 5 percent in 2013. But compared with other variables important to debt dynamics, debt-service payments are quite stable in the short-term. (Over longer periods, changes in effective interest rates are a ] bigger deal.) It’s worth noting in particular that the dramatic reduction in the federal funds rate in 2007-2008 had a negligible effect on the average interest rate paid by households.

In 2009-2012, the household debt-income ratio does fall, by around 5 points per year. But note that household surpluses (i.e. negative deficits) are no larger in these years than in 2008; the difference is that we see resumed positive growth of inflation and, a bit later, real incomes, raising the denominator of the debt-income ratio. This is what failed to happen in the 1930s. Equally important, there is a sharp rise in the share of debt written off by default, exceeding 3 percent in each year, compared with a writeoff rate below one percent in all pre-recession years. Note that the checked bar and the white bar are of similar magnitudes: In other words, repayment and default contributed about equally to the reduction of household debt. If deleveraging was an important requirement for renewed economic growth then it’s a good thing that it’s still possible to discharge our debts through bankruptcy. Otherwise, there would have been essentially no reduction in debt-income ratios between 2007 and 2012. [*]

This much is in the paper. But in 2013 the story changes a bit. The household debt-income ratio rises again, for the first time since 2008. And the household balance movers into deficit, for the first time since 2007 — for the first time in six years, households are receiving more funds from the credit markets than they are paying back to them. These events are linked. While the central point of our paper is that changes in leverage cannot be reduced to changes in borrowing, for the US households in 2013, it is in fact increased borrowing that drove the rise in debt-income ratios. Inflation and income growth were basically constant between 2012 and 2013. The 5-point acceleration in the growth of the household debt-income ratio is explained by a 4.5 point rise in new borrowing by households (plus a 1.5 point fall in defaults, offset by a 1-point acceleration in real income growth).

So what do we make of this? Well, first, boringly perhaps but importantly, it’s important to acknowledge that sometimes the familiar story is the correct story. If households owe more today than a year ago, it’s because they borrowed more over the past year. It’s profoundly misleading to suppose this is always the case. But in this case it is the case. Secondly, I think this vindicates the conclusion of our paper, that sustained deleveraging is impossible in the absence of substantially higher inflation, higher defaults, or lower interest rates. These are not likely to be seen without deliberate, imaginative policy to increase inflation, directly reduce the interest rates facing households, and/or write off much more of household debt than will happen through the existing bankruptcy process. Otherwise, in today’s low-inflation environment, as soon as the acute crisis period ends leverage is likely to resume its rise. Which seems to be what we are seeing.

[*] More precisely: By our calculations, defaults reduced the aggregate household debt-income ratio by 20 points over 2008-2012, out of a total reduction of 21.5 points.

Functional Finance and Sound Finance


Anyone who who has been following debates on fiscal policy over the past few years will have noticed that, among those who think fiscal policy can be effective, there are two distinct camps. There is a minority who think that fiscal policy is not subject to a budget constraint; that is, that as long as a government borrows in its own currency, its existing liabilities never limit its ability to adjust taxes and spending to bring the economy to full employment. And there are the majority who think that governments are subject to a binding budget constraint; that is, that while adjusting spending and taxes can in principle be used to bring about full employment, it may be impossible or undesirable to do so when the level of government debt is already high. In this view, maintaining full employment should be left to monetary policy. Following Abba Lerner, I call the first position “functional finance” and the second position “sound finance.”

I believe there are important differences between these two positions. But I also believe that these differences have not been clearly articulated, and as a result these debates between them been unproductive. It is my view that there are no important differences in terms of economic theory between the two positions. A perfect application of a functional finance policy rule and of a sound finance policy rule are indistinguishable. The difference between the camps is with respect to policy errors — which errors are most likely, and which are most costly.

Alternative Policy Rules

The starting point is the idea of instruments, which are variables directly controlled by the policymaker; and targets, which are the variables the policymaker wants to set at some level but cannot control directly. When the target variable is not at its desired level, the policymaker adjusts one or more instruments to try to bring it there. This creates relationship between the current level of the target and the chosen level of the instrument. We call this relationship a policy rule. Both functional finance and sound finance represent policy rules in this sense. Tinbergen’s Rule says that for policy rules to be successful (in the sense that all targets converge to their desired levels), there must be at least as many instruments as targets. One policy lever cannot be relied on to achieve two separate outcomes.

We have two instruments in macroeconomic policy: the government budget balance, and the central bank-controlled interest rate. What are our targets?

At first glance, full employment and price stability appear to be two separate targets. But in fact, both Lerner’s functional finance and the sound finance of modern textbooks agree that inflation is the result of demand-determined expenditure departing from a technologically determined level of potential output. Less than full employment means falling inflation, or deflation; overfull employment means high or rising inflation. So full employment and price stability are not two separate targets, they are two ways of describing the same target.

Both camps agree that we can identify a unique target level of output, and they agree on what that target should be. They also agree that output rises with higher government deficits, and falls with higher interest rates. So when interest rates are too high, or budget deficits too small, we will see unemployment (and perhaps deflation); when interest rates are too low or deficits are too large, we will see inflation (and perhaps bottlenecks and rising relative prices of factors in inelastic supply).

This consensus is shown in Figure 1. The full employment locus shows all the combinations of interest rates and fiscal balances that are compatible with full employment and price stability. A fall in private demand will require a rise in the deficit and/or a fall in interest rates to maintain full employment, so it will shift the full employment locus down and to the left. Similarly, a rise in private demand will shift the locus up and to the right. But for any level of private demand, with two instruments and only one target, there are an infinite number of combinations that achieve full employment.

(It is convenient to think of the fiscal balance on the horizontal axis as the primary balance, that is, the balance net of interest payments. So we are implicitly assuming that interest payments do not raise aggregate demand. It is also convenient to think of the interest rate as the real rate, that is, net of inflation. It would be straightforward to incorporate the effects of interest payments and inflation into the story, but would not change it in any interesting way.)

The first point of disagreement is what to do at a point like a. Output is below potential, but which instrument should be used to raise it? Functional finance says, the fiscal balance: government spending should be raised (or taxes should be lowered), moving the economy to the left, until we reach the full employment locus. The modern sound-finance consensus says that the interest rate should be lowered, moving the economy downward to the full employment locus. Both agree that government should do something to raise output. The disagreement is over which instrument to use.

Whichever instrument is used to keep output at potential, there is one instrument left over for some other target. The logical candidate is the sustainability of government debt.

We’ve discussed the math of government debt dynamics quite a bit on this blog. (See here and here and here and here.) The important thing for our purposes is that the long-run trajectory of the debt-GDP ratio depends on the primary balance, the interest rate on government borrowing, and the growth rate of GDP. If we write the ratio of government debt to GDP as b, and the primary deficit as a share of GDP as d, then for a given deficit, the equilibrium condition is b=d* 1/(g-r), where g is the average or expected growth rate of GDP over the period of interest. So for a given debt-GDP ratio b, the primary deficit required to hold it constant is d = b(g-r). (This is all just accounting; it does not depend on any economic assumptions.) It’s evident that, if we take the growth rate as exogenous, then for any given debt-GDP ratio there is a set of r, d combinations for which the debt-GDP ratio is constant. We can represent these values graphically in Figure 2. The dotted horizontal line is the growth rate. The diagonal line is the constant debt ratio locus. With a deficit or interest rate above the diagonal line, the debt-GDP ratio will rise; below, it will fall.

Note that the slope of the diagonal depends on the starting debt-GDP ratio — the higher it is, the shallower the slope will be. With no government debt, the line is vertical at the primary balance = 0 axis. So in any period in which the economy is at a point above the debt-sustainability locus, the diagonal rotates clockwise; in any period in which the economy is below the debt-sustainability locus, the diagonal rotates counter-clockwise.

What happens if the economy is off the constant-debt locus? It depends. In the area marked A (everything above the heavy line), the debt-GDP ratio rises without limit. In B, the debt-GDP ratio rises but converges to a finite value. In C the ratio falls to a finite value. In D, the debt-GDP ratio falls to zero and the government then accumulates a positive asset position, which eventually converges to a finite fraction of GDP. Finally, in area E the debt-GDP ratio falls to zero and the government then accumulates a positive asset position that rises without limit as a share of GDP. (If you are unconvinced we can go through the math.) Since the government budget constraint is normally taken to be the condition that debt-GDP ratio not rise without limit, we can ignore the distinctions between cases B through E and regard the heavy line as the government budget constraint.

We then combine this constraint with the full employment locus to give Figure 3.

Now we have two instruments and two targets. Or rather, one and a half targets: Since there is nothing special about the current debt-GDP ratio, we don’t need it to stay constant; we just need it not to go to infinity. So we don’t need to be on the debt-sustainability curve, we need to be on or below it. Point b, which satisfies the budget constraint exactly, is fine, but so is anywhere on the full employment locus below and to the right of b.

The functional finance-sound finance divide is just this: Functional finance says the fiscal balance instrument should be assigned to the full employment target and the interest rate instrument should be assigned to the debt sustainability target. Sound finance says the interest rate instrument should be assigned to the full employment target and and the fiscal balance instrument should be assigned to the debt sustainability target.

Functional finance and sound finance agree that the economy should be at a point like b. If policy were executed perfectly, the economy would always be at such a point, and there would be no way of knowing which rule was being followed. Since both target should always be at their chosen levels, it would make no difference — and be impossible to tell — which instrument was assigned to which target. The difference between the positions only becomes apparent when policy is not executed perfectly, and the economy departs from a position of full employment with sustainable public debt.

Consider a point somewhere above b, where we are have high unemployment but the debt-GDP ratio is rising without limit. What to do? Both orthodoxy and Lernerism want to get the economy back to a point like b, but they disagree on how.

In the sound-finance view, the interest rate instrument is committed to the output target. This means we must use the fiscal balance instrument free to meet the debt sustainability condition. This is how policy is normally discussed: An unsustainable upward trajectory in the debt position requires the government balance to move  toward surplus. In this case, that means that the government must cut spending or raise taxes, despite the fact that demand is already too low. Under Lernerian functional finance, on the other hand, the fiscal balance is committed to the output target, so the rule calls for higher deficits even though the debt position is already unsustainable. It is then the responsibility of monetary policy to adjust to maintain debt sustainability.

These alternatives are shown in Figure 4. The right-hand trajectory from c to b is the orthodox path. The left-hand trajectory is the Lernerian path. Implicit in the orthodox path is the idea that deficits must be brought down first, meaning a substantial period of high unemployment and output below potential; only once debt is on a sustainable path can interest rates be reduced to move back toward full employment. While the Lernerian path says in effect: If government debt is rising out of control, the central bank should intervene to force interest rates down to a level where the debt is sustainable. Then, if the resulting liquidity raises expenditure above the full employment level, you can subsequently raise taxes or cut transfers to bring demand back down.

Orthodoxy says that budget problems must be addressed fiscally. But this is true only on the implicit assumption that the interest rate is not available as an instrument to target debt sustainability. Sound finance’s policy rule is a Taylor-type rule for monetary policy, combined with a long-term government budget position that satisfies the debt-sustainability constraint at that interest rate. Functional finance’s policy rule: (1) fix the interest rate at a level at or below the expected growth rate (maybe even zero); (2) adjust transfers and taxes until output is at the full employment/stable prices level. The claim that fiscal policy must be subject to a budget constraint, comes down to the claim that the central bank cannot or will not keep r sufficiently low to make the full-employment fiscal position sustainable.

Why is there such disagreement about which instrument should be assigned to which target? It seems to me that the most important argument from the sound finance side is that elected governments cannot be trusted with the instrument of discretionary fiscal policy. They will not set taxes and transfers to bring aggregate demand to the full employment level, but will choose a higher, inflationary level of demand. Only independent central banks can be trusted to bring output to its socially optimal level. In this sense, the functional finance-sound finance divide is not a debate about economic theory, but about politics and sociology.

There are also more specifically economic disagreements. The sound finance side is more confident than the functional finance side about how quickly and reliably a change in interest rates will affect output. If there is a long lag between the change in the instrument and its effect, hitting the target requires accurate prediction of the state of the economy farther into the future. The existence of the ZLB reinforces this concern, since it is really just a special case of interest-inelasticity. (The statement “output does not respond strongly to any feasible change in interest rates” is equivalent to the statement “the interest-rate change needed to achieve a strong output response is not feasible.”) The functional finance side also tends to see a greater social cost in falling below full employment than rising above it, while the sound finance side tends to see the costs as symmetrical.

That is the framework. Now consider some modifications and special cases.


A natural objection to the functional finance view is that it may not be possible for the central bank to maintain interest rates low enough to keep debt sustainable. If we live in a world of high capital mobility and our government’s liabilities are close substitutes for liabilities elsewhere in the world, then the private sector will not hold them if their yield is too much lower. In this case — which is not unrealistic for small, open countries — the interest rate ceases to be a policy variable. This is shown in Figure 5, where r* is the exogenous work interest rate.

At a point like d in the figure, the public debt is stable but output is below potential. A move toward a primary deficit would raise output but put the debt on an unsustainable path. This case is not inherently implausible — one would need to think carefully about the concrete assumptions it embodies — but it is important to recognize that it rules out sound finance as well as functional finance. If the interest rate is set exogenously at the world level, it cannot be used to stabilize public debt or to stabilize output. An additional instrument is needed; the exchange rate is the natural choice. Since the exchange rate cannot straightforwardly be used to achieve debt sustainability, in this case there is a natural argument to switch the assignment of fiscal policy to debt sustainability and achieve full employment via the exchange rate.

Another possibility, which has been getting increasing attention recently, is that very low interest rates are destabilizing for the financial system. (I have criticized this idea before, but I don’t think it can be ruled out definitively.) Then we have another condition to satisfy, a asset price stability condition. Like the debt sustainability condition, this is asymmetrical, it doesn’t have to be satisfied exactly. But this one is a floor on interest rates rather than a ceiling. The is shown in Figure 6. Here, the asset price stability constraint does not initially prevent achieving both the other targets: As in Figure 3, point b initially satisfies all the constraints, as does any other point along the full employment locus below and to the right of it, down to the dotted line.

But what if a fall in private demand shifts the full employment locus far to the left? Here there is an important difference between the sound finance and functional finance rules. The functional finance rule says that the fall in private demand requires the government budget to move toward deficit. That is, we move left from b to the new full employment locus. This may in turn require a fall in interest rates, if the higher deficits would otherwise put the public debt on an unsustainable path. But public debt sustainability never requires an interest rate below the long term growth rate. So, since it is not plausible that the minimum interest rate compatible with asset price stability condition is greater than the growth rate, the possibility of asset bubbles should not limit the application of the functional finance rule.

The sound finance rule, on the other hand, says that the response to a fall in private demand should be a reduction in the interest rate. In other words, faced with the fall in private demand shown in the figure, we should move downward from point b  to the new full employment locus. Now there is the possibility that the required interest rate is incompatible with asset price stability. (In some views, this is precisely what happened a decade ago, setting the stage for the housing bubble.) This becomes an argument for setting interest rates higher than the conventional policy rule implies, even at the cost of higher unemployment.

Formally, the ZLB is identical to the asset price stability condition: both set floors to allowable interest rates. It is curious that, while concern with the ZLB and with the destabilizing effects of low interest rates often come from opposite political positions, they are — at least in this framework — equivalent in their implications for policy. Both are arguments for a reliance on fiscal policy to offset fall in private demand in general, rather than waiting for the floor to be reached — that is, for some form of functional finance.

Finally, consider the case where the fiscal balance is exogenously fixed, as shown in Figure 7. I think this is the case most critics of functional finance have in mind. If the budget authority, for whatever reason, is committed to tax and spending policies corresponding to a primary deficit, there may be no interest rate that can deliver both debt sustainability and full employment. The central bank must choose one. If it chooses debt sustainability, we have a situation known in the literature as “fiscal dominance.” The central bank must increase its liabilities as needed to finance the government deficit, even if that results in aggregate demand rising to inflationary levels. This is the situation at point e.

It is important to stress that Figure 7 is not what is advocated by functional finance. There is an understandable but unfortunate confusion between the claim “deficits can be at whatever level is needed to reach full employment” and “deficits can be at whatever level you want.” Functional finance says the former, not the latter. A functional finance rule would call for the government to raise taxes or cut spending at a point like e — not to balance the budget, but to eliminate the inflation. The practical problem for functional finance supporters is to convince skeptics that such a rule will be followed by an elected government.


Advocates of functional finance say that a government that borrows in its own currency never needs to adjust its taxes or spending on account of its current deficit or accumulated debt. The fiscal balance can always be set at whatever level is needed to achieve full employment. Their sound-finance critics reply, “It’s true that a deficit will raise current output. But over the long run you need a primary surplus to ensure that the government stays on its budget constraint. If the central bank is forced to monetize the debt instead, you will have runaway inflation.”

The critics are correctly describing the situation in Figure 7, where it is true that the government budget position has been set without regard for debt sustainability, the central bank is monetizing the debt (this is simply another way of describing holding interest rates low enough to maintain a stable path for government liabilities), and there is uncontrolled inflation. But the inference the critics draw from this possibility — that fiscal policy must target debt sustainability — is not correct. The correct inference is that at least one of the two instruments must target debt sustainability, and at least one must target full employment. The problem in Figure 7 is that budget balance is being set without regard for either condition — that is, it is in violation of both policy rules. Either the sound finance rule, or the functional finance rule, or any linear combination of the two, would ensure that the economy does not remain at a point like e but instead converges to one like b in Figure 3.

The debate between sound finance and functional finance cannot be resolved as long as they are framed in terms of what kind of rule is feasible in principle, and what outcome results when it is followed exactly. The disagreement is about what kinds of rules policymakers can be expected to adhere to in practice, and about the relative costs of different policy errors.

[This post was inspired by this talk by Brad DeLong, and by some comments by Nick Rowe which I cannot locate now.]

Borrowing ≠ Debt

There’s a common shorthand that makes “debt” and “borrowing” interchangeable. The question of why an economic unit had rising debt over some period, is treated as equivalent to the question of why it was borrowing more over that period, or why its expenditure was higher relative to its income. This is a natural way of talking, but it isn’t really correct.

The point of Arjun’s and my paper on debt dynamics was to show that for household debt, borrowing and changes in debt don’t line up well at all. While some periods of rising household leverage — like the housing bubble of the 2000s — were also periods of high household borrowing, only a small part of longer-term changes in household debt can be explained this way. This is because interest, income growth and inflation rates also affect debt-income ratios, and movements in these other variables often swamp any change in household borrowing.
As far as I know, we were the first people to make this argument in a systematic way for household debt. For government debt, it’s a bit better known — but only a bit. People like Willem Buiter or Jamie Galbraith do point out that the fall in US debt after World War II had much more to do with growth and inflation than with large primary surpluses. You can find the argument more fully developed for the US in papers by Hall and Sargent  or Aizenman and Marion, and for a large sample of countries by Abbas et al., which I’ve discussed here before. But while many of the people making it are hardly marginal, the point that government borrowing and government debt are not equivalent, or even always closely linked, hasn’t really made it into the larger conversation. It’s still common to find even very smart people saying things like this:

We didn’t have anything you could call a deficit problem until 1980. We then saw rising debt under Reagan-Bush; falling debt under Clinton; rising under Bush II; and a sharp rise in the aftermath of the financial crisis. This is not a bipartisan problem of runaway deficits! 

Note how the terms “deficits” and “rising debt” are used interchangeably; and though the text mostly says deficits, the chart next to this passage shows the ratio of debt to GDP.
What we have here is a kind of morality tale where responsible policy — keeping government spending in line with revenues — is rewarded with falling debt; while irresponsible policy — deficits! — gets its just desserts in the form of rising debt ratios. It’s a seductive story, in part because it does have an element of truth. But it’s mostly false, and misleading. More precisely, it’s about one quarter true and three quarters false.
Here’s the same graph of federal debt since World War II, showing the annual change in debt ratio (red bars) and the primary deficit (black bars), both measured as a fraction of GDP. (The primary deficit is the difference between spending other than interest payments and revenue; it’s the standard measure of the difference between current expenditure and current revenue.) So what do we see?
It is true that the federal government mostly ran primary surpluses from the end of the war until 1980, and more generally, that periods of surpluses were mostly periods of rising debt, and conversely. So it might seem that using “deficits” and “rising debt” interchangeably, while not strictly correct, doesn’t distort the picture in any major way. But it does! Look more carefully at the 1970s and 1980s — the black bars look very similar, don’t they? In fact, deficits under Reagan were hardy larger than under Ford and Carter —  a cumulative 6.2 percent of GDP over 1982-1986, compared with 5.6 percent of GDP over 1975-1978. Yet the debt-GDP ratio rose by just a single point (from 24 to 25) in the first episode, but by 8 points (from 32 to 40) in the second. Why did debt increase in the 1980s but not in the 1970s? Because in the 1980s the interest rate on federal debt was well above the economy’s growth rate, while in the 1970s, it was well below it. In that precise sense, if debt is a problem it very much is a bipartisan one; Volcker was the appointee of both Carter and Reagan.
Here’s the same data by decades, and for the pre- and post-1980 periods and some politically salient subperiods.  The third column shows the part of debt changes not explained by the primary balance. This corresponds to what Arjun and I call “Fisher dynamics” — the contribution of growth, inflation and interest rates to changes in leverage. [*] The units are percent of GDP.
Totals by Decade
Primary Deficit Change in Debt Residual Debt Change
1950s -8.6 -29.6 -20.9
1960s -7.3 -17.7 -10.4
1970s 2.8 -1.7 -4.6
1980s 3.3 16.0 12.7
1990s -15.9 -7.3 8.6
2000s 23.7 27.9 4.2
Annual averages
Primary Deficit Change in Debt Residual Debt Change
1947-1980 -0.7 -2.0 -1.2
1981-2011 0.1 1.3 1.2
   1981-1992 0.3 1.8 1.5
   1993-2000 -2.7 -1.6 1.1
   2001-2008 -0.1 0.8 0.9
   2009-2011 7.3 8.9 1.6

Here again, we see that while the growth of debt looks very different between the 1970s and 1980s, the behavior of deficits does not. Despite Reagan’s tax cuts and military buildup, the overall relationship between government revenues and expenditures was essentially the same in the two decades. Practically all of the acceleration in debt growth in the 1980s compared with the 1970s is due to higher interest rates and lower inflation.

Over the longer run, it is true that there is a shift from primary surpluses before 1980 to primary deficits afterward. (This is different from our finding for households, where borrowing actually fell after 1980.) But the change in fiscal balances is less than 25 percent the change in debt growth. In other words, the shift toward deficit spending, while real, only accounts for a quarter of the change in the trajectory of the federal debt. This is why I said above that the morality-tale version of the rising debt story is a quarter right and three quarters wrong.

By the way, this is strikingly consistent with the results of the big IMF study on the evolution of government debt ratios around the world. Looking at 60 episodes of large increases in debt-GDP ratios over the 20th century, they find that only about a third of the average increase is accounted for by primary deficits. [2] For episodes of falling debt, the role of primary surpluses is somewhat larger, especially in Europe, but if we focus on the postwar decades specifically then, again, primary surpluses accounted for only a about a third of the average fall. So while the link between government debt and deficits has been a bit weaker in the US than elsewhere, it’s quite weak in general.

So. Why should we care?

Most obviously, you should care if you’re worried about government debt. Now maybe you shouldn’t worry. But if you do think debt is a problem, then you are looking in the wrong place if you think holding down government borrowing is the solution. What matters is holding down i – (g + π) — that is, keeping interest rates low relative to growth and inflation. And while higher growth may not be within reach of policy, higher inflation and lower interest rates certainly are.

Even if you insist on worrying not just about government debt but about government borrowing, it’s important to note that the cumulative deficits of 2009-2011, at 22 percent of GDP, were exactly equal to the cumulative surpluses over the Clinton years, and only slightly smaller than the cumulative primary surpluses over the whole period 1947-1979. So if for whatever reason you want to keep borrowing down, policies to avoid deep recessions are more important than policies to control spending and raise revenue.

More broadly, I keep harping on this because I think the assumption that the path of government debt is the result of government borrowing choices, is symptomatic of a larger failure to think clearly about this stuff. Most practically, the idea that the long-run “sustainability” of the  debt requires efforts to control government borrowing — an idea which goes unquestioned even at the far liberal-Keynesian end of the policy spectrum —  is a serious fetter on proposals for more stimulus in the short run, and is a convenient justification for all sorts of appalling ideas. And in general, I just reject the whole idea of responsibility. It’s ideology in the strict sense — treating the conditions of existence of the dominant class as if they were natural law. Keynes was right to see this tendency to view of all of life through a financial lens — to see saving and accumulating as the highest goals in life, to think we should forego real goods to improve our financial position — as “one of those semicriminal, semi-pathological propensities which one hands over with a shudder to the specialists in mental disease.”

On a methodological level, I see reframing the question of the evolution of debt in terms of the independent contributions of primary deficits, growth, inflation and interest rates as part of a larger effort to think about the economy in historical, dynamic terms, rather than in terms of equilibrium. But we’ll save that thought for another time.

The important point is that, historically, changes in government borrowing have not been the main factor in the evolution of debt-GDP ratios. Acknowledging that fact should be the price of admission to any serious discussion of fiscal policy.

[1] Strictly speaking, debt ratios can change for reasons other than either the primary balance or Fisher dynamics, such as defaults or the effects of exchange rate movements on foreign-currency-denominated debt. But none of these apply to the postwar US.

[2] The picture is a bit different from the US, since adverse exchange-rate movements are quite important in many of these episodes. But it remains true that high deficits are the main factor in only a minority of large increases in debt-GDP ratios.

A History of Debt/GDP

“Probably more uninformed statements have been made on public-sector debt and deficits,” says Willem Buiter, “than on any other subject in macroeconomics. Proof by repeated assertion has frequently appeared to be an acceptable substitute for proof by deduction or proof by induction.”

It’s hard to disagree. 
But at least we know where an informed discussion starts. It starts from the least controversial equation of macroeconomics, the law of motion of public debt:
b is the ratio of public debt to GDP, d is the ratio of primary deficit to GDP, i is the nominal interest rate, g is the real growth rate of GDP, and pi is inflation. In principle this is true by definition. (In practice things aren’t alway so simple.) The first thing you realize, looking at this equation, is that contrary to the slack-jawed bleating of conventional opinion, there’s no necessary connection between the evolution of public debt and government spending and taxes. Interest rates, growth rates and inflation are, in principle, just as important as the primary balance. Which naturally invites the question, which have been more important in practice?
There have been various efforts to answer this question for different countries in different periods, but until recently there wasn’t any systematic effort to answer it for a broad sample of countries over a long period. I was thinking of trying to do such an exercise myself. But it looks like that’s not necessary. As Tom M. points out in comments,  the IMF has just undertaken such an exercise. Using the new Historical Public Debt Database, they’ve decomposed the debt-GDP ratios of 174 countries, from 1880 to the present, into the four components of the law of motion. (Plus a fifth, discussed below.) It’s an impressive project. Ands far as one can tell from this brief presentation, they did it right. Admittedly it’s a laconic 25-page powerpoint, but there’s not even the hint of a suggestion that microfoundations or welfare analysis would contribute anything. The question is just, how much has each of the components contributed to shifts in debt-GDP ratios historically?
As I’ve noted here before, the critical issue is the relationship between g and i, or (g + pi) and i as I’ve written it here. On this point, the IMF study gives ammunition to both sides.
From roughly 1895 to 1920, and from 1935 to 1980, nominal growth rates (g + pi) generally exceeded nominal interest rates. From 1880 to 1895, from 1920 to 1935, and from 1980 to the present, interest mostly exceeded growth. It’s impossible, looking at this picture, to say one relationship or the other is normal. Lernerian-Keynesians will say, why can’t the conditions of the postwar decades be reproduced by any government that chooses to; while the orthodox (Marxists and neoclassicals equally) will say the postwar decades were anomalous for various reasons — financial repression, limited international mobility of capital, exceptionally strong growth. The historical evidence doesn’t clearly resolve the question either way.

Given the unstable relationship between g and i, it’s not surprising there’s no consistent pattern in episodes of long-term reduction in debt-GDP ratios. I had hoped such episodes would turn out to be always, or almost always, the result of faster growth, lower interest rates, and higher inflation. This is basically true for the postwar decades, when the biggest debt reductions happened. Since 1980, though, it seems that countries that have reduced their debt-GDP ratios have done it the hard way, by taxing more than they spent. Over the whole period since 1880, periods of major (at least 10 percent of GDP) debt reduction has involved primary surpluses and g > r in about equal measure.

Another interesting point is how much the law of motion turns out to have exceptions. The IMF’s version of the equation above includes an additional term on the right side: SFA, or stock-flow adjustment, meaning the discrepancy between the flow of debt implied by the other terms of the equation and the stock of debt actually observed. This discrepancy turns out to be often quite large. This could reflect a lot of factors; but for recent episodes of rising debt-GDP ratios (in which SFA seems to play a central role) the obvious interpretation is that it reflects the assumption by the government of the banking system’s debts, which is often not reflected in official deficit statistics but may be large relative to the stock of debt. The extreme case is Ireland, where the government guarantee of the financial system resulted in the government assuming bank liabilities equal to 45 percent of GDP. To the extent this is an important factor in rising public debt generally — and again, the IMF study supports it — it suggests another reason why concern with balancing the long-term budget by “reforming” Medicare, etc., is misplaced. One financial crisis can cancel out decades of fiscal rectitude; so if you’re concerned about what the debt-GDP ratio will be in 2075, you should spend less time thinking about public spending and taxes, and much more time thinking about effective regulation of the financial sector.
The bottom line is, the dynamics of public debt are complicated. But as always, intractable theoretical controversies become more manageable, or at least more meaningful, when they’re posed as concrete historical questions. Good on the IMF for doing this.

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.

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.