Pricing the anonymity of banknotes

Banknotes are useful. Not only do they provide their owner with a standard set of payments services, they also offer financial anonymity. This post introduces the idea of trying to price the anonymity component. 

To help think about why we might want to price anonymous banknote usage, I’m going to make an analogy. Imagine Walmart sells special suits that allow people to become invisible. While most Walmart customers always pay for the goods they find in the aisles, a few try these invisible suits on, grab a bunch of stuff, and sneak out without paying. The product is weaponized and turned against its provider.

This same sort of weaponization characterizes the modern provision of banknotes. The government, like Walmart, provides citizens with a privacy-enhancing product: cash. Because its coins and banknotes don’t leave a paper trail, they act as a financial cloak. In the same way that an invisible suit can be used to evade Walmart’s checkout counter, a government-issued banknote can be turned against its provider by allowing users to avoid paying for the government services they have consumed. 

Walmart may wish to do something about the weaponization of invisible suits, especially if the costs imposed by abusers of suits begin to exceed the amount of income the company gets from buyers of invisible suits. One option Walmart has is to stop selling the product. No one would fault them for putting an end to an unprofitable business line. Invisible-suit aficionados could just shop elsewhere. 

But what if Walmart is society’s only provider of invisibility? This complicates things. While a few bad apples regularly abuse Walmart’s invisible suits by using them to steal, many others use the suits in legitimate ways. So while a decision to stop selling invisible suits might improve Walmart’s finances, it might also make society worse off. 

This same tension crops up in the debate over the future of cash. A ban on cash would help reduce tax evasion and improve government finances. But since banknotes are the only anonymous financial product, and no other entity is permitted to provide banknotes, a ban would put an immediate end to financial privacy. Because privacy is something that regular folks value for licit reasons, their welfare would be reduced.

Say Walmart does the noble thing. It continues to stock invisible suits to meet the public’s demand for privacy. But the company still has costs it must meet, including wages, inventories, and rent, and with a steady loss of payments facilitated by the weaponization of invisible suits, that hurdle becomes much harder to clear. To plug deficits, Walmart may have to ask all its rule-abiding customers to pay a little bit more for their purchases by raising all of prices by a little bit. 

But an across-the-board price increase hardly seems fair. Those abiding by Walmart’s rules are being asked to make up for a shortfall that is entirely the fault of suit-stealing rule breakers. Honest shoppers who don’t generally like to use invisible suits will be particularly furious — and who can blame them? They are being asked to pay more for the goods they hold dear in order to support the use of a single product they never cared for much anyway. 

This same lack of fairness plagues modern tax systems. The government needs to fund (via taxes) the services it provides, but the presence of cash is weaponized against the system by tax cheats. The funding gap that emerges must be made up for by all of the remaining citizens — the non-cheaters. So taxes, or the price of government services, will be higher in the presence of cash than in a world without cash. Non-cheaters, particularly those who don’t use cash, will feel betrayed because they must pay higher taxes to support the ongoing provision of a product they don’t necessarily value. 

Walmart may have a better option. Instead of increasing the price of all goods to make up for the behavior of a few invisible-suit users, it can just raise the price of suits high enough to make up for the shortfall. So customers who like invisibility end up bearing the costs imposed by thieves who weaponize suits. This targeted approach seems like a fairer path for Walmart to take. It releases a large chunk of its customer base from the obligation of offsetting the invisibility-induced shortfall while still giving those who value the privacy provided by invisible suits the option of buying them.

If setting a higher price for invisibility is the best option for Walmart, what about modern banknote-providing governments? In the same way that Walmart increases the price of invisible suits to offset the shortfall created by those who weaponize them, a government can introduce a levy on cash users. Rather than placing this levy on all banknote denominations, it might target high-denomination banknotes instead. The idea is that bulky $1s and €5s may be less useful in large-scale tax evasion than $100s and €200s. 

By setting a levy or negative interest rate of 5 to 10 percent per year on high-denomination notes (there are various ways to do this), the government would be able to earn a large-enough stream of revenue to help offset the shortfall created by cash-using tax evaders. The effect would be a lower tax bill for all non-cheaters, both for those who generally do not use cash and those who use only small-denomination notes ($1 and €5s). In effect, the anonymity provided by $100s and €200s would now be directly paid for by the users of those $100s and €200s. Unlike an all-out ban on banknotes, financial anonymity would still be provided. 

I think it makes sense for the Walmart in our thought experiment to give anonymity pricing a shot. Maybe governments should entertain the idea, too.

[This post was originally published at the Sound Money Project. I've modified it slightly for clarity.]

Supernotes

The U.S. $10,000 was available till Nixon nixed it in 1969

For the last few years the conversation about cash has been dominated by Ken Rogoff's proposal to remove high-denomination banknotes. In an effort to broaden the discussion, last year I wrote an essay for Cato Unbound about introducing a new U.S. supernote. The value of the current highest denomination note--the $100 bill--has deteriorated over the decades thanks to inflation. Is it time to restore the purchasing power of U.S. cash by bringing out a $1,000 note?

In the same essay I also floated the idea of taxing the supernote. Why a tax? A new $1,000 bill could be used for both good and nefarious purposes. Given that nefarious supernote usage (tax evasion and crime) could impose costs on society, a tax would make up for this by transferring wealth from note users to the rest of us. (I also blogged about the idea of taxing cash here and here). 

Josh Hendrickson, Will Luther, and Jamie McAndrews all had responses. Do read them, as they give a good sense of all the various nuances and complications involved in issuing a supernote and taxing it.

---------------------

Say we introduce a new supernote worth $1,000. What would Walter, a seasoned drug dealer, think about this new policy? Let's walk through the day-to-day costs that Walter absorbs as an illicit cash user.

Walter makes large value payments using banknotes. He also stores plenty of the stuff. A million dollars worth of $100 notes (i.e. 10,000 notes) takes up a lot of space. But one thousand $1000 bills can be packed into a container a tenth the size. This will make Walter's business much easier to expedite. His costs of counting, transporting, storing, and sorting notes will all drop significantly.

The risk of detection will also be much lower with supernotes. Hiding twenty supernotes in a car is a lot easier than hiding two-hundred $100 notes. Detection by authorities imposes costs on Walter and his associates. Banknotes can be seized under civil asset forfeiture laws. In many cases the police can seize cash on mere suspicion of wrongdoing--they don't even have to charge the owner with a crime.

Example of an asset forfeiture case involving cash [source]

These seizures can be contested by Walter and his associates, but this will involve significant time and legal expenses. There are also non-pecuniary losses associated with detection. If Walter or one of his associates is pulled over for speeding and the cops find a bag full of $100 notes in his car trunk, that may provide law enforcement with information and insight into his network.

Finally, Walter also incurs a "tax" on his cash holdings. Specifically, his cash does not earn interest. If Walter regularly stores $100,000 in cash, and the interest rate is 3%, he is effectively forfeiting around $3,000/year. This loss is the same whether Walter holds his stash in $100 notes or supernotes. Walter's $3000/year loss goes directly to the public. He is providing the rest of us with an interest-free loan, or a subsidy.

Weaving this all together, from Walter's perspective the new supernote is a great product. It reduces his storage & handling costs (S) as well as any costs arising from detection (D), and does so without increasing his taxes (T).

Civil society isn't quite as well off with a supernote. We've provided Walter with a superior means of avoiding detection. Not only does this mean that we've increased the odds of Walter staying out of jail. We've also reduced asset forfeiture revenues. Since law enforcement agencies uses forfeitures to fund their operations, any diminution in this flow means that the rest of us will have to pay higher taxes to compensate.

----------------------

Why don't we strike a deal with Walter? If supernotes allow him to enjoy lower S and D, why don't we ask for higher T in compensation? Setting a higher T involves an increase in the tax rate on supernotes relative to $100 notes.

One way to do this is to make the supernote depreciate a bit each day. The central bank will buy the note back today for $1000, but tomorrow it will only buy it back at $999.95. This constitutes a 5¢/day transfer from Walter to the public. At a yearly interest rate of 3%, he also loses around 5¢/day in forgone interest. This combination of a capital loss and forgone interest comprise the supernote tax.

Now when Walter and his colleagues switch from using the $100 bill to the supernote, society's decline in forfeiture income is compensated by higher tax income. Even with the higher tax, Walter prefers the supernote to the $100 because he saves enough on S and D to make it worth his while. So everyone wins if we issue a supernote.

Or as Hendrikson says in his response essay:

"the introduction of the supernote is in this instance welfare-improving (given the premise that illegal trade creates a social cost) because it allows policymakers to engineer a transfer from criminals to law-abiding citizens that would not be available otherwise."

--------------------

There may be some additional improvements in efficiency to be gained by replacing a bad tax--asset forfeiture--with a good one. Having the police directly raise funds by confiscating people's property is ripe for abuse.

Wooooow. This has huge implications, since cities are increasingly relying on fees and fines for their budgets. https://t.co/dnHPNTWYIQ

Thanks for passing this along, @jbenmenachem! pic.twitter.com/s6KMS1MwTg

— Michael Hobbes (@RottenInDenmark) April 16, 2019

By contrast, a supernote tax is automatic, predictable, transparent, and easier to collect.

--------------------

A supernote would provide at least some benefit to non-criminals. Say that Sarah wants to sell her car for $8000. She may be wary of accepting a check from the buyer, Todd, who she doesn't know. If she provides the car to Todd but his check bounces, then she's out of hand. Cash is a simple way to solve this problem. The moment that cash passes hands from Todd to Sarah, the payment is 100% certain.

Without a supernote, Todd will have to pay for the $8000 car with eighty $100s. Wouldn't it be more cost effective for him to make the payment with just eight $1000s? Less counting is required and the bills easily slip into a wallet. So S is reduced. (Detection, or D, is not a cost that licit users need worry about.)

Unfortunately the imposition of a tax will reduce the supernote's potential for improving the lives of non-criminals like Sarah and Todd. Since the tax raises the cost of the supernote relative to alternatives like the $100 note, many people who would otherwise have consumed the supernote just won't bother. Put differently, the  consumer surplus (for licit users) that is created by the introduction of a taxed supernote will be small than if the supernote was untaxed.

If the tax is set quite high, then usage of supernotes may be entirely confined to criminals. This the sort of monetary future that David Birch would probably say was first described by novelist William Gibson in Count Zero. Cash still exists, but it will have disappeared from polite society.

William Gibson imagined a future where 'polite society' won't accept cash. From 'Count Zero' ht @dgwbirch pic.twitter.com/Bh9ZKVDmJz

— JP Koning (@jp_koning) October 3, 2016

-------------------------

A taxed supernote is a neat idea, but does it qualify as a "fancy monetary standard" i.e too abstract and academic to inspire confidence? "Fancy" is the word that Irving Fisher's critics used to denigrate his early ideas about price targeting.

Admittedly a taxed supernote doesn't present a very clean user interface. Having a round face value is one of the conveniences of a note. This feature ensures that it can be easily divided into smaller amounts. But the supernote tax means that the face value of the note will very quickly fall to some inconvenient number like $999.33. As McAndrews points out: 

"...the differential rates of exchange among the different denominations of notes is an inconvenience. The cost of all those calculations required to make change and set different prices based on which note a customer offers must be counted against whatever benefit a tax might achieve."

It might be possible to avoid the rounding problem by finding a different means for assessing the tax. In his paper Taxing Cash, Ilan Benshalom describes a withdrawal tax. This tax would be assessed whenever money is taken out of an ATM or bank teller. However, supernotes will probably circulate for long periods of time without every being deposited, which means the withdrawal tax will rarely be activated.

For now, taxed supernotes are science fiction. But who knows? Irving Fisher's fancy monetary standard was science fiction for decades, but it has slowly become the standard way of doing monetary policy these days.

The demonetization gap

Two years ago, Indian PM Narendra Modi suddenly demonetized all of the nation's ₹1000 and ₹500 banknotes. His stated goal was to exact justice on all those holding large amount of dubiously-earned cash. But since these two denominations constituted around 85% of India's currency supply, the demonetization immediately threw the entire nation into chaos.

After suffering from a nine-month note shortage, enough new notes were printed to meet India's demand for cash. But in the interim, what had happened to Indians' demand for cash? Did their experience with demonetization lead them to hold less cash than before, or did they simply revert to their pre-demonetization habits and patterns? I wrote an article in September 2017 dealing with these questions. With another year having passed we now have more data—so I'm going to provide quick update.

My claim is that a demonetization gap continues to exists. This gap is evidence that the cancellation of ₹1000 and 500s has had an enduring effect on Indians' behaviour surrounding cash.

To measure the gap, we need to compare the evolution of India's cash supply to the path it would have taken in a world in which Modi's demonetization never occurred. We know that the supply of rupee banknotes grew at an average rate of around 12.3% from 2011 to 2016, and on the eve of demonetization there were around ₹17.5 trillion in banknotes and coins in circulation. Taking these numbers and extrapolating forward, November 2018's cash-in-circulation count would have clocked in at around ₹21.5 trillion rupees had the demonetization not occurred. But in our actual world, the one where demonetization occurred, India's cash count registers at just ₹19.5 trillion rupees.

So thanks to demonetization, Indians are holding around ₹2 trillion fewer paper rupees than they otherwise would have. I've illustrated the demonetization gap below:

Today is the two-year anniversary of Modi's rather inept demonetization.

Interestingly, the demonetization gap—the difference between India's current banknote count and where it probably would have been without demonetization—is still quite large... pic.twitter.com/DvUnOlEjim

— JP Koning (@jp_koning) November 8, 2018

What sort of assumptions do we need to make in order for the demonetization gap to be zero? Let's say that demonetization had never occurred. To get from a currency stock of ₹17.5 trillion in November 2016 to ₹19.5 trillion by November 2018, we need to assume an absurdly low 6% growth rate for the stock of currency stock. I doubt India has ever experienced such a slow growth rate in cash-in-circulation. So while you can quibble with the size of the gap, I think it's undeniable that some sort of gap exists i.e. demonetization has had long lasting effects on cash holdings.

There are two potential explanations for why a demonetization gap exists. My guess is that both are to some extent true, although as time passes the influence of the second will tend to disappear:

1. Demonetization might have had a permanent effect on Indians' taste for cash. Prior to demonetization, a money launderer might typically have built up an inventory of ₹100 lakh (US$135,0000) worth of banknotes before laundering them. But the demonetization frightened him, so now he launders his ill-gotten gains whenever he holds just ₹50 lakh worth of notes.

Or maybe a family that typically conducted most of their day-to-day transactions in cash opened a bank account during demonetization so that they could deposit their notes. And now they've fallen into the habit of paying for half their family expenses with cash, and the other half with debit cards.

These sorts of changes to transactions preferences would get expressed in the nation's overall stock of notes by a reduction relative to trend.

2. Demonetization might have caused large and lasting damage to the informal sector of the Indian economy. With 85% of the nation's money stuck suddenly came unusable, and so many businesses dependent on cash, these businesses may have been forced to go under. With informal production cratering, fewer banknotes would be required for transactions purpose than would otherwise be the case. Over the long term, however, one would expect these sectors to rebuild, any drag they had once placed on cash demand being removed.

If Indian's taste for cash changed, how might these new tastes have manifested themselves? Did Indians swap cash for deposits in the regulated banking system or did they simply swap one form of anonymous "black money" for another (i.e. cash for gold, diamonds, real estate)? In my post from last September I found some interesting charts. I'm going to update them below.

As the chart above illustrates, the number of point-of-sale (POS) terminals installed has experienced a one-time shot to the arm after the November 2016 demonetization announcement.

The second chart shows that the value of POS transactions using debit and credit cards moved to a new and higher plateau.

The last chart shows the growth in value transacted using mobile wallets. Demonetization gave mobile wallet usage a quick shot to the arm, but it is difficult to determine if growth stayed above trend in 2017-18 or below. Given that mobile wallets are recent and started from a very low base, usage had already been growing very fast before demonetization.

In any case, I think the charts provide at least some evidence that the shift out of cash has been captured by digital finance.

---------------

The existence of a demonetization gap does not mean that Modi's effort was a success. If someone comes up with a great monetary innovation, expect it to be quickly copied. Polymer banknotes, real-time gross settlement systems, and inflation targeting are all examples of monetary technologies that have spread from their original adopter to the rest of the world. But not a single nation has copied India's demonetization. I would be surprised if any ever do. The costs imposed by the event—lost labour time, foregone transactions, chaos—were all too apparent, and its benefits dubious.

That being said, I sympathize with the intuition that was at the core of Modi's demonetization. Let's face it, plenty of people use cash as a way to avoid taxes. These cheats force everyone else to pay more than their fair share for shared infrastructure. It would be nice if there was a way to rebalance the load by taking back resources lost to the cheats. A classic way to fix this problem is to have the tax department hire more inspectors. An alternative is to design the nation's cash system in a way that corrects for any unfairness. Modi's demonetization is an example of the second approach, a massive cash dragnet designed to flush out cheats.

But it was an incredibly clumsy effort. The tricky thing with cash is that it is simultaneously a vessel for tax evasion for a few cheats and also a vital monetary fluid for the many. Punishing the first group means that the second will also be hurt. If the costs incurred by the second group are too high, then the calculus behind the whole effort fails.

Modi's demonetization tried to lessen the blast radius by targeting users of large denomination ₹500 and ₹1000 notes while leaving users of the ₹10, ₹20, ₹50, ₹100, and ₹200 untouched. The motivation behind this was that presumably large tax cheats will concentrate their cash holdings in higher denomination notes, while regular note users will tend to concentrate in the lower denominations. But even with this filter in place, the ₹500 and ₹1000 were so widely held by Indians that the demonetization of these denominations forced a large proportion of the population to endure massive lineups for weeks. Retail trade ground to a halt.

Over the last two years I suggested a few ideas that would have improved the effectiveness of Modi's demonetization. Instead of targeting all ₹500s and ₹1000 notes, demonetizing notes by serial number would have resulted in a much smaller blast radius. Rather than withdrawing ₹500s and ₹1000s, it would have been easier to overstamp them with stickers, and then slowly withdraw these overstamped notes over time. This would have helped prevent massive cash shortages.

But even after these modifications, demonetization is too blunt of a tool to effectively solve the complicated inequities arising from cash-based tax evasion. So should Indians (and the rest of us too) simply live with these imperfections, accepting unfairness as an acceptable cost of maintaining cash systems?

Maybe not. In his paper Taxing Cash, Ilan Benshalom has suggested a less invasive technique for reclaiming resources from cash-using tax evaders. Rather than demonetizing all ₹500 and ₹1000s, Modi could have introduced a recurring withdrawal fee of ₹10 for each ₹500 note and a ₹20 rupee fee on each ₹1000 note.

Imagine that Rohit needs to pay Indira ₹10 lakh. The two can avoid taxes if they agree to transact using cash rather than making a digital payment. So Rohit withdraws one thousand ₹1000 bills from his bank. He incurs a fee of ₹20,000 (₹20 for each note), the bank forwarding the full amount to the government. Rohit might consider avoiding the withdrawal tax by withdrawing ₹50s and ₹100s (which don't incur fees), but he is unlikely to go this route since ₹10 lakh in small denomination notes would be terribly awkward.

The upshot is that Indian tax payers would get ₹20,000 in compensation for Rohit and Indira's evasion of taxes. Compared to Modi's demonetization, the blast radius of a large denomination withdrawal tax is much smaller. Regular Indians could have easily continued about their business using untaxed ₹100s or migrating to digital payments. It sounds promising, but after Modi's explosive demonetization, Indians are probably much less open to new monetary experiments, and who can blame them.

---

There are several other ways to visualize Indian demand for cash over time. For instance, here is the cash-to-GDP ratio:

The idea here is that for each unit of GDP, some amount of cash is used as means of circulating production. (Note: While the cash-in-circulation numbers are current, 2018 Q2 nominal GDP has still not been published. I estimated it by assuming 11.5% nominal growth, the average growth rate over the last few years.)

Vivek Dehejia and Rupa Subramanya measure the ratio of cash-in-circulation to the total money stock, or M3. They find little evidence of a reduced reliance on cash. For the chart below, I've used M4 which includes not only chequing and savings deposits held at banks but also total postal office deposits:

The cash-to-M4 ratio is a bit lower than it was on the eve of demonetization. For each ₹100 held in accounts, Indians now only hold ₹14.9 in banknotes and coins, down from ₹16 in October 2016. Be careful with using the cash-to-M4 ratio as a measure of preferences for banknotes. If Indians want to hold fewer deposits and more government bonds, M4 declines, and so the cash-to-M4 ratio will rise. But preferences for cash haven't changed at all.

A tax, not a ban, on high denomination banknotes

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.

---

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."

The odd relationship between gangster and central banker

In my recent post for the Sound Money Project, I touched on the odd relationship between central banker and gangster. I want to focus a bit more on this relationship.

An awkward truth of central banking is that one of the central bank's most important lines of business—the business of providing cash, specifically high denomination banknotes—primarily serves hoodlums, gangsters, tax evaders, and the mafia. Yes, non-criminals certainly make some use of high denomination banknotes, say a few notes hidden in the cookie jar in case the electricity goes down. But the largest base of users is comprised of folks who hold notes—not in cookie jars—but by the suitcase full; criminals. Banknotes are anonymous after all, so they are an excellent way for criminal organizations to make large-scale transactions without being traced.

Providing criminals with high-denomination banknotes is a lucrative line of business. For each $100 note put into circulation, a central bank holds $100 worth of interest earning assets in its vaults. Since note holders don't have the right to receive any interest, the central banks gets to keep all this interest income for itself.

For instance, by the end of 2016 the Bank of Canada had placed $80.5 billion worth of banknotes into circulation. Large denomination banknotes—the $50, $100 and $1000 notes—accounted for $58.4 billion of this, or around 72% of all banknotes. The assets standing behind all outstanding banknotes allowed the Bank of Canada to earn $1.53 billion in interest in 2016. Of this amount, around $1.1 billion (72% of $1.53 billion) can be attributed to high denomination banknotes, the majority of which comes courtesy of the largest holders of high denomination notes: gangsters.

So you can begin to see why the Bank of Canada might not want to get out of the business of producing $50, $100, and $1000 notes. $1.1 billion is a lot of profit! Of course, were the Bank to get out of producing high denomination notes altogether, it wouldn't forgo the entire $1.1 billion in yearly income. Criminals might choose to use $10 and $20 notes in the place of the demonetized high denomination notes. However, $10s and $20s are a bulky way to store value. They surely wouldn't be capable of recapturing all of the criminal wealth formerly held in the form of $50, $100, and $1000 notes. Which means that the total amount of banknotes outstanding would fall and Bank of Canada profits would shrink.

Why might central bankers care about their profits? As I wrote here, any government bureaucrat who can provide their master with an ongoing revenue stream will always have more say in their department's fate than a bureaucrat who has to ask for funding each year. And of all government bureaucrats, none is more jealous of their independence than the central banker. The process of ratcheting the interest rate lever higher or lower requires a complete absence of political meddling, so say central bankers. One might imagine that this autonomy is worth so much to central bankers that it justifies taking on a clientele dominated by gangsters.

There is a better reason for why it might be in the public interest for central bankers to continue serving criminals with high denomination banknotes. Consider the fact that if high denomination notes were to be rescinded, criminals would simply use other forms of payment in their place. If the substitute payments medium that criminals select places a new and extremely onerous set of burdens on society, then maybe the public provision of high denomination notes should not be discontinued.

What alternative payments media might criminals use in the place of $100 and $50 notes? In his screed against high denomination banknotes, Ken Rogoff suggests that gold, uncut diamonds, and bitcoin might become popular as a criminal payments media. The fact that these instruments are cumbersome relative to cash would make criminals easier to catch, and Rogoff claims that the crime rate might even drop.

In a provocative article, James McAndrews counters that rather than turning to commodities, criminals will instead select private debts as their preferred payments medium. A thief who sells stolen goods to a fence would accept some sort of IOU as payment rather than cash or diamonds. This IOU wouldn't be anonymous. Like any debt, the debtor and creditor would be a matter of record. But as long as the system of debts is secret—i.e. only criminal participants can see the record—then the users can't be tracked by the authorities, like cash.

When an IOU defaults, the traditional legal system provides a means for sorting things out. But this system would be out of bounds to criminals trafficking in IOUs. What is required is some sort of underground administrator or third-party to act as arbiter. According to McAndrews, the party that is likely to emerge as enforcer of criminal debts is organized crime: the mafia. 

In addition to enforcing IOUs, the mafia would also be in a position to fabricate new IOUs for use in the criminal monetary system. McAndrews uses the example of inflated invoices. The mafia would coerce legitimate businesses into writing IOUs, or invoices, for goods they never bought, or bought  at inflated prices. These invoices would circulate among criminals as money. To assure that the police ignored their extortion of legitimate business, the mafia would resort to stepped up bribery of the police.

All of this changes the calculus of a central bank withdrawal from the business of providing criminals with banknotes. Sure, a demonetization of high denomination notes might lead some gangsters to go legit because the lack of $100 and $50 notes makes their business too expensive to operate. But a whole new range of crimes could emerge. Violence could grow as the mafia executes defaulters in order to maintain the sanctity of the new IOU payments system that has taken the place of high denomination banknotes. Legitimate businesses could get blackmailed into feeding the criminal monetary system, those run by immigrants likely being the most vulnerable. And police departments will be corrupted.

McAndrews uses the public provision of free condoms and clean needles as an analogy. Restrict free condoms and it is possible that the rate of sexual intercourse goes down. But surely there will be an increase in unsafe sex, unplanned pregnancy, and sexually transmitted diseases. As for the provision of clean needles, restrict it and heroin use might fall. However, the prevalence of HIV will rise. Both unsafe sex and dirty needle usage impose costs not only on those directly afflicted but also indirectly on us—i.e. taxpayers who pay increased health care expenditures.

Likewise with cash. A restriction of $50 and $100 notes could very well lead to attrition in the ranks of existing criminals, as Ken Rogoff reasons. However, this could be twinned with an increase in mafia activity and the potential subordination of us—i.e. legitimate business—to the needs of the underground payments system. Keeping high value banknotes may thus be the wise decision, in the same way that choosing to keep free condom and clean needle programs going makes everyone's lives better off.

Cash, cat, and mouse

Bruno Liljefors, 1899, link

The tax authority and the tax payer are engaged in an age-old cat and mouse game, tax payers trying to perfect tricks that allow them to pay as little tax as possible and the tax authority trying to close these loopholes. Retail cash payments are one of the fields on which this battle is waged. It's interesting to see how sophisticated this cat and mouse game has become.

There are two weak points in the sales process that allow cash-accepting retailers to avoid paying sales taxes or VAT. The first weak point is at the very outset of a payment. When a customer pays with cash, the person behind the till can avoid ringing up the payment. Without a record of the payment having been made, the retailer needn't pay tax.

But even if a retailer rings up all cash payments and provides receipts, they can still avoid paying taxes. At the end of the business day, they need only doctor the cash register's data using a zapper—add on hardware or software designed for this purpose—in effect purging all or a portion of the cash payments registered during the course of business. With the only record of that day's cash payments now being the paper receipts held in customers' wallets—most of which will have been thrown away—the retailer needn't worry about the tax authority discovering the doctoring. (Erasing card based payments is much riskier for the retailer because a paper trail still exists with the card-issuer.)

Tax authorities have been targeting the second point of weakness for a few decades now by requiring retailers to use certified cash registers that have tamper-proof memory units. These are variously known as a fiscal control units, electronic tax registers, or fiscal tills. These tills are designed in such a way that any attempt on the part of the retailer to break into its memory using a zapper or some other technique will be discovered. Additionally, these units have the potential to be connected directly to the tax authority, allowing for instantaneous transmission of sales data and constant real-time tax auditing. That sounds a bit intrusive, no?

Below is a chart from the IMF showing nations that have implemented fiscal till plans:

Source: IMF, Electronic Fiscal Devices, 2015

Progressing to the next stage of the cat and mouse game, retailers will try to evade tamper proof memory units in the cash register by making recourse to the first weak point in the sales process; not entering the transaction into the cash register in the first place. Recognizing this, the tax authorities who have implemented fiscal till schemes have made it illegal to not issue a sales receipt. But illegality doesn't seem to me like a big hindrance to a retailer who has already set their mind on evading taxes.

One neat trick to get retailers to provide receipts—and therefore run all transactions through the tamper-proof cash register—is to recruit the customer into the cat and mouse game as helper. Public information campaigns exhorting people to ask for receipts are one technique. But the more interesting trick is implementing a tax-receipt lottery. All invoices issued from the tamper-proof cash register come with a unique lottery number. Anyone who keeps their invoices will be able to participate in a periodic lottery. Customers thus have an incentive to ask the retailer for a receipt, obliging the retailer to run the transaction through the fiscal till.

Taiwan implemented the first tax receipt lottery back in the 1950s, the Uniform Invoice lottery. I've included a picture below, and here is the website. In the last fifteen years, a number of nations have begun to copy it including Czech, Slovakia, Slovenia, Malta, Portugal, Poland, China, Sao Paulo, and Lithuania.

Taiwan sales receipts with lottery numbers on them

The next stage of the cat and mouse game occurs as the retailer, desperate to adapt to the government's crafty invoice lottery, tries to coax the customer over to his side. On a $50 meal, a restaurant may be able to save $2.50 in tax (assuming a 5% tax rate) if the the fiscal till is avoided. If the restaurateur says that he will share some of this savings with the customer, he may be able to induce her to not ask for an invoice and thus avoid the till. The amount of money he must dangle in front of her will have be large enough to compensate her for the foregone fun of playing the lottery, potential lottery winnings, and guilt.

China is the most interesting example of the cat and mouse game being played at this level. To incentivize cash-paying customers to ask for invoices, or fapiao, the Chinese authorities have created a scratch and win game. Restaurateurs have reacted by offering customers a free soda, or a discount, if they don't ask for the fapiao. Presumably the value of a soda is just sufficient to compensate the customer for foregoing the lottery. More entertaining accounts of fapiao here and here. 

I'm sure these methods of attacking tax avoidance work to an extent. In Québec, for instance, as of March 2016 the tax authorities say that they have recovered CAD$1.2 billion in taxes following the introduction of fiscal tills in the restaurant industry. However, I'll hazard that the biggest determinant of tax avoidance is good government. If people trust the government to do smart things with tax revenues and they don't see evidence of corruption, then they will be more likely to view paying taxes and reporting on cheaters as one of their public duties.

---

Other sources:
OECD: Technology Tools to Tackle Tax Evasion and Tax Fraud (link)
Ainsworth: Québec’s Sales Recording Module (SRM) - Fighting the Zapper, Phantomware, and Tax Fraud with Technology (link)
Steenbergen: Reaping the benefits of Electronic Billing Machines (link)

Aggressive demonetizations

Prime Minister Narendra Modi surprised Indians today by announcing that India's highest denomination notes, the 500 and 1000 rupee, will cease to be legal tender. On first blush, India seems to be enacting Ken Rogoff's idea of cutting down on criminality and tax evasion by phasing out high-denomination notes, which I recently discussed here.

But this isn't the case. Rather than removing the Rs. 500, the Reserve Bank of India is replacing it with a new bill. Furthermore, it will also be issuing a Rs. 2000 note, a new highest denomination note. What India is doing is enacting what I'll call an aggressive demonetization. I'd argue that this is an alternative (though not mutually exclusive) idea to Rogoff's. Both schemes are intended to create a logistical nightmare for money launderers; but whereas Rogoff's entails altering the denomination structure of banknotes to get this effect, Modi's aggressive demonetization keeps that structure intact while using note redemption and re-issuance as its lever.

Demonetizations are usually non-aggressive drawn-out affairs. For instance, when Canada announced that it would withdraw its $1000 note, it gave Canadians an eternal window to bring them in for redemption. The $1000 remains legal tender in Canada, meaning that it can be used to discharge any debt. As another example, take the euro. The introduction of the euro meant an end to all the national European currencies. While each of these currencies lost legal tender status in 2002, many enjoy an unlimited time frame for conversion into euros, including the Deutsche mark and Belgian franc. See below:

India's demonetization is an aggressive one because legal tender status is to be removed immediately and the time limit for redemption is incredibly tight and scripted. Here is Modi's announcement:

All details on the announcements made today can be found here. https://t.co/UoiCjCyupV #IndiaFightsCorruption pic.twitter.com/WKpgsdTcjg

— Narendra Modi (@narendramodi) November 8, 2016

To summarize, Indians have just a few weeks to exchange old notes for new ones at banks or post offices. Proof of ID is required and switches are limited to Rs 4000, around US$60. There is no size limit for directly depositing old notes in bank of post office accounts. But of course, this means that the depositor's identity will be known by the bank and transactions will be traceable. Deposits can be made at banks until the end of the year. After that date, the central bank will exchange old notes until March 31, 2017, although this will require some sort of declaration of origin.

The point of all this is to suss out anyone with large amounts of cash that has been earned from dubious sources. Say you've got one million paper rupees, worth around US$15,000. If you've got the receipts to show why you have that much cash, then you can safely bring it to the bank. But if you don't, you'll have to get rid of it as quick as you can by spending it, say on gold (or any other good). However, this will be an incredibly difficult task given the fact that there will be many other Indians trying to spend their undocumented Rs. 1000 and Rs. 500 notes on gold at that very same time, and only a limited number of gold dealers willing to accept them. After all, any gold dealer who accepts notes now inherits the same problem: what to do with newly-demonetized banknotes. Any gold dealer who starts to bring in larger-than-normal amounts of paper money to their bank for redemption will surely face questions. To compensate for this risk, gold dealers will either impose a large penalty on cash payments or they'll stop accepting cash altogether.

Some undocumented rupees will no doubt be successful in evading Modi's aggressive demonetization, but large quantities will be left stranded. Significant damage will have been dealt to anyone working in the underground economy.

As Tony Yates points out, the most aggressive demonetization in history was probably Saddam Hussein's recall of the Swiss dinar in 1993. Swiss dinars were Iraqi banknotes printed on high quality paper whereas dinars printed after the 1992 U.S. invasion were issued on shoddy and easily counterfeitable material. On May 5, Saddam announced that all Swiss dinars had to be turned into the central bank for an equivalent amount of post-war currency over a tiny six day exchange period. He then proceeded to close the border, preventing Kurds and other foreigners from making the switch. Huge amounts of currency was left stranded, although unlike the Indian situation it was foreigners, not criminals/tax evaders, who were the target. (I went into the Iraq story here. The Burmese kyat and North Korean won demonetizations of 1985 and 1999 were also quite awful, see here.)

If you think Modi's strategy is new, or confined to developing nations, think again. A few years ago, Sweden carried out out a (somewhat less) aggressive demonetization in order to catch illicit cash users. In 2012, the Riksbank announced that all  1000 krona banknotes without foil strips were to be declared invalid by the end of 2013 (each 1000 krona note is worth around $110). Until December 31, 2013, Swedes were permitted to get rid of 1000 krona notes by either using them to buy stuff or depositing them at a bank. To tighten the noose, no anonymous conversions of old notes into existing notes were permitted. Swedes had to have bank accounts, and therefore had to forgo their anonymity, in order to rid themselves of old currency.

Anyone who's seen Breaking Bad knows that laundering money takes time and patience. A Swedish criminal with ten million dollars worth of high denomination krona was suddenly faced with a significant problem; how to get this stash back into the legitimate economy within 400 or so days.

How tough was this challenge? We know that at the start of 2013 there were fourteen million 1,000 krona notes in circulation (worth 14 billion SEK, or US$1.6 billion). After the expiry date, the Riksbank noted that there were still some three million 1,000 krona notes that had not been redeemed, worth around $330 million. This gives a rough indication of the value of banknotes left stranded by criminals and tax evaders, around 25% of all notes outstanding.

After the December 31, 2013 deadline, the Riksbank itself offered to redeem invalid banknotes (it still does), albeit for a 100 krona fee. However, criminal and tax evaders have no doubt steered clear of this offer as the declaration form includes the following question:

Sweden is the only country in the world in which cash holdings are in decline. Might this have had something to do with the damage inflicted by the Riksbank's 2013 demonetization on the psyche of participants in the underground economy?

So let's compare the advantages of Modi's aggressive demonetization to Rogoff's abolition of high denomination notes. If an aggressive demonetization is chosen, then a central bank gets to enjoy high profits, or seigniorage, since it continues to issue an extended range of banknotes, unlike Rogoff's abolition. The more float, or 0% cash liabilities that remain outstanding, the more interest the central bank will earn on its bond portfolio. The central bank also earns significant earnings from 'breakage.' All illegitimate banknotes that never get redeemed are recognized as a one-time unusual gain on the central bank's statement of income. Finally, people engaging in legal activities who enjoy the anonymity afforded by high denomination notes still get to use them; they don't under Rogoff's abolition.

Unfortunately, an aggressive demonetization can only be effective for a little while. It's hard to see why people won't quickly re-adopt the highest denomination note as a medium for evading taxes and engaging in illicit activity. In response, the central bank will have to enact an followup demonetizations every few years, but of course the underground economy will do its best to anticipate these by moving into low-denomination notes or foreign paper whenever it suspects something is afoot.

To create a logistical nightmare for money launderers, maybe Peter Garber's idea beats Rogoff's abolition and Modi's demonetization?:

"Why not simply increase the physical dimensions of high-denomination notes without jumping through the flaming hoop of elimination? Before 1929, U.S. currency was 40 percent physically larger than it is now. Restoring that size or making it even larger would instantly work the wonders of decades of inflation. The iron law for subverting illicit economies: a percentage increase in physical note size is equivalent to the same percentage increase in the price level."

Thoughts on Rogoff's 'Curse of Cash'

The US$5000 banknote, destroyed in 1969 along with the $10,000, $1000, and $500 notes

With the publication of his new book The Curse of Cash, economist Ken Rogoff has ignited a big debate over the future of paper money. Both the book, which is packed with information and accessible to a mainstream audience, and Rogoff's series of blog posts are well worth reading, even if you already disagree with his premise that the way the world currently handles cash needs to be modified.

The key observation motivating Rogoff's book is this one: with $1.3 trillion worth of U.S. currency in existence, a back-of-the-envelope calculation says that the average four person family should be holding around $16,800 in cash. However, this simply doesn't reflect the personal experience of most Americans. Indeed, 2012 survey data shows that consumers generally report holding just $56 per person, leaving the majority of cash unaccounted for. Nor is this anomaly confined to the U.S. Given $78 billion in Canadian currency outstanding, a four person family in Canada should hold around $6,000. Instead, survey data shows the average person only holds a median $38 in their wallets. The same pattern occurs in Europe, Japan, Australia, and elsewhere.

According to Rogoff, much of the unaccounted cash is being held by those who participate in the underground economy, both by those engaged in criminal activity and those employed in legal activity (dentists, contractors, retailers, etc) who use cash as a way to avoid taxes. Rogoff's premise is that if we can alter the institution of cash, then maybe we can flush some of these people out of the underground economy and back into the legal, tax-paying economy.

The denomination structure of cash

Having read through many of the criticisms that Rogoff has received over the last few months, I've noticed that there is a tendency on the part of his opponents to frame this debate as an either/or one. Either keep cash and the personal liberty it provides—anonymity and uncensored access to the payments system—or sacrifice cash and in the process throw out that liberty.

This mischaracterizes the debate. Rogoff isn't advocating an end to cash or the liberties that go with it. Rather, he wants a modification of the existing denomination structure of banknotes such that the $100, $50, and $20 are removed while the $1, $2, $5 and $10 are left in circulation. Over the long-term, he proposes replacing these small bills with heavy coins. The set of personal liberties afforded by cash will be allowed to live on, albeit through the reduced convenience of small banknotes like the $10.

The term denomination structure refers to the top and bottom-most denominations issued by the monetary authority, the spacing between denominations, and the point at which the transition between coins to notes begins. As per Tyler Cowen's second law ("There is a literature on everything"), academics have been writing on the topic of optimal denomination structure for a few decades. The goal of this literature is to find the range and spacing of notes/coins that reduces the amount of monetary work that all participants in a currency system must engage in. By monetary work, I mean the effort that goes into printing money, carrying it, storing it, counting it, making calculations with it, paying with it, and breaking it into smaller amounts. If a denomination structure can be found that allows everyone do a little bit less work, society is much better off.

Rogoff takes the opposite approach. His abolition of large denomination banknotes is designed to increase rather than reduce the amount of monetary work that users of cash must engage in. After all, ten thousand dollars worth of Rogoff's preferred highest value note—the $10 bill—requires far more effort to count, store, and lug around than a hundred $100 bills.

Rogoff believes that the increase in monetary work brought about by a reduction in the purchasing power of the highest value note can be a useful filtering mechanism for improving societal welfare. Assume that there are "bad" and "good" users of cash, the former being criminals and tax evaders and the latter being regular people who want to enjoy the speed, anonymity, and convenience of paper money. "Good" cash users only need small quantities of notes from time to time and therefore will only be slightly inconvenienced by the increase in monetary work caused by a constriction in the purchasing power of the highest denomination note. "Bad" users tend to make regular use of large amounts of cash, and will therefore be severely affected by a constriction.

While Rogoff's abolition won't stop crime or tax evasion, it will surely make these activities trickier. This should in turn push activity out of the non-taxed underground economy into the legal economy.

Burdening cash is the status quo policy  

These ideas aren't entirely novel. In fact, I'd argue that since the 1800s, the U.S. has been implicitly adopting Rogoff's strategy of increasing the amount of monetary work involved in using cash. The chart below illustrates both the nominal and real value (in 2015 dollars) of the U.S.'s highest denomination banknote going back to 1871.

In general, the purchasing power of the highest denomination note has been gradually declining. This has been mostly due to the fact that even as inflation erodes the dollar's value, American monetary authorities have chosen to avoid introducing new higher value notes. Nor is the U.S. unique in this respect. Correct me if I'm wrong, but I can't think of a single developed nation that has introduced a higher denomination note over the last fifty years.

In the U.S.'s case, the decline in the purchasing power of the highest denomination note hasn't been entirely due to the combination of inflation and a lack of new large value U.S. notes. Take a look at what happened in 1969. Throughout the 19th century the U.S. Treasury was an issuer of $10,000 certificates, a practice the Federal Reserve would continue after its founding in 1913. However, on July 14, 1969 the Fed announced that it would put an end to this tradition by destroying all $10,000, $5000, $1000, and $500 denominations, leaving the $100 as the U.S.'s largest denomination. It did so on the very same day that Richard Nixon launched his famous war on drugs. Although the Fed claimed that its decision was motivated by the declining usage of large value banknotes over the previous two decades (PDF pg 624), the timing indicates that Nixon's crime push must have been a big reason.

So largely through a policy of benign neglect (i.e. by passively allowing inflation to eat away at its purchasing power), the U.S. along with most developed nations have been gradually increasing the workload involved in using the highest value note. Assuming inflation of 2%, by 2095 or so the US$100 will buy as much as the $20 does today. By 2130, it will buy as much as the $10 does today.

Rogoff isn't content with the gradual approach to increasing monetary work. He wants to add a one-time increase in the level of monetary work involved in using cash. This would involve a quick Nixon-style "tightening" of the filter, removing in one fell swoop all denominations above the $10 bill. Put differently, rather than waiting till 2130 for the $100 bill to be worth $10, he wants this event to happen now. Once a Rogoff-style high denomination notes abolition has been carried out, inflation will once again determine the rate of increase in the monetary work involved in cash usage.

So ultimately, the great cash debate isn't about cash vs. cashlessness. For decades developed nations have been gradually increasing the burden of using banknotes. Should we stick with the status quo or speed things up a little?

The case of Sweden

Rogoff makes one mistake in his book. As many people may know, Sweden is the only nation in which cash usage is in decline, a precedent Rogoff wants other nations to emulate. Several times in his book, Rogoff mentions that the Swedes have removed their highest denomination note, the 1,000 kronor, and that this removal helps to explain the nation's dramatic drop in cash usage. But this isn't the case. All that the Riksbank did was replace the old 1,000 kroner note in 2013 (which had Gustav Vasa on it) with a new Dag Hammarskjöld version. The 1,000 is still alive and kicking.

This puts Rogoff in a somewhat uncomfortable position. Some other policy than the one he prefers is at work in the very country he puts forth as an example for all to follow. I think I might know what this policy is. As discussed in this excellent post by Martin Enlund, the Swedes implemented a tax deduction in 2007 for the purchase of household-related services such as the hiring of gardeners, nannies, cooks, and cleaners. 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.

Enlund's chart shows how the decline in krona outstanding closely coincides with the timing of the introduction of RUT and ROT:

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 claim their tax credits, many of these transactions would have been pulled into the open. Note the rise in RUT and ROT payments on Enlund's chart, for instance. Calleman reports that  the number of customers using registered domestic service companies rose from 92,000 in 2008 to 537,600 in 2013. Since the implementation of RUT and ROT, Swedish opinions on paying for undeclared work have changed dramatically. In 2006, 17% said it was completely wrong to to hire undeclared labour. In 2012, 47% felt it was completely wrong.

Using data from a survey of the general public conducted by the Swedish tax authority, the charts below show how much knowledge Swedes have about those around them engaged in tax evasion. In the bottom chart, the number of Swedes who are aware of businesses that are evading taxes has fallen from 27% in 2007 to just 9% in 2013. That is an especially large and fast decline. As the tax authority points out, RUT and ROT is the likely explanation.

Rogoff himself maintains in The Curse of Cash that the largest holdings of cash in the underground economy are due not to criminals but those engaged in legal work (like contractors) who are avoiding taxes. By cutting down dramatically on tax evasion among those engaged in household services and repairs, the RUT and ROT deductions may explain a significant chunk of the decline in Swedish currency in circulation.

This post has gone long enough, so let me get to my final point. I agree with Rogoff's general point that it makes sense to burden cash users with ever more work since this burden disproportionately falls on heavy users like criminals. But Rogoff hasn't yet convinced me that the status quo policy of gradually increasing the workload involved in cash usage (via inflation) needs to be sped up by a sudden removal of every bill above the $10. After all, the Swedes are setting an example of how a policy of gradualism can be twinned with tax policy in order to get some of the very effects that Rogoff advocates, namely pulling people out of the underground economy into the legal economy.

Is the Swede's approach better than Rogoff's high denomination note abolition? I'm not sure, I don't know enough about the economics of tax policy to arrive at a firm conclusion. But it seems to me that a more complete analysis of the real reasons for Sweden's cash miracle needs to be conducted before we go about killing the $20, $50, and $100.