The Astonishing Case of the Impenetrable Zero Bound

By Dan Kervick

In a small, peaceful town there once lived three people: Abbie, Baker and Carlie.

Abbie was a very wealthy aristocrat, and also a philanthropist.  Her fortune and position in the town were the fruit of the hard work of her ancestors, but her life was dedicated now only to managing that fortune.  She lived to make the common people of the town happy, especially Carlie, who was her personal favorite.

Baker was much more selfish, and looked out for his own interests.  He wasn’t terrible and mean, just obstinately self-interested.  It seems he was born that way; it was in his DNA.

Abbie frequently lent money to Baker, and Baker frequently lent money to Carlie.  But in accordance with the ancient and venerable laws of the town, enacted to maintain a decorous distance between the aristocrats and common people, Abbie was forbidden from loaning money directly to Carlie.  Nevertheless, Abbie was usually able to help out Carlie indirectly when necessary.  She found that when she lent money to Baker, Baker was sometimes more willing than before to lend money to Carlie.  And if Abbie loaned the money to Baker at lower rates of interest than previously, Baker would usually reduce the rate of interest he charged Carlie in turn.

Baker didn’t reduce these rates out of kindness.  (He was selfish after all.)  No, he reduced these rates because Carlie was sometimes willing to borrow money at the lower rate but unwilling to borrow the money at a higher rate.  So he was glad when Abbie loaned money to him at low rates of interest, because then he could loan money to Carlie at a rate of interest that was higher than the rate Abbie charged him, but not so high that Carlie was unwilling to borrow from him.

There were two other lenders in the town: Wells and Bancroft.  They were just as selfish as Baker, but they also loaned money to Carlie and to the other common people of the town.  Whenever Baker tried to charge Carlie too much, Wells and Bancroft would espy an opportunity.  They would immediately borrow money from Abbie and then offer Carlie loans at a lower rate of interest than the one offered by Baker.  Opportunities for loaning money to townsfolk like Carlie were limited, so none of the three could make very much money if they didn’t compete aggressively to offer the lowest possible interest.

Sometimes Carlie or one of the other commoners had a little bit more money than needed to meet immediate expenses.  They would then ask Baker, Wells or Bancroft to hold the money for them.  The main reason they did this, instead of holding onto the money themselves, is that Baker, Wells and Bancroft were willing to pay Carlie and the others for the privilege of holding onto their money.  And the reason they were willing to pay for that privilege is because they could then lend that money to other people.  Suppose Carlie had a thousand dollars she was willing to give to Baker for one month, and suppose Baker knew someone who was willing to borrow those thousand dollars from him for three weeks at 5% interest.   Then as long as Carlie was willing to accept less than 5% from Baker for allowing him to hold her money for a month, Baker could make money on the three-party transaction.

Abbie was enamored of this whole system.  It was time-honored, and she thought it worked beautifully.  When Carlie needed more money, Abbie could get it to her by reducing the rate of interest she charged Baker, Wells and Bancroft.  And if Carlie was growing a little too exuberant and carefree, as she sometimes did when things were going well for her, Abbie would temporarily increase the rate of interest she charged Baker, Wells and Bancroft.  This would make it harder for Carlie to borrow money.  Abbie didn’t like to do this, but she knew it was sometimes for Carlie’s own good.

Then something very strange happened.  Abbie heard that Carlie needed more money, and Abbie responded by reducing the rate of interest she charged Baker and the others.  But Baker didn’t make any more loans to Carlie.  So Abbie reduced the interest rate further.  But Baker still did not make any more loans.  Finally she reduced the interest rate lower than it had ever gone before: ¼ of one percent for a one month loan.   But Baker still did not make any more loans.

Flustered and perplexed, Abbie invited Baker to her office to find out what was going on.  Baker explained, “Well, for one thing, it costs me money just to run my loan business.  So even though you charge me only ¼ of one percent, I still have to charge Carlie significantly more than that to stay in business.”

“But also,” Baker continued, “Carlie doesn’t seem to want to borrow money right now at even my lowest rate.  She’s afraid she won’t be able to pay me back.  And to tell you the truth, I’m also afraid she won’t be able to pay me back.  She doesn’t have a job right now.  So even on the days when she does want to borrow money from me, I don’t want to lend it to her.  She will spend the money I lend her, I fear, but have no way off earning enough to pay back even the principle of the loan.   Wells and Bancroft say the same thing.”

“Well, can’t she pledge something else to you,” asked Abbie.  “Something she already owns?  You and Carlie can agree that if she is unable to pay back the money, then you can take the things she has pledged.”

“She has already done that to some extent,” said Baker.  “She has even pledged her house to Wells.  But Carlie isn’t very well-off, to tell you the truth.  She doesn’t have much of value left to pledge, and what she has is very valuable to her and so she does not want to risk losing it by pledging it.”

After Baker left the office, Abbie thought and thought and thought.  “There must be some way around this problem,” she thought.   Finally she hit on it: she would just have to give money to Baker.  Then Baker would be willing to give money to Carlie.  If Baker gave Carlie less money than Abbie gave Baker, then it stood to reason that Baker could still make money on the total transaction.

And money was no object for Abbie, because she had virtually unlimited stocks of money.  Although not everyone realized it, Abbie owned the town’s money-printing machine, and could manufacture as much money as she needed at virtually no cost.  The only reason that she did not print unlimited quantities of money for the town was that experience had convinced her that increasing the amount of money available in the town at a faster pace than the town’s economy was growing would generally just raise the prices of everything without helping anybody.    So limiting the amount of money printed during any period of time was the best way to make sure the prices of things remained relatively stable.  This made it easier for people to make deals with one another in which one party to the deal would deliver some good or service right away in exchange for some promised quantity of money to be delivered later by the other party.  If people didn’t know how much the town’s money would be worth in the future, it would be harder for them to make those deals.  So Abbie considered the stabilization of prices and the prudent control of the supply of money to be part of her role as the town’s chief philanthropic benefactor.

But things were very bad right now, so Abbie had decided that she would just have to give Baker some money.  Abbie also decided that, for the sake of propriety, she wouldn’t say she was giving the money to Baker.  Instead she would say she was charging him negative interest.  She would charge Baker -5% interest for a one month loan.  If Baker borrowed $10,000, then a month later he would have to pay back $9,500.  He would thus make $500 on the transaction.  He could then give free money to Carlie.  Maybe he would loan her the $10,000 of borrowed money for one month at -4% interest.  Carlie would then pay him back $9,600 one month later.  Baker could then pay Abbie the $9,500 he owed her and still make $100.

Abbie called Baker to inform him of the new arrangements.

“Excellent!” he said.

“So, how much money would you like to borrow?” Abbie asked.

Baker replied, “Oh, for a start, let’s say

$1,000,000,000,000,000,000,000,000,000,000,000.”

He actually had to write this number down, because it contained so many zeros that neither he nor Abbie knew the English word for the number.   Abbie realized she would have to revise her plan and asked Baker to come back the next day.  After pondering the matter a bit, she hit on a solution.  The next day, when Baker returned to the office, Abbie offered the new terms:

“You may borrow for one month at -5% interest,” she said, “but there is a $10,000 limit on the amount you can borrow each month.  How much would you like to borrow today?’

“I would like to borrow $10,000,” said Baker.

“Fine,” answered Abbie.

A month passed, during which time Abbie congratulated herself on the ingenious beneficence of her plan.  The town was surely blessed to be guided by enlightened aristocrats like her, with advanced ideas about the proper role of money in society.   One month later, Baker returned to her office, and repaid the $9,500 he owed.  “Outstanding,” Abbie said, “and how much did you lend to Carlie?”

“Nothing,” Baker replied.  “Why should I have loaned any money to Carlie?”

“That was the whole point,” Abbie said, with a touch of aristocratic pique in her voice.  “You could have loaned Carlie money at negative interest, just like I did for you, and still have made a profit.  If you had loaned at -4%, you still would have made $100.”

“True enough,” answered Baker.  “But I profited even more by not lending her money at a negative interest rate.  I made $500 instead of $100.  No matter what rate I charged Carlie, so long as it was negative I would have made less than $500.  And Carlie won’t borrow money at a positive rate of interest.”

“But my dear Baker,” continued Abbie, “Wells and Bancroft did loan money to some of the common people.  I have spoken to them about it, and they behaved exactly as I expected, loaning money to the townsfolk at -4% interest, and thus making a 1% profit on the total transaction.”

“Yes, I spoke to them about it,” smirked Baker.  “They said, ‘You fool Baker, we undersold you again!  We were able to get people to take loans at the extremely low rate of -4% thanks to these -5% loans we’re getting from Abbie.  We made a profit of 1% on each loan!’ “

“But I explained to them that they were idiots, and that I made much more money – by borrowing from you at negative 5% and not making negative interest loans – than they had made by borrowing from you at negative 5% and making negative interest loans.   They grasped my point immediately, so I don’t think they will be lending out any of the money you give them again, not unless they can they can get a positive rate of interest from the borrower.”

Abbie realized that she would have to rework the plan again.  The problem seemed to be that, with a negative interest loan from her, Baker could make money simply by holding onto the money she had lent him.  So she considered charging Baker a holding fee for the money, so that he couldn’t profit on her loan to him.  She would charge him a percentage of the quantity loaned for each day he held onto it.

But she quickly realized that made no sense.  The holding charge was nothing but an adjustment to the interest rate.  If she loaned him the money at -5% per month, but then charged him back 4% per month for the money as he held onto it, that was no different than a -1 % interest rate with no holding fee.  If she charged him 6% for holding the money, that would be no different than a 1% interest rate.  The holding charge did nothing to get around the fundamental problem.  Somehow she needed to give Baker a negative overall interest rate, so that he could give a negative overall interest rate to Carlie and still make money.

She realized what she wanted to do was charge him for holding the money himself, but also let him avoid the holding charge if he lent it to Carlie.  “Aha,” she thought.  “I will loan Baker the money at -5% and put the money in a special metered box.  I will then charge him 5% per month for keeping the money in the box.  However, the interest rate is reduced by the amount of time the money is absent from the box. If the money is in the box for only 1/5 of the time during the month, for example, the total holding charge would be only 1%.”

Abbie tried this, but the problem was immediately apparent.  Baker took the money out of the box and put it in his desk drawer.  He avoided the holding charge in this way, but still did not lend any money to Carlie.  Then he paid the amount he owed to Abbie at the end of the month, and earned the entire $500 profit for himself.

Growing somewhat less rational as her frustration increased, and more determined than ever to exercise control over what was happening, Abbie first thought that she must somehow force Baker to keep the money in the box instead of putting it in his desk drawer to avoid the holding charge.   But she quickly realized that approach only returned the situation to the previous one: the holding charge was just an adjustment to the interest rate.  Also, if Abbie forced Baker to hold the money in the metered box, what was he supposed to lend to Carlie?  She was reasoning in circles.

Abbie thought extremely hard about this problem.  She consulted the works of great economists, philosophers and financial geniuses throughout history who had studied the problems of money, interest and exchange.  She also reflected on the advice of her father, who had once told her, “If you are failing in your job as an aristocrat, try an approach that makes things more complicated.   If you succeed, that will be wonderful, but if you continue to fail then people will have to spend so much time just figuring out what is going on that at least your failure will not be so apparent.”

At last she devised a plan.  The plan was comprehensive in scope, and would require the involvement of all three lenders, Baker, Wells, and Bancroft.  She summoned them to her office.

“I will assign a box to each one of you,” Abbie began, “and post an executive assistant to watch over the boxes.   The owner of any one of the boxes may only remove money from that box to transfer it to another box.  My assistant will supervise the transfers.  You may make whatever deals you like among yourselves to bring about these transfers. “

Abbie continued, “The boxes will be metered, and the owner of each box will be charged for holding money in a box, at a rate of 5% per month.  The primary way any one of you can avoid these charges is to succeed in getting money in your box moved to another box.”

“And what, then, are we supposed to lend to the common people such as Carlie?” asked Baker.

“I am giving you these signed credit vouchers,” replied Abbie.  “Each one is good for a certain quantity of dollars, and also specifies which box the dollars are held in – Baker’s box, Wells’s box, or Bancroft’s box.  You may give these to the townspeople in exchange either for actual dollars, or for their promise to give you some other number of vouchers in the future.  Although none of you is permitted to remove money from any of the boxes, my assistant will be authorized to remove money and transfer it from one box to another if you present him with the appropriate voucher. ”

“For example,” continued Abbie, as her listeners strained to listen and follow, “If Carlie has a voucher that represents $100 held in Baker’s box, and gives that voucher to her friend Carl in exchange for something else, Carl might then take that voucher to Wells.  Wells might be willing to give one of his own vouchers to Carl in exchange for the Baker voucher, but instead of giving Carl a Wells-voucher with the same face value as the Baker-voucher, Wells will probably give Carl a little bit extra, just as he now pays Carl for the privilege of holding onto his regular dollars.  Wells can then take the Baker-voucher to my assistant, who will transfer the number of dollars indicated on the voucher from Baker’s box to Wells’s box.”

“But since the common people have no vouchers right now, and are rather poor and short on dollars, how will they acquire enough vouchers or dollars to pay us back for loans of vouchers we make to them?”

“Well,” said Abbie, with a self-satisfied smile spreading across her face, “You can lend them the vouchers at negative rates of interest!  Since I am lending you dollars at negative interest, you can still make a profit that way.”

Baker, Wells and Bancroft looked at one another, with blank and searching expressions.  They squinted.  Then they grinned and shook their heads just slightly, rolled their eyes and left the meeting room to begin working with this complicated new system.

Abbie soon realized that despite the nearly byzantine complexity of the system, and its innovative audacity, nothing fundamental at all had changed.

First, suppose she charged a -5% rate of interest on the loans and a 4% holding fee for holding money in one of the boxes.  She realized that because the money could only move around among the boxes but was always in some box or other, then the situation was no different than if she were working with only one lender and one box.   If the money was loaned out for a month, then the whole system of Baker, Wells and Bancroft had effectively borrowed it at -1% per month.  And that system, as a whole, made money by holding the money in the boxes collectively, rather than lending it out via the new voucher system.  And if the holding fee was such that the effective borrowing rate was positive, then they were right back at the starting point.  The system of lenders as a whole wouldn’t want to borrow from Abbie, since the townspeople were unwilling to borrow from the lenders at a rate that would make positive interest loans from Abbie profitable.

The vouchers were really just ownership claims on the money in the boxes.  Whether the three lenders loaned money to Carlie by giving her actual dollars, as they had in the old system, or by giving her claims on their store of dollars held in the boxes, as in the new system, the underlying logic of the situation  was the same: lending money at negative interest is the same as giving money away.  And there was no circumstance under which the three lenders benefited, either individually or as a group, by giving money (or claims on their money) away for free.   It didn’t matter whether Abbie was giving them money for free as well.  Since Baker, Wells and Bancroft were selfish, then no matter how much free money Abbie gave them they would only end up with less than that amount if they also gave some portion of that money away for free to Carlie and her fellow townsfolk.

It was at this point that Abbie had a sort of revelation.  She hoped it wouldn’t turn out to be just as delusional a revelation as some of the previous revelations.  The revelation was this:  the fundamental problem here was that her transactions with Baker were too independent of Baker’s transactions with Carlie.  Baker was a profit-seeker, and all the choices were in Baker’s hands.  Baker could choose to borrow or not to borrow from Abbie on whatever terms Abbie was offering.  As far as those transactions were concerned, Baker could take them or leave them.   Similarly, Baker would them decide whether to offer Carlie a loan at whatever rate he wished, and Carlie could then take or leave those offers.  But because these decisions were independent, and because Baker’s ability to take the loan from Abbie, or not take the loan, had nothing to do with whether or not he made a loan to Carlie, then there was never a circumstance in which making the negative interest loan to Carlie made sense for Baker.

Suppose X were the loan transaction between Abbie and Baker and Y were some negative interest loan transaction between Baker and Carlie.  Then clearly Y alone, considered only in itself, loses money for Baker.  So what about X and Y together?  Would the combined transaction X+Y be profitable for Baker?   It might be, but that would depend on the terms offered by Abbie to Baker and the amount of negative interest offered by Baker to Carlie.  But one thing was obvious: Since Baker lost money on Y alone, considered only in itself, then if Baker made money on the transaction X, he would make less money from X+Y.  And if Baker lost money from X alone, then he would lose even more money from X+Y.   No matter what happened between Abbie and Baker, there is no way Baker came out ahead by making the negative interest loan to Carlie.

The only solution would be for Abbie to offer Baker profitable terms on her loan to him, but make his ability to obtain these terms contingent on whether or not he offered terms to Carlie that were acceptable to Abbie.

So Abbie’s next innovation was this: Baker, Wells and Bancroft would still operate with the system of vouchers and boxes set up previously, but they would now also be given a collection of official loan affidavit forms on which they could inscribe the terms of any loans they made to any of the townsfolk.  The affidavits needed to be signed by both the lender and the borrower, with the amount of the loan, the interest rate on the loan, and the length of the loan clearly indicated.   The lender could then take one of these signed affidavits to Abbie, and then – only then – would Abbie make a negative interest loan to the lender.  Abbie would offer a rate 1% lower than whatever rate the lender had given to Carlie or one of the other townsfolk.   If Baker made a 30 day loan to Carlie at -4%, then when Baker presented the loan affidavit Abbie would give Baker a 31-day loan for -5%.  After Carlie had paid back Baker, Baker would then pay back Abbie, but still make a 1% profit.  But Baker had to make a loan to Carlie first in order to get the loan from Abbie, so he no longer had the option of making an independent transaction with Abbie and then foregoing a transaction with Carlie.

In practice, this is how it worked: Baker didn’t need to obtain a money loan from Abbie first, before making a loan to Carlie, because he had the vouchers to give out.  So he would lend Carlie $10,000, for 30 days at -4% interest, by giving her 100 vouchers with a face value of $100 each.   Carlie and Baker then filled out the affidavit and signed it, indicating these terms.   Baker would take the affidavit to Abbie’s assistant, would would verify it, and move $10,000 from Abbie’s money box to Baker’s money box.  The terms of this loan were -5% for 31 days.   Carlie would spend $400 of the vouchers she had been given, and save the remaining $9,600 worth of vouchers.   At the end of 30 days, she would give Baker those $9,600 worth of remaining vouchers, completely discharging her debt to Baker.  Baker would then go to Abbie’s assistant the next day and authorize a transfer of $9,500 from his box back to Abbie’s box.

Baker might end up initially with $500 more in his box than he had before.  But the $400 dollars Carlie wasn’t required to pay back would have been spent around town among the townsfolk.  As before, that would result in money being transferred from Baker’s box to some other box.  Even if it weren’t transferred, he always knew it might be at any time, so did not count those sums as part of his own profits.  His profit was the $100 extra that would remain in his box no matter what.  He could then spend that money on things for himself, if he liked, by paying for the things he wanted with his vouchers.

It worked!  Baker, Wells and Bancroft began loaning money to the townsfolk at negative interest, and then applied for loans from Abbie at a rate of interest 1% lower than they had given.  And so long as Abbie limited the total monthly size of the loans she gave out, she could make sure that this lending activity did not overly expand the money supply and lead to instability and unpredictability in prices.

But something had clearly changed in the town.  According to the ancient and venerable laws of the town, Abbie was not supposed to lend or give money directly to Carlie.  But it was clear to both Baker and Abbie that Baker now effectively worked for Abbie, and was delivering money to Carlie as a sort of agent or emissary from Abbie.  Baker was now not much different than Abbie’s assistant.  Baker could charge higher or lower rates of interest to Carlie, but he would always make the same amount of money.  Abbie effectively set Baker’s profit margin, so Baker’s profit was really just a sort of salary that was determined entirely by Abbie.

And Abbie decided that even if the town returned to prosperity, it was probably best that the same system stay in place.  Baker might then loan money to Carlie at 4% interest, and then apply for a loan from Abbie at 3% interest, making his 1% as always.  Abbie could exert direct control on the interest rate Baker charged Carlie by announcing to Baker in advance the bottom limit on the interest rate she would charge him.   And she could modulate the amount Carlie borrowed by telling Baker what the monthly limit on his own borrowing would be.   All in all, the new system seemed to be working, and seemed like it would continue to work in the future.

Then something else went wrong.

Even though Carlie and the other townsfolk appeared to be getting more money now, they were not spending more money.  Their little shops and cafes were rather empty.  The big factories had previously cut down on production because Carlie and her fellow townspeople weren’t buying things.  Because the factories were producing less, they had laid off many workers.  That meant that the townspeople had even less income than before, and there were even fewer people with money to spend in the small shops and cafes.  And things weren’t getting any better.  Abbie was dumbfounded.

Having already abandoned the hoary pretense of the ancient and venerable laws against consorting directly with Carlie and her fellow townsfolk, Abbie decided to invite Carlie directly to her office.  She was sure Carlie would be delighted with this opportunity to meet her great benefactor face-to-face, and would explain what was happening.

“Carlie, my dear friend,” started Abbie, “what is the matter?  Why are you and your friends not spending the extra money I am providing you?”

“We are very happy for the extra money,” said Carlie.  “But, I still have many old debts that are owed to Baker, Wells and Bancroft.  My friends have these debts too.  The interest on those debts is very high, and we can barely keep up with the interest payments.   I have decided to use the extra money to pay down those debts.  Also, I never want to go through this business of high, suffocating debt again.  So even after I have paid the debts down, I don’t think I will ever spend as much as I did before.   I am going to save most of the extra money.”

“Carlie, while I admire your values of prudence and thrift, the money was not intended to be saved.  I wanted it to be spent to revive the businesses in my town.”

“Your town?”

“You know what I mean.  Our town.”

“Well, there are other things you could do.  My new job is very hard, and I am not paid much.  My friends are also not paid very much and their incomes have been going down for years.   Perhaps you could use your influence with the employers in the town to get them to pay us more.   My brother’s job was also very hard, until he got laid off.   He would desperately like to work.  Why don’t you hire him?”

Abbie’s face clouded.  Giving away free money in an emergency as a charitable endeavor was one thing.   That is what philanthropic aristocrats like Abbie did.  For the common people of the town these handouts were acts of grace and mercy from above, for which they should be thankful.  But what Carlie was now suggesting was a more systematic change to the fundamental social order of the town.  Abbie began to harbor suspicions that Carlie was a dangerous radical.

“I really don’t think that is an advisable course of action,” Abbie replied primly.

“Well then,” answered Carlie, “perhaps you could have Baker forgive some of the debts.  He works for you now, does he not?”

Abbie gasped.   The effrontery of this young woman knew no bounds!   Didn’t Carlie realize that the system of borrower and lender, debtor and creditor, bondholder and bondsman, was part of the foundation of the entire social order of the town?  A person who owned a debt owned a claim on the person who had taken on the debt.  That debt was the creditor’s property, and Carlie was therefore suggesting tampering with the iron laws and relations of property itself!  The laws and historically established allotments of property kept each person within his own proper social sphere, performing his assigned social function.   If Abbie disturbed these laws even once, where would it all lead?   Not just to a change in status for a few selfish money-lenders, she feared.  No, the changes could ripple upward to threaten enlightened aristocrats as well!

Abbie curtly dismissed Carlie, and then thought hard about what she must do.  She had to regain control of the situation!   She must revive spending and economic prosperity in the town, but also restore firm social discipline and respect for the social order.

Abbie moved swiftly and took some very bold steps.  She assumed even more complete control of the lending and payment system.   Baker, Wells and Bancroft would now just work for her as odd-job assistants and not make loans at all.  She then set up a system of boxes and vouchers for the townspeople that was very similar to the one she had originally set up for Baker and his colleagues.  Each citizen of the town and each business in the town would now have a box.

She then eliminated the old money of the town altogether.   She adjusted the settings on the money-printing machine to produce money that looked very different from the old money, and in conjunction with the mayor – whose salary she paid – announced a date at which the old money would cease to be valid.  The townspeople were permitted to bring in their old money and trade it in for the new money.  But they had to agree to keep their new money in their assigned boxes.

Each citizen and business was then issued an electronic voucher, and all of the people and businesses in town were supplied with small devices for processing these electronic vouchers.   If someone wanted to buy even so much as a cup of coffee, they would present and swipe their electronic voucher through the payment device owned by the coffee shop.  This would send a signal to Abbie’s assistants to transfer the appropriate amount of money from the purchaser’s box to the seller’s box.   If a business wanted to pay an employee, they had to use the same method.   Even a grandmother who wanted to give 50 cents to her grandson, or a passerby wanted to give a donation to a street musician, had to use this electronic system.

Then Abbie did something else, something that shocked everyone.

She announced that she would begin to charge a fee for holding the money in the boxes.  No one was permitted to hold any money outside the boxes at all, but any quantity of money one held inside the boxes was diminished in quantity by a pre-determined monthly rate.  If the holding rate was 5%, then at the end of each month, Abbie’s assistants would go to each box, and remove 5% of whatever quantity of money was in the box at that time.  Abbie also decided to stop issuing the negative interest loans.  Her expectation was that as people realized their money was diminishing in quantity each day, and that they had no control over this process, they would adopt a “use it or lose it” mindset and begin to spend money faster.  This would revive the economy of the town.

That’s what seemed to happen at first, and there was a slight pickup in business around town.  But then something else happened.   People understood that since Abbie was the sole source of the money they used, and was enforcing the extractive holding fee rule, then the total quantity of money in the town was shrinking every day.  At the current rate of reduction in the supply of money, one year hence there would be just a little more than half of the amount of money that was circulating initially.  And there was a practical limit on the speed at which any existing quantity of money could circulate though the town, so the decline in the quantity of money couldn’t be offset by an increase in the pace at which the money circulated.  As a result, the prices of everything began to fall to accommodate the drop in the quantity of money.  And the more prices dropped, the less eager people were to spend the money they had.  They realized that if they held onto their money, the prices of the things they wanted to buy might be lower the next day, and so they could buy more of those things.

Also, since no one had ever lived in a world with the topsy-turvy rules that Abbie had imposed, they didn’t know how to function in that world.  The confusion and strangeness of the new system, which required calculations very different from the kinds of calculations people were accustomed to making, added to uncertainty and fear, which wasn’t at all good for the economy of the town.

And then people found that they were having increasing trouble paying their debts.  As prices fell, employers received less money for the products they sold, and in turn they pressured their employees to take lower monetary wages.  That wasn’t a huge problem in itself, so long as the wages and prices adjusted at more or less the same rates.  But since the debts people owed were fixed by the contracts they had made in taking on those debts, and since those contracts specified particular amounts of money that never changed, then as the townspeople’s money wages went down, the difficulty of paying their debts went up.  This quickly led to panic and fear of mass bankruptcy.

Abbie also began to learn something about the limits of control from the top.  If Abbie would not supply a stable monetary vehicle for people to use to save their earnings and store the value they had built up, people would create vehicles of their own.  She learned that the townspeople were beginning to barter goods, so that they could avoid trading in Abbie’s bizarre shrinking money.   A $5 jar of jam preserved its value longer than $5 of Abbie’s money.  And when bartering was impractical, people issued IOU’s for various goods.  Soon the IOU’s had taken on a life of their own, and were traded against one another at relatively stable rates according to circulating price lists.

Abbie tried having the mayor declare these IOUs illegal, and sent Baker, Wells and Bancroft – now reduced to the role of mere henchmen – out to find and destroy the IOU’s wherever they located them.  But this solution was impractical.  The three henchmen could never locate more than a fraction of the IOU’s.   And in any case the popular resistance to this draconian step was fierce.  The fact is that people always desire to save some portion of whatever they possess or have earned that is of value, and to convert saved value into a stable medium that they can hold until they are ready to exchange that medium for something else.  And if their saving desires cannot be met in conventional ways, they will find some other ways to meet them.

As people moved away from Abbie’s dollars by fits and starts, and as confusion reigned, the value of these dollars vacillated wildly.  Abbie could see that the deflationary pressure caused by the fact that the quantity of dollars was rapidly shrinking was doing battle everyday with the inflationary pressure caused by the fact that people were moving to IOUs and exhibiting less demand for the dollars themselves.  The monetary situation was now highly volatile, unpredictable and unstable, and economic activity was suffering tremendously as a result.

Abbie was alarmed by the chaos, and realized she was losing control of the situation utterly.  She initially concluded that she would have to restore the negative interest loans so that she could inject money into the town’s economy to offset the money that was being drained away by the holding fees.  But as soon as she reached that conclusion she realized that she had put herself back in a situation that was eerily similar to the situation she had been in when she was charging Baker, Wells and Bancroft both a negative interest rate and a holding fee at the same time.   Either the overall effect of the two rates amounted to charging negative interest for money or the overall effect amounted to charging positive interest for money.  If she offset the bad effects of the holding fee entirely, she would be back in a situation in which she was giving money to the townspeople rather than taking it away.  And when that was going on, the townspeople had responded by not spending rapidly, but by paying off their debts.

The only solution appeared to be to do something about those debts, as Carlie had suggested.   But that solution was very radical, and Abbie was determined not to do anything that would set a dangerous and disruptive precedent by interfering with the iron laws of property and contracts.  Like all of those in the town who possessed a great deal of property, Abbie had been raised to regard property rights and institutions as sacred boundaries in an inviolable natural order.   She dared not interfere with these boundaries.

Abbie decided that a better approach would be to do something about the debts indirectly.   She would turn her policies around in precisely the opposite direction.  She would flood the town with money by offering the negative interest loans once again, and cancel the holding fees.  As the supply of money increased, she surmised, so should prices.  As prices went up, the town’s workers would press for higher monetary wages.  And as their wages went up, it would become very easy for the townsfolk to pay off their debts.

Abbie also realized that to stabilize the currency, she needed to rely on the ancient practice of using the tax code to support the value of the currency.  She had the mayor push through a town income tax that could only be paid with the official town dollars that Abbie issued.  Since the townspeople could not pay their taxes with the unofficial IOUs or with real goods and services, the imposition of the tax caused an immediate surge in the demand for dollars, and people quickly began to move savings out of the IOU’s and back into dollars.  If Abbie had still been inflicting the draconian holding fee on dollars, then the imposition of the tax would have been the last straw for the town.   But now that she was augmenting monetary income once again with negative interest loans, rather than extracting monetary income via the holding fee, the tax was acceptable.  People were even relived because they understood the stabilizing role the tax would play in re-establishing a single uniform currency.

So this is what Abbie tried, and it was definitely a step in the right direction.  But she had failed to account for something.   Many of the people in town were still unemployed.  There were many fewer jobs available in the town’s businesses than there were people in town who wanted to work.  So as prices on goods and services went up, wages did not go up as expected.  Because so many people were unemployed, the town’s workers had no bargaining power.  Businesses were happy to take the higher prices for the goods they sold while keeping their employees’ wages right where they were.  If the workers complained too much, they could always be replaced with some of the unemployed who would be only too happy to take the same job at almost any wage.

So prices went up and wages stayed where they were.  As a result, many people’s standards of living went down.  They couldn’t afford to buy as many things as they could before, and business sales suffered.  Businesses fired even more people as a result in a self-destructive cycle.  Even though the proprietors of these businesses realized what was happening to them, they were trapped.   All of the business people realized that they would all be better off somehow if they all hired more people and produced more things.  Then many more workers would be employed and have more income, and could buy the additional goods that were produced.   Since they would all then be selling more things, the increased sales would justify the costs the businesses had to incur to hire the workers in the first place.  But the problem was that no single business found that it was in their interest to hire more people so long as they couldn’t be sure that all of the other businesses were doing the same thing.  But in their system of private enterprise, no business had any control over what all the others would do, so they couldn’t afford to take that risk.  They were mutually imprisoned by this mutual dilemma.

Needless to say, by this point the town had lost all confidence in Abbie’s management of the economy and her hidebound and paralyzing aristocratic traditions.  While Abbie might have meant well initially and was willing to attempt various philanthropic maneuvers to alleviate the town’s economic problems, she was unwilling to do anything that would challenge the established social order.  She was a defender of the social status quo at bottom, and it was turning out that the social status quo was bad for the town.  And the worse things got, the more determined Abbie grew to control and manage everything.   Nobody but Abbie was permitted to decide what the town’s economic policies would be.   Increasingly, the townspeople couldn’t tolerate the situation.

What was especially frustrating to the town was Abbie’s insistence that only certain ways of attempting to influence the economic life of the town for the better were morally and socially permissible.  Abbie was only willing to adjust interest rates and holding rates up and down as she deployed her money machine, but she was unwilling to use her monetary power to participate in the economy in other more direct ways to fix what was broken.   Abbie struck them as something like a fussy and obsessive mechanic who, when faced with an obviously broken and damaged automobile, is only willing to drain oil or add oil to get it to run properly again, but is unwilling to put his hands into the actual machinery, get her hands dirty, and change the damaged parts.

Because they were not so bound to the incapacitating conservative traditions that Abbie venerated, the townspeople could see the fundamental problem with their town much more clearly than Abbie could.  They saw that what the common people lacked was not something that could be repaired by the adjustment of borrowing rates or holding rates, or by changing the form of money first from paper to vouchers and then from vouchers to electrons.  What they lacked was sufficient initial income they could spend to restart the engines of their town’s economy; and they lacked the opportunity to work and produce to build their town’s wealth and generate even more income.   They began to realize that Carlie had been right when she had suggested that in order to address the problems of unemployment, Abbie should simply hire people.

One day, the townspeople en masse visited Abbie in her office.   Carlie was there, along with her friends and her brother.  The shopkeepers and cafe owners were there.   All of the town’s unemployed were there too.  Even Baker, Wells and Bancroft were there.  What happened next the expunged town records do not reveal.   Some say Abbie moved to another town and was never seen again; but others say Abbie changed her name and now runs one of the small cafes in town.

But what is known is that Carlie and the others took control of the town’s money machine for themselves, and from that point forward the townspeople voted together on the best ways to use the money machine.   They made some mistakes, but all-in-all they did a good job with their new responsibilities.  One of the things they did was to create a contingency employment plan for dealing with hard times when business was slow, incomes were down, and people were being laid off.  The plan involved using the town’s money-creating power to hire the unemployed directly and invest in the town’s people and public services.  They hired people to work on the parks and the roads, and to improve the schools and other town buildings.  Some of the people the town hired were paid to teach others in the town the things they had learned how to do in their previous jobs; and some were even paid to learn these skills from others so they could move into new lines of work that were more in demand by local businesses.

Prices sometimes rose a bit due to the money printing, but not that much because the spending was generating new goods and services to purchase.  And because everyone was employed, business didn’t fall off much in response to the layoffs.  The workers also had more bargaining power, so wages stayed high and strong while the more greedy and rapacious business owners were forced to pay themselves less.   As the demand for products returned businesses would hire back people who were employed by the town; and the town was then able to decrease the number of people they employed.  In the meantime, the town had accomplished a large amount of needed public work that could be attended to best during the downturns.   The later downturns in the town’s economy were also much milder, and didn’t last as long.

Perhaps the most important change was in the morale of the townspeople.  Things didn’t always go well for them, but the people took heart from the fact that they were now governing their own community, rather than being governed by others in a system characterized by secrecy, hierarchy and unaccountability.  When they disagreed, they fought it out in public debate and made a decision, which they then knew was their decision, not the decision of an aloof ruler whose goals and values were not their goals and values.

The town got back to work, and put the chaotic years of deep economic downturns and aristocratic misrule behind them.  And if they didn’t exactly live happily ever after, they did live happily most of the time.

___________________

[The ideas for this story came from a long discussion at Steve Randy Waldman’s blog Interfludity of negative interest rate proposals.  The proposals had been discussed earlier by Matt Yglesias and Ryan Avent.   Special thanks are due to the commenters known as “K” and “JW Mason” for a long and stimulating discussion.  The subject of negative interest rates has also been discussed here by Scott Fullwiler in two July, 2009 posts at New Economic Perspectives, but with a somewhat different focus.  In those posts the topic was the money multiplier and proposals to boost lending by charging a penalty rate on excess reserves.  Fullwiler thoroughly critiques these proposals and the classical money multiplier from an MMT perspective.]

60 Responses to The Astonishing Case of the Impenetrable Zero Bound

  1. Very well done! The story isn’t simple, and it’s long! But, in the end, it is a very good narrative and will help people to understand what the economy is going through and where we have to end up.

  2. Nice parable!

    I suggest that you are missing a few intermediate steps (long as it already is).

    You see, sometimes Abbie wants to spend money herself to purchase luxury goods from the common people (she is, after all, an aristocrat!). However, it would be a grievous affront to the ancient and venerable laws of the town if Abbie just used her money printing machine in order to finance her expenditures. So, when she wanted a new carriage to ride in or a decorative lawn ornament to look at, what she would do is, yes, pay the appropriate commoner with her own money. But since Abbie realized that simply spending money would lead to a breakdown in the sense of separateness dividing her from the commoners by transmitting money to them without using Baker, Wells, and Bancroft as intermediaries.

    Luckily, years earlier, she had come up with an ingenious plan – she began issuing pieces of paper she called “certificates,” which really were very similar to boxes. She would sell people these people these certificates (although certainly not directly – she had, well, let’s call them “primary dealers” for that), and in exchange, she agreed to pay the holders the original money back plus a certain rate of interest.

    So, back to our story. Somewhere in the middle, Abbie decides that if she just exchanges some of her certificates for money, this will get Baker, Wells, and Bancroft lending again.

    After that doesn’t work (still somewhere in the middle of our story), Abbie decides to do something slightly different. You see, it turns out that her certificates have varying term structures – some of the certificates are for 1 month, but some are for as long as 30 years! So Abbie goes through a phase of buying back some of the longer term certificates, because she thinks that this will get Baker, Wells, and Bancroft lending again.

    After a certain period, Abbie remembers that she has a wand. It’s true, when she is in a contemplative mood and sits down to think about it, Abbie will sometimes acknowledge that it is really more of a stick with a knob on it. But this wand is an ancient wand, which has been handed down from aristocrat to aristocrat for centuries, reaching back into the shadowy depths of time. This is the wand of

    And when she waves this wand – this mystical wand of Spoc-tack’etions – it has a profound effect upon the commoners. She has only to walk to the podium of Oz, to look straight ahead, to ruffle her brow slightly, and to repeat 10 times:

    I wish I may I wish I might. Summon Spoc-tack’etions of prices rising tonight!!! I wish I may I wish I might.
    I wish I may I wish I might. Summon Spoc-tack’etions of prices rising tonight!!! I wish I may I wish I might.
    I wish I may I wish I might. Summon Spoc-tack’etions of prices rising tonight!!! I wish I may I wish I might.
    I wish I may I wish I might. Summon Spoc-tack’etions of prices rising tonight!!! I wish I may I wish I might.
    I wish I may I wish I might. Summon Spoc-tack’etions of prices rising tonight!!! I wish I may I wish I might.
    I wish I may I wish I might. Summon Spoc-tack’etions of prices rising tonight!!! I wish I may I wish I might.
    I wish I may I wish I might. Summon Spoc-tack’etions of prices rising tonight!!! I wish I may I wish I might.
    I wish I may I wish I might. Summon Spoc-tack’etions of prices rising tonight!!! I wish I may I wish I might.
    I wish I may I wish I might. Summon Spoc-tack’etions of prices rising tonight!!! I wish I may I wish I might.
    I wish I may I wish I might. Summon Spoc-tack’etions of prices rising tonight!!! I wish I may I wish I might.

    And then… **Poof** !

    (After this there follows several variations of this, in which Abbie uses the new more powerful wand of Gehn-pe-deeeeeh-neeeigh, which has been developed in a secret lab by her research elves. With this wand, you see, she can target Gehn-pe-deeeeeh-neeeigh. There are probably a few variations of this as well. And perhaps at some point she tries to alter the balance of trade between her town and the neighboring village of Merloo.)

  3. Hi Dan,

    Lots of stuff in here. Even a (failed) Gesellian stamp fee (it left out the Gesellian citizen’s dividend)! But none of the details (e.g. bank balance sheet operations, competitive interbank equilibrium) that would actually lead us to make any progress on the technical feasibility of negative rates in an *inside* money economy without a physical medium of exchange. I was kind of hoping for a stripped down ten sentence or less description of the legal money operations of the central bank, commercial banks and economic agents, from which we could work out the competitive equilibrium. What you’ve written is a story of a succession of banking systems, none of whose allowable operations are completely examined. And are we only considering 100% reserve economies (Abbie lends to bank lends to Carlie – Carlie deposits at bank deposits at Abbie)? Why was there no lending in the Gesellian scenario? Why do we never get to the scenario with only electronic inside money created by lending? I’m not actually sure if you concluded whether negative rates are possible or not, and if so, under exactly what conditions. But maybe that wasn’t your goal. A valiant effort though. Too valiant, perhaps.

    • Dan Kervick

      But none of the details (e.g. bank balance sheet operations, competitive interbank equilibrium) that would actually lead us to make any progress on the technical feasibility of negative rates in an *inside* money economy without a physical medium of exchange.

      Hi K,

      I thought that was covered by all the scenarios in which the money is required to stay inside the boxes. At that stage, the physical money has been reduced to little more than beads on an abacus. The boxes make things more vivid, but essentially the boxes+dollars mechanism is just a kind of account book, and moving money from one box to another is just a way of marking up or debiting accounts. It could just as easily take place electronically, and the people in the town’s economy don’t handle that actual medium. And then once they move to the electronic vouchers with scanners, there is no physical medium they hold at all.

      The system that eventually evolves is, it seems to me, clearly not a 100% reserve scenario in the strictest sense – since the the lenders are ultimately permitted to lend vouchers before acquiring the “reserves” for the box-based payment system. But you are right that I didn’t go on to consider explicitly the question of whether they are then subsequently required to borrow reserves that cover the full amount loaned. I could have pursued it both ways, but the story was already too long. And I thought it was already clear at that point that the logic of the situation is that changing the % of reserves the lender is required to borrow after the fact would not in any way give the lender more or less incentive for issuing negative interest liabilities.

      I ultimately arrived at a situation in which Abbie does manage to get the lenders to lend at negative interest: The solution requires using the “affidavits” that require the negative interest loan to be made to the public first before the lender can borrow the reserves at negative interest from the central banker. This corresponds to the claim I made in Comment #17 (and one later one I believe) in the long Interfluidity thread. And ultimately, in the story, Abbie transforms the lending system into what is effectively a public banking system, where banker profit motives no longer play a role and the banker profits have been transformed into what are effectively just salaries for helping to administer the public system. This was also referred to in comment #17:

      http://www.interfluidity.com/v2/3212.html#comment-24158

  4. Golfer1john

    What Abbie needed to do was buy stuff from the commoners in the amount of S (what they wanted to save from their incomes) plus T (the amount of the taxes she levied on them). And if she didn’t need so much stuff, she could lower the taxes. Then there would be no deflation and no layoffs, because all the town’s production would be sold. Then if there were still unemployment, she could buy a little more or lower taxes a little more, and the increased sales would prompt the shop owners to hire more people and make more stuff.

  5. Dan,

    I have an idea. Two banks: I own and run K Bank, you own and run D Bank. The economy works as follows:

    1. There is no physical money. Money is electronic deposit entries on banks’ balance sheets.

    2. All consumers are perfect credits: borrowing only occurs for liquidity/coordination purposes.

    3. No bank reserves or capital are required: banks have no equity, just overnight loans and deposits.

    4. “Liabilities must be backed by an equal quantity of assets or I’ll declare you insolvent and shut you down,” Abbie insists. If Carlie transfers a deposit from K Bank to D bank, K Bank must either borrow that amount from another bank or Abbie, or K Bank must sell a loan of equal value.

    5. If K-Bank and D Bank make a profit on overnight lending/borrowing they immediately pay it out to K and Dan as a bonus (just like the real world!). If they incur a loss, K and Dan are required to top up their bank (but, unlike the real world, they actually never lose money). Equity value is exactly zero.

    6. Abbie will borrow from either K Bank or D Bank at -5.5% and lend to them at -4.5%.

    There. The rules in ten sentences.

    K Bank pays -5.5% on deposits and is willing to borrow from or lend to D Bank as necessary at -5% (as long as Abbie says D Bank is solvent). Carlie wants to borrow $10,000. She first comes to K Bank who offers her a rate of -4%. She then walks across the street to D Bank to see if she can do better. What rate will D Bank offer her?

    This seems like a good description of a the current system but without paper money or the complications of credit risk. But it doesn’t look to me like a public banking system.

    PS. If anybody else wants to open a bank, feel free. Carlie needs cash and Abbie is handing out bank charters!

  6. Dang! Scrap 4. It’s stupid. D bank isn’t going to take on a liability without being compensated with a matching asset. God! Just scrap it!

  7. OK, So I merged the previous 4 and 5…

    There are *five* rules:

    1. There is no physical money. Money is electronic deposit entries on banks’ balance sheets.

    2. All consumers are perfect credits: borrowing only occurs for liquidity/coordination purposes.

    3. No bank reserves or capital are required: banks have no equity, just overnight loans and deposits.

    4. If K-Bank and D Bank make a profit on overnight lending/borrowing they immediately pay it out to K and Dan as a bonus (just like the real world!). K Bank and D Bank don’t ever have losses because nothing unexpected happens to their assets. Equity value is exactly zero.

    5. Abbie will borrow from either K Bank or D Bank at -5.5% and lend to them at -4.5%.

  8. Dan Kervick

    I just want to see if I understand the system first K.

    First, I think some of the confusions about these issues in earlier discussion is due to an ambiguity in the word “deposit.” So let’s just get that one cleared up first. Suppose we’re still in the physical money world. You go to a bank with $1000 in your pocket to open up an account. You give the banker $1000. That money is put in the vault, and in return the bank creates an account for you. The account is credited with a balance of $1000. The balance on the account is a liability of the bank: it represents the fact that the bank owes you $1000. The cash in the vault is an asset of the bank: it is now part of the bank’s total reserves. The bank has expanded its balance sheet, and now has both greater liabilities and greater assets, but with the same net equity position.

    If you later clear your account and the bank gives you $1000 from the vault, then the account balance goes to zero, so the bank’s liabilities have decreased by $1000. But the bank’s vault cash and total reserves shrink by $1000 too. So the bank’s balance sheet has contracted and its net equity position is unchanged.

    Now my understanding is that when bankers and economists use the term “deposits”, they are almost invariably referring to the deposit account balances, and therefore classify deposits as liabilities. However, sometimes people seem to use the term “deposit” to refer to the $1000 cash in the vault, because that cash has been deposited. (This, I think, was the way Krugman was using the term in his exchange with Scott Fullwiler, because he was saying that in order to make more loans the banks had to get more assets in the form of deposits .) So to avoid future confusion, let’s try to use the terms “deposit balances” when we want to talk about account balances, which are liabilities; and let’s try to use “deposited cash” when we talk about the vault cash which is an asset.

    So now let’s imagine the world where there is no physical cash, and thus no vault cash and no physical bank reserves. The only way anyone is capable of possessing a monetary asset is in the form of a balance at a bank. If I have an account at my bank with a positive $1000 balance, then that account represents a $1000 asset for me and a $1000 liability for my bank. And in this world, ordinary customers aren’t the only people who have accounts at banks. Banks also possess accounts at banks. If Bank D has an account at Bank K with a balance of $2 million then that account balance represents a $2 million asset of Bank D and a $2 million liability of Bank K. If Bank K also has an account at Bank D with a $1 million balance, then that account represents a $1 million asset of Bank K and a $1 million liability of Bank D. Considering the two accounts together, Bank D has a net $1 million claim on Bank K, and Bank K has a net -$1 million liability to Bank D.

    You ask that we assume no reserves. So I take it that means there is no central bank at which any of the other banks have an account. All the banks are on a par.

    You also asked that we assume the total equity value of the banks is zero. So I take it that that means that the sum of all customer accounts at a bank with positive balances (a “customer” here means any entity that is not itself a bank but has a deposit balance at a bank) is matched dollar-for-dollar by customer accounts at banks with negative balances.

    Is that the picture so far?

  9. In the “old” system, if you deposit $1000 at K Bank, we take that paper money and exchange it for electronic reserves with Abbie (who then burns it). We then take those reserves and lend them in the interbank market at a rate greater than the rate we pay on your $1000 deposit account. When I speak of deposits, I am referring to the $1000 debt I owe you in your account. Not some asset I own. I never hold “deposited cash” except maybe a small quantity of till money. Our assets are essentially entirely loans, even in the old system.

    We could call the balance between our banks a deposit, though it would be better to call it an interbank loan. There’s a market for interbank balances, and I think it’s worthwhile to think about the mechanism by which it clears.

    I did not intend to rule out reserves. What I said was that there are no *required* reserves. You can borrow reserves from Abbie at -5.5%. Those reserves yield -4.5% so you definitely don’t borrow from her in order to hold those reserves yourself. You borrow them because you have no cheaper way to repay a loan.

    And, yes, on the dollar for dollar match of customer loans and deposits.

    Speaking of the interbank market…

    Immediately effective, K Bank is making the following modifications to its interbank lending policy :-)

    If by entering into an interbank lending transaction, we expect that transaction to make our balance of assets and liabilities equal at the end of the day, then we will enter into that transaction at a rate of -5%. If, as a result of the transaction, we expect an increased probability of having to borrow from Abbie, we will transact (borrow or lend) at a rate closer to -4.5%. If, on the other hand we expect an increased probability of having to lend to Abbie (excess reserves), then we will transact at a rate closer to -5.5%. We apologize for any inconvenience this change in policy may have caused.

  10. Oops…

    You can borrow reserves from Abbie at -4.5%. Those reserves yield -5.5%…

  11. Samuel Conner

    Re:

    “The main reason they did this, instead of holding onto the money themselves, is that Baker, Wells and Bancroft were willing to pay Carlie and the others for the privilege of holding onto their money. And the reason they were willing to pay for that privilege is because they could then lend that money to other people.”

    This sounds a bit like the “loanable funds” fallacy. Would it be more accurate to say that the reason is that the townspeople are willing to “lend” to the local bankers at a lower rate than the bankers would have to pay Abbie for the same funds?

    • Dan Kervick

      The story starts in more primitive conditions. I didn’t describe any particular reserve requirements, so I just left it implicit that lending will require the acquisition of some quantity of additional assets, whether before the fact or after the fact. But yes, as always it’s the price. The lenders want to loan, and expanding the loan books calls for getting some additional quantity of assets from some source. They will take the best price they can get.

      • Samuel Conner

        Hi Dan,

        Abbie is pretty plainly the local Central Bank. In your starting scenario, the private banks seem to be able to borrow from the Central Bank as much as they want, when they want. That sounds like a post 1971 system, not a primitive system in which the total currency in circulation is limited, and a loanable funds theory is valid. Abbie seems to have a money printing machine from the very outset of the scenario.

        I’m not criticizing so much as suggesting that your initial scenario provides an opportunity to “in passing” debunk “loanable funds.” I don’t think that you want to complexify this story more by incorporating a transition from hard money to fiat money. You already have fiat money at the outset.

        • Dan Kervick

          Point taken. Yes, it would be good to add a part to show the evolution from an explicit loanable funds picture to a more contemporary endogenous money picture.

      • Samuel Conner

        Or else DO complexify it it further, with a primordial hard money system with its
        idiosyncratic failure modes, and break the story into several chapters. It’s a good
        teaching tool and fund to read.

      • Samuel Conner

        Perhaps make it into a graphic novel! Borrow a subtitle from “Susan of Texas”, an
        Agony in N Fits.

        Perhaps a YouTube video. It would be delightful, and helpful, if some clear thinking about the
        financial system and the present troubles could go viral.

  12. Dan Kervick

    OK, I went off on a tangent then because I thought you wanted to imagine a reserve free system.

    You can borrow reserves from Abbie at -5.5%. Those reserves yield -4.5% so you definitely don’t borrow from her in order to hold those reserves yourself. You borrow them because you have no cheaper way to repay a loan.

    Lost here. If I can borrow at -5.5% then why wouldn’t I want to hold them if holding is an option? They yield -4.5% if I lend them in interbank market, right? Why would I do that?

    And we’re only imagining a tax on excess reserves, not all reserves? If there is no reserve requirement, how does the CB decide how much of the reserves are excess?

  13. Dan,

    “Lost here.” Yes, I made a mistake. It was corrected in the comment immediately below.

    “How does the CB decide how much of the reserves are excess?”

    To the extent that there are any outstanding reserves, those reserves are excess. All of them. Ideally there are none, because somebody is borrowing reserves at -4.5% and somebody else is holding them at -5.5%. If those two banks could find each other, then they could both make a profitable trade by the second bank lending the first those reserves at -5%, in which case the first bank could cancel its discount window loan and there would be no outstanding reserves. In a zero reserve system like Canada’s it is normal for there to be no outstanding reserves. But sometimes it happens, perhaps because nobody wants to lend to some bank who then has to go to the discount window. What happens then is that there are excess reserves among the rest of the banks and as they all try to get rid of them, the interbank rate drops to the rate on reserves. Effectively you get a “floor” system rather than a corridor, which happens sometimes.

    “But yes, as always it’s the price”

    I didn’t really follow this whole comment. What are you saying? Do you have a strategy for competing with K Bank?

    • Dan Kervick

      Sorry, I’m still really lost K. Could you please spell things out for me more slowly?

      For example, when you say I can borrow reserves from Abbie at -4.5% and they yield -5.5%, what do you mean? The discount rate is -4.5% and the interbank rate is -5.5%?

      And are we imagining the central bank is also paying interest on reserves? What is the rate? And on which reserves is the rate paid? All reserves? Only some?

      What are “outstanding reserves”? Reserves borrowed from the discount window? Maybe I’m just hung up because I’m not familiar with the Canadian system? My understanding is that every dollar of reserves in every reserve account, no matter how it got there, is ultimately a liability of the central bank and an asset of the bank who has the account.

      Here’s my basic question: however you are imagining the system to be set up, I’m a banker and I borrow $X in reserves for 30 days, does it cost me money or not. If so, how much? Or if I make make money, how much do I make?

  14. Dan,

    Sorry, I get it. That comment wasn’t for me.

    Carlie called me, BTW. She’s *very* interested I’m my loan. Apparently she has a line of credit at “another” bank that’s charging 0% and she wants to pay it off!

    • Dan Kervick

      You shouldn’t give it to her if it’s for negative interest. There is no way you can profit :)

  15. Dan,

    The discount rate is -4.5% and the IOR rate is -5.5%. Abbie didn’t announce a target interbank rate, because then we’d have to discuss how she might enforce it. I don’t think it really matters. K Bank figures it’s safest to operate near the middle of the band, but we’ll have to see how that market develops.

    Reserves are a liability of the CB. All reserves pay IOR. Real central banks buy some assets using reserves. This happens, for example when a bank needs paper currency. The CB then buys some government bonds in exchange for reserves which the clearing bank can then convert to paper money. Then there’s QE which also involves an actual purchase of assets with reserves. Mandatory reserves may also be purchased (I’m not sure) but I think that’s pretty well it for permanently issued reserves.

    The CB will also *lend* out (rather than sell) reserve units. This typically occurs via OMO repos or at the discount window. The CB creates reserve units and *lends* them against collateral. The borrower must pay the agreed lending rate, but receives the IOR rate on the reserves (assuming they don’t pass those reserves on to someone else). In our case that would *cost* the borrower net 1% annually (the bank pays -4.5% at the discount window, but only earns -5.5% IOR).

    There is no mandatory reserves or paper money in our story. So all of Abbie’s reserves are created only at the moment when they are borrowed at the discount window and destroyed when they are returned. So in Abbie’s case the quantity of her discount window loans (her assets) are exactly equal to her outstanding reserves. This also means that for every discount window borrower there is some bank holding (excess) reserves. Since nobody wants to borrow at the discount window or hold reserves at IOR, there should be *zero* discount window borrowings or reserves outstanding overnight. All balances should clear via interbank lending at a rate somewhere in between discount and IOR.

    I hope that makes sense :-(

    • Dan Kervick

      OK, very good. I think I’ve got it.

      Yes, I think you are right that the interbank rate makes no difference here, because the central issue is the systemic situation with all the banks taken together. We could just as easily imagine that there is only a single bank. The cost of reserves is on average 1% per year. Every dollar borrowed at the discount window into the system earns the system money at 4.5% per year due to the -4.5% discount rate, but also loses the system money at a rate of 5.5% per year due to the -5.5% interest rate on reserves.

      So then the question is this: In a system run with these parameters, what would induce banks to lend money to non-bank customers at a negative rate of interest?

  16. Kevin de Bruxelles

    But Carlie’s town did not live in isolation. In fact there were several other towns, much poorer towns, in the vicinity. One of the reasons for Carlie’s economic problems is that Diego and Esperanza and their friends were moving into Carlie’s town and agreeing to work for much lower wages than the local’s would work for. Diego and Esperanza meant no harm; to them they were getting paid much more than back in their poor towns. The rich people of Carlie’s town pretended to not be happy about Diego and Esperanza but in truth they were very, very excited to have these new people work even harder than the locals for much less money. Soon many of the original people of Carlie’s town started to see certain jobs as beneath their dignity to perform.

    So when Carlie’s town decided to make a job for everyone, they were forced to decide who “everyone” consisted of. Would these jobs be open to Diego’s and Esperanza’s friends back in the neighbouring poor towns? Some argued that if these jobs were open to all then they would serve as a magnet and a flood of cheap labor would wash over Carlie’s town. Others argued it was racist to even ask the question and tried to shut down the discussion. But was Carlie’s printing press really strong enough to support all these people. And wouldn’t this flood people really mean that Carlie’s town would in a very short period of time be just as poor as all the neighbouring towns?

    So no, Carlie’s town did not live in isolation at all. The other, even more important problem her town faced was that most of the town’s factory owners had stopped making their products in Carlie’s town. And this made many of Carlie’s friends unemployed. No, the factory owners preferred to build their products in Fong’s huge town, which many years ago used to be the richest town in the world but was now among the poorest – and largest. Now sure, the products may have cost a little less since Fong’s people were only paid a tiny pittance compared to what Carlie’s friends used to get paid. But after a while, when Carlie’s friends no longer had jobs, they couldn’t afford to buy these cheap trinkets in any case.

    So when Carlie and her friends got the idea to gain sovereignty over the town’s printing press, others, especially Marine, asked if this was coherent given the other two problems (jobs going to other towns and other towns coming to take the existing jobs). While she certainly agreed with gaining sovereignty over the printing press, Marine also supported gaining sovereignty over the town’s borders and the town’s trading policy. Marine wanted to protect the town from unfair trade with poorer towns. Marine knew that if they ran the printing presses without stopping unfair trade and without securing their borders, then most of the newly printed money would just go to Fong’s friends who made the products and most of the jobs would go to Diego and Esperanza’s friends who worked cheaply. She saw Carlie’s emphasis on monetary sovereignty as a “nationalist” policy in a “globalist” context.

    But Carlie was scared by the word “nationalist” and besides Marine’s father was a really bad man. Also, Carlie’s town was dominated by two High Priests named Paul and Randy. Now these two priests and their different groups of disciples didn’t agree on everything, but one thing they did agree that stopping unfair trade and securing their borders with poorer towns was not compatible with their sacred texts. They much preferred to argue endlessly over esoteric central bank theories than to face the real problems. So Carlie called Marine a heretic and continued to try to convince people that currency sovereignty is important but trade and immigration sovereignty are not.

  17. Dan,

    I just did! Carlie didn’t want to wait anymore so she took me up on my offer. She is borrowing $10,000 at -4% (let’s say per day) to pay off a 1% line of credit at D Bank. I’ve already given the Abbiewire instructions to send you the money.  I need to borrow $10,000, but I called your funding desk and they offered me 1%. Are you kidding??? So I went to Abbie and she is funding me at -4.5%. Anyways, I’m making $50 a day on the loan.

    Now there’s a throng of people outside my door wanting loans. I’ve moved my lending rate to -2%, for a 2.5% profit margin assuming I have to keep borrowing from Abbie. I just made a $100,000 loan to Farley who is buying a house from Harley who is going to put his money in his deposit account at D Bank. What rate are you offering him?

    I can’t play this game all by myself, Dan. You know the rules. At what rates are you 1) lending to consumers, 2) taking their deposits, 3) offering to lend interbank, and 4) bid to borrow interbank? In the real world I would know all those numbers. I know you aren’t lending but I can’t know where deposits are going unless you tell me your rates!

    Abbie, BTW, is angry at you for not lending to me inside the corridor, even though she told you there’s nothing wrong with my bank. I hear you aren’t doing much business and Abbie is getting concerned about the lack of competition so she is giving out banking charters *for free*. Also, I hear she is contemplating putting in place a $100/day fee for holding banking charters because some banks aren’t using their balance sheets productively. That all really sucks, man, cause we had a good thing going here with just two banks. Anyways, I’ll be lending at an outrageous profit margin for the time being.

    I’ve moved my interbank bid to -4.5% because I don’t want to keep borrowing from Abbie and I want to prove to her that you are the one who is being difficult.

  18. Dan Kervick

    So I went to Abbie and she is funding me at -4.5%.

    How did that happen? Did Abbie cancel the interest on reserves rate of -5.5%? I thought we agreed that the net cost of reserves for you was 1%. Now you are paying Abbie 1% for additional reserves and also paying your customers to borrow from you?

    But if Abbie is now offering you funding at -4.5%, then I think you should review this passage in the story:

    “But my dear Baker,” continued Abbie, “Wells and Bancroft did loan money to some of the common people. I have spoken to them about it, and they behaved exactly as I expected, loaning money to the townsfolk at -4% interest, and thus making a 1% profit on the total transaction.”

    “Yes, I spoke to them about it,” smirked Baker. “They said, ‘You fool Baker, we undersold you again! We were able to get people to take loans at the extremely low rate of -4% thanks to these -5% loans we’re getting from Abbie. We made a profit of 1% on each loan!’ “

    “But I explained to them that they were idiots, and that I made much more money – by borrowing from you at negative 5% and not making negative interest loans – than they had made by borrowing from you at negative 5% and making negative interest loans. They grasped my point immediately, so I don’t think they will be lending out any of the money you give them again, not unless they can they can get a positive rate of interest from the borrower.”

  19. OK, Dan. I have no idea what you are doing, but I’m making lots of loans to all the town’s people at big profits. You, apparently, have your own little printing machine. So what *exactly* are you doing??? You still haven’t told me. I take it you are borrowing reserves from Abbie (or me?) at -4.5%. So now you have to “pay” -4.5% on the loan, but you are “receiving” -5.5% on the reserves you are holding. So you are losing 1% per day. How big is this operation of yours? You know I’m borrowing reserves at -4.5%, so why are you holding them when IOR is -5.5%??? You don’t like money? What have you done with the reserves you have borrowed??? I have literally no idea what you are doing.

    • Dan Kervick

      K, what are you doing with your reserves? You can’t give your reserves to your customers. You seem to be describing a situation in which the quantity of your deposits is going up dramatically as you make loans, but in which your reserves are either holding steady or going down, even as you borrow them. How is that happening? How are you making your interbank payments payments? You’re the one who told me that there was a -5.5% rate of interest on reserves. How are you avoiding those payments and managing to get an effective – 4.5% borrowing rate. Where did your reserves go?

      I suppose its possible that for every loan you make, the borrower spends that money by giving it to depositors at other banks, so you are experiencing a net drain of reserves as those payments are made. So I guess no reserves are flowing into your reserve account from other payments made by borrowers at other banks? But even if one bank were getting lucky doing this, clearly the banking system as a whole can’t do it. The reserves are always just moving around inside the system, and total reserves don’t decrease by one cent unless the central banker drains them. So the system as a whole is always holding all of the reserves it has borrowed, and thus the system as a whole is paying 1% for additional reserves. And yet we are to imagine that the system is at the same time offering loans to customers at -4%?

  20. Samuel Conner

    Perhaps it’s time to do some Steve Keen style ODEs to explicitly illustrate
    the dynamics.

  21. Dan,

    You said you were carrying out an arbitrage and that the other bankers were idiots for not doing it. Now you are refusing to tell me what it is. WHAT IS IT?

    I told you: I can’t tell you where the deposits are going if you REFUSE to tell me what rate you are paying on deposits. If you are paying less than me, then all the deposits will end up at K Bank and I wont need to borrow from anybody. If you are paying the same then some of them will end up at both our banks. If you pay more, then you’ll get most of the deposits. Tell me what you are doing, and I will explain how the money moves around.

    I *only* need to borrow reserves if somebody transfers a deposit from me to another bank. In that case I don’t hold those reserves, I SEND THEM TO THE OTHER BANK. So I’m replacing deposit funding with discount window funding which costs me an extra 1%. But I still make money borrowing at the discount window and lending to consumers (just less than before). But seeing as D Bank appears to be closed, *all* of my lending is ending up as deposits so I’m no longer borrowing at the discount window. Why do you think I’m holding reserves? I have *zero* reserves. I *might* be borrowing at the discount window if you are paying high rates on deposits, in which case I don’t get a lot of deposits. But I don’t know since you aren’t telling me what you are doing. I’d be an idiot to borrow at the discount window and then hold reserves. At K Bank we are either borrowing from Abbie or holding reserves. We never do both at the same time.

    You said you understood the rules of the game, but you are refusing to tell me

    1) Your big arbitrage operation whereby you borrow at negative rates and do “nothing”
    2) What rates you set on *anything*. Am I running this banking system all by myself?

    Come on. You’ve made big claims, but when it comes time to back them up you just keep changing the topic and making new claims. Just answer some simple questions. Be a capitalist for a second, Dan. Turn on the money machine. Tell me how you are going to destroy K Bank. The towns people are investing in new projects and I’m getting rich while we all wait for you to open your doors. Come on!

  22. Dan Kervick

    You said you were carrying out an arbitrage and that the other bankers were idiots for not doing it. Now you are refusing to tell me what it is. WHAT IS IT?

    That episode takes place in the part of the story where Abbie is offering -5% negative interest loans, and that’s all. Nothing corresponding to IOR. I borrow at -5%, pay back less than I borrow and make money. I make more money that way than I do by borrowing at -5% and lending at -4%.

    If we then move to the scenario where there is negative interest on reserves – a holding fee – bringing the total cost of borrowing and reserves to 1%, then I will not borrow additional reserves at all unless I am making loans at a rate exceeding 1%. If the demand for loans won’t support a rate above that – and won’t even support a positive rate of interest – then I don’t make additional loans.

    So I’m replacing deposit funding with discount window funding which costs me an extra 1%. But I still make money borrowing at the discount window and lending to consumers (just less than before).

    That doesn’t add up – not if you are only charging the loan customer -4% interest. Then you lose money by borrowing at 1% and lending at -4%.

    This all started with a debate about how the central bank could induce commercial banks to move into a negative interest rate regime. You need to tell a plausible story about how that could happen. It doesn’t help to tell a story about how a single bank in the system might make money from negative interest because it is successful in getting all of its additional borrowed reserves transferred to other banks. With the hypothetical borrowing and IOR rates as described by you, a single bank might get lucky and be successful in getting an effective cost of borrowing of -4.5% if it somehow offloads all its reserves to other banks after borrowing them. But for every payment that is made out of some bank’s reserve account an equal payment is made into other bank’s reserve account. So there is no way that the system as a whole is getting a -4.5% borrowing rate. Instead the system as a whole is getting a +1% borrowing rate. So I see no way that the banking system could move to a prevailing negative rate of interest on commercial loans.

  23. Dan!

    “That episode takes place in the part of the story where Abbie is offering -5% loans… Nothing corresponding to IOR”

    Then why did you bring it up after we *fully* agreed on the rules with -5.5% IOR??? It’s so hard discussing with you! Honestly, it’s like your memory is less than 5 minutes.

    “Then you lose money by borrowing at 1% and lending a -4%”

    I *said* replacing deposit funding with the discount window costs me an *extra* 1%. How do you suddenly imagine that I’d be borrowing at 1%? You know I can borrow at -4.5%! If you read what I wrote, and looked at the numbers we agreed on you’d see that there is a 1% difference between deposit funding and discount window funding at K Bank. So things get 1% worse for me. But *still* profitable.

    “getting all of its additional borrowed reserves deposited in other banks”

    What reserves are you talking about. If I’m the only bank, there are *no* reserves. I didn’t move my reserves anywhere. I currently lend at -2% and pay -5.5% on deposits. So I make 3.5% *net* profit when I make a loan. That’s what I’m doing right now. I’m making tons of money because
    everybody wants my loans and there is nowhere else in town to get a loan. For now *that’s* the status. One bank. I have:

    1) $1 million of loans at a rate of -2%
    2) $1 million of deposits at a rate of -5.5%
    3) I have no reserves or discount window borrowings.
    4) I’m offering to lend/borrow interbank at -5%

    I’m assuming that we can agree that that is a possible state of affairs (however it came about). The confusing part before was that I didn’t know what your rates or actions were so I had no idea how my loans were likely to be funded. I wasn’t *assuming* that I could just dump my reserves on you. There happened to be a wire transfer to your bank so I made it. I would have much preferred if there was no wire transfer and I could just fund from deposits. As I said, I can’t play this game alone. I need to know *your* policies so I can respond.

    I’m making $35,000/day and I’m making tons of new loans every day. I used to have a $10,000 discount window loan because I needed to fund a wire transfer to your bank. If you had made the loan to me, there would have been no reserves in existence. Anyways, D-Bank has since stopped actively doing business and all the clients have transferred their deposits and renewed their loans with me.

    All I know is that you are offering loans at 1%. Are you just going to sit there and let me make all the money by lending at negative rates? Or are you going to start competing by doing something and thereby showing me that in a competitive equilibrium rates would not be negative? Do
    something and lets track the movement of deposits, loans and reserves around the system based on transactions that we both agree are correct. So you’ve given me your lending rate. Now give me your deposit rate and your interbank lending policy.

    You have an empty bank and you are making no money. Abbie has imposed a $100/day bank charter license fee and you are going to suffer if you don’t do something. I have *huge* margins and I’m making money hand over foot. There’s plenty of room for two banks in this town. If you want, I’ll even hand over half my loans and deposits to you. Give it a shot. Where’s the capitalist in you?

  24. Dan Kervick

    What reserves are you talking about. If I’m the only bank, there are *no* reserves.

    I haven’t the slightest idea what you are talking about when you say that K. If you are a bank, you have an account at the central bank. If you have a positive balance in that account, then you have reserves since every dollar in that account is part of your total reserves.

    In my fictional world, if you are Baker, and you have borrowed from Abbie, and you have some sum of money in your box, then you have reserves. It doesn’t matter whether Baker is the only bank, or one of many.

    Then why did you bring it up after we *fully* agreed on the rules with -5.5% IOR??? It’s so hard discussing with you! Honestly, it’s like your memory is less than 5 minutes.

    Because that was at a point where you had seemingly shifted back to saying that you were profiting on negative interest loan because you borrowing from Abbie at -4.5%. Look, I’m trying to get a straight answer out of you on something that you don’t seem to want to answer straight out. If you borrow some sum of money from Abbie for any length of time, do you end up paying Abbie, or does Abbie end up paying you? You keep moving back an forth, invoking the negative borrowing charge when you want to make it look like you can profit by making negative interest loans, and then remembering the offsetting holding charge (negative IOR) when you want to make it look like there is no way for the lender who borrows from Abbie to profit from the loan from Abbie by holding it.

    I didn’t move my reserves anywhere. I currently lend at -2% and pay -5.5% on deposits. So I make 3.5% *net* profit when I make a loan. That’s what I’m doing right now. I’m making tons of money because
    everybody wants my loans and there is nowhere else in town to get a loan.

    This is a strange hypothesis. We are considering a world in which there is no physical cash, and all money is held as deposit balances, remember? Why does everyone want your loans? If people borrow money from you at -2% interest, they have to hold the money as deposits at your bank. The interest rate on the deposit is -5.5%. They lose money from borrowing. Why do they want your loans?

    If I borrow $1000 from you for one year, and the loan rate is -2% per year, and the interest rate on deposits is -5.5% per year, and I hold it in my account for a year, then at the end of the year I have lost $35 dollars as a result of taking the loan. If I had not taken the loan, I would have lost $0.

    The only way I can make money on the loan is if I manage to exchange my deposit balance, after I borrow it, for some good or service. But the whole town can’t operate this way, because every dollar that leaves one deposit account enters another deposit account, where it is always losing money. So for the town as a whole, every dollar borrowed incurs a loss of 3.5%. This is a much worse situation than they were in originally, when there was little demand for borrowing and the interest rate was just above zero.

  25. Dan,

    “In my fictional world, if you are Baker, and you have borrowed from Abbie, and you have some sum of money in your box, then you have reserves”

    Why would I borrow from Abbie. If I’m the only bank and I extend a loan, I get an equal deposit. I’m not borrowing from Abbie.

    “If you borrow some sum of money from Abbie for any length of time, do you end up paying Abbie, or does Abbie end up paying you?”

    It obviously depends whether I hold on to the reserves or not, right? I told you, I would never borrow reserves in order to hold them. If I borrow reserves it’s because I have to send you a wire transfer and *you* wont lend me the money. Anyways, if you insist: If I borrow reserves *and* hold them (which I *never* do) I lose 1%/day. If I borrow reserves and send them to you, then it obviously depends what I get back in return, right? I don’t just give you something for nothing. If I send you reserves, maybe I send you a deposit with that. It all depends. The only way I don’t have to assume what happens between K Bank and D Bank is if *you* decide what happens at D Bank. For now I’m assuming that D Bank is empty and is not doing anything. Therefore I have loans and deposits and no reserve balance of any kind.

    If you want to know where the reserves go as a result of interbank transactions, then *do* something. Give somebody a loan, take a deposit, ask me or Abbie for a loan, or whatever. Just do something. I wont run your bank anymore.

    “If people borrow money from you at -2% interest, they have to hold the money as deposits at your bank.”

    Well, not necessarily. They could deposit the money at your bank. Who knows? Do you even take deposits? But anyways… How is that different from a positive interest rate environment. Borrowing money and depositing it is a pretty stupid trade. Deposits earn less than loans, right? People who borrow have higher returning investment projects, or greater utility for current consumption, or greater risk tolerance than people who save and keep their money in a low yielding bank account. That’s got nothing to do with the sign of rates.

    “So for the town as a whole, every dollar borrowed incurs a loss of 3.5%. This is a much worse situation than they were in originally, when there was little demand for borrowing and the interest rate was just above zero.”

    No, it isn’t. That statement only depends on the *difference* between the loan rate and the deposit rate, right? It has nothing to do with the sign of rates. Lets assume that the difference between the loan and deposit rate is the same for positive and negative rates.

    Now can we play this game according to the rules? I’m making a *killing*, Dan.

    Here’s the situation:

    1) $1 million of loans at a rate of -2%
    2) $1 million of deposits at a rate of -5.5%
    3) I have no reserves or discount window borrowings.
    4) I’m offering to lend/borrow interbank at -5%

    and I’m offering to give you half my loans and deposits. If you actually care to find out if negative rates are possible, then make a move and see what happens. And don’t complain that I’m stuffing reserves in your bank! I’m not. I’m just trying to guess what you would do because you aren’t helping. Make a move!

  26. Dan Kervick

    No, it isn’t. That statement only depends on the *difference* between the loan rate and the deposit rate, right?

    Sure, but their world was something like ours. Interest rates right above the zero bound. Very low interest on loans; very row positive rates on deposits. Surely the net for the borrower is less than a 3.5% loss.

    Of course nobody is borrowing anyway since the economy is depressed and there is insufficient demand for credit, but that’s a different problem.

    As for the rest, I literally don’t even know what we’re talking about any more. You are offering to lend in the interbank market, but you also say you have no reserves to lend? You are making loans but have no reserves? Apparently the public is lending money to you by placing deposits at your bank even though you are offering them -5.5% on their deposits? You are either just making everything up as you go along, or we’re speaking a completely different language .

    Like you did at Interfluity, you are just declaring yourself to be at a desirable endpoint without explaining how the market could arrive at that endpoint.

  27. “Surely the net for the borrower is less than a 3.5% loss.”

    It used to be 1.5%, because I thought there’d be competition. But then you refused to lend, so I’m charging a profit optimizing rate. I’m a price setter, not a price taker. If you were lending maybe it would be less than 1.5%. It’s up to you.

    “You are either just making everything up as you go along, or we’re speaking a completely different language .”

    NONE of the rules has changed since I set out the five rules, and proposed that we try to discover the competitive equilibrium by *competing*, and you said “OK!” The only thing I’ve made up is what I thought your response *might* be in certain situations, because you weren’t telling me.

    “you are just declaring yourself to be at a desirable endpoint without explaining how the market could arrive at that endpoint.”

    What endpoint? How can we be at equilibrium if we don’t know what one of the two banks is doing? The only reason I’m proposing states of the banking system is because you aren’t. We can start wherever you want and see where the equilibrium goes.

    Let me try another one… Lets say each bank starts with $1m of deposits and $1m of loans each. Nobody has reserves or reserve loans from Abbie and there are no outstanding interbank loans between us. Abbie is setting IOR at 4.5% and the discount rate (DR) at 5.5%. K Bank and D Bank are both lending at 6% and paying 4.5% on deposits. Does that sound reasonable? Are we in an endpoint that you believe could be attained?

    Something bad happens and Abbie lowers both IOR and DR by 10% to -5.5% and -4.5%. K Bank immediately lowers its lending rate to -4% and its deposit rate to -5.5%. Does something break? What does D Bank do? What do the clients do?

  28. Dan Kervick

    D bank lowers its lending rate to 5.75% and keeps its deposit rate at 4.5%.

  29. OK. Carlie has accounts at both K Bank and D Bank. She wants to transfer $10,000 from her K Bank account to her D Bank account. I give Abbie instructions to transfer $10,000 of reserves from K Bank to D Bank after the close of the day. I call you to tell you that the wire is for Carlie’s account at D Bank. Since I don’t have $10,000 of reserves I have to arrange to borrow them *before* the end of the day. If you don’t lend me the $10,000 of reserves then I’ll have to borrow from Abbie at the DR, and you are going to have excess reserves earning IOR at the end of the day. Since that would be bad for both of us, I’m hoping you’ll lend me the money. I’m asking to borrow $10,000 from you at -5% which would improve both our positions compared to having to deal with Abbie. Do you accept my bid, or will you make me a counterproposal?

  30. BTW, I’m not saying you *have* to take Carlie’s deposit. It’s your bank. I don’t want to be accused of stuffing reserves into other people’s banks. If you want, I’ll just tell her D Bank refused to accept the transfer.

    • Dan Kervick

      Sorry, I had a busy day yesterday.

      I’m not going to lend you the money. I’ve decided to close my loan desk completely, accept no new deposits and reduce interest on existing deposits to 0%.

  31. OK. I’ve moved my lending rate to -3.5%.

    In rule 3 we agreed that all loans are overnight. (I know that in reality many loans are longer term, but most, like lines of credit and floating rate loans are repayable without a fee, and fixed rate mortgages are repayable with a nominal fee.) Anyways, Harley, the contractor, apparently has a $100,000 line of credit from you for financing receivables. He wants to borrow from me instead. I have given him a line of credit at -4%. He has written a $100,000 check to himself that he is using to pay off your loan. I’ve taken the liberty of assuming that you are going to ask me for payment since the cheque was written from an account at K Bank. I’ve borrowed $100,000 from Abbie at -4.5% and instructed her to wire $100,000 to D Bank.

    *All* of the other towns people are outside my office and also want to renew their loans with me. I told them that I am going to call you to give you a last chance to save your bank, but that they will otherwise all have their loans before the end of the day. The way I see it, you can either reopen your lending business at around -3.5% (and move deposits below that rate) and make a profit, or you can get destroyed. Since the game requires agents to behave in a rational self-interested manner, economic suicide is not a valid move.

  32. Dan Kervick

    *All* of the other towns people are outside my office and also want to renew their loans with me.

    Why do they want loans? Money now has negative value. Since people can only hold money in your bank at -5.5%, the very act of acquiring money represents a drain on stocks.

  33. For now, they want my loans so they can stop paying the 5.75% they are paying you on yours. Don’t forget, Dan: the people who hold your deposits are not the same as the ones who hold your loans. And each person has a different quantity of loans and deposits. 99% of the people have vastly bigger loans than deposits. A few of them, like you, me and Abbie have very large deposits and no loans. But none of them wants to hold your loans when they can replace them with mine at 9.25% less. It’s a no brainer. What other option do they have? They are debtors. They don’t *have* the money to pay off those loans or they already would have.

    Why will they *continue* to borrow after they’ve replaced the borrowing from you with borrowing from me? Yes, I explained that in my comment May 2, at 5:50 PM. But now that I’ve explained how the people’s immediate reactions are rational, it’s your job to explain how you are going to save your bank.

  34. Dan Kervick

    I don’t want them to repay their loans now. If someone repays a loan that means some quantity of reserves moves from some other bank’s reserve account to my reserve account. But I don’t want to hold any money in my reserve account since it just loses value there. I prefer to renegotiate each loan for the same rate but with an extended repayment period – and no interest charges accruing for lets say one year. Holding an extended loan asset in the form of a promise to pay later is more valuable for me now then holding an asset of the same nominal value in the form of a reserve balance. I also don’t need any reserves to make payments. Since I am paying 0% on deposits and you are paying negative interest on the deposits, and there is no way of withdrawing a deposit in the form of cash, then no one wants to withdraw their deposit from my bank and deposit it in yours. So I don’t need any reserves to make any payments.

    So I don’t think people are borrowing any money from you now.

  35. Samuel Conner

    I haven’t been following the K/Dan controversy aside from noticing all the back and forth
    showing up in my in-box, but I’d like to raise another issue related to NIRP that is not
    present in the toy economy of this parable.

    The banks in this economy do traditional “boring” banking. That is not our present
    problem. Cheap Central Bank money (or cheap money from commercial banks) can
    be used by banks and shadow banks for commodities speculation and all varieties
    of financial engineering. Perhaps this economy is not complex enough to serve
    as an adequate parable for the present problems

  36. Dan,

    You are changing the rules. Loans are supposed to be single period (rule 3). If for some reason you thought the economy we agreed on lacked some critical feature in order to make negative rate lending impossible, then you should have said so from the start. The fact that you accepted our proposed economy as a good model and spent a week arguing about it, means you thought your theory of the Impenetrable Zero Bound (IZB) was consistent with *that* economy. Now that it clearly turns out that negative rates *are* a stable competitive equilibrium in that economy, it’s not very credible when you want to change the rules. It means your original theory was no good. Do you have a new theory?

    If for some reason you do want to change the rules, you need to say something like “I see that you are right K. In the economy that we have defined negative lending rates *are* a stable equilibrium. But there’s a crucial feature of the real economy that I hadn’t thought of earlier that make negative rates impossible, which is…” And then you carefully lay out the new rules and say “if, in *this* economy, negative lending rates are a stable equilibrium then I’m obviously wrong about my claim.” So what is your new theory of the IZB? What’s the missing rule?

    Since we don’t know the future path of Abbie’s rates, you cannot give out fixed rate term loans. What if Abbie raised rates to 19.5%/20.5%? Now your one year 0% loan (no accrued, right?) will blow up in your face. You will lose all your deposits if you don’t hike your deposit rate to near 20% (cause I will) and you’ll have to borrow from Abbie at 20.5%. If you are making some particular assumption about the path of rates, you kind of need to share that with me. It’s part of the model right.

    If you must have long term loans I propose that they must be floating rate loans. I.e. I propose that you can lend term only if the rate is some non-negative spread to Abbie’s DR.

    As far as your specific loan proposal, I don’t see why I can’t offer them whatever you offer them after the first year, but I give them a floating rate equal to the DR+0.5% for the first year instead of your 0% initial rate. They are going to like that way better than your proposal. Your funding costs are way higher than mine because you are paying 0% on deposits *for no good reason*. Unless you lower your deposit rate, you can’t offer lending terms that I can’t do cheaper!

    Samuel: “Perhaps this economy is not complex enough to serve as an adequate parable for the present problems”

    We are not debating whether this economy is sufficiently complex to model the present problems. The model doesn’t even have credit risk! We are debating whether there is an obstacle to negative lending rates once paper money is gone. If you have any proposal as to what feature of the real world that isn’t present here would make negative rates impossible, and why, please let us know. Otherwise the suggestion is as interesting as my claim that the moon is made of green cheese, just not in the places where anybody’s ever looked, and I can’t tell you where.

  37. I shouldn’t have said so much. I don’t want to end up in some interminable ill defined debate.

    Bottom line: My funding costs are 4.5% lower than yours. There is nothing you can offer your clients that I can’t do at a lower rate. Long term, short term, whatever. Makes no difference how your loans are structured. Unless you lower your funding cost (your deposit rate) the clients are going to be borrowing from me.

  38. Dan Kervick

    Now that it clearly turns out that negative rates *are* a stable competitive equilibrium in that economy, it’s not very credible when you want to change the rules.

    Where did the stable equilibrium come from, K? I thought we were supposed to be gaming out the moves we would make in this situation to see where things are headed. My judgment is that they are headed for crisis and currency collapse, so I have decided to cut my losses, freeze myself in the positive equity position I started in, and leave it to you to do what you want. I didn’t change the rules, I’m just adapting to the rules of a radical situation whose outcome seems very hard to predict. That seems to me to be the logical conclusion of the ill-advised central bank decision to try to engineer a currency that is an intrinsic liability. People are now rushing out of the currency and into barter, gems, wampum, cans of creamed corn, anything they can find and trade that will serve as a savings vehicle that loses its value less rapidly than the central bank’s money.

    • Elfin Cleric lvl 12

      Boy am I glad to hear you say that, Dan! I was starting to wonder what kind of freak show I had gotten myself mixed up with. Fact is, with the CPI running between 2-6% and the banks and treasury offering somewhere between 0-2%, the dollar is already a liability with very significant downside risk and virtually no upside. The only thing holding it together is the stupidity of the American public and our aircraft carriers overseas.

  39. I take it you are relinquishing your borrowing clients to me? You agree that I can beat any offer you can make them because my funding is cheaper than yours?

  40. “People are now rushing out of the currency and into barter, gems, …”

    That sounds like inflation. I thought you said it would be deflationary up higher?

    Are you claiming that a dollar has a “positive value” for all interest rates above zero but suddenly gets a “negative value” the moment rates go to -0.01%? So at 0% the dollar is worthless?

  41. Dan,

    In the real world, banks find an interest rate equilibrium in an instant following a a rate decision by the central bank. Lets say the rate went from 5%/year to -5% a year. In reality if one obstreperous bank decided to follow your policy it would take a few weeks, possibly a couple of months before essentially all its loans had been lost to competing banks. A real bank would see how the end game would play out and would buckle and move its rates in line with everyone else almost instantly. The only winning move is to match my rates which will allow you to profit from lending.

    I understand that you are claiming that there will be an impact in the real economy. But that impact (inflation, whatever) will take much longer than the equilibrating rates game that we are playing, which ought to play out in a matter of seconds. I’m happy to explore the effects on the real economy. But first we have to let the rates market equilibrate. If you refuse to make the decision to let your bank survive based on claims about what’s going to happen in the real economy over the much longer term, then we can’t get to that equilibrium where we can explore the impact on the real economy. *If* we go to that equilibrium and then you prove that the real economy ends up unstable and somehow you get forced into losing money as a result, then you’ll be able to say “look, I told you it couldn’t work. If banks lend a negative rates they end up losing money, and they are better off shutting down first” But, you have nothing to lose if, for example, you move your deposit rate to slightly below mine, and your lending rate to slightly above. Then in the worst case, you would just slowly lose clients but be profitable in the meanwhile. You can always shut down at *any* point in the future, but between now and then you will make money. The only rational move is to move your rates in line with mine.

  42. Dan,

    Should I stop checking for responses from you?

  43. Dan Kervick

    I’m sure we’ll return to this at some point.

  44. It seems to me that we quit just as we were about to get to the actually interesting part: the impact on the real economy of no lower bound on interest rates. Alas, till next time.