Plumbing the depths of the effective lower bound

Unfathomable Depths by Ibai Acevedo

Denmark's Nationalbank and the Swiss National Bank are the world's most interesting central banks right now. As the two of them push their deposit rates to record low levels of -0.75%, they're testing the market's limit for bearing negative nominal interest rates. The ECB takes second prize as it has been maintaining a -0.2% deposit rate since September 2014.

At some point, investors will flee deposits into 0%-yielding cash. This marks the effective lower bound to rates. Has mass paper storage begun? The last time I ran through the data was in my monetary canaries post, which was inconclusive. Let's take a quick glance at the updated data.

To gauge where we are relative to the effective lower bound, I'm most interested in the demand for large denomination notes, which bear the lowest costs of storage. Once a central bank reduces its deposit rate so deep into negative territory that the carrying cost of deposits exceeds the cost of storing a nation's largest value banknote, then it has hit the effective lower bound. Small denominations notes, which have higher storage costs, are not a pivotal part of the picture given the ability of note holders to freely convert low value notes into higher ones.

European Central Bank

The ECB issues the €500 note, which has the second highest purchasing power out of the world's currency notes. I've charted the quantity of €500 euro notes in circulation below, as well as the percent change in the value of all euro denominations:

After declining through 2012 and 2013, we saw a sharp rise in demand for €500 notes, particularly in December 2014 and the first few months of 2015. The red line illustrates the general demand for all denominations of euro cash. Over the last four months the seasonally-adjusted growth rate of banknotes outstanding has risen to its highest level in the last five years.

It's hard to determine how much of this increase can be attributed to the ECB's negative rate policy, initiated when Mario Draghi brought the deposit facility rate to -0.1% in June and -0.2% in September, and how much is due to the Greek fiasco. Growing fears that Greece will either leave the euro or impose capital controls have led to a steady jog out Greek banks. There are two escape routes: Greek's can convert their deposits can into German deposits or into cash.

In an interesting article, Bloomberg's Lorcan Roche Kelly backs out the Greek-specific demand for European cash. Read it for the full details, but the shorter rendition is that a line item on the Bank of Greece's balance sheet allows us to see how many banknotes Greeks are demanding in excess of the Bank of Greece's regular allocation. Kelly finds a large spike beginning in December and extending into 2015, which we can attribute to the bank jog. I've recreated the chart below:

Source: Bloomberg, data to end of March

The approximately €12 billion jump in Greek cash demand corresponds nicely with the recent €7.2 billion spike in €500 notes in circulation across the entire eurozone. The upshot is that a large chunk of the rise in €500 notes over the last few months is probably due to a run on Greek banks, not an escape from negative-yielding ECB deposits. Remove the run and the rise in demand for €500 notes would have been unremarkable, indicating that the eurozone is still far from hitting the effective lower bound.

Swiss National Bank

Because Swiss banknotes are not a direct escape route from the ongoing Greek bank run, SNB cash data should provide a clearer signal of the whereabouts of the effective lower bound than ECB data. The SNB issues the world's most valuable banknote in terms of purchasing power; the 1000 franc note. Below I've plotted the yearly percent change in demand for both the 1000 note and Swiss cash-in-general to the end of February.

There's been slight pickup in the demand for Swiss cash, but nothing dramatic. Its worth pointing out that Swiss paper currency has historically played a safe haven role. Demand tends to spike during episodes of uncertainty, including the 2008 credit crisis and the 2011-12 period, when it seemed like the euro could be torn apart. This means that it is difficult to be sure how much of the recent pickup in demand for Swiss cash stems from the SNB's -0.75% deposit rate and how much is due to fear of a Greek government default, which would create havoc in world markets.  

Danmarks Nationalbank

Our final canary is the Danmarks Nationalbank. Unlike the demand for Swiss paper francs, the demand for Danish paper krone does not usually spike during times of crisis. For instance, during the 2008 credit crisis demand remained muted. This leads me to believe that demand for paper krone provides the clearest indicator yet of the presence (or not) of the effective lower bound. I've charted the year-over-year change in Danish currency in circulation.

In the 55 days that have passed since the Danmarks National bank reduced its rates to -0.75% (February 5), there has been a sustained rise in the demand for cash, as the red data indicate. But I don't think we can describe it as anything out of the ordinary, at least not yet.

Interestingly, in late March the Nationalbank granted Danish banks some wiggle room by providing them with greater access to the Bank's 0% current-account facility. This small adjustment would have reduced Danish banks' incentives to emigrate from -0.75% deposits into cash. Was the central bank's decision to provide this wiggle room a response to private data showing that it had hit the effective lower bound? Who knows.

It may be worth noting even if a central bank finds itself at the effective lower bound, it can forestall the demand for large denomination notes by using moral suasion. Willem Buiter mentions this possibility in his recent note High Time To Get Low, but maintains we have no evidence of this sort of pressure. I'm tempted to agree with him. If either the Danish or Swiss central bankers have put informal embargoes on cash, we would have known about it by now.

The use of moral suasion to prevent large denomination banknote storage would effectively freeze the quantity of high value notes in circulation. In such a scenario, we'd expect the 1000 Sfr note to rise to a slight premium to face value, say 1050 Sfr in bank deposits for each 1000 Sfr in banknotes. Traders would be willing to pay this premium as long as the storage costs on high value notes are lower than the -0.75% penalty set by the SNB on deposits, thus allowing them to earn an excess return on their note holdings. As long as moral suasion remains successful in choking off Swiss banks' demand for cash, each subsequent cut by the SNB into ever deeper negative territory would drive the premium on notes higher. (Assiduous readers will recognize this as the second of three ways for a lazy central banker to escape a liquidity trap.)

In sum, we probably haven't hit the effective lower bound yet. Stay tuned.

John Cochrane is too grumpy about negative rates

John Cochrane has written two posts that question the ability to implement negative interest rates given the wide range of 0%-yielding escape hatches available to investors. These escapes include gift cards, stamps, tax & utility prepayments, and more. In a recent post entitled However low interest rates might go, the IRS will never act like a bank, Miles Kimball and his brother rebut one of Cochrane's supposed exits; the Internal Revenues Service. I've responded to Cochrane's other schemes here.

Think of Cochrane's exits as arbitrage opportunities. As nominal rates plunge into negative territory, the public gets to harvest these outsized gains at the expense of institutions that issue 0% nominal liabilities. The Kimballs' point (and mine here) is that because these institutions will lose money if they continue to issue these liabilities, they will implement policies to plug the holes. Cochrane's multiple exits aren't the smoking gun he takes them to be.

In a new post, Cochrane tries to salvage his argument by making an appeal to symmetry. He points out that in the symmetrical case—a world with positive inflation and higher nominal rates—we don't actually observe people adopting the sort of behavior that Miles believes they would adopt in a negative rate world. So in practice, Cochrane doesn't believe that removing cash in order to implement negative interest rates will work.

This is a fair tactic to take. In general, people should demonstrate similar behavior whether nominal rates are positive or negative. However, is it true that in an environment with positive inflation and high nominal rates, institutions issuing liabilities (or those purchasing those liabilities) allow themselves to be systematically made the targets of arbitrage?

Take Cochrane's main example; gift cards. As I described here, once rates fall deep into negative territory, retailers will simply stop issuing gift cards since they won't care to earn a negative spread. Cochrane's appeal to symmetry implies that gift card issuers behave differently when rates are positive. Well let's imagine that rates are at 5%. An issuer of 0% gift cards is certainly not setting itself up to be arbitraged—in fact, given that it is funding itself at 0% in a 5% yield environment, it will be earning an excess return on each card issued. Nor will the liability-using public choose to subject itself to the money-losing obverse side of the trade. People can simply choose to avoid investing in 0% gift cards in favor of a 5% alternative. Likewise for the other liabilities that Cochrane mentions. Rather than prepaying taxes and earnings 0%, the public will pay at the last moment and harvest a 5% return until then. Instead of delaying the cashing of a check, they'll deposit it the day they receive it in order to earn interest.

So when interest rates are positive, people will try to avoid behaviour that allows them to be taken advantage of, whether they be an issuer or buyer or liability. Symmetrically, it follows that this same behaviour should prevail when rates are negative.

In his post, Cochrane seems to be changing the subject of the conversation from arbitrage to the indexing of contracts. His point is that during periods of positive inflation and high interest rates, nominal payments were not indexed to the nominal interest rate. His example is the IRS, which does not offer interest for early payment when market interest rates are high. Factually he is right. But this criticism is besides the point. The IRS doesn't offer interest to those who pay their taxes early because prepaid taxes aren't the government's main form of funding, treasury debt is. If the government's main form of financing *was* to offer savings accounts to tax payers, then you can be sure that those accounts would have to promise nominal payments that rise in line with the market's nominal interest rate—otherwise no one would open an account and the government would suffer a cash crunch. Nor would the government offer an excess nominal rate, since every American would exploit the situation and open an account—at the government's expense.

No one wants to be the dupe and end up on the wrong side of an arbitrage. If anyone is arguing for asymmetry, it is Cochrane. He needs to explain why liability issuers and users would exhibit such a degree of irrationality as to allow themselves to be exploited as rates fall into negative territory, but so rational as to avoid being exploited at positive rates.

A libertarian case for abolishing cash

Last week Citi's Willem Buiter published a note on the three ways to get rid of the effective lower bound to nominal interest rates, one of which is to abolish cash. He goes on to say that

politically, the abolition of currency would run into opposition from some of the legitimately cash-dependent poor and elderly, from those for whom the anonymity of cash is desired because they are engaged in illegal activities and from libertarians. The first constituency can be helped, the second can be ignored and the third one should take one for the team.

I think that Buiter is wrong to characterize libertarians as necessarily opposed to the abolition of cash. Their take on cash is probably (or at least should be) a bit more nuanced. Since libertarians generally advocate government withdrawal from lines of business like health care or liquor retailing, an exit of central banks from the cash business should be a desirable outcome.

What Buiter is advocating is a bit more extreme than just government exit, however. An across-the-board banning of cash would not only take the government out of the cash business but also prevent individuals and businesses from entering the product niche. The participation of the private sector in the provision of cash isn't just science fiction. Historically, commercial banks were intimately involved in the production of paper currency. In modern times, the majority of banknotes that circulate in Scotland are issued by three private banks—the Bank of Scotland, the Royal Bank of Scotland, and the Clydesdale Bank, while in Hong Kong, the major commercial banks are charged with issuing currency.

Buiter would probably object to private banknotes. After all, if private banks are able to issue negotiable bearer instrument that pay a zero nominal interest rate, a central banker will continue to be plagued by the problem that he/she can't reduce interest rates below zero—instead of fleeing into 0% government paper, the public will hide in private banknotes. It's the same liquidity trap as before, with private currency in the place of central bank currency.

However, there would be one key difference. Private banks must abide by the Darwinian calculus of profit and losses, central banks don't have to. Take a world with privatized cash. A recession hits and the rate of return on capital falls plummets. At the same time, the central bank drops its deposit rate deep into negative territory. As a private bank tries to match with deposit rate reductions of its own, say to -2%, customers will convert negative yielding deposits into the bank's higher-yielding 0% bank notes. The bank, whose survival depends on a healthy spread between the rates on borrowing and lending, faces a sudden spike in borrowing costs to 0%, the rate on their cash base. Spreads will shrink, even invert. Bankruptcy looms.

In order to avert this disaster, private issuers will quickly institute limits on their cash business. This could involve adopting any one of Buiter's three remedies: 1) cancel their note issue; 2) impose a fee on cash, or; 3) remove the fixed exchange rate between deposits and cash. Thus,the lower bound probably wouldn't be a problem in a banking system characterized by privatized paper issuance. The necessity of maintaining a spread would force private banks to rapidly innovate any one of these three escapes come recession and negative nominal rates. Upon recovery, they can remove these limitations and continue with their regular cash business.

Imagine that private banks all choose the first option when nominal rates fall below zero, cancellation. With cash no longer in existence, banks will have succeeded in restoring their margins to health. The population, however, will have effectively lost their ability to make anonymous transactions. This puts a libertarian in a tough philosophical position. On the one hand, a cashless world poses a serious threat to personal liberty. John Cochrane calls it an "Orwellian nightmare," and Chris Dillow has referred to banning cash as "a grossly illiberal measure - the banning of capitalist acts between consenting adults."

On the other hand, if cash threatens a bank's existence, no libertarian would advocate the use of force to prevent said bank from exiting the business of cash provision. Capitalistic acts cannot be forced upon non-consenting adults, or, put differently, Jack's desire for anonymity-providing products doesn't justify Jill being put into chains in order to provide those products. Therefore, a withdrawal of cash by banks as nominal rates fall below zero, and the loss of anonymity that comes with it, is consistent with libertarianism.

So oddly, Buiter's proposed end point—a cancellation of cash in order to rid the world of the lower bound—is very similar to what a libertarian end point could look like. Both institutions will elect to withdraw cash from circulation because it interferes with their institutional prerogatives. For a central bank, this mission boils down to the targeting of some nominal variable like inflation while in the case of a private bank it is its ability to earn a competitive return. That's not to say that a libertarian ought to support Buiter's abolition, only that the subject is more nuanced than it might seem upon a superficial reading.  

As a postscript, it's worth noting that neither Buiter's central banker nor a libertarian's private banker need go as far as abolishing cash in order to remove the effective lower bound. Buiter provides two other options, the best of which (in my opinion) is removing the fixed exchange rate between cash and deposits. Miles Kimball has gone through this option exhaustively. I've outlined some even less invasive, though not as effective, options here.

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Related links: 

Does the zero lower bound exist thanks to the government's paper currency monopoly? (link)
Is legal tender an imposition on free markets or a free market institution? (link)
Bill Woolsey on how the private sector would withdraw cash at negative rates (link | link )
FTAlphaville: Buiter on the death of cash ( link )

Note: I changed some wording on September 26, 2015. The message remains the same.

Liquidity as static

In his first blog skirmish, Ben Bernanke took on Larry Summers' secular stagnation thesis, generating a slew of commentary by other bloggers. If the economy is in stagnation, the econ-blogosphere surely isn't.

I thought that Stephen Williamson had a good meta-criticism of the entire debate. Both Bernanke and Summers present the incredibly low yields on Treasury inflation protected securities (TIPS) as evidence of paltry real returns on capital. But as Williamson points out, their chosen signal is beset by static.

Government debt instruments like TIPS are useful as media of exchange, specifically as collateral, goes Williamson's argument. Those who own these instruments therefore enjoy a stream of liquidity services that gets embodied in their price as a liquidity premium. Rising TIPS prices (and falling yields) could therefore be entirely unrelated to returns on capital and wholly a function of widening liquidity premia. Bernanke and Summers can't make broad assumptions about returns on capital on the basis of market-driven yields without knowing something about these invisible premia. (Assiduous readers may remember that I've used a version of the liquidity premium argument to try to explain the three decade long bond bull market, as well as the odd twin bull markets in bond and equity prices.)

Riffing on Williamson, liquidity premia are a universal form of static that muddy not only bond rates but many of the supposedly clear signals we get from market prices. Equity investors, for instance, need to be careful about using price earnings ratios to infer anything about stock market valuations. The operating assumption behind something like Robert Shiller's cyclically adjusted PE (CAPE) measure is that rational investors apply a consistent multiple to stock earnings over time. When CAPE travels out of its historical average, investors are getting silly and stocks are over- or undervalued.

But not so fast. Since a stock's price embodies a varying liquidity premium, a rise in equity prices relative to earnings may be a function of changes in liquidity premia, not investor irrationality. Until we can independently price these liquidity services, CAPE is useless as a signal of over- or undervaluation, a point I've made before. Hush, all you Shiller CAPE acolytes.

Liquidity also interferes with another signal dear to economists and finance types alike; expectations surrounding future inflation. The most popular measure of inflation expectations is distilled by subtracting the nominal yield on 10-year Treasuries from the equivalent yield on 10-year TIPS. The residual is supposed to represent the value of inflation protection offered by TIPS. But it is a widely known fact that this measure is corrupted by the inferior liquidity in TIPS markets. See commentary here, here, and here. The upshot is that a widening in TIPS spreads—which is widely assumed to be an indicator of rising inflation expectations—could be due to a degeneration  improvement in the liquidity of TIPS relative to the liquidity of straight Treasuries.

Interestingly, the Cleveland Fed publishes a measure of inflation expectations that tries to "address the shortcomings" of rates derived from TIPS by turning to data from a different source: inflation swaps markets. In an inflation swap, one party pays the other a fixed rate on a nominal amount of cash while the other returns a floating rate linked to the CPI. Given the market price of this swap, we can extract the market's prediction for inflation. According to the people who compile the Cleveland Fed estimate, inflation swaps are less prone to changes in liquidity than TIPS yields, thus providing a true signal of inflation expectations.

But how can that be? Surely the prices of swaps and other derivatives are not established independently of market liquidity. After all, like stocks and bonds, derivatives are characterized by bid-ask spreads, buyers strikes, and runs. Sometimes they are easy to buy or sell, sometimes difficult. When I first thought about this, it wasn't immediately apparent to me what liquidity premia in derivative markets would look like. With bond and equity markets, its easy to determine the shape and direction of the premium. Since liquidity is valuable, buyers compete to own liquid stocks and bonds while sellers must be compensated for doing without them. A premium on top of a security's fundamental value develops to balance the market.

Derivatives are different. Take a call option, where the writer of the option, the seller, provides the purchaser of the option the right to buy some underlying security at a certain price. In theory, the more liquid the option, the higher the price the purchaser should be willing to pay for the option. After all, a liquid option can be sold much easier than an illiquid one, a benefit to the owner. But what about the seller? I risk repeating myself here, but a seller of a stock or bond will require a *higher* price if they are to part with a more liquid the security. However, in the case of the option, the writer (or seller) will be willing to accept a *lower* and inferior price on a liquid option. After all, the writer will face more difficulties backing out of their commitment (by re-selling the option) if it is illiquid than if it is liquid.

This creates a pricing conundrum. As liquidity improves, the option writer will be willing to sell for less and the purchaser willing to buy for more. Put differently, the value that the writer attributes to the option's liquidity and the concomitant liquidity premium this creates drives the option price down, while the value the purchaser attributes to that same liquidity engenders a liquidity premium that drives the option price up. What is the net effect?

I stumbled on a paper which provides an answer of sorts (pdf | RePEc). Drawing on data from OTC options markets, the authors finds that illiquid interest rate options trade at higher prices relative to more liquid options. This effect goes in the opposite direction to what is observed for stocks and bonds, where richer liquidity means a higher price. The authors' hypothesis is that the liquidity premium of an option is set by those investors who, on the margin, are most concerned over liquidity. Given the peculiarities of OTC option markets, this marginal investor will usually be the option writer (or seller), typically a dealer who is interested in reversing their trades and holding as little inventory as possible, thus instilling a preference for liquidity. Buyers, on the other hand, tend to be corporations who are willing to buy and hold for the long term and are therefore less concerned with a fast getaway. The net result is that for otherwise identical call options, the overriding urgency of dealers drives the price of the more liquid option down and illiquid one up.

Anyone who has dabbled in futures markets may see the similarity in the story just recounted to a much older idea, the theory of normal backwardation. The intuition behind normal backwardation is that a futures contract, much like a call option, has two counterparties, both of whom need to be rewarded with a decent expected return in order to encourage them to enter into what is otherwise a very risky bet. If both require this return, then how does an appropriate "risk premium" get embodied in a single futures price?

None other than John Maynard Keynes hypothesized that the two counterparties to a futures trade are not entirely symmetrical. Hedgers, say farmers (who are normally short futures), simply want a guaranteed market for their goods come harvest and are willing to provide speculators with the extra return necessary to induce them to enter into a long futures position. Farmers create this inducement by setting the current price of a futures contract a little bit below the expected spot price upon delivery, thus providing speculators with a promise of extra capital returns, or a risk premium. That's why Keynes said that futures markets are normally backwardated.

Options writers who desire the comforts of liquidity are playing the same game as farmers who desire a guaranteed price. They are inducing counterparties to take the other side of the deal, in this case the liquid one, by pricing liquid options more advantageously than illiquid but otherwise identical options. And while I don't know the peculiarities of the various counterparties to an inflation swap, I don't see why the same logic that applies to options wouldn't apply to swaps.

So returning to the main thread of this post, just as the signals given off by TIPS spreads are beset by interference arising from liquidity phenomena, the signals given off by inflation swaps are also corrupted. A widening in inflation swap spreads could be due to changing liquidity preference among a certain class of swap counterparties, not to any underlying change in inflation expectations. Its not a clear cut world.

What about the most holy of signals given off by derivative markets: the odds of default as implied by credit default swap spreads? A CDS is supposed to indicate the pure credit risk premium on an underlying security. But if the marginal counterparty on one side of a credit default swap deal is typically more interested in liquidity than the other counterparty, then CDS prices will include a liquidity component. According to the paper behind the following links ( pdf | RePEc ), it is the sellers of credit default swaps, not the buyers, who typically earn compensation for liquidity, the theory being that sellers are long-term players with more wealth than buyers. The paper's conclusion is that CDS spreads cannot be used as frictionless measures of default risk.

Liquidity is like static, it blurs the picture. The clarity of the indicators mentioned in this post—Bernanke & Summers' real interest rates, stock market price earnings ratios, inflation expectations implied by both TIPS and swap markets, and finally the odds of default implied in corporate default swap spreads—are all contaminated by liquidity premia that vary in size over time. Models created by both economists and financial analysts contain abstract variables that map to these external data sources. I doubt that this data is irrevocably damaged by liquidity, but it may be warped enough that we should be wary about drawing strong conclusions from models that depend on them as input.

Before I slide too far into economic nihilism, there may be a way to resuscitate the purity of these indicators. If we can calculate the precise size of liquidity premia in the various markets mentioned above, then we can clean up the real signals these markets give off by removing the liquidity static.

One way to go about calculating the size of a liquidity premium is by polling the owners of a given security how much they must be compensated for doing without the benefits of that security's liquidity for a period of time. Symmetrically, a potential owner of that security's liquidity is queried to determine how much they are willing to pay to own those services. The price at which these two meet represents the pure liquidity premium. Problem solved. We can now get a pure real interest rate, a precise measure of inflation expectations, a true measure of credit default odds, or a liquidity-adjusted price-to-earnings multiple.

Unfortunately, its not that easy. The only way to properly discover the price at which a buyer and seller of a particular instrument's liquidity services will meet is by fashioning a financial contract between them,  a financial derivative. These derivatives will trade in a market for liquidity or 'moneyness' that might look something like this. And therein lies the paradox. Much like the option and CDS of our previous example, this new derivative will itself be characterized by its own liquidity premium, thus impairing its ability to provide a clean measure of the original instrument's liquidity premium. We could fashion a second derivative contract to measure the liquidity premium of the first derivative contract, but that too will be compromised by its own liquidity premium, taking us down into an infinite loop of imprecision.

So... back to economic nihilism. Either that or a more healthy skepticism of those who confidently declare the economy to be in stagnation or the stock market to be a bubble. After all, there's a lot of static out there.

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Note: David Beckworth has also written about the difficulties of using bond yields as indicators of secular stagnation. (1)(2)(3). And now Nick Rowe has a post on secular stagnation and liquidity.