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Wednesday, September 23, 2020

Fiscal Sustainability And The Fiscal Folk Theorem

Fiscal sustainability is often invoked in mainstream discussion of fiscal policy. However, "sustainability" is rarely defined in editorial pieces. The reason for this reticence is straightforward: there is no agreed-upon definition. Unfortunately for the concept, there is no clear way of testing whether real-world fiscal policies are sustainable, nor what are the side effects of being unsustainable.

This is related to what I refer to as the Fiscal Folk Theorem. If the technical definition of sustainability is not specified, nor the alleged problems created by unsustainability is specified, the discussion is inherently non-quantifiable -- no matter how many numbers are mentioned. The resulting discussion collapses to the Fiscal Folk Theorem. The theorem suggests that bad things can happen due to a high level of debt. However, this does not mean that something bad will happen -- as the Widowmaker Trade demonstrated.

Gold Standard -- Can Define Sustainability

If we are in a peg situation -- like the Gold Standard -- sustainability analyses can be done. Assume that the government has pegged its currency to gold. The peg can only hold as long as the government's gold reserves are positive.

We can do analyses of the gold reserves, and offer projected dates for depletion. So long as the projected depletion dates are soon, one can plausible describe policy as "unsustainable." Within a reasonably forecastable horizon, gold reserves run out, and the peg will have to break. (The exact consequences of the peg will break is unknown, since the government has a few options in response to a loss of gold cover.)

Unfortunately, this analysis does not extend beyond currency peg situations.

Floating Currency Sovereigns

The exact definition of a floating currency sovereign is somewhat ambiguous, a point which Modern Monetary Theory critics pretend is extremely important. However, the operational definition is straightforward: the government is essentially invulnerable to involuntary default.

If we are worried about a default and think it can be analysed in a fashion similar to the Gold Standard case, one runs into the problem of digging into the institutional structure of the jurisdiction. For the developed countries, the story is generally the same: even if a hypothetical default dynamic exists, it can happen at (almost) any positive level of debt. As such, there are no magic "tipping points," unlike the concrete problem of running out of reserves. We are back to the non-quantifiable Fiscal Folk Theorem.

Definitions of Fiscal Sustainability

The problem with "fiscal sustainability" is that there is no agreed-upon definition in the mainstream literature. I am not the only one saying this, even the Wikpedia entry agrees: "There is no consensus among economists on a precise operational definition for fiscal sustainability, rather different studies use their own, often similar, definitions." (Wikipedia entry for Fiscal Sustainability, quote for the page as of 2020-09-21.) Wikipedia is not authoritative, but I see no need to waste my time doing a literature survey to prove the obvious.

I do not expect serious dissension from neoclassicals when I say (like the Wikipedia entry) that there is no single definition, or even that there are flaws with measures that are used (the Wikipedia article lists some concerns, I have seen others in the literature). However, they will not be happy with my summary of the deeper problems. The definitions that I am aware of face one or more of the following defects.
  • They make little economic sense.
  • The sustainability of real-world countries' fiscal policies cannot be evaluated by these definitions (not measurable with observable data).
  • There is no attempt to link unsustainable fiscal policies to alleged negative outcomes. 
Taken together, the implication is that sustainability definitions offer no useful quantifiable information. They are equivalent to the Fiscal Folk Theorem. Given the popularity of invoking "fiscal sustainability" by neoclassical economists, the ubiquity of the Fiscal Folk Theorem is no surprise.

I will now discuss possible definitions.

Debt Ratio Going to Infinity

One traditional definition of fiscal sustainability is the debt-to-GDP ratio not going to infinity. This is often the test in simplistic spreadsheet models that project government debt-to-GDP ratios. Pretty well any argument that just refers to "r" and "g" fall into this category.

The empirical problem with this definition is straightforward. For a debt-to-GDP ratio to go to infinity, it has to achieve values that are larger than any arbitrary number. Unless the government issues bonds with a face value of "infinity" (I am not a lawyer, but that seems sketchy), this will not happen on any finite horizon. Therefore, we could never evaluate this in the real world.

What we can do is make a model projection. However, this has turned from a test of a real-world government's policies to a test of a model. The reality is that the models being used contain no behavioural information for the private sector. The policy did not fail, rather the model did.

In order for the debt-to-GDP ratio to get arbitrarily large, consumption in the private sector has to become arbitrarily small relative to debt (since consumption is a component of GDP). Using economic jargon, the propensity to consume out of wealth is zero.

In other words, there has to be some sector (or sub-sector) that acts as a black hole for government debt: debt enters the sector, but the sector will not proportionally raise consumption. This is not merely something that holds for a short period -- a population cohort saving for retirement might act like this during some portions of their working life -- it has to hold on any observable time frame. Other than strange corner cases -- the government writing itself I.O.U.'s that grow in an exponential fashion -- it is hard to see how this seems like a sensible description of any real-world actors.

The argument is straightforward: an unsustainable trajectory is a property of a pathological model, and not a property of a real-world government's policies. Having the model being the source of the weakness raises an issue that is unintuitive. People like myself enjoy describing long-term fiscal forecasts as "garbage in-garbage out exercises." My feeling is that people assume that the the input garbage refers to the data. In this case, the problem could actually be "high quality data in - garbage out," since the model contaminates data that might be reasonable. It is entirely likely that massive efforts will be expended on tuning the estimates for the model inputs, but the model dynamics are where the problems lie.

The Inter-Temporal Governmental Budget Condition

I discussed the inter-temporal governmental budget condition (IGBC) in Section 7.3 of Understanding Government Finance, but I will offer a short version tailored to the question at hand.

The IGBC is a component of complex dynamic stochastic general equilibrium (DSGE) models, but we can try to discuss the condition independently of a particular model. For reasons I cannot put my finger on, most treatments focus on a complicated statement of the IGBC, perhaps because it uses a cool infinite summation. It is mathematically equivalent to the much simpler transversality condition, even though this transversality condition seems to be the reason why the IGBC (allgedly) holds.

The transversality condition is: the discounted value of expected government debt will tend to zero as time goes to infinity. This condition ends up being equivalent to one about the infinite sum of discounted primary fiscal surpluses, and the initial debt level.

The immediate point is that we cannot observe any of the variables within this formulation, with the potential exception of the discount rate (if the government issues consols). Real-world governments do not specify fiscal policy as an infinite sequence of lump sum taxes and consumption levels, which matches the formal definition of the test. The only exception to the previous statement is if you believe the Fiscal Theory of the Price Level. In that case, the test is simple: if the price level is finite, fiscal policy is sustainable. Nevertheless, there is a certain amount of disbelief about the Fiscal Theory of the Price Level, so it will be brushed aside.

We see that if we are going to apply this condition, we need to find a means to project governmental fiscal policy. Since things like taxes are conditional on economic outcomes, we need to project economic variables going forward. We end up testing a model; different models have different outcomes. 

The sting in the tail here is that if we believe that the DSGE model is being solved properly, there is no solution if the IGBC does not hold. All we know is that the model wigged out and cannot converge -- and we cannot be sure why this happened. One can work around this (modify policy until a solution is found, then try to have policy converge to the desired model representation of fiscal policy). I have never heard of anyone attempting this complex a task -- but at the same time, I largely disregard the DSGE literature due to perceived weaknesses.

Even if we manage to deal with observation issues, it is unclear whether the results make any economic sense.
  • If the growth rate of the economy is greater than the discount rate, the transversality condition implies that the debt-to-GDP ratio must go to zero. There is no obvious reason why this must happen.
  • If the growth rate of the economy is less than the discount rate, government debt may be allowed to grow faster than GDP. By implication, the debt-to-GDP ratio can march off to infinity. This conflicts with the earlier definition, and might raise a lot of eyebrows.
Finally, there is no explanation why this matters (unless you believe the Fiscal Theory of the Price Level). All that happens in the DSGE model is that there is no solution. That is, the model offers no information as to what happens with economic variables. Why should we care about a defective model specification? There are an infinite number of models with no solutions.

The folk story that seems to be behind the logic appears to have something to do with a willingness to hold government debt. This does not work, since the transversality condition is based on a representative household, and the assumption is that every household does the exact same thing. There is no way for a representative household to trade with any other entity than the government or business sector (which does not appear in this model setup), since literally every household wants to be on the same side of the trade. (This can only happens if the trade volume is zero.) As was obvious to outsiders with mathematical training, this aggregation method is defective.

Conditions Based on Fiscal Variables

The end run around the measurability issue is to pick a mathematical test on observable fiscal variables, that are presumably projected forward a finite number of years.

This eliminates most empirical issues, other than arguments about the means of making projections of fiscal variables. But if we are willing to accept things like scenario analysis, that can be done, at least on a medium-term horizon.

Although the measurement issue is solved, we are left with the "why do we care?" problem. A mathematical condition on some fiscal variables by itself tells us very little. The test needs to be tied to a mathematical model, and we end up circling back to the problems that popped up in the previously discussed variants.

Lines on Charts

The final catch-all method is doing an analysis of government debt in the equivalent of a spreadsheet (but preferably implemented in code, to avoid pulling an R&R). We project variables, and see what various lines on charts do (debt-to-GDP ratio, debt service, etc.).

Since my preferred idiom is to use lines on charts, I cannot complain too loudly. Showing lines on charts offers far more information to readers than statements about big numbers, which is the preferred idiom of crackpots.

The issue is that the information conveyed is limited -- unlike a projection of gold reserves going to zero. As Japan showed, a rising debt-to-GDP ratio implies almost nothing.

Out of all the potential charts, the only one that might matter are debt service based on interest rate scenarios over a horizon of a decade or so. This might allow us to judge the odds of the need for central banks to think more carefully about how interest rate policy actually works.

Is There a Better Definition?

The obvious rejoinder to the previous discussion is that there is a rigorous definition of "fiscal sustainability" that meets my objections. This is certainly possible, but at the same time, this alternative is certainly doing a good job of hiding from outsiders.

My argument is that we would only see an interesting definition of "fiscal sustainability" if we see some negative effect of debt (or debt service) that shows up in finite time intervals. Running out of gold cover for a currency in the Gold Standard fits the bill. However, free market-oriented researchers have been scouring time series databases for decades trying to find the magic econometric bullet that proves that government debt is bad. It is safe to say that they have not found anything that has convinced anyone other than themselves.

Fiscal Folk Theorem

Finally, once one accepts the Fiscal Folk Theorem, then it is very easy to digest articles that discuss fiscal sustainability. Unless the article gives a specific technical definition of sustainability as well as specific consequences of unsustainability, the article has zero added information beyond the Fiscal Folk Theorem. If it does add information, one then needs to address the specific quantifiable claims. (Just invoking Japan is enough to torpedo most articles.) 

Can We Do Better?

One predictable reaction to my arguments would roughly run like this: "OK, Dr. Smarty-Pants, can you do better?" As always, it depends on your definition of "better."

Unless we are discussing a country with a currency peg, there is no simple sustainability condition of the format that conventional economists wish to exist. So if one wants a "better" sustainability rule, you are out of luck.

Instead, we always need to ask ourselves: what exactly do we want to do? You then do that.
  • If you are worried about debt default, model debt default. For non-euro developed countries, default mechanisms are much more awkward than fables from sell side economists.
  • If you are worried about inflation, model inflation. Does it make sense to worry about inflation in 40 years, given our difficulties projecting growth over a decade?
  • If you are worried about a line on a chart, don't look at charts.

Forecast Implications?

A response I often see on other forums when I write something like this is "So you think the debt can be run up forever?" This is quite often in response to articles like this one, where I argue that long-term debt forecasting is an impossible task -- which is somewhat frustrating to me as a writer.

The answer is really simple, and yes, I learned about this courtesy of my exposure to MMT: sooner or later, if government spending is excessive, inflation will rise (unless alternative methods are used to control inflation, which is not on the political radar). How do we know if the spending is excessive? Inflation rises.

I am not pretending to be a forecaster, so I am not the source who is going to tell you what is up with inflation. Nevertheless, I will point out that the pandemic has blown a massive hole in the job market, and there is an incredible demand deficiency. Governments are injecting income to hold off the mass default event that takes out banking systems. Sooner or later, labour markets will tighten, and then the deficit will close on its own. Debt will be a big number.

The only sensible thing to ask is whether central banks really understand the effects of raising rates. Will raising rates increase debt service payments, pushing inflation higher? I am not seeing any evidence of serious consideration of that topic, which is far more important than 50-year debt-to-GDP ratio forecasts.

(c) Brian Romanchuk 2020


  1. I think the root of your argument is that we have no clear definitions.

    I would suggest trying to define what a government is giving away when it gives away 'money'.

    When I try that exercise, I conclude that a government is giving away coupons of entitlement. Entitlement to what? What does a government own that a government can give away in a similar fashion as a store owner can give away coupons of some sort?

    A discussion along this line of thought should be able to find definitions, except possibly for what happens when too many coupons are given away, which is not really a question of definitions.

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