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Tuesday, April 14, 2020

Why Fiscal Sustainability Is An Unsustainable Concept

One frequently encounters variations of the phrase "unsustainable debt trajectory" (or similar) in statements by mainstream economists. The phrase is popular as it offers what appears to be a sophisticated criticism of some fiscal policy setting that is disapproved of, but without having any content that can be used to prove the speaker wrong. Modern Monetary Theory (MMT) largely rejects that "debt sustainability" has theoretical validity for a floating currency sovereign. I will focus on the analysis of a paper by Scott Fulwiler to justify this stance.

(Note: This article is a draft section in a chapter on fiscal policy in my MMT primer. I will cover some important concepts in earlier sections, but not repeat them here. The first is the notion that inflation is the constraint on fiscal policy, which comes from Functional Finance (primer). The next concept is that a floating currency sovereign can always avoid default. I would note that this chapter is covering much of the material seen in Chapter 7 of Understanding Government Finance.)

The concept of "debt sustainability" is the usual alternative to the argument that inflation is the only constraint on floating currency sovereigns. Technically, there is the related idea of the inter-temporal governmental budget constraint, which is a mathematical construct that appears in neoclassical models. I discussed this constraint in Section 7.4 of Understanding Government Finance. The complexity level of that constraint is beyond what I wish to discuss in this text. Unless one wants to get into the mathematics, the notion of "fiscal sustainability" I use here covers most of the issues of the governmental budget constraint.

This section is based on some of the discussions found in the paper "The debt ratio and sustainable macroeconomic policy," by Scott Fullwiler.[1]  I am simplifying certain concepts, and not attempting to cover all the topics in that paper; they will be addressed in later sections. Much of the content of that paper is a critique of neoclassical theory. Since I am not assuming that my readers are familiar with that theory, discussing that material would be mainly a source of confusion. Readers with a more advanced knowledge of economic theory would be advised to read that article if they wish to have further details on what distinguishes MMT from neoclassical theory.


A formal definition of fiscal sustainability is that the interest burden of government debt does not rise beyond the productive capacity of the economy, or alternatively, the debt-to-GDP ratio does not become arbitrarily large.[2] (The looser way of describing the debt-to-GDP ratio condition is to say that the ratio does not go to infinity.) For simplicity, I will drop the discussion of the interest burden, and just use the notion of the debt-to-GDP ratio being bounded.

The first thing to keep in mind is that we are looking at a ratio, and if we assume that the economy is growing forever, both the level of debt and the size of nominal GDP will become arbitrarily large ("go to infinity"). The absolute level of debt does not matter, what matters is its size relative to the economy.

In less formal discussions (such as opinion columns), mainstream commentators are typically using a looser version of this definition. The issue is not what is happening at times infinitely far in the future, rather a concern about the debt-ratio on some forecast horizon (like 75 years). Shortening the horizon is reasonable, as we should not be worried about what is happening to government debt long after the Sun has reduced the Earth to a cinder. However, by moving away from this formal definition, "fiscal sustainability" is quite vague, and it does not have much more theoretical content than saying "Gee willikers, the debt-to-GDP ratio will get really high!" (What percentage is "really high"?) This lack of precision on such an important topic is rather awkward.

Primary Deficits and Long Run Averages

We cannot really hope to create an exact forecast of the long-run trajectory of the economy. We mighty be able to get a handle on the upcoming year, but we do not what will cause future business cycles. The usual convention is to assume that the economy will revert to a long-run average behaviour.

The usual assumption made is that the economy will revert to some average growth rate in real terms, which cannot be controlled by policymakers. The idea is population growth cannot be determined by policymakers, and the productivity of workers will follow trends in technology. Although this might be misleading, it is safe to say that there is no easy method for a country to decide that it would like its output to grow faster; development economics is a difficult problem.

Conversely, average inflation rates appear to be under the control of policymakers. For example, if inflation is too high, there are many mechanisms by which a recession can be forced, and recessions tend to reduce inflation rates. One may note that countries like Canada were able to hit their 2% inflation targets from the mid-1990s until the Financial Crisis (but many were below target afterward).[3]

Taken together, we can see that nominal or GDP growth is assumed to tend to some average level, with average nominal GDP growth equaling real GDP growth plus the inflation target.

We then need to come up with a way of specifying the long-term tendency for fiscal policy settings. The conventional way of specifying fiscal policy is in terms of the primary fiscal balance (which can either be a deficit or surplus). This is the fiscal deficit without interest expenses. For example, if the fiscal deficit is 4% of GDP, and interest expense is 3% of GDP, the primary fiscal balance is a deficit of 1% of GDP.

The apparent reason for looking at the primary fiscal balance is that it is the difference between taxes and programme spending -- and programme spending is to accomplish desired goals (medical care, military, welfare programmes). Interest expenses are just welfare payments for bond holders. The long-term tendency of fiscal policy is expressed by assuming that the primary fiscal balance is steady near some value.

Sustainability Conditions

Whether or not a steady state fiscal policy is sustainable depends upon the relationship between the growth rate of the economy, and the interest rate on debt. Please note that the relationship described here is outlined in the Fullwiler paper, but I am giving a longer explanation that explains it without relying up on the use of equations.

We can understand this easily by approximating the relationship that determines the debt-to-GDP ratio in a particular year. It is the sum of two terms.
  1. Take the previous debt-to-GDP ratio, and multiply it by the factor of one plus difference between the interest rate on debt minus the GDP growth rate. (This can be described as the growth differential between the debt stock on its own, and GDP.) For example, if the interest rate is 4%, and the GDP growth rate is 5% (variables could either be both real or nominal), multiply the previous debt-to-GDP ratio by 0.99 (=1 - 1%). If the debt-to-GDP ratio was 50%, the new ratio is 50(0.99) = 49.5%. Note that this term is multiplying the debt ratio, not adding to it.
  2. Add the year's primary balance as a percent of GDP. So if the primary deficit in the previous example is 4%, the debt-to-GDP ratio is 53.5% (=49.5% + 4%).
(Author's note: I might add a technical appendix to justify that claim. The approximation comes from assuming that we are working with annual data, and more importantly, using a first order approximation of debt and GDP growth rates. The error would be small for small growth differentials, which is normally the case. It would start to break down if the differential 10% or above.)

If we assume that growth rates and the primary deficits are constants[4], we can use the above approximation to see that the debt-to-GDP ratio will remain bounded if GDP growth is greater than the interest rate. In that case, the first term in the approximation is shrinking by the growth rate different. Once the debt-to-GDP ratio is large enough, that shrinkage will be larger than the addition provided by the primary deficit.

For example, assume that the primary deficit is a whopping 10% of GDP, while the GDP growth rate is 1% greater than the interest rate. If the debt-to-GDP ratio somehow reached 2000%, the first term of the approximation tells us that the debt-to-GDP ratio falls by 20% (1% of 2000%), then the primary deficit adds back 10% -- so the debt-to-GDP ratio would fall. According to the approximation, the two terms imply an equilibrium ratio of 1000%. (The growth differential implies a drop of 10%, and the primary deficit adds back 10%.)

Conversely, if the interest rate on government debt is greater than the GDP growth rate, the debt-to-GDP ratio will spiral off to infinity unless there is a primary surplus to stop growth. As the debt-to-GDP ratio rises, larger surpluses are needed to stop the spiral.

Implausibility of an Ever-Rising Ratio

The possibility of the debt-to-GDP ratio rising to infinity is quite curious. If we were to take the model seriously, the economy would evolve such that interest payments are more than 100% of GDP. That is, bond holders receive more interest from the government than is needed to buy everything produced by the economy, and put the excess income into buying more bonds.

This seems like an implausible outcome. Why would you want to hold more debt, when you can already buy everything within the economy? Instead, you might as well bid up the price of goods and services, so that you get a bigger portion of real output (remembering that it is extremely unlikely that all the debt is owned by a single individual, and that workers get incomes that will also want to buy goods and services).

Fullwiler describes the situation as follows:
In other words, a primary budget balance not at least as high as 0.6 percent of GDP on average would grow deficits, the national debt, and debt service all to the point that eventually paying the debt service would result in high and rising inflation. While this second row puts the convergence ratios at infinity for convenience, in fact at some point the increased debt service would simply pass through to inflation to raise nominal GDP in kind. Thus, CBO’s [CBO = U.S. Congressional Budget Office] regular practice of assuming a long run nominal GDP growth rates equal to the potential real GDP growth rate plus inflation at around 2 percent is inconsistent with its own projections of unbounded growth in debt service payments.
The problem appears straightforward: the assumption that long-run GDP growth rates and interest rates are fixed (at "natural rates") makes very little sense. If we look at stock-flow consistent (SFC) models (as discussed in my book An introduction to SFC Models Using Python),we see that SFC models do not exhibit such behaviour. An increase in government debt implies that private sector wealth is rising, and we should see increased consumption out of that wealth. If the increase in nominal demand is beyond the capacity of the economy to provide real goods and services, the price of goods and services would be bid higher. That is, the debt-to-GDP ratio would be inflated away by nominal GDP growing faster than the nominal interest rate.

In other words, the entire premise of debt sustainability analysis is based on obviously defective macroeconomic models. It is abundantly clear that the debt-to-GDP ratio will not go to infinity, rather the issue is the inflation risks posed by excessive aggregate demand.

Continuing the Discussion

The next article in this sequence will turn to the meatier aspects of the Fullwiler paper: the issue of what determines the interest rate on government debt. To spoil the argument, the interest rate is a policy decision, and not set by natural laws of economics.


[1] Fullwiler, Scott T. "The debt ratio and sustainable macroeconomic policy." World Economic Review 7 (2016): 12-42.

[2] If we allow for permanently zero or even negative interest rates, we might have to drop the notion of interest burden, and just look at the debt-to-GDP ratio. For example, if we lock the interest rate at 0%, interest burden is always zero, no matter what the debt-to-GDP ratio is.

[3] The exception to this might be Japan, which was unable to hit a 2% inflation target; instead inflation was below target. I am unconvinced about the seriousness of the desire to hit that target; it may have been announced to stop the lectures by Western neoclassical economists.

[4] If we wanted a more realistic situation where these variables are changing, we would need to put bounds on these variables. For example, we could assume that the primary deficit is no larger than 5% of GDP.

(c) Brian Romanchuk 2020


  1. Good post. The potential issue as i see it is one of timing. Fiscal deficits correspond to private "wealth." Of course we can't know the real value of that wealth until the point when it is converted into consumption...presumably in the future. As long as the population is content stockpiling wealth this is sustainable. But let's say in a future state of the world (baby boomer aging perhaps?), the preference for wealth vs consumption falls. In that case we may find we've created too much wealth relative to the economy. The academic answer is easy: reduce wealth (raise interest rates, less govt spending, etc).

    But...the blind spot among economists is politics. Once you've created what feels like wealth, the groups that own it become very powerful and are staunchly opposed to any drop in wealth (as evidenced by central bank panic over any fall in wealth). You may easily end up in a situation where it is not politically feasible to do anything that negatively impacts wealth. In that scenario you've painted yourself into a corner where you have to accept inflation.

    There is no market signal that will tell you if such a situation is lurking in the future. I'd argue wealth/gdp is something we should try to keep stable...but plenty disagree.

    1. Wealth is a market value. Keeping it stable is extremely difficult, as how is that to be accomplished? Price control in the stock markets?

  2. I think something as simple as including home prices in inflation calculations would get us part of the way there. Not all excess money creation shows up in the can just as easily show up in asset prices (even though most economists refuse to believe that).


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