On Fiscal Sustainability

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 a fiscal policy stance that is disapproved of, but without having any substantive content that can be used to rebut the speaker. Modern Monetary Theory (MMT) largely rejects that “debt sustainability” has theoretical validity for a floating currency sovereign.

(Note: This is a re-written unedited draft of a manuscript section on fiscal sustainability. Material was added to a previously published draft.)

This section leans mainly on a heavily cited paper by Scott Fullwiler to describe the MMT stance (along with a pre-print that was released at the time of writing). However, the wording is largely my own, and I have greatly simplified the discussion to be an outline of the MMT stance – without worrying about the debates that are the concerns of the Fullwiler articles. There are many other subjects (for example, “fiscal dominance”) that are discussed therein, that are too tangential for this text.

I have chosen this radical simplification for a straightforward reason: unlike the academic articles by Fullwiler, I make no assumption that the reader is familiar with the mainstream views that Fullwiler is debating. It is impossible for me to summarise those mainstream views in a good faith fashion, for a simple reason: I view the mainstream position to be an incoherent mess. As such, I do not want to waste the reader’s time explaining something I view as trivially incorrect. Instead, I outline the basic principles, which will hopefully allow the reader to understand the debates,

Debt Sustainability

The concept of “debt sustainability” is the usual alternative to the argument that inflation is the only constraint on floating currency sovereigns. This section is based on some of the discussions found in the paper “The debt ratio and sustainable macroeconomic policy,” by Scott Fullwiler, albeit with simplifications.

A formal version of “debt sustainability” is the so-called inter-temporal governmental budget constraint (IGBC) of the neoclassical literature. It should be noted that the IGBC is controversial, even within the neoclassical literature. If one wanted to have a sophisticated discussion of economic theory, it would be in respect to the IGBC. However, this is being skipped in this text, for the following reasons.

• If the reader is familiar with the IGBC, the Fullwiler paper discusses its shortcomings. (Section 7.4 of my book Understanding Government Finance also discusses the IGBC.) My feeling is that if the reader is familiar with the IGBC, they are also likely to be familiar with the critiques.
• If the reader is unfamiliar with the IGBC, it can be summarised as: complicated as well as incorrect and/or misleading. For the same reason that chemistry textbooks do not discuss the Philosopher’s Stone, I see no need to waste anyone’s time trying to explain the material.

As a result, this section will only discuss a simpler-to-understand version of “sustainability.” This definition of fiscal sustainability is that the interest expenditures implied by government debt is not supposed to rise beyond the productive capacity of the economy, or alternatively, the debt-to-GDP ratio does not become arbitrarily large (the ratio “goes to infinity”). Since the interest expenditures/debt-to-GDP ratio are essentially equivalent, I will focus on the version that uses the debt-to-GDP ratio.

(A point about terminology. Interest spending by governments is typically called the “interest burden” by mainstream economists, which is a good example of how mainstream economists insert moral judgements within their “scientific” terminology.)

The first thing to keep in mind is that we are discussing the ratio of debt-to-GDP, 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"). As such, we should not care about the absolute level of debt (but that does not stop fiscal conservatives).

In less formal discussions, 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. It is equivalent to saying, “good golly, the debt-to-GDP ratio will be really high!” (What ratios qualify as “really high”? Why do we care?)

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. This is defensible, although one could question the standard way this is done.

• We assume that the economy follows an average nominal or real growth rate. Economists tend to love working with real quantities, so the typical variable is the real growth rate, normally denoted g.
• The next assumption is that interest rates also have a long-term average. If we look at real GDP, we need to look at real interest rates, with the long-term average typically denoted r.
• Government non-interest spending is assumed to be a steady percentage of GDP. 
• The tax take is also assumed to be a fixed percentage of GDP. An astute reader will note: should not the tax rate be a level of tax that is consistent with a desired average inflation rate? This is of course the correct answer – but we need to do things incorrectly to understand conventional fiscal analysis.

There are two key implications of the above assumptions. The first is that the difference between the interest rate and the growth rate – r – g – is critically important for analysis (as will be seen). The second implication is that there is an expectation that the primary fiscal balance – taxes minus non-interest expenses – is a constant percentage of GDP. (The fiscal balance is the primary balance with interest expense subtracted.) Academics will often jump right into discussing this topic in terms of the primary fiscal balance and the importance of r-g without explaining why they are looking at those quantities.

Debt-Ratio Dynamics

The question then turns to: how does the debt-to-GDP ratio evolve under those steady-state conditions? The actual equations are relatively simple, but messy. It is easier to discuss an approximation of the dynamics. The assumption is that we want to calculate the debt-to-GDP ratio on an annual basis.

As a simplification, I listened to my advice to abolish money from economic theory, and I assume that there is no money issuance. One could incorporate money (a liability with an interest rate of 0%) in two easy ways: either by assuming that the money/debt ratio is constant (which implies that we just use the weighted average interest rate of all liabilities as r), or assume that money creation is a constant percentage of GDP – which cancels out an equivalent amount of the primary balance. More complex solutions require incorporate some kind of dynamics that moves us away from a steady state condition.

The next year’s debt-to-GDP ratio is (roughly) given by the following two steps.

1. Take the ratio as a number (e.g., a 50% ratio is 0.5), and compound this number by the (r-g) differential. If the differential is 2%, then the ratio goes from 0.5 to 0.5(1.02) = 0.51 (or 51%). In other words, this term has the ratio growing at the interest rate/growth rate spread.
2. Subtract the primary fiscal balance (or add the primary fiscal deficit) as a percentage of GDP to the above figure (as a percentage). If we continue the previous example, and the assumed primary surplus is 2% of GDP, we then subtract 2% from 51% to get a new debt-to-GDP ratio of 49%.

With low interest/growth rates, the above procedure gives numbers that a close enough for government work. As a reminder: if one insists on adding money creation, one needs to pick the rule that determines the growth of the money stock. If the money/debt ratio is constant, just replace government debt-to-GDP ratio with the government liability-to-GDP ratio, and use the weighted average interest rate in the Step 1 calculation. Otherwise, if money growth is a fixed percentage of GDP, subtract (money growth plus the primary balance) in Step 2.

We can now ask: under what conditions can the debt-to-GDP ratio go to infinity?

• If r<g, it cannot happen – no matter how large the primary fiscal deficit is. The reason is that the compounding step (step 1 in the calculation) will eventually imply such a large drop in the ratio, that the primary deficit cannot push it above the previous level. For example, if r-g is -1%, and the primary deficit is 10% of GDP, if the debt-GDP ratio started at 2000%, it would be (2000×0.99 + 10 = 1990%; i.e., it falls.
• If r>g, the government has to run a primary surplus – or else the ratio would (allegedly) march off to infinity. The primary surplus must be big enough so that subtracting it in step 2 counters the compounding in step 1. This is the case that all the debates are about.

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 is 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). This is what happens when you pull an arbitrary assumption about average tax takes out of your nether regions.

This implausibility infects the budgetary analysis of the American Congressional Budget Office (CBO). 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 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.

Fixing the Problem with SFC Models

As always, the problems with conventional analysis revolves around assumptions. In this case, the assumption that long-run GDP growth rates and interest rates are fixed (at “natural rates”) makes 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.

Interest Rates are a Policy Variable

Another important principle discussed in the Fullwiler article is the argument that the interest rates on government debt is a policy variable. (This debate was returned to in a 2020 article of his “When the Interest Rate on the National Debt Is a Policy Variable (and ‘Printing Money’ Does Not Apply).”)

As the chart above shows, the 3-month Treasury Bill rate is effectively glued to the Fed Funds target, while the level of the 10-year Treasury tends to be near the target. (I chopped the data off to 1995, to roughly match the period of Fed transparency. The same story holds over longer periods.)

This is no accident. As Fullwiler noted in his second piece, short-term instruments like fed funds, Treasury repurchase agreements (“repos”), and Treasury bills are money market instruments that all have the same credit risk – the U.S. Federal government. Small spreads open up for technical reasons (including the expectation of rate changes, as can be seen if one applies a magnifying glass to the Treasury bill history).

One could delve into the econometrics of the situation (as Fullwiler did) to validate there is a statistical relationship. The brute force analytical alternative is to observe the following: the U.S. government could just overhaul its operating procedures and stop issuing bills and notes – locking rates at zero. Yes, the payment of interest is a policy decision, not a law of nature.

Once we accept that the interest rate paid on debt is a policy decision, the entire discussion is a non-issue: just pay a rate of interest less than the growth rate, and situation is always “sustainable.”

To what extent the neoclassical position is coherent, is that although it looks like the Federal Reserve is free to set policy rates as they wish, they need to set the policy rate in a fashion to control inflation. This is related to the debates between neoclassicals and MMT proponents about the effectiveness of interest rate policy (Section 2.5). Once again, I cannot hope to resolve that debate here.

One final note is that we see the problems with the neoclassical position (that neoclassicals generally attempt to obfuscate with terminology). The problem with “run-away debt” is almost certainly going to show up with increased demand from interest expenditures driving demand (otherwise we have the silliness of interest expenditures being larger than the economy). This interest rate/inflation spiral is only possible if the central bank keeps hiking rates – allegedly to control inflation!

Concluding Remarks

The analysis of fiscal sustainability is important, but it is done almost entirely within the framing chosen by conventional economists. The problem is that the framing makes no sense. As such, although the analysis is part of MMT, it is only there because of analytical errors by conventional economists.

References and Further Reading:

• “The debt ratio and sustainable macroeconomic policy,” by Scott T.  Fullwiler. World Economic Review 7 (2016): 12-42.
• “When the Interest Rate on the National Debt Is a Policy Variable (and ‘Printing Money’ Does Not Apply),” by Scott Fullwiler. Pre-print, 2020. URL: https://sci-hub.tw/downloads/2020-09-01/3c/10.1111@pbaf.12249.pdf

(c) Brian Romanchuk 2020