*Fiscal Folk Theorem*. It might surprise people to read this, but the folk theorem is correct. The issue is that the predictive content of the theorem is limited, and if mis-applied, it leads to

*The Widowmaker Fallacy*.

Neoclassical economists are not going to be happy with my message. For them, the most palatable possibility is that this is purely a communications problem. Even if this is true, it is a

*catastrophic*communications problem - this sample may have been relatively small, but I have digested so much financial market commentary to know that this is a widespread condition. Very simply, any neoclassical theory that goes beyond the Fiscal Folk Theorem is not making a dent in the wider conversation.## The Fiscal Folk Theorem

Since this argument has nothing to do with multiplier analysis, fiscal may not have been the best word. But since I like the acronym FFT, the Fiscal Folk Theorem it is. Technically, this is not a theorem, but rather a meta-theorem: it is a generic statement about a wide range of possible mathematical frameworks. It sounds fuzzy, because it has to be -- you need to specify the details in response to the mathematical model of the economy chosen.

There are three legs to the argument.

- Government debt is a really big number.
- If we multiply that number by an arbitrary real positive number (i.e., assumed average interest rate), we get a really big number.
- If the number in Step (2) is too big, some unspecified bad thing happens to the economy.

Possible choices for

*bad things*in step 3 include debt default, hyperinflation, government bond yields increasing, inflation going up by some amount, or even the*Wall Street Journal*disrespecting your currency.## Proof of the Folk Theorem

This might be a surprising statement, but yes -- the FFT is correct.

Given the latitude in the numerical relationships within the statements, we realise that that the FFT collapses to: if the government has a positive amount of debt outstanding, something bad can happen.

Proof is by contradiction: if the FFT were false, it would mean that it would be impossible for anything bad to happen to a government that has a positive amount of debt outstanding. Since we have observed hyperinflations, debt defaults, and the WSJ dissing the Canadian dollar, bad things have happened.

My argument is that this explains the "what about Greece/Zimbabwe/Weimar/Canadian peso?" retorts we see in popular argument: they are invoking the proof of the FFT.

## The Widowmaker Fallacy

The immediate problem with the FFT is that if one assumes that a "high" debt level means that something bad "must" happen, you have fallen for

*The Widowmaker Fallacy*. The FFT only says that something bad*might*happen, and there are no quantitative metrics to any of it.## Why Is The FFT Weak?

In addition to leading to the Widowmaker Fallacy, we can summarise the main problems with the FFT.

- Non-quatifiable trigger levels for debt and debt service levels. Without them, any level of debt fulfils the criteria.
- No quantifiable description of what negative things will hit the economy. Many economists make a big deal out of probability theory, and as options markets have proved, there is a large group of people who understand it and can explain it.
- There are no notions of trade-offs. A reduction in debt is always considered a good thing. Despite being a "fiscal" theorem, there is no serious attempt to model the effect of changing fiscal policy, so there is no notion of what the costs of debt reduction are.
- An extension of the previous point is the discussion of when tightening fiscal policy is appropriate. The typical hand-waving version of this is to accept that tightening fiscal policy during a recession is perhaps not the best idea. However, the reality is that we quite often do not know when the economy is in recession, and this formulation leaves open the possibility of tightening one month afterwards, driving the economy into a second recession.

Any analysis that has these failings are equivalent to invoking the FFT.

## The Treasury Bill Test

Before continuing to the further analysis of the FFT, we need to look at

*The Treasury Bill Test (TBT)*This is a test as to whether a set of theoretical statements has useful predictive value, or is just an accounting statement that is true by definition.The motivation for the TBT is that we are looking at the total return of a portfolio that is just rolled Treasury bills, with no management fees. If we abstract away from the technical details, we can see that the total return is the (geometric) average of the mathematical interest rate implied the Treasury Bill purchase prices.

If we abstract away from quote convention (and reinvestment) issues, someone could correctly observe that the Treasury bill portfolio will have a greater return over 10 years than a 10-year bond when held to maturity if the compounded average rate is greater than the purchase yield of the bond.

The observation is just a version of rate expectations, and contains no predictive content. A statement about the Treasury bill yields is interesting only if it provides information that allows us to predict (in some fashion) whether the future compounded rate is greater or less than the spot bond yield. Note that somebody might make the correct guess one or more times, but that is not the same thing as a systematic rule (which might give probabilistic estimates, which can be accounted for with multiple trials).

We say that any set of statements about a mathematical system that only give "accounting" information that describe past outcomes but cannot offer quantifiable predictions fail the TBT.

## Debt Spreadsheet Analysis: Fail the TBT

Returning to government debt analysis, any analysis that projects debt ratios based on arbitrary assumptions about realised variables fail the TBT test. If we guess the variable values correctly, we get the correct answer. But if we do not have a systematic project to project the values, the exercise offers nothing other than accounting information.

I can assert from authority that if we randomly choose a non-journal articles that invokes the variables

*r*and*g,*there is an extremely high probability it will fail the TBT. This can be extended to any article that could be summarised by sticking a debt trajectory in a spreadsheet.If the article fails the TBT, it offers no useful quantitative information, and is equivalent to the FFT. This explains why such a large portion of debt management commentary fall prey to

*the Widowmaker Fallacy*.## Breaking Past the FFT

If analysis that wants to paint a negative picture of government debt and offer information that is not contained in the FFT, it needs to offer testable quantitative predictions.

One of the best-known examples of a thesis that offered more information than the FFT was the famous Reinhart and Rogoff "90% debt ceiling" paper. There was a minor inconvenience with the quantitative predictions being incorrect, but at least they tried.

## MMT and the FFT

My guess is that the FFT description might not make MMT proponents happy, but I doubt that there would be a serious objection. The point is to emphasise the lack of information provided. Meanwhile, if the "bad thing" to be avoided is inflation (and not hyperinflation), the FFT does fit the MMT narrative. The possibility of replacing all debt with base money admittedly does an end run around the FFT, but perhaps there could some riders associated with money that could be attached to it to cover this.

The MMT narrative is not equivalent to the FFT by going in a different direction. Many people are unhappy with the fuzziness of high-level descriptions of MMT, and so could attempt to reverse the arguments I make here. Nevertheless, MMT provides us an idea as to what predictions to test, and which can be scoffed at (e.g., bond vigilantes).

## Neoclassical Communication Woes

There is no doubt that this line of argument is awkward from a neoclassical perspective. If we assume that neoclassical theory offers information beyond the FFT, this is not being communicated to a wider audience. If there are quantitative predictions that could be tested, people are not looking at those tests.

I write popularisations about economic theory as it pertains to bond markets. I have been trained as an applied mathematician. On paper, it should be easy to offer a clean explanation of the added value provided by neoclassical theory. The commercial reality is that my target audience is currently not interested in any theory beyond the FFT or MMT, and I see no way to give a compelling reason that they should broaden their horizons.

Fiscal Folk Theorem is one of the best things I have read on your blog.

ReplyDeleteSo far I do not follow the logic behind the Treasury Bill Test (TBT) based on the description here. Is the logic an if-then proposition like this: If one cannot predict the rolling T-bill return with certainty then ... (fill in the logical implication)?

The text probably needs a re-work. The idea is that the observation about the realized forward rolling yield is only useful if we can forecast (in some sense) the rolling yield. Otherwise, it’s just a statement that offers colour on historical dynamics.

DeleteWhen we look at any paper that blathers on about r>g, (or r<g), it adds no information unless we can independently forecast r-g in some fashion (maybe probability-based, whatever). Otherwise, we are just hand-waving and saying the debt ratio can go up or down, who knows? Sure, most of these papers have discussions of r-g, but these are just backwards story-telling.

Thanks. So TBT does relate to forecast uncertainty in commonly generated narrative models that I might call the fudge factor fiscal fear theorems.

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