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Monday, April 26, 2021

A Response to "Unpleasant Asset Pricing Arithmetic"

Zhengyang Jiang, Hanno Lustig, Stijn Van Nieuwerburgh and Mindy Xiaolan have a working paper "What Determines the Government’s Funding Costs when r=g?:  Unpleasant Fiscal Asset Pricing Arithmetic." They argue that the "fiscal cost" of deficits is not expected to be driven by the gap between the "risk free rate" and GDP growth (the famous r-g equation). Their target is something or other Olivier Blanchard wrote. In a completely non-surprising development, I am not happy with their logic.


If I were a referee on this paper, I would target four main points of concern. 
  1. I would re-phrase a lot of their arguments as follows: people are sloppy with the use of "risk-free rate." In my academic days, I was very much anti-sloppiness. That said, I was in a academic field that was attempting to make useful observations, and we needed a good reason to be pedantic. In this case, the sloppy people are closer to being correct in terms of what matters from a practical perspective.
  2. They do some theoretical analysis that looks fishy to me. However, the justifications for their theories are mainly contained within another paper.  Since I have not read that other paper, I obviously cannot give a definitive statement here. If I had to give an academic review, my review would be conditional on that other paper passing muster, which is a situation I ran into when I was actually an academic.
  3. They have something about "convenience yields" which is some version of a "reserve currency" argument. Once again, relies on another paper that I have not read.
  4. There is a final concern that would be extremely controversial: they skip over the entire mechanism of default. Why does it happen? If I were an academic reviewer, I would probably not want to get drawn into this issue. However, it is rather interesting that neoclassical academics insist that "everybody knows that floating currency sovereigns cannot default, therefore MMT has nothing new" when we have an entire paper produced by people at a well-known university where the entire premise is that floating currency sovereign default risk is a significant part of pricing.

1. Pedantic Observations About "Risk-Free Rates"

Since I see no reason to read what Blanchard wrote, so I am not entirely sure whether he used "risk free rate" incorrectly. However, most people will use "real risk free rate" and the variable "r" interchangeably.

The phrase "risk free rate" is sloppy. Firstly, bonds have duration risk, underpeformance risk, etc., which every financial market practitioner is aware. It is a shorthand for "default risk free rate" -- but even that is a shorthand. It really means "the rates associated with the curve for an issuer who has no plausible credit risk scenario that does not involve having the currency's entire financial infrastructure melting down at the time of default, at which point I’m stuffed anyway, so whatever.” 

What Jiang et al. are implicitly arguing: you cannot use the central government curve to define the risk-free rate, you need to imagine some hypothetical entity that is completely default risk free and also issues bonds. 

This is arguably correct. However, it also has no practical value, and is a misunderstanding of what other people in this debate are saying.

The possibility of there being another curve that is risk-free relative to a given sovereign within a currency is well-known for countries that do not qualify as a "currency sovereign": notably, issuers that borrow in a foreign currency, or members of the euro peg system. Nobody in their right mind would discuss "r-g" logic for such countries without bringing in default risk analysis.

Conversely, for floating currency sovereigns, no such hypothetical absolutely default risk free issuer exists. Central banks might qualify, but none of the major ones (currently) issue bonds. The "risk free" curve they provide is at most overnight, and only available to selected banks. There is no observable "truly, absolutely risk free" bond curve in the market, so it makes no sense to use it in "asset pricing arithmetic."

Derivatives people might jump up and down at this point and yelp about OIS. My response is simple: swaps are not a lending instrument. If you disagree, feel free to call up your friendly neighbourhood derivatives salesperson and ask about lending $200 million to them via a swap (or better yet, try to borrow $200 million, a more unscrupulous salesperson might find a way to take your $200 million).

In any event, this misses the substantive point: people are using "risk free rate" as a shorthand for "government yield curve" -- or more importantly, the funding cost. If you look at the models. the variable r is what is used to determine debt dynamics. Even if an "absolutely default risk free curve" existed, the interest rate that matters in analysis is the rate on government debt.

And when anyone does empirical work, they are comparing observed government debt yields to growth rates. Since no other risk-free curve can be observed, discussion of it has zero added value in empirical analysis.

2. Is the Math/Theory Correct?

The analysis in the paper is very hard to describe, since the authors follow an unusual way to analyse governmental debt.

For example, they have a confusing first example. They state that the economy is static, with zero interest rates, inflation, and real growth. That is, GDP is stuck at $10 trillion forever. They then state that taxes are 25% of GDP, and spending is 20% of GDP, and debt/GDP at year zero is 100% ($10 trillion debt).

This implies a primary surplus of 5% of GDP, which they note. Somehow, debt/GDP is stable. Elementary mathematics tells us that this is only possible if there are interest payments of 5% percent of GDP. (Otherwise, the government debt level will march merrily off to negative infinity.)

But wait, did we not say that interest rates were 0%? Well, that's the interest rate on some hypothetical “absolutely risk free” curve. The govvie curve is apparently trading at 5%.

It seems extremely obvious that if the govvie curve is trading with a real rate of 5%, that's the "r" you need to use. Nobody would debate that; the only issue would be pesky MMTers asking why the government that issues a currency resource cost-free is worried about nominal dollars?

But if we dig into this paper, there's some equations and theory. The justifications for them are buried in another paper. I have not read it (and I have other projects to deal with at present).

However, the logic outlined looks dubious. They do a discounted cash flow analysis from the government's perspective. The government uses a discount rate of 5% based on the highly scientific principle of: why not 5%? It needs to use something that allows the infinite summation of taxes and spending to converge.

The problem is: there is no law of nature that suggests that other entities need to value assets using the discounted cash flow analysis of a particular entity.

They state:
Investors who buy the government debt portfolio are net long in a claim to output as long as the government has positive debt outstanding.
This is incorrect. I suggest that any academics reading this mosey over and read a bond prospectus. What you see is that bond investors have is a claim on future dollars. In particular, a bondholder at time t has a claim on asset at that time that pays a set of cash flows up to a maturity date T. Anything after time T has no effect on the price, using basic asset pricing arguments. (One could try to sell a story about consols, but consols are not a significant part of any real-world country's funding strategy.)

Looking at the attempts to justify this unusual description of bond pricing, it looks like the authors are basing their theories on "insurance” or some theory about “owning the government bond portfolio.” However, unless the Galactic Empire sets up shop on Earth selling fixed income derivatives, there is no entity able to provide net insurance to the private sector -- other than the government. Meanwhile. governments do not sell "insurance" on their own debt. And one does not simply purchase "the government bond portfolio," one buys "government bonds" that each have a fixed maturity.

An alternative characterisation of their theory is that they somehow believe that bondholding is akin to holding equity in a firm. They attach great importance to the risks to cash flows created by recessions, for example. However, since there is no actual default mechanism proposed before the maturity date of a bond created by future volatility in economic output, there is no reason for this to matter. In any event, output fluctuations are not purely a random walk; welfare states show mean-reverting behaviour.

Once again, I could try digging further, but that will not happen soon.

3. Convenience Yields

The authors state:
The U.S. Treasury is in a unique position. The Treasury can sell securities at prices that exceed those of other securities with similar risk characteristics. We call the difference between the yields on Treasurys and equivalent securities the convenience yields. Krishnamurthy and Vissing-Jorgensen (2012) estimate convenience yields on U.S.
Treasurys of around 73 bps per annum between 1926 and 2008.
This is incorrect, since (a) there are no USD securities with similar risk characteristics to Treasurys and (b) credit spreads for high quality USD paper trade within 73 bps most of the time. (Municipal bonds trade under Treasurys, based on tax effects that are easily priced.) Based on the description, the other paper must have been comparing yields across currencies -- which should not be done. Moreover, it makes no sense to draw conclusions about floating currencies from Bretton Woods era data.

4. Default - How?

The premise of this paper is that fixed income investors insert significant default risk into pricing. Is there any evidence of this? What are the mechanisms that cause default for a floating currency sovereign?

Once again, it is abundantly clear that not "everyone" knows that floating currency sovereigns do not face involuntary default risk.

(c) Brian Romanchuk 2021


  1. I think they are trying to say something different from what you describe.

    First, they are trying to say that the fiat money supply (created by government when issuing debt) used by this economy is represented by $200t in debt. That debt is rolled over every year but only $190t of wealth is received annually because of the discount. Because the bonds issued each year are for nominal $200t, the money supply represented by debt obligation remains constant.

    However, they also (in example one) allow the government to have a revenue surplus of $10t. This represents a transfer of wealth from private sector ownership to government ownership.

    Now we can see that government annually takes in $190t + $10t = $200t which just happens to equal the $200t repaid to investors annually. We have a stable economy.

    So how do we calculate r and g in this situation?

    They go on to say that "the (r sub f) - g measure of the fiscal cost of deficits is incomplete."

    I think it would be fair to say that here (in this example) we see government being used to transfer wealth between members of the private sector.

    1. Under the normal definition of “interest rates,” the discount would be zero if interest rates are zero. The discount is just another way of specifying an interest rate.

  2. I was just saying on twitter, that government budgets are a perfect example of conditional convergence. The positive terms diverge to infinity and the negative terms diverge to negative infinity, ergo, you get conditional convergence and by commuting terms(ie borrowing), you can make the series converge to any desired value.

    Initially, I was thinking of this more like "oh it's sort of silly to talk about intertemporal budget constraints", but the more I look at it, why not? If we are going to do the math here, why not do it right? It's just impossible to talk further and further in the future, and a conditionally convergent series, seems as reasonable as anything.

    1. I’ve got a lot of complaints about the budget constraint, the most important of which: why does it hold? I’ve never seen a single person justify why it would hold. I think I know why they think it holds, but it’s clear that the logic does not work.


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