Why the discrepancy?

Vitalik Buterin had a thought-provoking tweet a few days back about interest rates.

Lending DAI to Compound offers 11.5% annual interest. US 10 year treasuries offer 1.5%. Why the discrepancy?

— Vitalik Non-giver of Ether (@VitalikButerin) August 23, 2019

Today's post explores what goes into determining interest rates, not blockchain stuff. So for those who don't follow the blockchain world, let me get you up to speed by decoding some of the technical-ese in Buterin's tweet.

DAI is a version of the U.S. dollar. There are many versions of the dollar. The Fed issues both a paper and an electronic version, Wells Fargo issues its own account-based version, and PayPal does too. But whereas Wells Fargo and PayPal dollars are digital entries in company databases, and Fed paper dollars are circulating bearer notes, DAI is encoded on the Ethereum blockchain.

Buterin points out that DAI owners can lend out their U.S. dollar lookalikes on Compound, a lending protocol based on Ethereum, for 11.5%. That's a fabulous interest rate, especially when traditional dollar owner can only lend their dollars out to the government—the U.S. Treasury—at a rate of 1.5%.

Why this difference, asks Buterin?

Interest rates are a lot of fun to puzzle through. I had to think this one over for a bit—so let's slowly work through some of the factors at play.

Let's begin by flipping Buterin's question around. When the U.S. Treasury borrows from the public, the bonds it issues are promises to pay back regular dollars (i.e. Federal Reserve dollars). But what if the U.S. Treasury decided to borrow DAI by issuing bonds promising to repay in DAI? What would the interest rate on these Treasury DAI bonds be? Would it be 11.5% or 1.5%? Perhaps somewhere in between?

Credit risk

First, there's the question of credit risk. The U.S. Treasury is a very reliable debtor. It won't welch. If it issues both types of bonds, it'll be just as likely to repay its DAI bond as it will its regular dollar bond. Since the market already requires 1.5% from the Treasury to compensate it for credit risk (and a few other risks), the Treasury's DAI bonds should probably yield 1.5% too. (I'll modify this later as I add some more layers).

Now let's look at Compound. A DAI loan made on Compound (for simplicity let's just call it a Compound DAI bond) is surely much riskier than our hypothetical Treasury DAI bond. Compound is a blockchain experiment. It could malfunction due to buggy code. Maybe every single Compound borrower goes bust. To compensate for this risk, a prospective bond buyer will require a higher return from Compound DAI bonds than they will U.S. Treasury DAI bonds.

So Compound credit risk (Buterin's third option) probably explains a big chunk of the huge gap between the 11.5% interest rate on Compound DAI bonds and our hypothetical 1.5% interest rate on the U.S. Treasury's DAI bonds. But not all of it.

Collapse risk

Buterin mentions a second risk: the chance that DAI, the entity that creates blockchain dollars, collapses. Like Compound, DAI is a new monetary experiment. The code could be buggy. It might get hacked. By comparison, conventional dollar issuers—say Wells Fargo or PayPal—are far less likely to malfunction.

How does DAI collapse risk get built into the price of a hypothetical Treasury DAI bonds

The average market participant (I'm not talking about crypto fans here, but large & smart institutional actors) should be genuinely worried about purchasing a Treasury DAI bond—not so much because the Treasury is unlikely to pay it back—but because the DAI tokens that the Treasury ends up repaying could, in the even of DAI breaking, be worth 99% less than their original value. Average bond buyers will expect some compensation for bearing this risk. How much? Say 5.5% (I'm just guessing here).

Earlier I said that a Treasury DAI bond would yield 1.5%. But if we add 5.5% worth of failure risk to 1.5% in basic risk, a Treasury DAI bond should yield 7.0% before the average investor is going to hold it.

Now let's go back and look at a Compound DAI bond. As Buterin pointed out, they yield 11.5%, which is much higher than the 7.0% yield on our hypothetical Treasury DAI bond. We've already assumed that DAI collapse risk works out to 5.5%. If we subtract collapse risk from a Compound DAI bond's 11.5% yield, the remaining 6% is accounted for by risks such as Compound failing (11.5% - 5.5%). Put differently, investors in Compound DAI bonds will require 5.5% and 6.0% to compensate for collapse risk and credit risk respectively, for a total of 11.5%. Again, these are hypothetical numbers. But they help us puzzle things out.

Two different blockchain dollars: USDC vs DAI

Interestingly, Compound doesn't just facilitate DAI loans. It also expedites loans in another blockchain dollar, USDC. We'll refer to these as Compound USDC bonds. As Buterin points out later on in the thread, the rate on Compound USDC bonds is 6.5%, quite a bit lower than Compound DAI bonds.

What might explain this discrepancy?

Not credit risk, since in both instances the same creditor—Compound—is responsible for creating the bonds. Which leaves varying levels of collapse risk as an explanation. USDC is a regulated stablecoin (i.e. it has the government's approval). DAI isn't. And USDC has genuine U.S. dollars backing it, whereas DAI is backed by highly volatile cryptocurrencies. So the odds of USDC collapsing are surely lower than DAI.

How much interest do USDC bond holders require to compensate them for collapse risk? Assuming that Compound's risk of failing is worth 5.5% of interest (as we already claimed), that leaves just 1% attributable to the risk of USDC failing (6.5%-5.5%). Put differently, investors in Compound USDC bonds will require 5.5% and 1.0% to compensate for credit risk and collapse risk respectively, for a total of 6.5%.

Oddly, the yield on a Compound USCD bond is less than the hypothetical yield on our safe Treasury DAI bond (6.5% vs 7.0%). Why is that? Even though Compound is riskier to lend to than the Treasury, a DAI-linked return is riskier than a USDC return. Another way to think about this is that if the Treasury were to also issue USDC bonds, those bond would only yield 2.5%. To account for credit (and other) risks investors would require a base 1.5% with an extra 1.0% on top for the risk of USDC breaking.

The convenience yield

Let's bring in one last layer. Something called the convenience yield is lurking behind this.

When you lend me some tokens, you need to be compensated for more than just credit risk i.e. the risk that I won't pay back the tokens. You are also doing without the convenience of these tokens for a period of time. The replacement, my IOU, won't be very handy. For instance, the convenience of a dollar bill can be though of as the ability to mobilize it whenever you need to meet some pressing need. But if you've lent a $100 bill to me then you've given up all that bill's usefulness. Instead, you're stuck with my awkward $100 IOU. You need some compensation for this. (Unconvinced? Head over to Steve Randy Waldman's classic ode to the convenience yield).

So when we break down the components of the interest rate on DAI bonds, there must be some compensation required for forgoing the convenience of DAI, its convenience yield. Earlier I attributed the big gap between rates on Compound DAI and USDC bonds to varying odds of each scheme failing. However, the gap could also be explained by varying convenience yields. If the convenience yield of a DAI token is higher than that of a USDC token, we'd expect an issuer of a DAI bond to pay a higher rate than on a USDC bond, in order to compensate DAI holders for giving up on those superior conveniences. 

If DAI's convenience yield is higher than USDC's, what might explain this gap? DAI is completely decentralized and can't be monitored. USDC isn't. It is less censorship-resistant than DAI. So perhaps USDC just isn't as handy to have around.

So some of the 11.5% rate on Compound DAI bonds—say 2%—may be due to the convenience yield forgone on lent DAI. If DAI had the same features as USDC, and thus had a lower convenience yield, a Compound DAI bond might only yield 9.5% (11.5% - 2.0%). If so, the discrepancy between the Compound DAI and USDC bonds—9.5% vs 6.5%—wouldn't be as extreme.

Summing up, let's revisit Buterin's tweet:

Lending DAI to Compound offers 11.5% annual interest. US 10 year treasuries offer 1.5%. Why the discrepancy?

— Vitalik Non-giver of Ether (@VitalikButerin) August 23, 2019

If my line of thinking is right, the discrepancy is accounted for a messy mix of the higher risk of lending to Compound (3), the danger of DAI cracking (2), and whatever convenience yield one forgoes when one no longer has DAI on hand (4-other). And of course, Buterin's first option is right too. I'm assuming that people are rational and can easily buy and sell various assets. But the sorts of large institutional players who set market prices may not be operating in crypto markets.

How I learned to stop worrying and accept deflation

Why can't we create inflation anymore? Maybe it's because money isn't what it used to be.

Money used to be like a car; the market expected it to depreciate every day. When we buy a new car we accept a falling resale value because a car provides a recurring flow of services over time; each day it gets us from point a to point b and back. And since these conveniences are large, the market prices cars such that they yield a steady string of capital losses.

Money, like cars, used to provide a significant flow of services over time. It was the liquidity instrument par excellence. If a problem popped up, we knew that money was the one item we could rapidly exchange to get whatever goods and services were necessary to cope. Given these characteristics, the market set a price for money such that it lost 2-3% every year. We accepted a sure capital loss because we enjoyed a compensating degree of comfort and relief from having some of the stuff in our wallets.

These flows of services are called a convenience yield. Assets that throw off a convenience yield, like cars and money, typically have negative expected price paths. Let's call them Type 1 assets.

Type 2 assets, things like stocks and bonds, don't boast a convenience yield. Without a convenience flow, people only buy them because they promise a real capital return. One way a Type 2 asset provides a capital return is via a positive expected price path. We only hold Google shares because we expect them to rise by around 5-10% a year. Same with treasury bills. The government issues a bill at, say, $97, and they mature a year later at $100.

Another way for a Type 2 asset to provide a capital return is via periodic payments. A bond or an MBS doesn't rise over time. Rather, it provides its return in the form of regular coupon payments.

Could it be that money has steadily lost its convenience yield? If so, it's shifted from being a Type 1 asset with a negative expected price path towards being a Type 2 asset. That would explain our new deflationary era. In the same way that Type 2 assets like Google and t-bills have to offer a positive expected price path if they are to be held, the purchasing power of money needs to improve over time. And since everything in the world is priced in terms of money, that means that the price level can no longer inflate, it has to deflate.

Where has money's once considerable convenience yield gone? The costs of creating liquidity have been steadily diminishing. Wall Street has been able to make a wide variety of assets like stocks and bonds much more liquid at less cost. So whereas money was once the liquidity instrument par excellence, people now have a multitude of liquid instruments that they can choose from. At the same time, central banks, via quantitative easing, have create massive amounts of central bank liabilities. With a sea of liquid assets, maybe liquidity just isn't a valuable commodity anymore.

Welcome to deflation, folks. Into the vacuum left by money's retreating convenience yield, a promise of capital returns has sprung up.

Reversing deflation?

Even if money has become a Type 2 asset, central bankers can still get the inflation rate back to 3%. To do so, they'd have to change the nature of the capital return that it offers. Like Google shares, money now seems to promise a rising expected price path (i.e. deflation). Central bankers need to switch that out with a bond-style promise of juicier periodic payments. This would involve a central banker ratcheting up the interest rate on money balances, or reserves, to an above-market level. Only with an unusually high interest rate on reserves would people once again accept a declining expected price path for money (i.e. inflation).

For an analogy, imagine that tomorrow the U.S. Treasury were to issue a new 10-year bond with an outlandishly high 10% coupon. With the market-clearing yield on existing 10-year bonds sitting at just 2%, the new bond would start trading at a large premium to its $1000 face value and slowly fall over time. Likewise, money that sports an outlandishly high interest rate would steadily lose purchasing power. 

Ratcheting up rates in order to get us back to a 3% inflation path could be a ghastly experience. Before it can start rolling down the hill again, money's purchasing power would have to rise sharply in value. But money is the unit in which everything else is priced, which means the price level would need to rapidly deflate. If prices are sticky, this could result in a glut of unsold labour and goods; a recession.

Alternatively, might a central bank rekindle inflation by forcing interest rates below their market level? In the short term we'd get a quick one-time dose of inflation. But after the adjustments had been made the price level would only continue its previous deflationary descent. A central banker would have to consistently ratchet down interest rates to generate a perpetual series of one-time inflationary pops in order to keep hitting its 2-3% inflation target. This strategy would run into problems. Go much below -1% and a central bank will hit the lower bound. Unless it wants to risk mass cash storage, it won't be able to go further. Even if a central bank devises ways to get below -1%, it'll have to perpetually ratchet rates down in order to spur the next one-time pop in inflation. Once it hits -20%, or -30%, one wonders whether the market won't simply adopt an alternative currency.

Given that these two options don't seem too comforting, maybe we should just get used to a bit of deflation.


Tony Yates responds here and here.

Gold's rising convenience yield

While I may have taken some jabs at the gold bugs in two recent posts, please don't take that to mean that I have it in for the metal itself. Gold is a fascinating topic with a history that is well worth studying. (See this, for instance). In that vein, what follows is some actual gold analysis.

Something weird is happening in gold markets. The future price of gold (its forward price) has fallen below the current gold price. Now in fairness, this isn't an entirely new phenomenon. Over the last year or two, the price of gold one-month in the future has traded below the current, or spot price, a number of times. However, this observation has grown more marked as both the three-month and six-month rates have also recently fallen below the spot price.

This degree of inversion is rare. Except for a brief flip in 1999 when near-term forward prices fell below zero for a day or two, future gold has almost always traded for more than current gold. See chart below, which illustrates the one-month to twelve-month forward price premium/deficit in annual percent terms:

Here's why this pattern has dominated:

Gold's forward price indicates the level at which a buyer and seller will contract to exchange gold at some point in the future. The seller must be compensated for a number of costs they will incur in holding the gold until the deal's consummation, including: 1) taking out a loan to buy the gold and stumping up interest expenses; and 2) paying to store and insure it in a vault. Together, these are called carrying costs.

The buyer of future gold needs to compensate the seller for these costs. Rather than paying the seller an up-front fee, the buyer builds a premium into the price they pay for future gold in-and-above the current spot price, say $5. The future seller of gold can use this $5 premium to cover their carrying costs, thereby coming out even in the end. So future gold trades above spot gold by the size of its carrying costs.

The current inversion of spot and future gold prices seems to break all these rules. The premium that sellers have traditionally required has not only shrunk to 0 but become a deficit. Put differently, sellers of future gold are no longer demanding a compensatory fee for storing and financing the metal. In fact, they seem willing to provide these expensive services at a negative price!

One explanation for the inversion is that with interest rates being so low, the costs of carrying gold have become negligible. This is only party correct. Minuscule carrying costs would imply a future gold price that is flat relative to the current gold price, when in actuality future prices are below present prices.

That leaves only one explanation for the inversion: there is some sort of hidden non-pecuniary benefit to holding the stuff. In futures-speak, this benefit is typically referred to as a commodity's convenience yield, a term coined by Nicky Kaldor in 1939. An analogy to oil markets may be helpful. Oil prices often invert because merchants see potential for future supply disruptions. Having oil on hand during these disruptions is immensely useful as it  spares our merchant the hassle of negotiating his or her way though an oil supply chain that may be severely crippled while ensuring that customer demand is smoothly met. So the convenience yield can be thought of as a flow of relief, or uncertainty-shielding services, provided to owners of inventories of a commodity. If that relief is sheer enough, than the convenience yield will be larger than the twin costs of financing and storage, resulting in inverted markets. (For an excellent explanation of the convenience yield in oil markets, check out this Steve Randy Waldman post).

That's what appears to be happening in gold. Gold merchants seem to be anticipating choppiness in the future supply and demand of the metal, and see growing benefits in holding inventories of the stuff in order to cope with this choppiness. The convenience yield on these inventories has jumped to a high enough level that it currently outweighs the costs of storing and financing gold, resulting in an inverted gold market.

Gold's convenience yield spikes every every few years due to market disruptions, with the last spike occurring during the 2008 credit crisis, the one prior to that in 2001, and the one before that in 1999 when central banks announced plans to limit gold sales. It just so happens that these earlier disruptions occurred when U.S. interest rates were already high enough that they continued to outweigh the metal's suddenly-augmented convenience yield. Inversions were brief and only on the 1-month horizon. Now that a disruption is occurring when interest costs are near zero, a more sharply inverted market is the result, dragging the 3 and 6-month horizons into negative territory. Going forward, all gold market disruptions could very well create sharp inversions of -1 to -2% in the 1 to 12-month horizons, insofar as we are living in an era of permanently low interest rates.

Is gold becoming money?

A number of gold bugs see the current inversion as something quite momentous. To understand why, you need to know that a gold bug's nirvana is when gold is once again 'money'. When something is money, it is highly liquid. The beauty of owning a highly liquid medium is that it can be mobilized to deal with almost any disruption to one's plans and intentions. Put differently, the convenience yield on stored money is very high. One measure of a paper dollar's convenience yield is the interest rate a government-insured certificate of deposit. Locking away cash for, say, 24 months means that the owner loses all the benefits of its liquidity. With 24-month certificates of deposit currently yielding 0.34% a year, the value of those forgone conveniences is 0.34%.

So when a gold bug's dream becomes reality and gold overtakes the dollar, yen, pound etc. as the world's most-liquid exchange medium, that is the equivalent of saying that gold is providing investors with the market-leading monetary convenience yield. And a permanently high convenience yield would result in a permanently inverted gold market (or at least a much flatter one).

Is the current inversion an indication that gold is becoming money? I don't think so. If the augmented convenience yield on gold was in fact rising due to gold's liquidity having surpassed that of fiat money, we'd expect this to be reflected not only in near-term forward prices but along the entire horizon of forward prices. Not only should the 3-month forward prices be inverted, but so should the 3-year forward price. Is this the case? Not really. If you've seen Crocodile Dundee, I'd suggest you go and check out this hilarious post by Bron Suchecki illustrating the extent of gold's inversion. If you haven't seen the movie (you should), check out the chart below.

The first data point is the spot price. Gold forward prices are inverted after that, but only over a narrow range of five or six-months. By mid-2015, forward prices return to their regular pattern of trading at a premium to current prices.

So no, gold is not becoming money. Rather, we are running into some short-term jitters, and merchants think that holding the stuff provides a few more ancillary benefits than before.

Could these short-term supply & demand problems crescendo into longer-term problems, resulting in inversion beyond 2015? I don't think so. Unlike oil and most other commodities, the supply of mined gold is never used up. Ounces that were brought out of the ground by the Romans are still in existence. This means that supply disruptions should never pose a significant problem in the gold market since gold necklaces and fillings can be rapidly melted down into bars and brought to market. While we care if Saudi stops all oil production or if the U.S. corn harvest is terrible,  if South Africa ceases to produce gold—meh.

This means that the convenience yield on inventories of gold will almost always be less than the convenience yield on stocks of oil, since the sorts of disruptions in the gold market will always be shorter and less extreme than in oil markets. Oil supply shocks can be so sharp and enduring that oil's convenience yield remains elevated for long periods of time. The result is an inverted oil market over the entire time horizon. Such inversions are fairly common events in oil markets (once again, see Bron's post).

Gold shocks can never be enduring, so the types of price inversions we'd expect will be fleeting and only appear in the near-term time horizon. Like the one we are seeing now. In sum, we've seen this all before, and no, it's not the end of the world.

Does QE actually reduce inflation?

There's a counterintuitive meme floating around in the blogosphere that quantitative easing doesn't do what we commonly suppose. Somehow QE reduces inflation or causes deflation, rather than increasing inflation. Among others, here are Nick Rowe, Bob Murphy, David Glasner, Stephen Williamson, David Andolfatto, Frances Coppola, and Bill Woolsey discussing the subject. Over the holidays I've been trying to wrap my head around this idea. Here are my rough thoughts, many of which may have been cribbed from the above sources, though I've lost track from which ones.

Let's be clear at the outset. Inflation is a rise in the general price level, deflation is a fall in prices. QE is when a central bank purchases assets at market prices with newly issued reserves.

In equilibrium, the expected returns on all goods and assets must be equal. If they aren't equal then people will rebalance towards superior yielding assets until the prices of these assets have risen high enough to iron out their superior return (and away from low yielding assets until their prices have fallen enough so that their expected return is once again competitive with all other assets).

Central bank reserves are one of the many assets whose yield is included in this calculus of returns. The return on reserves can be decomposed into two specific categories of return: expected capital gains, or price appreciation, and a liquidity return, sometime referred to on this blog as a monetary convenience yield.

Regarding the first return, this is typically negative. People expect the purchasing power of central bank reserves to be lower in the future than in the present—they anticipate inflation.*

The liquidity return exists because reserves are highly marketable. The ability to quickly mobilize reserves to deal with unanticipated events yields a flow of liquidity services, specifically the alleviation of felt uncertainty. The expected return on these liquidity services outweighs the expected capital loss on reserves, providing reserve owners with a combined return that is competitive with other assets like cars, olive oil, education, t-bills or houses.

When a central bank conducts QE, the quantity of reserves in the economy increases so that they are less scarce. All else staying the same, the marginal value that people attribute to the flows of liquidity services provided by reserves declines. With their liquidity return having fallen, reserves now yield a lower overall return than competing assets.

Given these unequal returns, reserve owners will want to rebalance their portfolios into higher yielding alternatives. However, existing owners of these assets will be unwilling to accept this trade since the return they can expect to receive on reserves is no longer competitive with the return on the assets that they would be forgoing. Reserve owners will have to sweeten the deal by offering potential counterparties an improved return on reserves held. The way they can do this is to offer to sell their reserves at a reduced price today relative to their price tomorrow. In doing so, reserve owners are offering counterparties an improved potential for capital appreciation to counterbalance the diminished liquidity return on reserves.

Another way to describe this trade is that reserve owners must create some inflation, or a higher price level, in order to attract interested buyers. From this higher plateau, prices will rise at a much slower rate than before, or, put differently, the purchasing power of reserves will fall much slower than previously expected. The new expected price trajectory of reserves may even be a deflationary one—the market anticipating prices tomorrow to be lower than those today. In any case, only when the expected capital gain on reserves has been sweetened enough to sufficiently compensate would-be owners of reserves for bearing their diminished liquidity return will potential counterparties be willing to trade away their existing assets for reserves.

So back to our initial question: does QE reduce inflation? Not quite. By diminishing the liquidity return on reserves, QE reduces *expected* inflation. This change in expected inflation occurs via a leap in inflation in the present. Subsequent rounds of QE will continues to breed inflation and lower expected inflation until the liquidity return has been reduced to zero, at which point further QE will have no effect.

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But let's introduce another wrinkle. What happens if other assets also carry a liquidity return? And let's assume that there are different kinds of liquidity returns, so that the liquidity services provided by one asset can't be easily substituted with the liquidity services of another. Thus, when the economy is flooded with reserves and their marginal liquidity return hits zero, the liquidity return on alternative assets needn't also decline to zero.

Let's take up where we left off. QE has reduced the liquidity return on reserves to zero and subsequent rounds of QE no longer cause inflation or reduce expected inflation. Let's assume that short term bills, specifically those issued by, say, Microsoft, provide a unique set of collateralizability services, and therefore yield a liquidity return > 0.

When our central bank purchases Microsoft bills, the supply of Microsoft collateral in the economy shrinks, which increases the liquidity return on Microsoft bills. The total return on Microsoft bills, the sum of their liquidity return and expected capital gain, is now superior to all other assets. This spawns a mass effort by investors to sell other assets for Microsoft bills. The only way that existing bill owners will agree to sell away their superior yielding Microsoft debt is if potential buyers offer to pay a higher price. As short term Microsoft bill prices are bid up, the expected capital gain on bills is reduced, counterbalancing the higher liquidity return. At some appropriately higher bill price, the total expected return on bills will be reduced to a level competitive with all other assets, restoring equilibrium.

This process, however, doesn't have any impact on inflation. All that is happening is that the relative price of a certain asset—the short term Microsoft bill—is rising.

Subsequent rounds of QE will further reduce the supply of short term Microsoft bills, increasing their liquidity return and eventually driving their price above par. At any price above par, capital returns on bills are effectively negative—bills, after all, never pay out more than their par value. People will continue to be attracted to a <0% yielding short term bill as long as it sports a sufficiently large liquidity return. The latter can outweigh the negative capital return, providing a total return that is competitive with other assets.

One problem with QE is that it drives the price paid for the liquidity service on Microsoft short term bills above the cost that Microsoft must incur in maintaining those liquidity services. People are effectively paying more to enjoy Microsoft liquidity services than they would in a competitive economy in which prices are pushed down to the cost of production. The artificially high price for bills that has been caused by QE incentivizes people to acquire a smaller flow of Microsoft liquidity services than they would otherwise prefer. This represents a deadweight loss to the economy, or what is termed an allocative inefficiency by economists. The surplus that consumers enjoy is smaller than it would be in a world in which large scale purchases of Microsoft bills had not pushed their liquidity return to artificially high levels.

This loss of allocative efficiency, however, does not equate to deflation. While QE involving Microsoft bills may not be ideal for the economy, it doesn't cause the price level to fall.

Given QE's effect on Microsoft bills, it would be odd if Microsoft did not choose to continually issue new short term bills until the marginal value of liquidity services yielded by bills was driven back down to the cost of maintaining those services. This would goose Microsoft's profits while simultaneously increasing the consumers' surplus, removing all of the inefficiency created by QE.

However, if the issuer of these unique collateralizable bills is the government, not Microsoft, things might be different. Because the government isn't profit-driven, it may be less motivated to issue new bills and reduce the allocative inefficiency created by QE. Is this a big deal? The excess of liquidity's price over cost is similar to any other monopolistic distortion, take for intance the diamond or potash oligopolies that price their products above cost. Situations like these are unfortunate, but I'm not so sure that they have large macroeconomic consequences. The benefit of not doing QE because one might create inefficiencies in a few lone markets for collateral are surely not as large as the benefits of doing QE in order to boost the economy's price level.

So the best I can do in my mental meandering is that QE either produces inflation or is irrelevant. It does not cause lower inflation or deflation. The by-product of any QE-inspired jump in inflation is lower *expected* inflation than before. A few inefficiencies may be created in various markets targeted by purchases, but as interesting as these inefficiencies are I don't see how they produce severe macroeconomic consequences.

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*For the sake of simplicity I assume that reserves don't pay interest.

Rates or quantitites or both

Roaming around the econ blogosphere, I often come across what seems to be a sharp divide between those who think monetary policy is all about the manipulation of interest rates and those who think it comes down to varying the quantity of base money. Either side get touchy when the other accuses its favored monetary policy tool, either rates or quantities, of being irrelevant. From my perch, I'll take the middle road between the two camps and say that both are more-or-less right. Either rates, or quantities, or both at the same time, are sufficient instruments of monetary policy. Actual central banks will typically use some combination of rates and quantities to hit their targets, although this hasn't always been the case.

Just to refresh, central banks carry out monetary policy by manipulating the total return that they offer on deposit balances. This return can be broken down into a pecuniary component and a non-pecuniary component. By varying either the pecuniary return, the non-pecuniary return, or both, a central bank is able to create a disequilibrium, as Steve Waldman calls it, which can only be re-equilibrated by a rise or fall in the price level. If the net return on balances is sweetened, banks will flee assets for balances, causing a deflationary fall in prices. If the return is diminished, banks will flock to assets from balances, pushing prices higher and causing inflation.

The pecuniary return on central bank balances is usually provided in the form of a promise to pay interest, or interest on reserves.

The non-pecuniary return, or convenience yield, is a bit more complicated. I've talked about it before. In short, it's sorta like a consumption return. Because central bank balances are useful in settling large payments, and they are rare, banks find it convenient to hold a small quantity of them as a precaution against uncertain events. This unique convenience provided by scarce balances is consumed over time, much like a fire extinguisher's property as a fire-hedge is consumed though never actually mobilized. By increasing or decreasing the quantity of rare balances, a central banker can decrease or increase the value that banks ascribe to this non-pecuniary return.

Now some examples.

The best example of a central bank resorting solely to the quantity tool in order to execute monetary policy is the pre-2008 Federal Reserve. Before 2008, the Fed was not permitted to pay interest on reserves (IOR). This meant that the only return that Fed balances could offer to banks was a non-pecuniary convenience yield, a point that I described here. By adding to or subtracting from the quantity of balances outstanding the Fed could alter their marginal convenience, either rendering them less convenient so as to drive prices up, or more convenient so as to push prices down.

The Bank of Canada is a good example of a central bank that uses both a quantity tool AND an interest rate tool, though not always both at the same time. Since 1991, according to Mark Sadowski, the BoC has paid interest to anyone who holds overnight balances. This is IOR, although in Canada we refer to it as the deposit rate. In addition to paying this pecuniary return, BoC balances also yield a non-pecuniary return. Banks who hold balances enjoy a stream of consumptive returns, or a convenience yield, that stems from both the rarity of BoC balances and their exceptional liquidity.

The best way to "see" how these two returns might be decomposed is by looking at the short term rental market for Bank of Canada balances, or the overnight market. In Canada, this rate is called CORRA, or the Canadian overnight repo rate. A bank will only part with BoC balances overnight if a prospective borrower promises to sufficiently compensate the lending bank for foregone returns. Assuming that the Bank of Canada's deposit rate is 2%, a potential lender will need to be compensated with a pecuniary return of at least 2% in order to dissuade them from socking away balances at the BoC's deposit facility.

The lender will also need to be compensated for doing without the non-pecuniary return on balances. If the overnight lending rate, CORRA, is 2.25%, then we can back out the rate that a lender expects to earn for renting out the non-pecuniary services provided by balances. Since the lender of balances receives the overnight rate of 2.25% from the borrowing bank, and 2% of this can be considered as compensation for foregoing the 2% pecuniary return on balances, that leaves the remaining 0.25% as compensation to the lender for the loss of the non-pecuniary return.

So in our example, the pecuniary and non-pecuniary returns on BoC balances are 2% and 0.25% respectively, for a total return of 2.25%.

The Bank of Canada meets each six weeks, as Nick Rowe points out, upon which it promises to provide banks with a given return on settlement balances, say 2.25%, for the ensuing six week period. When it next meets, the Bank will  introduce whatever changes to this return that are considered necessary for it to hit its monetary policy targets. The BoC can modify the return by changing either the pecuniary component of the total return, the non-pecuniary component, or some combination of both.

Say it modifies only the non-pecuniary component while leaving their pecuniary return untouched. For instance, with the overnight rate trading at 2.25%, the BoC might announce that it will conduct some open market purchases in order to increase the quantity of balances outstanding, while keeping the deposit rate fixed at 2%. By rendering balances less rare, purchases effectively reduce the non-pecuniary return on balances. As a reflection of this shrinking return, the overnight rate may fall a few basis point, or it may fall all the way to 2%. Whatever the case, the rate at which banks now expect to be compensated for foregoing the non-pecuniary return on balances has been diminished. Banks will collectively try to flee out of overpriced clearing balances into assets, pushing up the economy's price level until balances once again provide a competitive return. This sort of pure quantity effect is the story that the quantities camp likes to emphasize.

The story told by the quantities camp is exactly how the BoC loosened policy between April 2009 and May 2010. At the time, the BoC injected $3 billion in balances *without* a corresponding decrease in the deposit rate. The overnight rate fell from 0.5% until it rubbed up against the 0.25% deposit rate. The lack of a gap between the overnight rate and the deposit rate indicated that the injection had reduced the overnight non-pecuniary return on balances to 0%. After all, if lenders still expected to be compensated for forgoing the non-pecuniary return on balances, they would have required that the overnight rate be above the deposit rate.

The BoC's decision to reduce the overnight non-pecuniary return on balances to 0% would have generated a hot potato effect as banks sold off lower-yielding BoC balances for higher-yielding assets, thus pushing prices higher. A change in quantities, not rates, was responsible for the April 2009 to May 2010 loosening.

Likewise, in June 2010, the BoC tightened by using quantities, not rates. Open market sales sucked the $3 billion in excess balances back in, thereby increasing the marginal convenience yield on central bank balances. The deposit rate remained moored at 0.25%, but the overnight rate jumped back to 0.5%, indicating that the overnight non-pecuniary return on balances had increased from 0% to 0.25%. This sweetening in the return on balances would have inspired a portfolio adjustment away from low-yielding assets into high-yielding central bank balances, a process that would have continued until asset prices had fallen far enough to render investors indifferent once again along the margin between BoC deposits and assets. Once again quantities, not rates, did all the hard work.

While the BoC chose to tighten in June 2010 by changing quantities, it could just as easily have tightened by changing rates. For instance, if it had increased the deposit rate to 0.5% while keeping quantities constant, then the net return on balances would have risen to 0.5%, the same return that was generated in the last paragraph's quantities-only scenario. This sweetening in the return on balances would have caused the exact same chain of portfolio adjustments and falling asset prices that the quantities-only scenario caused.

Alternatively, the BoC could have tightened through some combination of quantities AND rates. It might have increased the deposit rate from 0.25% to 0.4%, and then conducted just enough open market sales to increase the non-pecuniary return on balances from 0% to 0.1%, for a total combined return of 0.5%. The ensuing adjustments would have been no different than if tightening had been accomplished by quantities-only or rates-only.

Putting aside the period between April 2009 and June 2010, does the Bank of Canada normally execute monetary policy via rates or quantities? A bit of both, I'd say. At the end of a six week period, say that the Bank wishes to tighten. It typically tightens by announcing a 0.25% rise in its target for the overnight rate combined with a simultaneous 0.25% rise in the deposit rate. The overnight rate, or the rental rate on clearing balances, will typically rise immediately by 0.25%, reflecting the sweetened return on balances.

Did rates or quantities do the heavy lifting in pushing up the return on balances? Put differently, was it the threat that open market sales might increase the convenience yield on balances that tightened policy, or was it the improvement in the deposit rate? I'd argue that the immediate punch would have been delivered by the change in the deposit rate. CORRA, the rental rate on balances, jumped because overnight borrowers of BoC balances were suddenly required to compensate lenders for the higher pecuniary rate being offered by the BoC on its deposit facility. Quantities don't enter into the picture at all, at least not at first. The rates-only camps seems to be the winner.

However, as the ensuing six-week period plays out, market forces will push the rental rate on BoC balances (CORRA) above or below the Bank's target, indicating an improvement or diminution of the total return on balances. The BoC has typically avoided any incremental variation of the deposit rate to ensure that the rental rate, or return on balances, stays true to target over the six week period. Rather, it has always used quantity changes (or the threat thereof) to modify the non-pecuniary return on balances during that period, thereby steering the rental rate back towards target. First rates, and then quantities, conspire together to create Canadian monetary policy.

To sum up, the Bank of Canada's monetary policy is achieved, it would seem, through a complex combination of rate and quantity adjustments. The rates vs. quantities dichotomy that sometimes pops up on the blogosphere simplifies what is really a more nuanced story. Monetary policy can certainly be carried out by focusing on quantity adjustments to the exclusion of rate adjustments (as was the case with the pre-2008 Fed) or vice versa . However, modern central banks like the Bank of Canada use rates, quantities, and some combination of both, to achieve their targets.

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Note: The elephant in the room is the zero-lower bound. But the zero lower bound needn't prevent rates or quantities from exerting an influence on prices. On the rates side of the equation, the adoption of a cash-penalizing mechanism along the lines of what Miles Kimball advocates would allow a central bank to safely push rates below zero. As for the quantity side of the equation,  the threat of Sumnerian permanent increases in the monetary base may not be able to reduce the overnight non-pecuniary return on balances once that rate has hit zero, as Steve Waldman points out... but they can certainly reduce the future non-pecuniary returns provided by balances. Reductions in future non-pecuniary returns should be capable of igniting a hot potato effect, albeit a diminishing one, out of balances and into assets.

Medieval QE

Hand operated rolling mill, for putting the edge impression on to coins

I've been reading about the medieval monetary system lately. What a fascinating and complex mechanism, and a good reminder that we should not be using the word medieval as a synonym for primitive or unenlightened. Medieval coinage, I've come to discover, is also a highly confusing subject. A quote that John Munro attributes to Karl Helleiner seems apropos: "There are two fundamental causes of madness amongst students: sexual frustration and the study of coinage."

Studying odd, imaginary, or historical monetary systems is rewarding not only because of the aha! moment that understanding provides, but also because of what these systems reveal about our modern one. Readers may have noticed that for the last two months I've been posting rather obsessively on monetary policy, a topic I've typically avoided. Here's my attempt to combine monetary policy and medieval coinage into one post, hopefully as a useful way to consolidate all my points in an interesting way.

In medieval days, mints were generally owned by a prince. A mint-master was put in charge of coining silver bullion into coin (gold and copper were also coined, but for simplicity I'll focus on silver). The prince set the official rate at which the mint-master could convert raw silver into a specific coin. For instance, one pound-weight of silver might be coined into 240 silver pennies, each with 1/240th a pound-weight of silver in them. Under the principle of free coinage, anyone could bring raw bullion, plate, jewelry, and foreign coin to the mint to be converted into coin of the realm.

Coins were far more convenient in trade than raw silver because they saved transactors from the laborious process of weighing and assaying silver powder or ingots. Because of this superior marketability, coins usually traded at a premium to an equivalent amount of raw silver. A coin with 1 gram of silver therein, for instance, might exchange in the market at a price of 1.1 grams of pure silver bullion. Munro refers to this premium as the agio.

The existence of an agio represented a potential arbitrage opportunity for the public. A merchant need only buy raw silver, bring it to the mint to be coined, and leave with the same weight of silver, but now in coin form and capable of purchasing, say, 10% more goods. He could then buy more bullion with this new coins, repeating the process and earning a 10% risk-free return each time.

While coinage was free, it was not gratuitous. The mint-master required a certain amount of silver as payment for the use of his time, minting tools, and wages for his employees. Since silver was usually mixed with base metals like copper to produce the final coin, the mint-master also required compensation for supplying the baser metals. This fee was called brassage. The prince exacted a fee too, or a tax. This was called seigniorage.

These costs restricted the opportunities for arbitrage. If the brassage and seigniorage costs were higher than the agio, the public would avoid the mint altogether since the transaction would result in a loss in purchasing power. Better to keep their silver in bullion form or search for a mint that produced identical coin at less cost.
However, as long as the agio was more than brassage and seigniorage, citizens would continue to bring bullion to the mint and enjoy a small return.

This process had a natural limit. Much like the water-diamond paradox (which tells us that the usefulness of something does not necessarily equate to a higher price) the fact that coins were more useful than raw bullion in transactions didn't mean that people would always pay to enjoy that benefit. As the public flocked to the mint, a coin glut would develop. The marginal value that the market placed on coin-as-transactions-medium would deteriorate, driving the agio down to the twin costs of brassage and seigniorage. Put differently, an increase in coin supply would push the marginal value of coin towards the cost of production. Just as water is extremely useful but essentially free, the marketability value of coins -- though still useful -- could be had at no cost once the quantity of coin was sufficiently plentiful.

Let's bring this back to monetary policy. The initial agio of coin over silver is very much akin to the liquidity premium I've mentioned in previous posts. The existence of an agio, or liquidity premium, is justified by the convenience, moneyness, or non-pecuniary return on a medium-of-exchange. As the supply of coin is allowed to increase, all other things staying the same the market's marginal valuation of this non-pecuniary return will fall, as will the associated agio/liquidity premium.

A modern central bank keeps the supply of reserves artificially tight and restricts competition. In doing so, it creates a positive marginal non-pecuniary return on reserves (or a convenience yield, see here). This drives the market value of reserves above the price at which they would otherwise trade were they subject to competition. In other words, a central bank creates a permanent agio.

In order to execute monetary policy, central banks will typically massage this agio. By emitting a small amount of reserves or sucking them in, a central banker can alter the marginal valuation that the market places on the convenience of reserves. This pushes the agio higher or lower. Any change in the agio translates into an economy-wide change in the price level.

Bringing this back to a medieval setting, imagine that the prince ceases free coinage (much like how a modern central banker would restrict reserve supply and competition). From time to time the public might be allowed access to the mint, and in limited numbers, but usually the mint would be closed to business. The supply of coin, therefore, is henceforth restricted. The ensuing lack of transactions media will cause a large agio to emerge as the market value of coin rises relative to bullion. I'm assuming here that counterfeiting is too dangerous to justify. If not, counterfeiters will be motivated to establish black market mints once the agio significantly exceeds brassage.

The prince is now in the same position as a modern central banker. By bringing a bit of silver bullion to the mint, turning it into coin, and spending it, he can increase the quantity of coin in the economy and thereby decrease the marginal non-pecuniary return on coin. The agio would thereby shrink, pushing the market value of coin down, or the price level up.   After all, the economy's unit of account in the medieval period was determined by a given link coin, usually the penny, so any change in the penny's value resulted in an economy-wide change in prices.

Both the prince and a central banker face a limit to the effectiveness of expansionary monetary policy. Once a prince has issued enough coin to drive the agio down to zero via mass "coin quantitative easing", further coin emissions will have no effect on the price level. A coin will now be worth no more than its intrinsic silver value. Nor can it fall to a discount to its silver content, since the public would simply buy coin and melt it into bullion until the discount has been removed. As for a modern central banker, once QE has reduced the convenience yield provided by reserves across the entire curve to zero, then further reserve emission cannot push the price level down any further. The agio has disappeared. In the same way that coin falls to its silver content, reserves will have fallen to their intrinsic "backing" value -- and will go no lower.

The prince still has an alternative. He can engage in outright debasement. By reducing the intrinsic silver content in coin, the price level will once again start to rise. Likewise, a central banker might attack the intrinsic value of central bank liabilities by destroying assets, or purchasing assets at bloated prices, or engaging in helicopter drops. Princes did in fact tend to reduce the price level via debasement and not by manipulating the agio, although they usually did so as a way to earn higher revenue, not to help the economy. No doubt due to the irresponsibility of the prince's who preceded them, modern central bankers are legally prohibited from outright debasement. Manipulating the agio on reserves, or playing with the interest rate on reserves, are the only tools left to them.

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Most of the actual facts about medieval coinage in this post come from John Munro's Warfare, Liquidity Crises, and Coinage Debasements in Burgundian Flanders, 1384 - 1482 (RePEc) and The Coinages and Monetary Policies of Henry VIII (RePEc), among other papers. Munro shouldn't be blamed for mistakes in my theorizing, nor the analogy to modern central bank QE. 

Woodford's forward guidance—why not use forward contracts instead?

...once the supply of reserves is sufficient to drive the short-term riskless rate to zero..., there is no reason to expect further increases in the supply of reserves to increase aggregate demand any further... Once banks are no longer foregoing any otherwise available pecuniary return in order to hold reserves, there is no reason to believe that reserves continue to supply any liquidity services at the margin; and if they do not, the Modigliani-Miller reasoning applies once again to open market operations that increase the supply of reserves, just as in the model of Wallace.

-Michael Woodford, 2012.  

On a whim, I wrote an email to Michael Woodford last week. Woodford, a macroeconomist at Colombia University, is the authour of Interest and Prices (pdf), an important contribution to modern monetary policy. I'll be the first to admit that I haven't been able to work my way through his book—too few words and too many equations. But I have read two excellent papers by him. The first is Monetary Policy Without Money, which I'll touch on in another post, and the second is a well-known paper that he presented at Jackson Hole in 2012 entitled Methods of Policy Accommodation at the Interest-Rate Lower Bound. If you're interested in monetary policy and you haven't read it yet, you really should.

My email, affixed below, had to do with the above quote from his second paper:

Dear Professor Woodford,

I have read your paper Methods of Policy Accommodation at the Interest-Rate Lower Bound several times and it has taught me quite a bit.

One question:

In Section 3.1 (Effects of Targeted Asset Purchases in Theory), you point out that once the supply of reserves is sufficiently plentiful, banks no longer forgo a pecuniary return that would otherwise be provided by reserves (ie a marginal convenience yield). This is the point at which the overnight interest rate hits the lower bound, additional reserve additions are irrelevant, and the Modigliani-Miller result applies.

It seems to me that the overnight rate doesn't shadow the general convenience yield on reserves per se, but rather it shadows the 24-hour convenience yield on reserves. Just like there is a term structure to bonds, there is a term structure to the convenience yield on reserves. In addition to a 24-hour convenience yield, there is a 1 week, 1 month, 1 year yield, each point allowing us to construct a convenience yield curve.

Although the overnight yield may be zero, convenience yields further down the convenience yield curve may still positive. Banks hold reserves not only to enjoy their overnight convenience, but also to enjoy expected flows of future convenience. This would seem to imply that the present discounted value of future flows of convenience can be positive even when the overnight convenience yield is zero.

Which would indicate that even when we are at the lower bound for overnight rates, purchases are not necessarily subject to the Wallace irrelevance critique insofar as they specifically target positive yields further down the convenience yield curve. If purchases today can reduce convenience yields tomorrow, the present discounted value of future flows of convenience will be reduced. Overnight purchases won't suffice since they only target overnight convenience yields. Open-ended outright purchases might not work if there is no commitment to avoid unwinding these purchases in the future. Perhaps long term repo operations that target the distant end of the convenience yield will be most effective in avoiding the irrelevance criticism. Repos precommit a central bank to avoid unwinding at a future point in time, thereby reducing future convenience yields and, as a corollary, the present value of total convenience flows.

Does that make any sense? I am curious what your thoughts on this are.

Cheers,

JP Koning

Frequent readers will notice that my letter was just a summing up of my three recent posts on the convenience yield.* If you've already read those three posts and reached your quota, don't bother reading further, since much of what I'm going to write follows in that general theme.

Surprisingly, Woodford got back to me. I'm not going to publish his response, but in brief he doesn't think that there should be a convenience yield curve. Woodford told me that he thinks reserves are an overnight asset, not a long-term asset like, say, Treasury bills, and an overnight asset doesn't supply a convenience yield for longer than 24 hours.

I agree with Woodford that the convenience yield supplied by a short-lived asset is negligible. No one holds a stock of ripe avocados because they might serve as convenient medium of exchange 30 days from now.

But reserves aren't avocados. They are infinitely-lived instruments that can be perpetually held without the necessity of paying storage fees. This means that even when overnight yields have hit 0% (as indicated by an overnight fed funds rate of zero) reserves still supply current reserve-owners with a positively-valued marginal convenience yield over longer time frames than the 24-hour window. The implication of this is that although central banks may no longer be capable of manipulating the 24-hour convenience yield lower, they may be still be able to conduct targeted financial transactions, or balance-sheet policy, that change distant parts of the convenience yield curve. This gives a central bank plenty of traction at the zero lower bound. After all, a reduction in the future convenience flows thrown off by reserves will reduce the present value of all convenience flows. The expected return on reserves having been reduced, reserves will be spent away in the present and this will stimulate today's inflation and/or real activity.

QE—what Woodford refers to as balance sheet policy—is a fairly blunt tool when it comes to reducing distance convenience yields.** This is because a one-time expansion of the central bank's balance sheet can be easily reversed at a future point in time by sucking reserves back in. Financial markets may therefore view QE as fleeting. If so, distant convenience yields will not budge much and, as a result, inflation and real activity will remain unaffected.

Rather than engaging in crude QE when the overnight rate hits zero, a central bank might enter into a more focused form of balance sheet expansion. Five-year repos, for instance, may be sufficient to ensure that excess reserves stay in the system for an extended period of time. Even more effective would be a policy of entering into forward contracts with banks. These transactions would commit the central bank to purchasing assets at various points in the future, thereby ensuring a series of large balance sheets down the road.

For instance, if the Bank of Canada faced the ZLB and wanted to reduce the future convenience yield on reserves after, say, 2015, it could contract with commercial banks to purchase assets at various dates in 2016, 2017, and 2018. It would enter into as many of these forward contracts as necessary to guarantee today a sufficiently large supply of reserves tomorrow. Unlike crude QE, forward contracts are irreversible. The permanency of these transactions should be sufficient to reduce the future convenience yield on reserves, thereby diminishing their expected return in the present and stimulating current spending.

A policy of using forward contracts to reduce the distant convenience yield on reserves could be a substitute for Woodford's verbal forward guidance. Rather than specifying in words the future time path of interest rates, the central bank need only add a sufficient amount of forward contracts to its balance sheet in order to ensure that it hits its targets (an inflation target, a nominal GDP target, whatever). The upshot is that balance-sheet policy needn't die at the zero-lower bound. Concrete actions that guarantee to alter the size of a central bank's future balance sheets and convenience yields can be just as effective as Woodford's carefully crafted wording.

In any case, I'm not holding my breath for Woodford to get back to me on that, he's a busy guy.

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*Interestingly, Woodford uses the term convenience yield in his paper, too.
** Miles Kimball has equated balance sheet policy at the ZLB to using a massive fan to move the economy.

The rise and fall (and rise) of the hot potato effect

Don Randi Trio +1 at the Baked Potato, Poppy Records, 1971. [link]

In this post I'll argue that:

1. When it comes to financial assets, the hot potato effect is irrelevant.
2. The hot potato effect is born the moment we begin to talk about non-financial instruments — things you can touch and consume, like gold or cows or houses or whatnot.
3. Because central bank reserves are simultaneously financial assets and a tangible consumables, they are capable of generating a hot potato effect.
4. The moment that central bank money ceases to be valued as a consumer good, its hot potato effect dies.

Here's a short illustration of the hot potato effect that should serve as my definition of the term. Imagine that a gold miner finds several huge gold nuggets and quietly brings them to town to sell. The gold miner approaches the town's merchant with an offer to exchange gold for supplies, but at current prices the merchant is already happy with the size of his gold holdings. He will only take the the miner's gold if the miner is willing to buy supplies at a premium to the prevailing market price. The miner grumbles but sells the gold anyways. Now the merchant approaches the town's largest landowner with an offer to exchange gold for land, but the landowner is already content with the size of his gold holdings. He will, however, accept the offer if the merchant is willing to improve his price. The merchant accepts and the transaction is consummated.

Each subsequent townsperson will require a higher price to convince them to part with their goods and hold the newly mined gold. In this fashion the gold miner's nuggets work through the town's economy like hot potatoes, pushing up all gold-denominated prices.

With non-tangibles like financial assets, the hot potato effect is irrelevant. Say that our merchant decides to issue new stock or bonds into the town's economy by purchasing other stocks/bonds, gold, or by funding viable projects. The landowner takes the merchant up on his offer and tenders some gold, land, and shares in return for the merchant's newly-issued financial instruments. The merchant's financial instruments are fairly liquid and function as useful exchange media.

A few days later the landowner decides to sell these financial instruments and approaches the miner. The miner, who earlier experienced the hot potato effect, says that he'll only buy the financial instruments if the landowner will sell them for less gold. The landowner is about to consummate the transaction when the merchant barges in. The merchant offers to buy back the financial instruments at a smaller discount. After all, the merchant still owns the same land, shares, and gold that the landowner originally submitted for shares, and he can make a quick profit by repurchasing and retiring the landowner's stock with a smaller quantity of land/gold than was initially tendered. The miner reacts to the merchants competing offer by reducing the discount he required of the landlord, but each time he does so the merchant will match him with a better price. After much haggling between merchant and miner, the landowner will be able to sell his shares to one of them at a price very close to their original gold-denominated value.

Financial asset prices are driven not by the hot potato effect but by a "modern finance effect". The market value of a claim on an issuer is determined by the issuer's earning power and the risk of its underlying assets. If an individual tries to sell claims away like they were hot potatoes, profit maximizing arbitrageurs will step in and bring their price back up to their fundamental value, thereby annulling any hot potato effect.

Now back to central banks. Much like a merchant will buy back the instruments he has issued, a central banker commits to mobilize whatever bonds, gold, and other assets he holds in his vaults to repurchase every reserve he has ever issued. Like any other financial asset, the price of reserves is determined by underlying earnings power. Should a central bank issue new reserves by swapping them for bonds or gold, this issuance will not ignite a hot potato cycle of declining prices because arbitrageurs will compete to buy up any underpriced reserves.

The story doesn't end here. In addition to functioning as financial assets, central bank reserves also function as consumables. A bank that holds reserves enjoys a convenience yield: they can be sure that come some unforeseen event, they'll have adequate resources on hand to cope. Reserves are consumed in the same way that fire extinguishers are used up. While it is unlikely that either will ever be mobilized to deal with emergencies, their mere presence is consumed by their owner as a flow of uncertainty-shielding services over time.

Unlike fire extinguishers, reserves can be created instantaneously and at no cost. If fire extinguishers were like reserves, we'd conjure up any amount of them that we desired, their price would fall to zero, and everyone would enjoy their convenience for free. The marginal value that the market places on the consumability of reserves, however, never plunges to zero because a central bank keeps their supply artificially tight.

A central banker's ability to set off a hot potato chain of rising prices stems from the role of reserves-as-consumable, not their role as financial assets. Say that the banker offers to loosen the supply of scarce reserves. Existing consumers of reserves are already well-stocked with reserves at current prices. They will only accept the new issue by reducing the quantity of goods or other assets that they're willing to swap for reserves. Put differently, the price level must rise. This is the same mechanism by which the miner's gold nuggets were passed on hot-potato-like.

On the other hand, when a central banker further constricts the supply of already-scarce reserves, the marginal consumer of reserves will face a deficit in their reserve inventories, a hole that the consumer can only fill by offering larger quantities of goods/assets in return for reserves. Put differently, the price level must fall.

As a central bank issues ever larger amounts of reserves, the marginal value the market places on their consumability, or their marginal convenience yield, falls towards zero. As this happens, the hot potato effect becomes almost negligible—each subsequent issue of reserves increases the supply of what has already become a free good. The consumptive quality of central bank reserves is now akin to oxygen. Just like an increase in the amount of air has no effect on air's price—we already value it on the margin at zero— increases in the quantity of reserves are irrelevant. With the hot potato effect officially dead, we've arrived at Scott Sumner's case 5b, or Stephen Williamson's not-your-grandmother's-liquidity-trap.

With the death of the hot potato, the market's valuation of reserves is now solely governed by what I referred to earlier as the modern finance effect. Subsequent increases in the quantity of reserves via open market operations have no effect whatsoever on the price level. Anyone who sells reserves as if they were hot-potatoes will be corrected by arbitrageurs who return the price level to its fundamental value. This is a world in which Mike Sproul's backing theory precisely applies, or what Miles Kimball calls Wallace irrelevance/neutrality holds absolutely.

Reintroduce a shortage of central bank reserves and the marginal consumptive value, or convenience yield, of reserves will once again move above zero. The ability to harness the hot potato effect arises once again.

The convenience yield as epicentre of monetary policy implementation

Let's not get carried away by the idea that central banks set overnight interest rates. Central banks exercise direct control over the economy by pushing down on one shiny red button, the convenience yield on reserves. By modifying the convenience yield, a central banker nudges agents to either flee from reserves or flock to them. This causes a change in the purchasing power of reserves, the mirror image of which is the general price level.

So how do overnight interest rates like the fed funds rate figure into the picture? Reserves are scarce and convenient, so agents will only part with them if they are compensated with an adequate amount of "rent". The higher the marginal convenience of reserves, the more rent they require. The market in which reserves are rented out for very short periods of time, usually 24 hours, is referred to as the overnight market.

By conceptualizing monetary policy this way, it immediately becomes apparent that overnight interest rates are little more than a reflection of the underlying convenience yield on reserves. Fed funds rates move only in the instant after the convenience yield has been modified. Nor are overnight rates the first to move in response to changes in the convenience yield. They are just one of an almost infinite number of market prices and rates to react in the moments after the convenience yield has been diminished or improved. We should stop thinking in terms of overnight-rate exceptionalism. Price changes radiate out from the convenience yield.

I've gone into much more detail on all these ideas in an earlier post. In this post I want to focus on one point I made earlier -- the fed funds rate can be a bad reflection of the underlying convenience yield. There are several reasons for this. First, in renting out reserves, banks are effectively replacing the central bank as their counterparty with another private bank. In normal times, banks make excellent counterparties. But during times of stress, rentors may require an extra amount of rent that has nothing to do with the usefulness or scarcity of reserves, but the riskiness of counterparties. A spike in the fed funds rate may have nothing to do with the underlying convenience yield, and everything to do with credit risk.

Secondly (and more importantly), the funds rate ceases to be a good indicator when it falls to zero. When this happens, there is a temptation to view monetary policy as spent. After all, it may seem that a central bank can't reduce the convenience yield below 0, which is to say that it can't push the fed funds rate into negative territory. We should resist this temptation. The current fed funds is an estimate of the 24-hour convenience yield on reserves. But agents hold reserves not only to enjoy their present convenience but to enjoy their expected future flows of convenience. So even if the market puts no value on the immediate 24 hour convenience yield, that isn't to say that the market doesn't value their convenience 1 week from hence, or 1 month, 1 year, or 1 decade.

Just like there is a term structure to government bill/bond rates, there is a term structure of the convenience yield on reserves. We can get an inkling of the term structure by looking at longer-term fed funds deals. In the term fed funds market, for instance, banks will rent reserves for up to one year. Federal funds futures give an indication of the expected convenience yield several years from now.

When the overnight convenience rate hits zero, central banks still have plenty of traction over the rest of the term structure. By attacking the convenience yield on reserves one year from now, for instance, a central bank hurts the discounted value of expected streams of convenience thrown off by reserves in the present. As a result, today's forward-looking agents will be nudged away from holding reserves, causing a rise in the price level. As long as there are portions of the convenience yield curve that are still positive, a central banker can do their job.

If thinking in terms of short term rates is misguided, so is a focus on base money. Once the short term convenience rate on reserves has hit zero, present changes in the quantity of base money will have little effect on convenience yields further down the curve. One way to reduce convenience yields five years hence would be to promise that the then-supply of base money will be sufficiently broad so as to ensure that the marginal deposit yields no convenience flows. But a central bank will only be able to affect future convenience yields if the market believes it will have the gumption to follow through on its promises.

Monetary policy at low convenience rates is all about making promises about future convenience yields and ensuring those promise are credible. Conventional monetary policy, on the other hand, is relatively simple -- all a central banker need do is manipulate the current convenience yield in order to have an effect on prices.

The fed funds rate was never the Fed's actual policy lever

The lever on which a central bank pushes or pulls in order to keep its target variable (say inflation) on track is commonly referred to as the central bank's policy instrument. The policy instrument is the variable that is under the direct control of a central banker. The classic story is that the pre-2008 Fed conducted monetary policy via its policy instrument of choice—the federal funds rate. By pushing the fed funds lever up or down, the Fed could change the entire spectrum of market interest rates.

I think this is wrong. The fed funds rate was never the Fed's actual policy instrument. Now this isn't a novel claim. Market monetarists tend to say the same thing. According to folks like Nick Rowe, the quantity of money has always been the Fed's true policy instrument. The fed funds rate was little more than a useful shortcut (a communications device) adopted by the Fed to convey to the public what it intended to do.

I'm sympathetic to the market monetarist's position, although I'm not entirely in the same corner. I agree that the Fed's policy instrument was never the fed funds rate. But I'm going to go one further than the market monetarists and say that the Fed's real policy instrument prior to 2008 was always the non-pecuniary return on reserves.

What do I mean by non-pecuniary return? All assets are expected to provide a sufficient return to their holder. This expected return can be decomposed into a pecuniary and a non-pecuniary component. Financial assets, for instance, tend to provide only pecuniary returns. These come in the form of expected interest payments, dividends, and capital appreciation. Non financial assets like couches, books, and cutlery tend to provide only non-pecuniary returns. These non-pecuniary returns come in the form of future consumption (dated consumption claims), protection from uncertainty, status, etc. Complex assets like houses provide both pecuniary and non-pecuniary returns. We expect to enjoy the shelter provided by our house, and we simultaneously expect it to provide a capital gain when we sell it.

Note that another word for non-pecuniary return is convenience yield. I'll use the two interchangeably from here on in.

For the first time ever on Moneyness, an equation to help clear the waters:

Total expected return of an asset = expected non-pecuniary return + expected pecuniary return

In well-functioning markets, all assets provide the same total expected return. If some asset begins to throw off excess returns, people will buy it up till its price has risen to the point that the cost of acquiring that asset offsets its superior return. Vice versa with an asset that begins to throw off deficient returns.

Central bank reserves are like any other asset. They provide an expected return that can be decomposed into pecuniary and non-pecuniary components. Perhaps somewhat oddly for a financial asset, reserves have never provided a pecuniary return, at least not before 2008. This is because reserves failed to pay interest. (In fact, reserves have always provided a slightly negative pecuniary return. They are generally expected to fall in price, burdening holders with a negative capital gain).

Reserves, therefore, are only held because their non-pecuniary return, or convenience yield, is sufficiently large to compensate their owners for a lack of a pecuniary return. [From here on in, it goes without saying that I am talking about the pre-2008 Fed]. What is the nature of this yield? Reserves are the main instrument used for interbank payments and settlement. Should an emergency arise necessitating an immediate payment, a banker can always put his or her inventory of reserves to use. If a banker foregos holding an inventory of reserves, he or she will have to bear the risk of not being able to quickly obtain sufficient reserves for potential unforeseen payments requirements. Reserves are to a banker what a fire alarm is to a household— while neither provides an explicit pecuniary benefit, both assets provide their owners with ongoing protection from the uncertainty of future events. Bankers and households alike expect to "consume" this convenience over the life of the asset, earning the same total return they would on their other assets.

It is the convenience yield on reserves, and not the fed funds rate, that serves as the Fed's policy instrument. By manipulating the convenience yield—the non-pecuniary return provided by reserves—the Fed exercises monetary policy. When the Fed improves the convenience yield on reserves, reserves will provide a superior expected return relative to all other assets in an economy. Rational agents will bid the price of reserves up, and the price level down. When it hurts the convenience yield, reserves will provide an inferior expected return relative to all other assets in an economy. Rational agents will now cry the price of reserves down, and the price level up.

One way to alter the convenience yield on reserves is to change their quantity via open market operations. As the supply of reserves shrinks via open market sales, the marginal reserve provides an ever improving convenience yield. Rational agents will seek to earn an excess return on their portfolios by buying superior-yielding reserves and selling other assets. This causes a fall in the price level until reserves no longer provide superior returns. Conversely, as the supply of reserves is increased via open market purchases, the marginal reserve provides an ever shrinking convenience yield. Rational agents will try to rid themselves of inferior-yielding reserves, causing a decline in the price of reserves, the mirror image of which is a rise in the price level.

There's a second way to change the convenience yield on reserves. Keep the quantity fixed, but make reserves more convenient! Just like an auto manufacturer can improve the expected convenience yield of a car by adding more features—cup holders, AWD, safety air bags, inboard TV, you name it—the Fed can also improve the expected convenience yield on reserves by souping them up. One popular add-on has always been the required reserve stipulation. As a condition of participation in the payments system, a central bank may require member banks to hold a certain quantity of reserves contingent on the number of deposits that each member has issued to the public. Where before central bank reserves were valued primarily for their role in settlement, now reserves can also be held to fulfill the reserve requirement, enabling the bank to continue as a payments system member in good standing. Voilà, reserves are now doubly-convenient since they can perform two roles, not just one. Henceforth, any increase in reserve requirements improves the convenience yield on reserves and any decrease will hurt their convenience yield.

If the Fed's monetary policy instrument has always been the convenience yield on reserves and not short term interest rates, as is commonly supposed, why all the hoopla about the federal funds rate? Why do central banks talk so much about manipulating overnight interest rates?

The problem with doing monetary policy in terms of convenience yields is that convenience yields are not directly visible. We know that they exist, but we can't really see them. This leaves the Fed in a conundrum, because if it tries to communicate about monetary policy, it can only talk about raising or lowering the hidden convenience yield on reserves, but it can't go into any numeric depth on the issue.

But wait! There are indirect ways to measure convenience yields. One way is to ask people how much money they expect to earn if they forgo the convenience of some asset for a duration of time. The rent they expect to earn in compensation should "shadow" the convenience yield. The more convenient an asset becomes, the higher the rent the asset holder expects to be compensated with if they are to do without that asset for a period of time. The less convenient, the lower the rent.

The federal funds market is the rental market for reserves. Banks can either hold reserves and enjoy their convenience, or they can rent their reserves out to other banks, foregoing the convenience of reserves for a period of time but earning compensatory payments. These payments are the rental value of reserves, or the fed funds rate. The fed funds rate is driven by the convenience yield on reserves. So when reserves are made more convenient by the Fed, banks will expect to earn a higher fed funds rate as compensation from borrowers. When the fed funds rate falls, that means that reserves have been made less convenient.

So the fed funds market provides a numeric manifestation of the unobservable convenience yield on reserves. The Fed can use this manifestation as a stand-in for communicating with the public, describing monetary policy as-if it was directly manipulating the fed funds rate whereas in actuality the convenience yield is the Fed's true policy instrument. In the 1990s and 2000s, when the Fed announced changes in the fed funds rate target, it was doing nothing more than describing to the public how a change in the underlying convenience yield would appear to the superficial observer. As Nick Rowe says, interest rate targeting is not reality, its a way of framing reality.

The fed funds rate also serves the Fed's Open Market Committee as a useful sign post, or indicator, that provides information on the way to hitting its final price target. For each modification it makes in the convenience yield, the FOMC can measure how successful it has been by referring to how far the fed funds rate has moved in response. Alternatively, the FOMC can use the fed funds rate as a guide for stabilizing what would otherwise be an invisible and difficult to manage convenience yield. In general, the Fed has tried to keep the convenience yield on reserves flat for extended periods of time between meetings. Whenever the fed funds market blips up or down in the interim, the Fed can use these blips as indicators that it is not keeping the underlying convenience yield steady. Action, either OMOs or reserve requirement changes, will be used to bring the convenience yield on reserves back into its holding pattern.

But the key point here is that the federal funds rate is NOT doing the heavy lifting in monetary policy. The federal funds rate only responds passively to changes in the Fed's true policy instrument—the convenience yield on reserves. Fed-induced changes in the convenience yield create an instantaneous and simultaneous reaction in all markets, including the fed funds market, bond markets, stock markets, labour markets, goods markets, and commodity markets. The fed funds rate isn't the first price to react, nor is it the pivot around which the full network of other market rates move. That we use the fed funds market to measure the reaction of the economy to a change in the policy instrument rather than using, say, commodity markets, is merely for the sake of ease. The funds rate just happens to be the one that provides the most noise-free signal for how much the convenience yield has been manipulated.

...but not a perfect noise-free signal. The fed funds rate's ability to act at a good reflection of the underlying convenience yield comes to an end when it gets too low. Even as the Fed continues to reduce the convenience yield, the fed funds rate falls to 0% from where it refuses to budge, conveying the impression—an improper one—that the Fed's policy instrument is powerless. But further reductions in the convenience yield, and a higher price level, ARE still possible.

My point here is very similar to the one that Nick Rowe makes when he says that interest rates "go mute" at zero. This is an important point I never grasped intuitively till I began to think of Fed policy as the manipulation of convenience yields. The main difference between the two of us is that  Nick takes the "money" view, which looks at absolute quantities of money, while I take a "moneyness view", which means I'm interested in monetary convenience yields [on money vs. moneyness]. We arrive at the same final destination, though, albeit by different roads.

Plenty of things changed after October 2008. I suppose I could go into this in more detail, but this post is already too long. Suffice it to say that reserves ceased offering a present non-pecuniary return and began offering a pecuniary return. The latter is IOR (interest-on-reserves). The non-pecuniary return has shrunk because there is currently such a glut of reserves in the system that the marginal reserve no longer offers its owner a present convenience yield. All of these changes complicate the picture.

There's plenty more to say on all this stuff, but this post is heavy enough. Just keep in mind that thinking in terms of convenience yields and not the federal funds rate opens up a whole new world. The idea that the funds rate was ever the policy instrument should be confined to the trash bin. More later.