Dan Kervick: The Astonishing Case of the Impenetrable Zero Bound

Yves here. I rather like the storytelling format of this post.

By Dan Kervick, who does research in decision theory and analytic metaphysics. Cross posted from New Economic Perspectives

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.

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[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.]