Interpreting the yield curve

There's been a lot of talk lately about the flattening of the yield curve, what's causing it, and what it portends. In this post, I describe a simple "neoclassical" theory of the yield curve and ask to what extent it serves as a useful guide for our thinking on the matter.
 
Let's start by defining terms. Let I(m) denote the yield (market interest rate) on (say) a U.S. treasury bond with maturity m. So, I(1) denotes the yield on a one-year bond and I(10) denotes the yield on a ten-year bond. The slope (S) of the yield curve is given by the difference in yields between long and short bonds. In this example, S = I(10) - I(1).

Here's what the yield curve looks like for the U.S. since 1961.

Normally, the slope of the yield curve is positive. But occasionally, it turns negative -- an event that is called yield curve inversion. Market analysts care about yield curve inversion because the event is frequently (though not always) followed by a recession (the shaded bars represent recessionary episodes).

The graph above plots the nominal yield curve. Economists frequently stress the importance of real (inflation adjusted) interest rates, which I will denote R. Because there is a ten-year Treasury-Inflation-Protected Securities (TIPS), we have a market-based measure of R(10). Let me compute     R(1) = I(1) - P(1), where P(1) denotes expected year-over-year inflation. Let me use the year-over-year change in core PCE inflation as my measure of P(1). That is, I am assuming that over the short-run, the market expectation of inflation is roughly last year's core (trend) inflation rate. Since TIPS data is only available since 2003, here is what we get:
 

The nominal and real yield curve share the same broad pattern. This is consistent with what we would expect if inflation expectations are stable. Note the slight bump up in the nominal yield curve following the November 2016 presidential election. Since then, both yield curves have been flattening--the real yield curve more so than the nominal curve. Does this mean we are heading for recession, or at least a growth slowdown? And if so, why? To answer this latter question, we need some theory. [Warning: what follows in blue is wonkish. If you are not a wonk, skip the blue section--some intuition follows.]

Consider this simple model economy. There are three periods (the minimum number I need to generate a yield curve). The economy is closed and is populated by individuals with identical preferences for consumption over time, c1, c2, c3. That is, people care about their material living standards over the course of their planning horizon. If people like to smooth their consumption over time, then the following representation of preferences serves to capture this idea W = u(c1) + u(c2) + u(c3), where u(.) is an increasing concave function. For simplicity, let u(.) = log(.). To make things even simpler than they need to be, assume an endowment economy so that the real GDP is expected to evolve according to y1, y2, y3. Finally, let Rij denote the real rate of interest between periods i and j. Then the equilibrium real interest rates are given by:
R12 = y2/y1
R23 = y3/y2
R13 = square root of (y3/y1)

Let me now explain in words what this model implies. First, the model predicts that real interest rates are proportional to expected economic growth. The economic intuition for this is that if incomes are expected to grow more rapidly, then in an attempt to smooth consumption (that is, bring future income back to the present) people will want to save less (or borrow more). The decline in desired saving (increase in desired borrowing) results in upward pressure on the interest rate until the bond market clears.

The slope of the yield curve in this model economy is given by S = R13 - R12. This is roughly the ratio of expected long-term growth (y3/y1) relative to expected short-term growth (y2/y1). Thus, a positively-sloped yield curve in this economy is symptomatic of a bullish economic outlook (growth is expected to accelerate). Conversely, a negatively-sloped yield curve is symptomatic of a bearish outlook (growth is expected to decelerate). The interpretation offered here of the flattening yield curve is that expectations are turning increasingly bearish--people are cutting back on planned consumption, increasing their desired saving (reducing planned borrowing)--all of which serves to put downward pressure on long rates.

As with all simple theories, it would be wrong to view this as "the" explanation for the yield curve. At best what the theory does is highlight certain forces that may be at work in the real economy. Whether the forces identified are quantitatively important is an empirical question. Nevertheless, I think the model offers a good place to organize our thinking on the matter.

A conventional view among economists is that the Fed has little or no control over long real interest rates. If long-rates are declining because of an increasingly bearish sentiment, then there's little the Fed can do about it. But what justifies the recent policy of raising the short-term rate? The model above suggests that the Fed is simply responding to market forces--the market "wants" higher short rates and the Fed is simply accommodating this want. I'm not sure this is the best way to think about what's happening. One thing missing from this simple model that may be important to consider is the liquidity premium on short-term government debt. Is the current Fed policy affecting this liquidity premium and, if so, what effect is it having on real economic activity? I'll try to address these and other questions in future posts.


Postscript 11/27/2017 Some further thoughts. ***********************

Consider a world where real economic growth remained constant, i.e., y2/y1 = y3/y2 = y4/y3 = ...
In such a world, the yield curve would be perpetually flat. In a world where output fluctuated around a constant trend, the slope of the yield curve would be zero on average. (I am abstracting from inflation risk, etc.)

In reality, the yield curve is usually positively sloped. It seems unlikely that the explanation for this is that investors are perennially bullish (in the sense of expecting accelerated growth). There are other factors that may impinge on bond yields at different horizons and hence on the slope of the yield curve. One such factor is the liquidity premium attached to short-maturity debt. If the short bond in the model above is valued for its liquidity (and if liquidity is "scarce" in a well-defined sense that I don't have room to explain here), then the market yield of the short bond will be lower than what is dictated by "fundamentals." In other words, short bonds will seem very expensive. If this is the case, then the yield curve may be positively sloped even if the growth outlook is stable (instead of bullish).

To the extent that the Fed can influence the liquidity premium on bonds (and there is good reason to believe it can), then raising the policy rate in the present environment would serve to diminish the liquidity premium on bonds. In the model economies I know of where such a liquidity premium exists, eliminating it actually stimulates economic activity. This is because liquid bonds, to the extent they are used as exchange media, actually complement investment spending instead of crowding it out (as is the case in other models that abstract from the liquidity services that bonds provide).

The interpretation in this case is that raising the policy rate is reducing "financial repression," which is likely to offer modest stimulus. This policy action in itself will have no measurable impact on inflation and the associated flattening of the yield curve is what we would expect if growth prospects remain stable (the flattening yield curve does not necessarily portend recession).

**************************************************************************

Tyler Cowen on Central Bank Cryptocurrencies

I enjoy reading Tyler Cowen and have learned a lot from his columns. So before I criticize his most recent effort, I want to thank him for all his fine contributions! Unfortunately, I think he drops the ball a little bit on his most recent effort. No worries--we all do sooner or later. What follows are some thoughts that came to my mind as I read his most recent article entitled "Cryptocurrencies Don't Belong in Central Banks." My (unedited/uncensored thoughts are recorded in blue...Tyler, take note: "uncensored"= risk-taking central banker!) 

Should central banks embrace cryptocurrencies, or even pioneer their own? In a nutshell, no. Crypto assets are an unusual innovation, still in flux and often poorly understood. Trying to centralize them in a bureaucracy is exactly the wrong way to go. 

"Crypo assets are an unusual innovation" -- this is a claim that makes little sense without first defining what is meant by the term. Most people have in mind some notion of a distributed (shared) append-only ledger of information updated and maintained by members of a community through some consensus algorithm that makes use of cryptography in securing information. I'm not sure how "unusual" this idea is where fintech is concerned (advances in information management systems have been happening for a long time). And, as I explain here, the concept of distributed ledgers updated via communal consensus is an ancient idea. 

"Trying to centralize them in a bureaucracy" makes no sense at all if the very concept depends on a decentralized record-keeping arrangement. And in any case, a central bank that experiments with such a protocol is not "centralizing" all crypto assets--just its own crypto asset. What is inherently wrong with this? The fact that a central bank is a "bureaucracy?" 

Yet China’s central bank claims it is working toward a blockchain-based digital currency. Singapore has already experimented in this direction. The phrase “Fedcoin” is sometimes bandied about, though I’ve seen no concrete sign of the U.S. Federal Reserve jumping on this bandwagon. In its recent quarterly review, the Bank of International Settlements asked central banks to consider whether cryptocurrencies might make sense for them.

The "Yet" beginning the paragraph does not belong there. It presumes we've accepted the premise laid out in the previous paragraph which, as I have suggested, makes little sense. 

Central banks, however, are intrinsically conservative bureaucracies. They shun bad publicity, and they don’t like to be “out there” ahead of the curve. They don’t want their names connected with potential mishaps -- because they value their credibility and their political capital so highly. That’s appropriate, because central bank independence is typically fragile.

Almost everyone shuns bad publicity. No one wants their names connected with potential mishaps. It's not that central banks don't like to be "out there"--it's that they are usually prevented from being "out there" by government legislation. Of course, central bankers should be "conservative" in the sense of respecting the legislation that is designed to govern them.  

Given that background, (which is wrong) should we foist a new and potentially risky responsibility on them? Central banks will feel some anxiety at having to manage a crypto project. (central bankers will always feel anxiety). To conserve their political capital, they will take fewer risks elsewhere, such as unorthodox monetary policy or larger balance sheets. (what justifies this bald speculation?) Yet the response to the 2008 financial crisis shows a certain amount of central bank risk-taking is needed. (those conservative central bankers again, I guess). I’m worried about central banks taking on unnecessary risky projects, thereby rendering them too cautious in other areas. (there's no need to worry about this in my opinion.)

 An additional reason for skepticism stems from the nature of crypto assets. The word “cryptocurrency” is far more common than “crypto asset,” but it’s a misleading term. Bitcoin, for instance, is used only rarely in retail transactions, and for all its success it isn’t becoming more important as a medium of exchange. Bitcoin thus isn’t much of a currency in the literal sense of that term. There is a version of bitcoin, Bitcoin Cash, that changed the initial rules to be better suited as an exchange medium, but it isn’t nearly as popular. (I don't disagree, but I also don't understand the point of this paragraph.)

If you think of these assets as “cryptocurrencies,” central bank involvement will seem natural, because of course central banks do manage currencies. Instead, this new class of assets is better conceptualized as ledger systems, designed to create agreement about some states of the world without the final judgment of a centralized authority, which use a crypto asset to pay participants for maintaining the flow and accuracy of information. (Good, I agree with all this.) Arguably these innovations come closer to being substitutes for corporations and legal systems than for currencies. (Except that in monetary theory, we understand money as a ledger -- a record-keeping system. See, e.g., Kocherlakota, 1998). 

Put in those terms, an active (rather than merely supervisory) role for central banks in crypto assets is suddenly far from obvious. Consider other financial innovations: Does anyone suggest that central banks should run their own versions of ETFs or high-frequency trading? Is there a need for central banks to start managing the development of accounting and governance systems?

Um, yes, yes, and yes. Central banks are already like bond ETFs (assets are bonds, liabilities are reserves and currency). High-frequency trading--like Fedwire, you  mean? And I'm not sure why better accounting and governance systems should not be employed by central banks if it makes sense for other institutions?

Finally, bitcoin and other crypto assets are still in the midst of rapid evolution, with basic questions still unanswered. Should bitcoin “fork” to allow for greater speed in processing transactions? Is the future going to favor bitcoin, the Ethereum platform, or something else altogether? How many initial coin offerings make economic sense, as opposed to being bubbles? Should initial coin offerings be used to fund startups? How many crypto assets should survive in the long run? Can blockchains be used to record and settle the transfer of property titles? Are there any circumstances when it should be possible to revise transactions on a blockchain?

Yes, there are always questions concerning the outcome of fintech. This has been happening for hundreds of years. What is the point of stating this obvious fact and why should the prospect of evolving information technology discourage central banks from experimenting with it? What if such an attitude was adopted when email first appeared on the scene? 

In general, I think the central banks in the world’s developed economies have done a pretty good job. But consider a simple question: Would any central bank have had the inspiration or taken the risk of initiating the bitcoin protocol in the first place?

Let's assume that the answer to this question is no. The only thing that follows from this is that we should not rely on central banks as our only source of fintech. But we already do not have such a reliance. So what is the point being made here? Let's experiment away, I say! 

Well, maybe not. My own sense of the discussion concerning central banks and cryptocurrencies is that people are confounding two conceptually distinct issues. 

The first issue is whether central banks should open the digital component of their balance to the general public (say, the way the U.S. Treasury does at https://www.treasurydirect.gov/). And why not? After all, central banks allow anyone in the world to hold the paper component of their liabilities. This idea is actually very old--it is related to the question of whether a central bank (or post offices) should permit people to open book-entry utility accounts.  This remains a good question and there are many issues to sort out, including what impact such an innovation would have on banks. But it has nothing to do with "cryptocurrencies" except to the extent that cryptography is used to secure communications--something that is already widely employed.

The second issue is whether central banks should issue "digital cash." The digital reserve money associated with the scheme in the paragraph above is not cash-like in the sense that it is not a bearer instrument. People have to identify themselves when they open accounts at the U.S. Treasury. Presumably, they'd have to do the same thing if they opened up a digital money account at at post office or central bank. Digital cash is something more akin to paper money. As far as I can tell, the technology to create digital cash has been around for a long time. That is, there is nothing technological that prevents a central bank (or anyone) from issuing numbered accounts (think of the good ol' anonymous Swiss bank account, for example). Even PayPal could issue digital cash--if it was legally permitted to, which it isn't. So, the question here is whether a central bank should issue digital cash. The wallet-to-wallet debit/credit activity could be done in-house via a central book-keeper, or the activity could be delegated to some third parties (e.g., Bitcoin miners). I don't really see central banks getting into this business, but they will have to think about how private-sector digital cash may impinge on their ability to conduct monetary policy. (Note: the innovation with Bitcoin is not digital cash per se, rather the innovation has to do with P2P digital cash--debit/credit operations that do not rely on a central book-keeper.)