Ken Rogoff has famously called for a ban on high denomination banknotes in order to help combat tax evasion and hurt criminals. But rather than banning notes, why not implement a market-based approach such as a tax? Among other advantages, a tax leaves people with flexibility to determine the cheapest way to reduce their usage of the targeted commodity. This is how society is choosing to reduce green house gas emissions. So why not go the tax route for banknotes too?

My recent post for the Sound Money Project on pricing financial anonymity delves into this idea. The anonymity provided by banknotes is both a "good" and a "bad". People have a legitimate demand for financial alone time; a safe zone where neither their friends, family, government, nor any other third-party can watch what they are buying or selling. These days, cash is pretty much the only way to get this alone time.

But cash's lack of a paper trail can be abused when it used to evade taxes. The resulting gap in government finances forces the honest tax-paying majority to pay more than their fair share for government services. This state of affairs isn't just.

One way to fix this inequity is to raise the price of banknote usage high enough so that it includes the costs that tax evaders impose on everyone else. A tax on banknotes, call it a financial privacy tax, can do this. It internalizes the externality, or the harm done to others. 

Interestingly, financial privacy taxes already exist. For each banknote that it has issued, a central bank typically holds a risk free interest-yielding asset in its vault. In a free market, this interest would flow through to banknote holders, say by the implementation of note serial number lotteries. Rather than allowing the interest to flow through, however, the central bank withholds it. The amount it withholds constitutes the financial privacy tax.

In Canada, for instance, the overnight risk-free interest rate is currently 1.25%. The yield on banknotes being 0%, the Bank of Canada is withholding $1.25 in interest payments for each $100 bill held. So a note-using Canadian is effectively being taxed $1.25 year for each $100 worth of financial privacy he or she chooses to use. Anyone who wants to avoid the tax need only deposit the note into a bank account and earn 1.25% per year.  But once they do that, they will be giving up their privacy.

Modern taxes on banknotes aren't consciously designed as financial privacy taxes. By that I mean, it's not like central bankers have sat down at a conference table and thought long and hard about the costs and benefits of anonymity only to settle on the most appropriate level for the tax. Rather, the size of the tax has been arrived at by accident. Historically, central bankers have simply assumed that it was technologically impossible for banknotes to yield anything other than 0%. (Fully adjustable interest rates on notes, both positive and negative, are actually quite easy to implement, as I'll show). Which means by default, the privacy tax has always been at least as large as the foregone overnight interest rate.

The overnight rate is in turn a function of an entirely different thought process: monetary policy. Central bankers ratchet the overnight rate up or down in order to to hit their chosen inflation target. The problem with this setup is that two separate decisions have been jumbled together. The level at which the central bank sets its financial privacy tax has become the ill-conceived byproduct of its chosen macroeconomic policy.

Here's an example of this muddle. If the Bank of Canada decides to tighten monetary policy tomorrow by increasing its interest rate from 1.25% to 1.5%, it has simultaneously made an entirely separate decision to increase the privacy tax on banknotes by 0.25%. But whereas the monetary policy decision is guided by plenty of data and number crunching, the increase in the privacy tax is purely arbitrary—no thinking has gone into justifying an increase. It's a fait accompli.

Or think about it from another angle. Say that the Bank of Canada has determined that it is appropriate to increase the financial privacy tax by 0.25%. Using its current toolkit, the only way it can accomplish this is by increasing the overnight rate by 0.25%. But this tightening of monetary policy could potentially send the entire economy into a tailspin, all for the sake of satisfying an entirely different policy goal, that of setting the appropriate tax on privacy.

There's no reason that the two decisions can't be split up. The tool that would allow central bankers to do this is the ability to pay positive and negative interest rates on banknotes. I talked about note serial number lotteries as one way to pay positive interest here. Later on in this post I'll discuss a way to pay negative interest. To see how these tools could successfully split the monetary policy decision from the privacy tax decision, let's return to our previous example. If the Bank of Canada were to increase the overnight rate for monetary policy purposes from 1.25% to 1.5%, but it did not want to alter the financial privacy tax, it could simultaneously increase the interest rate on banknotes from 0% to 0.25%. The original 1.25% privacy tax stays intact. While the owner of a banknote is now forgoing the 1.5% overnight rate, he or she is also collecting 0.25% in interest.  

Conversely, these tools would allow the privacy tax to be increased or lowered without requiring a potentially damaging change in monetary policy. Using our example, to increase the privacy tax from 1.25% to 1.5% per year while keeping monetary policy constant, for instance, the Bank of Canada would move the interest rate on banknotes from 0% to -0.25% while keeping the overnight rate at 1.25%. So a banknote owner is now taxed 1.5% per year, of which 1.25% is due to the forgone overnight rate while the other bit is the 0.25% negative interest rate. This has been accomplished without any tightening or loosening of monetary policy.

So there you go, the monetary policy decision has been split from the privacy tax decision. The advantage of having the ability to split up these two thought processes is that it is now possible to think long and hard about what the proper privacy tax rate should be.

One question we might ask is if the current financial privacy tax on banknotes is sufficiently high. Remember, the problem we are trying to solve is that a small group of citizens are not paying their fair share of income taxes by taking advantage of the untraceability of banknotes. The 1.25%/year financial privacy tax on banknotes that is currently being imposed by the Bank of Canada may not be enough to recoup the damage that this untraceability is doing to everyone else. Maybe we need a 2% tax on banknotes, or 5%, or 10%.

Say we increased the Canadian financial privacy tax rate from 1.25% to 5%. (For now let's not be too concerned about how the tax gets levied. I'll get into that later). One unfortunate side effect is that licit users of banknotes—the unbanked and those who want financial alone time for reasons other than evading taxes and crime—would be caught up in a tax net that is intended for illicit users. This doesn't seem very fair. Might there be a finer sorting mechanism that allow us to tax crooks while letting non-crooks through?

In his controversial book on banning high-denomination notes, Ken Rogoff has proposed exactly this sort of fine sorting mechanism. Based on the assumption that criminal usage of bills is largely confined to high-denomination note, he proposes that only $100s, $50s, and maybe $20 bills be banned. We are interested in a tax in this post, of course, not a ban. But if Rogoff's assumption about criminal usage is right, then a graduated tax on banknotes might be a better option than a flat tax, with higher denominations facing a more aggressive levy than low denomination notes.

All central banks currently tax the full range of banknote denominations at the same rate. In Canada's case, the 1.25% tax rate that is currently applied to a C$1000 bill (yes, we have them in Canada, see top) comes out to the same amount incurred by one hundred $10 bills: $12.50 per year. But a $1000 note is far better for evading taxes because it contains more anonymity services per gram than a $10 note. After all, a bag full of tens is bulky and visible, an envelope with a few $1000 bills isn't.

Given the outsized anonymity provided by the $1000, perhaps we should keep the 1.25% tax rate on $10 bills but boost the tax rate on $1000s to (say) 12.5%. A tax evader who holds a $1000 bill would now incur a tax of $125 instead of just $12.50 while a regular Joe with just a few $10 bills would see no increase in banknote-related taxes. (Heck, it might even be a good idea to reduce the tax on small notes to zero.) By boosting the tax on high denomination banknotes, the Bank of Canada enjoys a larger revenue stream than before. Which means that at least some of the revenue gap due to tax evasion can now be plugged, thus fixing some of the damage inflicted on honest tax payers.

How would we go about increasing the financial privacy tax on high denomination notes?

Central banks currently have a policy of maintaining perpetually fixed exchange rates between various note denominations. Your $10 bill is always convertible into ten $1 bills, and your $100 into ten $10 bills. But this needn't be the case.

To implement the tax, central banks would begin to vary the exchange rate between banknotes. Let's take the U.S. as our example. Instead of redeeming the $100 bill at par, the Federal Reserve would slowly reduce the rate at which it redeems the $100 over time. This ratcheting down of the price of $100s would be passed off to the cash-using public in the form of a capital loss, this capital loss functioning as a tax. (For those with long memories, this is basically Miles Kimball's crawling peg idea, applied to the idea of financial privacy rather than evasion of the zero lower bound).

Let's work through an actual example. Say that the Fed wants to impose an extra 5% financial privacy tax on the $100 bill, but not on other bills. It sets December 31, 2018 as the last day that it will redeem a $100 bill for either: a) $100 worth of central bank deposits; or b) $100 worth of bills in $1s, $5s, $10s, $20s, and/or $50s. On the first day of the new policy—January 1, 2019—a $100 bill can be redeemed for a tiny bit less, say $99.93. Daily reductions continue so that by the end of 2019, the Fed will have scaled its redemption rate back by 5% to $95.

This means that if you deposit a $100 banknote at your bank on December 31, 2019, your bank in turn depositing said note at the Fed, the Fed will credit the bank with just $95 in deposit balances, not $100. In anticipation of this, your bank would have only credited you with $95 when you initially deposited the note. Voila, a financial privacy tax. Everyone holding a $100 note for any period of time will have incurred an 5% annualized tax. But if you hold twenty $5 bills, the tax is avoided.


Continuing with our example, by the end of 2020 the Fed's redemption rate will have declined by another 5% to $90.25. And by the end of 2021, the $100 would be worth $85.74, and on and on.

At some point things start to get a bit silly. By 2031, the market value of the $100 will have fallen below the $50 bill, and by the the first decade of the next century it will be worth less than the $1. To prevent this inversion, the Fed will at some point—say in 2026—demonetize the old issue of $100 bills and introduce a new $100 bill, resetting its market value at $100. The whole process of steady reductions starts anew.

This post has been a heavy one, so I'll just quickly summarize it before signing off.

The anonymity provided by banknote is often abused, but rather than banning notes why not tax the abusers? We wouldn't have to start from scratch. Banknotes yield 0% when overnight rates are positive, so society is already imposing a financial privacy tax of sorts on notes. Unfortunately, central banks set the privacy tax arbitrarily, as the unplanned by-product of monetary policy. New tools for increasing /decreasing the return on banknotes could facilitate a separation of the two decision-making processes. These tools could be used to set a higher tax on large denomination notes while leaving smaller notes untaxed, the true costs of anonymity being recognized for the first time.

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P.S. If you're interested in this topic, David Birch has a good post on Austin Houldsworth's Crime Pays System or CPS. It's sort of tongue in cheek, but also quite relevant:

"During this talk, ‘Mr Rogers’ proposed the Crime Pays System, or CPS. Under this system, digital payments would be either “light” or “dark”. The default transaction type would be light, and free to the end users. All transaction histories would be uploaded to a public space (we were of course thinking about the bitcoin blockchain here), which would allow anybody anywhere to view the transaction details. This type of transaction is designed to promote an environment of social accountability.

The alternative transaction type would be dark. With this option, advanced cryptographic techniques would make the payment completely invisible, leaving no trace of the exchange, thus anonymising all transactions. A small levy in the region of 10-20% would be paid per transaction. The ‘Dark Exchange’ would therefore offer privacy for your finances at a reasonable price.

The revenue generated from the use of this system would be taken by the government to substitute for the loss of taxes in the dark economy."

Another worthwhile source is Josh Hendrickson's recent paper "Breaking the Curse of Cash" (written along with Jaevin Park). It's a pretty technical paper, but it explores a model in which coins and paper money circulate, but coins are a burden for illegal traders to use because they make noise, leading to detection.

"If illegal traders impose an externality on society,  the government can generate seigniorage from the illegal traders by setting low rate of return on paper money and providing transfers to legal traders by setting high rate of return on coins. Then the amount of illegal trade is reduced while the amount of legal trade increases. This is a standard solution to an externality problem."

Freigeld, or stamp scrip, is designed to pay negative interest, but it can be re-purposed to pay positive interest.

Remember when global interest rates were plunging to zero and all everyone wanted to talk about was how to set a negative interest rate on cash? Now that interest rates around the world are rising again, here's that same idea in reverse: what about finally paying positive interest rates on cash? I'm going to explore three ways of doing this. As for why we'd want to pay interest on cash, I'll leave that question till the end.


The first way to pay interest on cash is to use stamping. Each Friday, the owner of a bill—say a $50 note—can bring it in to a bank to be officially stamped. The stamp represents an interest payment due to the owner. When the owner is ready to collect his interest, he deposits the note at the bank. For example, say that 52 weeks have passed and 52 stamps are present on the $50 note. If the interest rate on cash is 5%, then the banknote owner is due to receive $2.50 in interest.

Alternatively the note owner can collect the interest by spending the $50 note, say at a local grocery store. The checkout clerk will count the number of stamps, or interest due, and tack that on to the face value of the note. With 52 stamps, the owner of a $50 note should be able to buy $52.50 worth of groceries, not $50. After all, the store has the right to bring the $50 note to its bank and collect the $2.50 in interest for itself.

Stamped currency seems like a pretty big hassle to me. The clerk behind the counter must count out the stamps on the note by hand, and the owner of the note has to trek back and forth to the bank each week to get the stamp affixed. Instead, imagine that each banknote has a magnetic strip that records how long the bill had been in circulation. This would remove some of these hassles. Weekly trips to the bank for stamping would no longer be necessary, and a note reader installed at a bank or retailer would automatically record how much interest was due, precluding painstaking counting of stamps.

"They use this magnetic strip to track you." says Byers to Agent Scully, The X-Files

Apart from stoking conspiracy theories, there's still a major problem with a magnetic strip scheme. Because each note has entered circulation at a different time, each is entitled to a varying amounts of interest. And this means that banknotes are no longer fungible. Fungibility—the ability to cleanly interchange all members of a population—is one of the features of money that makes it so easy to use. Remove it and money becomes complicated, each piece requiring a unique and costly effort to ascertain its value.


Our second way of paying interest on money doesn't destroy the fungibility of banknotes. The central bank needs to sever the traditional 1:1 peg between deposit money and cash, and then have cash slowly appreciate in value relative to deposits.

For instance, a central bank might start by setting an exchange rate of $1 note = $1 deposit on January 1, but on January 2 it adjusts this rate so $1 note is equal to $1.0001 deposits, and on January 3 adjust this rate to $1:$1.0002, etc. So the cash in your wallet is benefiting from capital gains. By December 31, the exchange rate will be around $1 note to $1.0365. Anyone who has held a banknote for the full year can deposit it and will have earned 3.65 cents in interest, or 3.65%. 

The major drawback with this scheme is the calculational burden imposed on the population by breaking the convenient 1:1 peg between cash and deposits. Assuming that retailers price their wares in terms of deposits, anyone who wants to pay in cash will have to make a currency conversion using that day's exchange rate. For instance, if the central bank's peg is currently being set at $1 note = $1.50 in deposits, then a popsicle that is priced at $1 will require—hmmm... let me check my calculator—$0.667 in cash. Phones will make this exchange rate calculation easy, but it is still likely to be a bit of a nuisance.

There are other hassles too. Would a capital gains tax have to be paid on the appreciation of one's cash? How would existing long-term contracts deal with the divergence? For instance, if my employer is paying me $50,000 per year, obviously I'd prefer this sum be denominated in steadily appreciating cash rather than constant deposits, and she will prefer the latter. What becomes the standard unit of account?


The last way to pay interest (at least as far as I know) is to run lotteries based on banknote serial numbers, an idea independently proposed by Hu McCulloch and Charles Goodhart back in 1986.

It's surprisingly easy to get banknotes to pay interest. Run a lottery based on note serial numbers. Hu McCulloch dreamt this scheme up in 1986, but no central bank has ever tried it. Source: https://t.co/pUUf1liuhH pic.twitter.com/5mil9B62FN

— JP Koning (@jp_koning) January 14, 2018

Central banks would periodically hold draws entitling the winning serial numbers to large cash prizes. For example, if there was $100 billion in banknotes in circulation, the central bank could set the interest rate on cash at 5% by offering prizes over the course of the year amounting to 5% of $100 billion, or $5 billion.

This technique of paying interest on cash solves the fungibility problem that plagues the earlier stamping technique. Every note has the same chance of winning the lottery, and non-fungible winners are immediately withdrawn. And unlike the crawling peg idea, banknotes and deposits remain equal to each other so burdensome exchange rate calculations don't need to me made.

However, it introduces the threat of bank runs. The day before the big lottery is set to occur, everyone will withdraw deposits for cash so that they can compete in the draw. To prevent a bank run, it may be necessary to randomize the date of the big lottery so that no one knows when to withdraw notes, an idea proposed by Tyler Cowen. Another way to preclude bank runs is to have a regular stream of small weekly lotteries rather than one or two big ones each year.

Another drawback to note lotteries is the cost that is imposed on society by having everyone constantly checking serial numbers. As Brian Romanchuk points out, employees who are working behind their employer's tills may be tempted to switch out winning notes with losers. Employers may protect themselves by setting up scanning hardware to read in serial numbers as banknotes enter the tills, maintaining their own internal database of cash inventories so that winners can quickly be isolated and returned. But all of that is costly. Would it be worth it?

Interestingly, there is some precedent for these sorts of lotteries. In Taiwan, receipts are eligible for a receipt lottery, a neat way to incentivize people to avoid under-the-table transactions (ht Gwern). Lotteries can also be useful in attracting depositors, as outlined in this Freakonomics podcast (ht Ryan). George Selgin and William Lastrapes have gone into the idea of lottery-linked money in some detail:

Though the suggestion may appear far fetched, in many countries lotteries are presently being used with considerable success to market bank deposits. According to Mauro Guillen and Adrian Tschoegl (2002), “lottery-linked” deposit accounts have been especially popular with poorer persons, including many who might otherwise remain “outside the banking system.” ... In two popular Argentine schemes, for instance, depositors receive one ticket or chance of winning for every $200 or $250 on deposit (ibid., p. 221). Lottery-linked banknotes, in contrast, would themselves serve as tickets, allowing persons to play for as little as the value of the lowest note denomination, and with no apparent cost to themselves save that of occasionally inspecting their note holdings.

Some readers may recognize these three techniques for paying interest on cash as the inverse of the three go-to ways of applying negative interest rates to cash being discussed a few years ago. For instance, one of the most well-known ways of imposing negative interest rates on owners of cash is to apply a Silvio Gesell style stamp scheme (see picture at top), whereby a currency owner must buy a stamp and affix it to the note in order to renew the validity of their currency each month. (I once discussed Alberta's experiment with Gesell's "shrinking money" here). Without the appropriate number of stamps, the note is illegitimate. In my first example above, Gesell's stamp tax has been re-engineered into a stamp subsidy. As for the magnetic strip modification, this is Marvin Goodfriend's 1999 update of Gesell, flipped around to award interest rather than docking it.

Miles Kimball has written extensively on escaping the zero lower bound to interest rates by setting a crawling peg on currency. But just as Kimball's crawling peg can impose a negative interest rate on banknotes, it can be used to pay interest, as I described above. Indeed, Miles (along with Ruchir Agarwal) frequently mention this possibility in his blog posts and papers (see this pdf).

Finally, remember Greg Mankiw's controversial 2009 article on imposing negative interest rates by serial number? He wrote:

Imagine that the Fed were to announce that, a year from today, it would pick a digit from zero to 9 out of a hat. All currency with a serial number ending in that digit would no longer be legal tender. Suddenly, the expected return to holding currency would become negative 10 percent.

Mankiw's idea is just the reverse of Goodhart and McCulloch's earlier lottery idea, the lottery replaced by with a demonetization.


So why pay interest on currency? I can think of two reasons. One is based on fairness, the other on efficiency.

The decision to avoid paying the market rate of interest on currency amounts to a tax on currency users. Who pays this tax? Cash is often the only means for the poor, new immigrants, and unbanked to participate in the economy. So the tax falls on those who can least afford it. This hardly seems fair. By conducting note lotteries or stamping notes, those consigned to the cash economy can get at least the same return on banknotes as the well-off banked receive on deposits.

Now hold up JP, some you will be saying at this point. What about criminals? Yep, the other group of people who suffer from the lack of interest on banknotes are criminals and tax evaders. Rewarding them with interest hardly seems appropriate. One would hope that if central banks did adopt a mechanism for rewarding currency with interest, it would be capable of screening out bad actors. For instance, criminals may be leery of collecting their interest or lottery prize if making a claim at a bank means potentially being unmasked. Another way to set up the screen would be to pay interest or prizes on small denominations like $1-$10 notes, and not on $20s and above. Since criminal organizations prefer high denomination notes due to their compactness, they wouldn't benefit from interest.

As for the efficiency argument, this is nothing but the famous Friedman rule that I described in my previous post. All taxes impose a deadweight loss on society. When a good or service is taxed, people produce and consume less of it than the would otherwise choose, tax revenues not quite compensating for this loss. From a policy maker's perspective, the goal is to reduce deadweight loss as much as possible by selecting the best taxes.

In the case of cash, the deadweight loss comes from people holding less of it than they would otherwise prefer, incurring so-called shoe leather costs as they walk to the bank and back to avoid holding too much of the stuff. If a 0% return on cash is an inefficient form of taxation relative to other alternatives types of taxes, then it would be better for the government to just pay interest on the stuff and recoup the lost revenues elsewhere, say through consumption taxes or income taxes.

David Beckworth argues that the U.S. Federal Reserve should stop running a floor system and adopt a corridor system, say like the one that the Bank of Canada currently runs. In this post I'll argue that the Bank of Canada (and other central banks) should drop their corridors in favour of a floor—not the sort of messy floor that the Fed operates mind you, but a nice clean floor.

Floors and corridors are two different ways that a central banker can provide central banking services. Central banking is confusing, so to illustrate the two systems and how I get to my preference for a floor, let's start way back at the beginning.

Banks have historically banded together to form associations, or clearinghouses, a convenient place for bankers to make payments among each other over the course of the business day. To facilitate these payments, clearinghouses have often issued short-term deposits to their members. A deposit provides clearinghouse services. Keeping a small buffer stock of clearinghouse deposits can be useful to a banker in case they need to make unexpected payments to other banks.

Governments and central banks have pretty much monopolized the clearinghouse function. So when a Canadian bank wants to increase its buffer of clearinghouse balances, it has no choice but to select the Bank of Canada's clearing product for that purpose. Monopolization hasn't only occurred in Canada of course, almost every government has taken over their nation's clearinghouse.

One of the closest substitutes to Bank of Canada (BoC) deposits are government t-bills or overnight repo. While neither of these investment products is useful for making clearinghouse payments, they are otherwise identical to BoC deposits in that they are risk-free short-term assets. As long as these competing instruments yield the same interest rate as BoC deposits, a banker needn't worry about trading off yield for clearinghouse services. She can deposit whatever quantity of funds at the Bank of Canada that she deems necessary to prepare for the next day's clearinghouse payments without losing out on a better risk-free interest rate elsewhere.  

But what if these interest rates differ? If t-bills and repo promise to pay 3%, but a Bank of Canada deposit pays an inferior interest rate of 2.5%, then our banker's buffer stock of Bank of Canada deposits is held at the expense of a higher interest elsewhere. In response, she will try to reduce her buffer of deposits as much as possible, say by reallocating bank resources and talent to the task of figuring out how to better time the bank's outgoing payments. If more attention is paid to planning out payments ahead of time, then the bank can skimp on holdings of 2.5%-yielding deposits while increasing its exposure to 3% t-bills.

Why might BoC deposits and t-bills offer different interest rates? We know that any differential between them can't be due to credit risk—both instruments are issued by the government. Now certainly BoC deposits provide valuable clearinghouse services while t-bills don't. And if those services are costly for the Bank of Canada to produce, then the BoC will try to recapture some of its clearinghouse expenses. This means restricting the quantity of deposits to those banks that are willing to pay a sufficiently high fee for clearing services. Or put differently, it means the BoC will only provide deposits to banks that are willing to accept an interest rate that is 0.5% less than the 3% offered on t-bills.

But what if the central bank's true cost of providing additional clearinghouse services is close to zero? If so, the Bank of Canada should avoid any restriction on the supply of deposits. It should provide each bank with whatever amount of deposits it requires without charging a fee. With bankers' demand for clearing services completely sated, the differential between BoC deposits and t-bills will disappear, both trading at 2.5%.

There is good reason to believe that the cost of providing additional clearinghouse services is close to zero. It is no more costly for a central bank to issue a new digital clearinghouse certificate than it is for a Treasury secretary or finance minister to issue a new t-bill. In both cases, all it takes is a few button clicks.

Let's assume that the cost of providing clearinghouses is zero. If the Bank of Canada chooses to  constrain the supply of deposits to the highest bidders, it is forcing banks to overpay for a set of clearinghouse services which should otherwise be provided for free. In which case, the time and labour that our banker will need to divert to figuring out how to skimp on BoC deposit holdings constitutes a misallocation of her bank's resources. If the Bank of Canada provided deposits at their true cost of zero, then her employees' time could be put to a much better use.

As members of the public, we might not care if bankers get shafted. But if our banker has diverted workers from developing helpful new technologies or providing customer service to dealing with the artificially-created problem of skimping on deposits, then the public directly suffers. Any difference between the interest rate on Bank of Canada deposits and competing assets like t-bills results in a loss to our collective welfare.


Which finally gets us to floors and corridors. In brief, a corridor system is one in which the central bank rations the number of clearinghouse deposits so that they aren't free. In a floor system, unlimited deposits are provided at a price of zero.

When a central bank is running a corridor system, as most of them do, the rate on competing assets like t-bills lies above the interest rate on central bank deposits. Economists describe these systems as corridors because the interest rate at which the central bank lends deposits lies above the interest rate on competing safe assets like t-bills and repo, and with the deposit rate lying at the bottom, a channel or corridor of sorts is formed.

For instance, take the Bank of Canada's corridor, illustrated in the chart below. The BoC lets commercial banks keep funds overnight and earn the "deposit rate" of 0.75%. The overnight rate on competing opportunities—very short-term t-bills and repo—is 1%. The top of the corridor, the bank rate, lies at 1.25%. So the overnight rate snakes through a corridor set by the Bank of Canada's deposit rate at the bottom and the bank rate at the top. (The exception being a short period of time in 2009 and 2010 when it ran a corridor floor).



Let's assume (as we did earlier) that the BoC's cost of providing additional clearinghouse services is basically zero. Given the way the system is set up now, there is a 0.25% rate differential (1%-0.75%) between the deposit rate and the rate on competing asset, specifically overnight repo. This means that the Bank of Canada has capped the quantity of deposits, forcing bankers to pay a fee to obtain clearing services rather than supplying unlimited deposits for free. This in turn means that Canadian bankers are forced to use up time and energy on a wasteful effort to skimp on BoC deposit holdings. All Canadians suffer from this waste.

It might be better for the Bank of Canada (and any other nation that also uses a corridor system) to adopt what is referred to as a floor system. Under a floor system, rates would be equal such that the rate on t-bills and repo lies on the deposit rate floor of 0.75%--that's why economists call it a floor system. The Bank of Canada could do this by removing its artificial limit on the quantity of deposits it issues to commercial banks. Banks would no longer allocate scarce time and labour to the task of skirting the high cost of BoC deposits, devoting these resources to coming up with new and superior banking products. In theory at least, all Canadians would be made a little better off. All the Bank of Canada would have to do is click its 'create new clearinghouse deposits'  button a few times.



The line of thought I'm invoking in this post is a version of an idea that economists refer to as the optimum quantity of money, or the Friedman rule, first described by Milton Friedman back in the 1960s. Given that a central bank's cost of issuing additional units of money is zero, Friedman thought that any interest rate differential between a monetary asset and an otherwise identical non-monetary asset represents a loss to society. This loss comes in the form of people wasting resources (or incurring shoe leather costs) trying to avoid the monetary asset as much as possible. To be consistent with the zero cost of creating new monetary assets, the rates on the two assets should be equalized. The public could then hold whatever amount of the monetary asset they saw fit, so-called shoe leather costs falling to zero.

In my post, I've applied the Friedman rule to one type of monetary asset: central bank deposits. But it can also be applied to banknotes issued by the central bank. After all, banknotes yield just 0% whereas a t-bill or a risk-free deposit offers a positive interest rates. To avoid holding large amounts of barren cash, people engage in wasteful behaviour like regularly visiting ATMs.

There are several ways to implement the Friedman rule for banknotes. One of the neatest ways would be to run a periodic lottery that rewards a few banknote serial numbers with big winnings, the size of the pot being large enough that the expected return on each banknote as made equivalent to interest rate on deposits. This idea was proposed by Charles Goodhart and Hugh McCulloch separately in 1986.

Robert Lucas once wrote that implementing the Friedman rule was “one of the few legitimate ‘free lunches’ economics has discovered in 200 years of trying.” The odd thing is that almost no central banks have tried to adopt it. On the cash side of things, none of them offer a serial number lottery or any of the other solutions for shrinking the rate differential between banknotes and deposits, say like Miles Kimball's more exotic crawling peg solution. And on the deposit side, floor systems are incredibly rare. The go-to choice among central banks is generally a Friedman-defying corridor system.

One reason behind central bankers' hesitation to implement the Friedman rule is that it would threaten their pot of "fuck you money", a concept I described here. Thanks to the large interest rate gaps between cash and t-bills, and the smaller gap between central bank clearinghouse deposits and t-bills, central banks tend to make large profits. They submit much of their winnings to their political masters. In exchange, the executive branch grants central bankers a significant degree of independence... which they use to geek out on macroeconomics. Because they like to engage in  wonkery and believe that it makes the world a better place, central bankers may be hesitant to implement the Friedman rule lest it threaten their flows of fuck you money, and their sacred independence. 

That may explain why floors are rare. However, they aren't without precedent. To begin with, there is the Fed's floor that Beckworth describes, which it bungled into by accident. At the outset of this post I called it a messy floor, because it leaks (George Selgin and Stephen Williamson have gone into this). The sort of floor that should be emulated isn't the Fed's messy one, but the relatively clean floor that the Reserve Bank of New Zealand operated in 2007 and Canada did from 2009-11 (see chart above). Though these floors were quickly dropped, I don't see why the couldn't (and shouldn't) be re-implemented. As Lucas says, its a free lunch.

 We are more than thirty days into Narendra Modi's demonetization campaign, and while many of the commentators I follow say that it is admirable of Modi to try to reduce the role of black money (wealth held by tax-evaders and criminals) and increase digital money adoption, most say that demonetization is not the way to go about it.

In short, the idea behind Modi's demonetization is to require everyone who owns old 1000 and 500 rupee notes to bring them to a bank before year-end for conversion into new banknotes or to be deposited into an account. By forcing Indians to re-familiarize themselves with dormant accounts, or open new ones, the architects of the plan hope that India's reliance on cash as a medium of exchange will be reduced. Any amounts above the ceiling require proper documentation. Those who own large amounts of cash for undocumented reasons, either because they are evading taxes or engaging in criminal behaviour, will therefore be unable to make the switch, their money expiring worthless by year's end. Having been taught a lesson, they may choose to permanently move some of their operations into the official sector.

Kaushik Basu, World Bank chief economist from 2012-2016, is particularly pessimistic about the policy, noting that while he agrees with the Reserve Bank of India's estimate that the economy will probably grow at 7.1% in 2016-17, from 7.6% estimated earlier, he expects a "huge drop" in the economy next year. "Money works like blood," says Basu, invoking one of the Physiocrat's classic analogies of the economy to the human body.

I certainly agree with Basu's use of the money-as-blood analogy, but my hunch is that temporary media of exchange will spring up to take the at least some of the space heretofore occupied by Modi's demonetized banknotes. My mental model for understanding demonetization is the Irish bank strike of 1970. For six months banks were shuttered, Irish citizens entirely cut off from their bank accounts. Cheques could not be deposited, nor could the central bank use the branch banking system as a means to get paper money into the economy.

India can cope without cash for a few days. In 1970, Irish banks closed for six month: the economy did just fine. https://t.co/TB8n53wqal pic.twitter.com/qXcw3EEc9v

— JP Koning (@jp_koning) November 14, 2016

Rather than suffering a huge blow, the Irish economy continued to function as it did before. Into the void vacated by banks and cash, post-dated cheques emerged as a the economy's blood, its circulating medium of exchange, with pub owners acting as informal credit evaluators.

Like Ireland in 1970, India suddenly finds itself deprived of a large portion of its money. In the place of 1000 and 500 rupee notes I expect informal credit to take some of its place, the effects on the economy therefore not being as devastating as Basu hints. See for instance this:


While many commentators are already declaring the demonetization to be a success or a failure, we won't have a good sense of this for several years. What sort of data should we be evaluating along the way? One of the effects we'd expect to see in a successful policy is a long-term reduction in the usage of cash, both as licit users of banknotes are diverted into the banking system and illicit users, burned by the forced switch out of old 1000 and 500 rupee notes, migrate out of the underground economy into the official economy. This should be reflected in data on India's currency in circulation, an attractive indicator in that is simple, accurate, not subject to revision, and comes out on a weekly basis. You can download the data here under the section 'Reserve money'.

The chart below shows the number of rupee banknotes outstanding going back to 2001. Prior to the demonetization, cash had been growing at a rate of 14-15% per year, as illustrated by the blue trend line. Since then you can see that there has been a huge collapse in quantity outstanding as Indians queue to deposit their cash in the banking system. At the same time, the Reserve Bank of India (RBI) hasn't printed enough new 500 and 2000 rupee notes to meet demand.


Cash in circulation will inevitably rebound in 2017 as the RBI catches up to demand by printing new rupees. If cash in circulation jumps back to the pre-demonetization level of ~18 trillion rupees and proceeds to readopt its growth path of 14-15%, than the demonetization will have failed to generate the desired effect. Despite suffering through queues and a relatively sluggish period of aggregate demand, Indians will have returned to their old habits, the whole demonetization campaign being a waste of time and effort.

But if cash in circulation only retraces part of the rebound, say rising to 16 trillion rupees by mid- 2017 (it is currently at ~10 trillion), and then sets out on a new and lower growth path (say 12-13%), then it will have achieved at least some of the desired effect. A new growth path starting from a lower level would imply that the demonetization has been successful in modifying the behaviour of licit cash users (i.e. converted them into digital money users) while driving illicit users of cash into the official economy.

My hunch is that of these two possibilities, the second is more likely: India will see a reduction in the growth path of rupee banknotes starting from a lower plateau. That being said, I find myself sharing many of the worries that Basu and other commentators have. Such a large and aggressive demonetization is a risky way to achieve the twin goals of broadening India's official economy and increase electronic money use. In order to catch people by surprise, much collateral damage must be inflicted, including time wasted in lineups and trades that go unconsummated due to a lack of cash (informal credit as in the case of Ireland not being able to completely fill the void). Suyash Rai makes a convincing argument that a demonetization of this size intrudes on property rights and rule of law.

Despite the chaos it has created, I still feel that the demonetization will make India at least a bit better off than before. However, other nations with large underground economies and low digital money uptake should be wary of copying India's example, waiting at least three or four years to gauge the final outcome. Rather than Modi's risky shock-and-awe approach, a better way to solve the problem is through a series of small and gradual measures. One of these steps might include implementing the approach Kaushik Basu writes about in his 2011 paper Why, for a Class of Bribes, the Act of Giving a Bribe should be Treated as Legal. See my post here for a full explanation.

Here's another incremental maneuver. Instead of imposing a short period of time for switching out of a limited quantity of 1000 and 500 rupee notes, why not allow three or four years for unlimited amounts of notes to be converted—but design the new notes to be 40% larger than the demonetized ones, as Peter Garber suggests, thus making it harder for Indians to store and handle cash?

Another step would be to copy Sweden which, thanks to several policies enacted over the last decade or so, is the only nation in the world with declining cash in circulation. One reason: retailers are required to use certified cash registers that prevent cash-induced tax gas. The Swedes have also adopted tax policies that encourage reporting of activities that typically remain in the unofficial economy, as I explain here. I also recently learnt from Miles Kimball that the Riksbank, Sweden's central bank, privatized the banknote distribution system in the 2000s, the effect being to end the subsidization of note transportation. If banks must bear the true (and higher) cost of moving notes around India, then this will be passed onto their customers, who in turn will react by switching into cheaper digital alternatives. I plan to write about this next week.

The advantage of many incremental steps towards increased digital money usage and a smaller underground economy is that should one step go bad, the blast radius will be small. One large Modi-style step might get you there faster, but if it goes awry, it risks upending the entire effort.

Last week I asked whether the Federal Reserve could get rid of the $100 bill. This week let's discuss whether it should get rid of the $100. I don't think so. The U.S. provides the world with a universal backup monetary system. Removing the $100 would reduce the effectiveness of this backup.

Earlier this week the New York Times took up the knell for eliminating high value bank notes, echoing Larry Summers' earlier call to kill the $100 in order to reduce crime which in turn was a follow up on this piece from Peter Sands. More specifically, Summers says that "removing existing notes is a step too far. But a moratorium on printing new high denomination notes would make the world a better place."

As an aside, I just want to point out that Summers' moratorium is an odd remedy since it doesn't move society any closer to his better place, a world with less crime. A moratorium simply means that the stock of $100 bills is fixed while their price is free to float. As population growth boosts the demand for the limited supply of $100 notes, their price will rise to a premium to face value, say to $120 or $150. In other words, the value of the stock of $100 bills will simply expand to meet criminals' demands. Another problem with a moratorium is that when a $100 bill is worth $150, it takes even less suitcases of cash to make large cocaine deals, making life easier—not harder—for criminals. To hurt criminals, the $100 needs to be withdrawn entirely from circulation, a classic demonetizaiton.

With that distinction out of the way, let's deal with three of the motivations for demonetizing high denomination notes: to reduce criminality, to cut down on tax evasion, and to help remove the effective lower bound.

Criminality

Summer's idea is to kill the $100 bill so that criminals have to rely on smaller denominations like $20s. Force criminals to conduct trade with a few suitcases filled with $20 bills rather than one suitcase filled with $100 bills and they'll only be able to jog away from authorities, not sprint. What sorts of criminals would be affected? The chart below (from this article by Peter Sands) builds a picture of cash usage across the different types of crime.


As the chart illustrates, the largest illegal user of cash is the narcotics industry. So presumably the main effect of a ban of $100s will be to raise the operating costs of drug producers, dealers, and their clients.

But should we be sacrificing the benefits of the $100 bill in the name of what has always been a very dubious enterprise; the war on drugs? An alternative way to reduce crime would be to redefine the bounds of punishable offences to exclude the narcotics trade, or at least certain types of drugs like marijuana. Law enforcement officers could be re-tasked to focus on the cash intensive crimes that remain, like human trafficking and corruption. In that way crime gets more costly and we get to keep the $100 to boot, which (as I'll show) has some very important redeeming qualities.

Tax Evasion

Cash is certainly one of the best ways to evade taxes, but there are other methods to reduce tax evasion. For instance, Martin Enlund draws my attention to a tax deduction implemented by Sweden in 2007 for the purchase of household related services, or hushållstjänster, including the hiring of gardeners, nannies, cooks, and cleaners. In order to qualify the services must be performed in the taxpayer’s home and the tax credit cannot exceed 50,000 SEK per year per person. This initial deduction, called RUT-avdrag, was extended in 2008 to include labour costs for repairing and expanding homes and apartments, this second deduction called ROT-avdrag.*

Prior to the enactment of the RUT and ROT deductions, a large share of Swedish home-related purchases would have been conducted in cash in order to avoid taxes, but with households anxious to get their tax credits, many of these transactions would have been pulled into the open.

We can evidence of this in the incredible decline in Swedish cash demand ever since:

@t0nyyates @jp_koning Starting in July 2007 it became 50% cheaper to buy services (cleaning, ironing, baby-sitting) pic.twitter.com/4EHshRAHWR

— Martin Enlund (@enlundm) February 18, 2016

Sweden has the distinction of being the only country in the world with declining cash usage. The lesson here is that it isn't necessary to sacrifice the $100 in order to reduce tax evasion. Just design the tax system to be more lenient on those market activities that can most easily be replaced by underground production.

Escaping the lower bound

Yep, those advocating a removal of $100s are right. Central banks can evade the effective lower bound on interest rates and go deeply negative if they kill cash, starting with high denomination notes.

But as economists such as David Beckworth have pointed out, you can keep cash and still go deeply negative. All a central banker needs to do is adopt Miles Kimball's proposal to institute a crawling peg between cash and central bank deposits. This effectively puts a penalty on cash such that the public will be indifferent on the margin between holding $100 bills or $100 in negative yielding deposits.

Another way to fix the lower bound problem is a large value note embargo whereby the Fed allows its existing stock of $100 bills to stay in circulation but doesn't print new ones (much like Summers' moratorium). This means that if Yellen were to cut deposit rates to -2% or so, the price of the $100 would quickly jump to its market-clearing level, cutting off the $100 as a profitable escape route. As for the lower denominations, the public wouldn't resort to them since $20s are at least as costly to hold as the negative rate on deposits. Unlike Miles' proposal a large value note embargo doesn't allow for a full escape from the lower bound, but it does ratchet the bound downwards a bit, and it keeps the $100 in circulation.

Why should we keep it?

The $100 bill is the monetary universe's Statue of Liberty. In the same way that foreigners have always been able to sleep a little easier knowing that Ellis Island beckons should things go bad at home, they have also found comfort in the fact that if the domestic monetary authority goes rotten, at least they can resort to the $100 bill.

The dollar is categorically different from the yen, pound or euro in that it is the world's back-up medium of exchange and unit of account. The citizens of a dozen or so countries rely on it entirely, many more use it in a partial manner along with their domestic currency, and I can guarantee you that future citizens of other nations will turn to the dollar in their most desperate hour. The very real threat of dollarization has made the world a better place. Think of all the would-be Robert Mugabe's who were prevented from hurting their nations because of the ever present threat that if they did so, their citizens would turn to the dollar.    

I should point out that the U.S. gets compensation for the unique role it performs in the form of seigniorage. Each $100 is backed by $100 in bonds, the interest on which the U.S. gets to keep. So don't complain that the U.S. is providing its services as backup monetary system for free.

Foreigners who are being subjected to high rates of domestic inflation will find it harder to get U.S dollar shelter if the $100 is killed off; after all, it costs much more to get a few suitcases of $20 overseas than one case of $100. This delayed onset of the appearance of U.S. dollars as a medium of exchange will also push back the timing of a unit of account switch from local units to the dollar. As Larry White has written, money's dual role as unit of account and medium of exchange are inextricably linked. People will only adopt something as a unit of account after it is has already been circulating as a medium of exchange. A switch in the economy's pricing unit is a vital remedy for the nasty calculational burden imposed on individuals and businesses by high inflation. The quicker this tipping point can be reached, the less hardship a country's citizens must bear. The $20 doesn't get us there as quick as the $100.

So contrary to Summers, I think we should think twice before killing the $100. The U.S. has a very special to role to play as provider of the world's backup monetary system; it should not take a step back from that role. Criminals, tax evaders, and the lower bound can be punished via alternative means. I'd be less concerned about killing other high denomination notes such as the €500, 1000 Swiss franc, or ¥10,000. That's because inflation-prone economies don't euroize or yenify—they dollarize.


Addendum: If Summers is genuinely interested in combing the world of coins and bills for what he refers to as a 'cheap lunch', then there's nothing better the U.S. can do than stop making the 1 cent coin, which is little more than monetary trash/financial kipple. Secondly, replace the $1 bill, which is made out of cotton and supported by the cotton lobby, with a $1 coin. The U.S. lags far behind the rest of the world in enacting these simple cost cutting efforts.


*See here and here for more details on RUT and ROT avdrag,
** Martin Enlund has a great post here on Sweden's cash policies.

Thomas Jordan, Chairman of the Governing Board of the Swiss National Bank

Negative interests rates are the shiny new thing that everyone wants to talk about. I hate to ruin a good plot line, but they're actually kind of boring; just conventional monetary policy except in negative rate space. Same old tool, different sign.

What about the tiering mechanisms that have been introduced by the Bank of Japan, Swiss National Bank, and Danmarks Nationalbank? Aren't they new? The SNB, for instance, provides an exemption threshold whereby any amount of deposits that a bank holds above a certain amount is charged -0.75% but everything within the exemption incurs no penalty. As for the Bank of Japan, it has three tiers: reserves up to a certain level (the 'basic balance') are allowed to earn 0.1%, the next tier earns 0%, and all remaining reserves above that are docked -0.1%.

But as Nick Rowe writes, negative rate tiers—which can be thought of as maximum allowed reserves—are simply the mirror image of minimum required reserves at positive rates. So tiering isn't an innovation, it's just the same old tool we learnt in Macro 101, except in reverse.

No, the novel tool that has been created is what I'm going to call a cash escape inhibitor.

Consider this. When central bank deposit rates are positive, banks will try to minimize storage of 0%-yielding banknotes by converting them into deposits at the central bank. When rates fall into negative territory, banks do the opposite; they try to maximize storage of 0% banknote storage. Nothing novel here, just mirror images.

But an asymmetry emerges. Central bankers don't care if banks minimize the storage of banknotes when rates are positive, but they do care about the maximization of paper storage at negative rates. After all, if banks escape from negative yielding central bank deposits into 0% yielding cash, this spells the end of monetary policy. Because once every bank holds only cash, the central bank has effectively lost its interest rate tool.

If you really want to find something innovative in the shift from positive to negative rate territory, it's the mechanism that central bankers have instituted to inhibit the combined threat of mass paper storage and monetary policy impotence. Designed by the Swiss and recently adopted by the Bank of Japan, these cash escape inhibitors have no counterpart in positive rate land.

The mechanics of cash escape inhibitors

Cash escape inhibitors delay the onset of mass paper storage by penalizing any bank that tries to replace their holdings of negative yielding central bank deposits with 0%-yielding cash. The best way to get a feel for how they work is through an example. Say a central bank has issued a total of $1000 in deposits, all of it held by banks. The central bank currently charges banks 0% on deposits. Let's assume that if banks choose to hold cash in their vaults they will face handling & storage costs of 0.9% a year.

Our central bank, which uses tiering, now reduces deposit rates from 0% to -1%. The first tier of deposits, say $700, is protected from negative rates, but the second tier of $300 is docked 1%, or $3 a year. Banks can improve their position by converting the entire second tier, the penalized portion of deposits, into cash. Each $100 worth of deposits that is swapped into cash results in cost savings of 10 cents since the $0.90 that banks will incur on storage & handling is an improvement over the $1 in negative interest they would otherwise have to pay. Banks will very rapidly withdraw all their tier-2 deposits, monetary impotence being the result.

To avoid this scenario, central banks can install a Swiss-style cash escape inhibitor. The way this mechanism works is that each additional deposit that banks convert into vault cash reduces the size of the first tier, or the shield, rather than the second tier, the exposed portion. So when rates are reduced to -1%, should banks try to evade this charge by converting $100 worth of deposits into vault cash they will only succeed in reducing the protected tier from $700 to $600, the second tier still containing the same $300 in penalized deposits. This evasion effort will only have made banks worse off. Not only will they still be paying $3 a year in negative interest but they will also be incurring an extra $0.90 in storage & handling ($100 more in vault cash x 0.9% storage costs).

Continuing on, if the banks convert $200 worth of deposits into vault cash in order to avoid -1% interest rates, they end up worsening their position even more, accumulating $1.80 in storage & handling costs on top of $3.00 in interest. We can calculate the net loss that the inhibitor imposes on banks for each quantity of deposits converted into vault cash and plot it:

The yearly cost of holding various quantities of cash at a -1% central bank deposit rate

Notice that the graph is kinked. When a bank has replaced $700 in deposits with cash, additional cash withdrawals actually reduce its costs. This is because once the first tier, the $700 shield, is used up, the next deposit conversion reduces the second tier, the exposed portion, and thus absolves the bank of paying interest costs. And since interest costs are larger than storage costs, overall costs decline.

If banks go all-out and cash in the full $1000 in deposits, this allows them to completely avoid the negative rate penalty. However, as the chart above shows, storage & handling costs come out to $9 per year ($1000 x 0.9%), much more than the $3 banks would bear if they simply maintained their $300 position in -1% yielding deposits.

So at -1% deposit rates and with a fully armed inhibitor installed, banks will choose the left most point on the chart—100% exposure to deposits. Mass cash conversion and monetary policy sterility has been avoided.

How deep can rates go?

How powerful are these inhibitors? Specifically, how deep into negative rate territory can a central bank go before they start to be ineffective?

Let's say our central banker reduces deposit rates to -2%. Banks must now pay $6 a year in interest ($300 x 2%). If banks convert all $1000 in deposits into cash, they will have to bear $9 in storage and handling costs, a more expensive option than remaining in deposits. So even at -2% rates, the cash inhibitor mechanism performs its task admirably.

If the central bank ratchets rates down to -3%, banks will now be paying $9 a year in interest ($300 x 3%). If they convert all $1000 in deposits into cash, they'll have to pay $9 in storage & handling. So at -3%, bankers will be indifferent between staying invested in deposits or converting into cash. If rates go down just a bit more, say to -3.1%, interest costs are now $9.30. A tipping point is reached and cash will be the cheaper option. Mass cash storage ensues, the cash escape inhibitor having lost its effectiveness.

The chart below shows the costs faced by banks at various levels of cash holdings when rates fall to -3%. The extreme left and right options on the plot, $0 in cash or $1000, bear the same costs.

The yearly cost of holding various quantities of cash at a -3% central bank deposit rate

So without an inhibitor, the tipping point for mass cash storage and monetary policy impotence lies at -0.9%, the cost of storing & handling cash. With an inhibitor installed the tipping point is reduced to -3.1%. The lesson being that cash escape inhibitors allow for extremely negative interest rates, but they do run into a limit.

The exact location of the tipping point is sensitive to various assumptions. In deriving a -3.1% escape point, I've used what I think is a reasonable 0.9% a year in storage and handling costs. But let's assume these costs are lower, say just 0.75%. This shifts the cash tipping point to around -2.5%. If costs are only 0.5%, the tipping point rises to around -1.7%.

This is where the size of note denominations is important. The Swiss issue the 1000 franc note, one of the largest denomination notes in the world, which means that Swiss cash storage costs are likely lower than in other countries. As such, the Swiss tipping point is closer to zero then in countries like the Japan or the U.S.. One way to push the tipping point further into negative terriotry would be a policy of embargoing the largest note. The central bank, say the SNB, stops printing new copies of its largest value note, the 1000 fr. Banks would no longer be able to flee into anything other than small value notes, raising their storage and handling costs and impinging on the profitability of mass cash storage.

Good old fashioned financial innovation will counterbalance the authorities attempts to drag the tipping point deeper. Cecchetti & Shoenholtz, for instance, have hypothesized that in negative rate land, a new type of intermediary could emerge that provides 'cash reserve accounts.' These specialists in cash storage would compete to reduce the costs of keeping cash, pushing the tipping point back up to zero.

The tipping point is also sensitive to the size of the first tier, or the shield. I've assumed that the central bank protects 70% of deposits from the negative deposit rate. The larger the exempted tier the bigger the subsidy central banks are providing banks. It is less advantageous for a bank to move into cash when the subsidy forgone is a large one. So a central bank can cut deeper into negative territory the larger the subsidy. For instance, using my initial assumptions, if the central bank protects 80% of deposits, then it can cut its deposit rate to -4.6% before mass paper storage ensues.

Removing the tipping point?

There are ways to modify these Swiss-designed cash escape inhibitors to remove the tipping point altogether. The way the SNB and BoJ have currently set things up, banks that try to escape negative rates only face onerous penalties on cash conversions as long as the first tier, the shield, has not been entirely drawn down. Any conversion after the first tier has been used up is profitable for a bank. That's why the charts above are kinked at $700.

If a central bank were to penalize cumulative cash withdrawals (rather than cash withdrawals up to a fixed ceiling) then it will have succeeded in snipping away the tipping point. This is an idea that Miles Kimball has written about here. One way to implement this would be to require that the tier 1 exemption, the shield, go negative as deposits continue to be converted into cash, imposing an obligation on banks to pay interest. The SNB doesn't currently allow this; it sets a lower limit to its exemption threshold of 10 million francs. But if it were to remove this lower limit, then it would have also removed the tipping point.

What about retail deposits?

You may have noticed that I've left retail depositors out of this story. That's because the current generation of cash escape inhibitors is designed to prevent banks from storing cash, not the public.

As central bank deposit rates fall ever deeper into negative territory, any failure to pass these rates on to retail depositors means that bank margins will steadily contract. If banks do start to pass them on, at some point the penalties may get so onerous that a run develops as retail depositors start to cash out of deposits. The entire banking industry could cease to exist.

To get around this, the FT's Martin Sandbu suggests that banks could simply install cash escape inhibitors of their own. Miles Kimball weighs in, noting that banks may start applying a fee on withdrawals, although his preferred solution is a re-deposit fee managed by the central bank. Either option would allow banks to preserve their margins by passing negative rates on to their customers.

Even if banks don't adopt cash escape inhibitors of their own, I'm not too worried about retail deposit flight in the face of negative central bank deposit rates of -3% or so. The deeper into negative rate territory a central bank progresses, the larger the subsidy it provides to banks via its first tier, the shield.  This shielding can in turn be transferred by a bank to its retail customers in the form of artificially slow-to-decline deposit rates. So even as a central bank reduces its deposit rate to -3% or so, banks might never need to reduce retail deposit rates below -0.5%. Given that cash handling & storage costs for retail depositors are probably about the same as institutional depositors, banks that set a -0.5% retail deposit rate probably needn't fear mass cash conversions.

So there you have it. Central banks with cash escape inhibitors can get pretty far into negative rate land, maybe 3% or so. And with a few modifications they might be able to go even lower.

The 1995 British two pound "Dove" coin

The Bank of England's chief economist Andrew Haldane recently called for central banks to think more imaginatively about how to deal with the technological constraint imposed by the zero lower bound on interest rates. Haldane says that the lower bound isn't a passing problem. Rather, there is a growing probability that when policy makers need three percentage points of headroom to cushion the effects of a typical recession, that headroom just won't be there.

Haldane pans higher inflation targets and further quantitative easing as ways to slacken the bound, preferring to focus on negative interest rates on paper currency, a topic which gets discussed often on this blog. He mentions the classic Silvio Gesell stamp tax (which I discussed here), an all out ban on cash as advocated by Ken Rogoff, and Miles Kimball's crawling peg (see here).

According to Haldane, the problem with Gesell's tax, Rogoff's ban (pdf), and Kimball's peg is that each of these faces a significant 'behavioural constraint.'  The use of paper money is a social convention, both as a unit of account and medium of exchange, and conventions can only be shifted at large cost. Tony Yates joins in, pointing out the difficulties of the Gesell option. Instead, Haldane floats the possibility of replacing paper money with a government-backed cryptocurrency, or what we on the blogosphere have been calling Fedcoin (in this case BOEcoin). Unlike cash, it would be easy to impose a negative interest rate on users of Fedcoin or BOEcoin, thus relaxing the lower bound constraint. Conventions stay intact; people still get to use government-backed currency as a medium of exchange and unit of account.*

While I like the way Haldane delineates the problem and his general approach to solving it, I'm not a fan of his chosen solution. As Robert Sams once pointed out, Fedcoin/BoEcoin could be so good that it ends up outcompeting private bank deposits, thus bringing our traditional banking model to an abrupt end. Frequent commenter JKH calls it Chicago Plan #37, a reference to a depression-era reform (since resuscitated) that would have outlawed fractional reserve banking. If Haldane is uncomfortable with the Gesell/Rogoff/Kimball options for slackening the lower bound because they interfere with convention, he should be plenty worried about BOEcoin.


I do agree, however, with Haldane's point that the apparatus adopted to loosen the constraint should interfere with convention as little as possible. We want the cheapest policies; those that only slightly impede the daily lives of the typical Brit on the street while securing the Bank of England a sufficient amount of slack.

With that in mind, here's what I think is the cheapest way for the Bank of England to slacken the lower bound: just freeze the quantity of £50 bills in circulation. Yep, it's that easy. There are currently 236 million £50 notes in circulation. Don't print any more of them, Victoria Cleland.**

I call this a policy of embargoing the largest value note. How does it work?***

Say that in the next crisis, the Bank of England decides to chop rates from 0.5% to -2.0%. Faced with deeply negative interest rates, the UK runs smack dab into the lower bound as Brits collectively try to flee into banknotes. After all, banknotes offer a safe 0% return, the £50 note being the chosen escape route since those are the cheapest to store and convey.

Flooded with withdrawal requests, banks will quickly run out of £50s. At that point the banks would normally turn to the Bank of England to replenish their stash in order to fill customers' demands. But with the Bank of England having frozen the number of £50s at 236 million and not printing any new ones, bankers will only be able to offer their customers low denomination notes. But this will immediately slow the run for cash since £20s, £10s, and £5s are much more expensive to store, ship and transfer than £50s. Whereas people will surely prefer a sleek high denomination note to a deposit that pays -2%, they will be relatively indifferent when the choice is between a bulky low denomination cash and a deposit that pays -2%. Thus the lower bound has been successfully softened by an embargo on the largest value note.

Once negative interest rates have served their purpose and the crisis has abated, they can be boosted back above 0% and the central bank can unfreeze the quantity of £50s. Everything returns to normal.

A few conventions will change when the largest value note is embargoed.

1. People will no longer be able to convert £50 worth of deposits into a £50 note. Instead they'll have to be satisfied with getting two £20s and a £10. That doesn't seem like an expensive convention to discard. And if folks really want to get their hands on £50s, they'll still be able to buy them in the secondary market, albeit at a small premium.

2. In normal times, £50 notes always trade at par. Because their quantity will be fixed under this scheme, £50s will rise to a varying premium above face value whenever interest rates fall significantly below zero. For instance, at a -2.0% interest rate a £50 note might trade in the market at £51 or £52.

The par value of £50 notes is a cheap convention to overturn. The majority of the British population probably don't deal in £50s anyways. Those who do use £50 notes in their daily life will have to get used to monitoring their market price so that they can transact at correct prices. But the inconveniences faced by  this tiny minority is a small cost for society to pay in order to slacken the lower bound.

3. Importantly, there will be no need to proclaim a unit of account switch upon the enacting of an embargo on £50s; the switch will be seamless.

Because the £50 was never an important part of day-to-day commercial and retail existence, come negative interest rates no retailers will set their prices in terms of a £50 standard. If they do choose to set sticker prices in terms of the £50 note, they will find that if they want to preserve their margins they will have to levy a small surcharge each time someone pays with £20s, £10s, and £5s and bank deposits. Given the prevalence of these payment options, that means surcharging on almost every single transaction. That's terribly inconvenient. Far better for a retailer to set sticker prices in terms of the dominant payments media—£20s, £10s, and £5s and bank deposits—and provide a small discount to the rare customer that wants to pay with £50s.

It's entirely possible that the majority of retailers will not bother offering any discount whatsoever on £50s. This would effectively undervalue the £50 note. Gresham's Law tells us that given this undervaluation, the £50 will disappear from circulation as it gets hoarded under people's mattresses. For the regular British citizen, never seeing £50s in circulation probably won't change much. And anyone who does want a £50 can simply advertise on Craig's list for one, offering a high enough premium to draw it out of someone's hoard.

In closing, a few caveats. The figures I am using in this post are ballpark. It could be that a policy of freezing the supply of £50 notes allows the Bank of England to get to -2%. But maybe it only allows for a level of -1.75%, or maybe it slackens the bound so much as to allow a -2.5% rate.

Haldane mentions that the Bank of England could need 3% of headroom to combat subsequent recessions. But as Tony Yates has pointed out, in 2008 bank officials calculated that a -8% rate was needed. The Bank could get part way there by not only embargoing the £50 but also the next highest value note; the £20. But that probably wouldn't be enough. As ever smaller notes have their quantities frozen, this starts to intrude on the lives of the people on the street, making the policy more costly. If it needs to slacken the lower bound in order to allow for rates of -8%, I think the Bank of England should be planning for a heftier policy like Miles Kimball's crawling peg. After all, when the sort of crisis that requires such deeply negative rates hits, the last thing we should be worried about is disturbing a few conventions. Until another 2008-style crisis hits, embargoing large value notes might be the least intrusive, lowest cost option. 

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*Of these policies, I think Miles Kimball's plan is by far the best one.
**Specifically, the Bank would only print new bills to replace ripped/worn out bills. Otherwise the outstanding issue will wear out and become easier to counterfeit. As for Scotland, which issues 100 pound notes, their quantity would have to be fixed as well.
*** I first mentioned the idea of embargoing large notes in relation to the Swiss 1000 CHF note, and later elaborated on it in the Lazy Central Banker's Guide to Escaping Liquidity Traps.