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.

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.

Bond Market Vigilantes: Invisible or Inconceivable?

Brad DeLong is annoyed with people who are scared of invisible bond-market vigilantes. And he’s right to be annoyed! It’s extraordinarily silly — or dishonest — to claim that the confidence of bondholders constrains fiscal policy in the United States. As he puts it, “Any loss of confidence in the long-term fiscal stability of the United States of America” is an “economic thing that does not exist.”

So he’s right. But does he have the right to be right?

I’m going to say No. Because the error he is pointing to, is one that the economics he teaches gives no help in avoiding.

The graduate macroeconomics course at Berkeley uses David Romer’s Advanced Macroeconomics, 3rd Edition. (The same text I used at UMass.) Here’s what it says about government budget constraints:

What this means is that the present value of government spending across all future time must be less than or equal to the present value of taxation across all future time, minus the current value of government debt. This is pretty much the starting point for all mainstream discussions of government budgets. In Blanchard and Fischer, another widely-used graduate macro textbook, the entire discussion of government budgets is just the working-out of that same equation. (Except they make it an equality rather than an inequality.) If you’ve studied economics at a graduate level, this is what government budget constraint means to you.

But here’s the thing: That kind of constraint has nothing to do with the kind of constraint DeLong’s post is talking about.

The textbook constraint is based on the idea that government is setting tax and spending levels for all periods once and for all. There’s no difference between past and future — the equation is unchanged if you reverse the sign of the t terms (i.e. flip the past and future) and simultaneously reverse the sign of the interest rate. (In the special case where the interest rate is zero, you can put the periods in any order you like.) This approach isn’t specific to government budget constraints, it’s the way everything is approached in contemporary macroeconomics. The starting point of the Blanchard and Fischer book, like many macro textbooks, is the Ramsey  model of a household (central planner) allocating known production and consumption possibilities across an infinite time horizon. (The Romer book starts with the Solow growth model and derives it from the Ramsey model in chapter two.) Economic growth simply means that the parameters are such that the household, or planner, chooses a path of output with higher values in later periods than in earlier ones. Financial markets and aggregate demand aren’t completely ignored, of course, but they’re treated as details to be saved for the final chapters, not part of the main structure.

You may think that’s a silly way to think about the economy (I may agree), but one important feature of these models is that the interest rate is not the cost of credit or finance; rather, it’s the fixed marginal rate of substitution of spending or taxing between different periods. By contrast, that interest is the cost of money, not the cost of substitution between the future and the present, was maybe the most important single point in Keynes’ General Theory. But it’s completely missing from contemporary textbooks, even though it’s only under this sense of interest that there’s even the possibility of bond market vigilantism. When we are talking about the state of confidence in the bond market, we are talking about a finance constraint — the cost of money — not a budget constraint. But the whole logic of contemporary macroeconomics (intertemporal allocation of real goods as the fundamental structure, with finance coming in only as an afterthought) excludes the possibility of government financing constraints. At no point in either Romer or Blanchard and Fischer are they ever discussed.

You can’t expect people to have a clear sense of when government financing constraints do and don’t bind, if you teach them a theory in which they don’t exist.

EDIT: Let me spell the argument out a little more. In conventional economics, time is just another dimension on which goods vary. Jam today, jam tomorrow, jam next week are treated just like strawberry jam, elderberry jam, ginger-zucchini jam, etc. Either way, you’re choosing the highest-utility basket that lies within your budget constraint. An alternative point of view – Post Keynesian if you like – is that we can’t make choices today about future periods. (Fundamental uncertainty is one way of motivating this, but not the only way.) The tradeoff facing us is not between jam today and jam tomorrow, but between jam today and money today. Money today presumably translates into jam tomorrow, but not on sufficiently definite terms that we can put it into the equations. (It’s in this sense that a monetary theory and a theory of intertemporal optimization are strict alternatives.) Once you take this point of view, it’s perfectly logical to think of the government budget constraint as a financing constraint, i.e. as the terms on which expenditure today trades off with net financial claims today. Which is to say, you’re now in the discursive universe where things like bond markets exist. Again, yes, modern macro textbooks do eventually introduce bond markets — but only after hundreds of pages of intertemporal optimization. If I wrote the textbooks, the first model wouldn’t be of goods today vs. goods tomorrow, but goods today vs. money today. DeLong presumably disagrees. But in that world, macroeconomic policy discussions might annoy him less.

What’s Good Enough for GE Is Good Enough for America

[Originally posted at New Deal 2.0.]

S&P’s threat to downgrade the US government’s credit rating has been dismissed by economist-bloggers as a political intervention by bondowners and compared to “adorable children wearing their underpants outside their trousers.” As far as the chances of the US someday defaulting on its debt go, the announcement has zero informational value.

Still, it’s true that federal debt held by the public has reached 60 percent of GDP, while tax revenues remain around 20 percent of GDP. 60 percent of GDP is a lot! And double, nearly triple, tax revenue! What would we call a company with outstanding debt double or even triple its revenues, and expected to keep the highest bond rating?

We could call it General Electric. 

As recently as 2007, GE had an S&P rating of AAA with outstanding debt at over three time revenues. Or we could call it the Tennessee Valley Authority; TVA managed outstanding debt of 3.9 times revenue in the late ’90s (it’s since come down a bit), and S&P never downgraded its bond rating from AAA. Or, we could call it Hydro Quebec, with debt of over 4.5 times revenues (altho, admittedly, its S&P rating is only A+). Or the natural gas and energy supplier TransCanada, with debt equal to 2.2 time revenues and an A rating from S&P. Even Transocean, which operated the Deepwater Horizon rig for BP, managed an A- rating prior to the spill, with a debt-revenue ratio similar to what the federal government has now.

Now, it’s perfectly sensible for a big utility, with its high proportion of long-lived fixed capital and stable revenue streams, to carry a lot of debt. If I ran Hydro Quebec (and converting the company to a worker- and consumer-owned cooperative wasn’t an option), I’d take on a lot of debt too. But here’s the point. If the question is, what if the government had to fund itself like a private business, the answer isn’t necessarily that it would do anything different from what it’s doing now.

In the real world, of course, there are lots of differences between the government of the United States and a private business. The federal government issues the currency that its debt is denominated in. It has effectively unlimited authority to increase taxes on the private sector. And its liabilities are the most important store of value and means of payment for the private sector. (When Alan Greenspan said that the financial system would have a real problem without holdings of federal debt, he may have been arguing in bad faith, but he wasn’t wrong.) And of course, the US government is responsible for output and employment in the economy as a whole, and not just for its own balance sheet. All these differences mean that it makes sense for the US government to carry more debt than a private business. If GE or Transocean are safe bets for lenders with debt of two or three times revenue, then the federal government must be ultra ultra safe. Which, interestingly enough, is just what the bond market says.

So perhaps we can get away from the “oooh, that’s a really big number!” school of analysis of federal borrowing. And instead ask what levels of federal deficit and outstanding debt are most compatible with economic growth and financial stability. For the foreseeable future, I’d suggest, the answer has a lot more to do with the role of government spending in aggregate demand, and with government debt as a risk-free asset for the private sector, than with the level of debt that’s “sustainable”. Because if you think there are more states of the world where TVA or GE make their payments to bondholders than where the US government does, you must be smoking something from S&P’s private stash.

UPDATE: This excellent post from Mike Konczal makes the same point more systematically.