Typing on a computer

The idea of deliberate practice is one that I have been very eager to get my students to understand. I found a nice passage in Moonwalking with Einstein: The Art and Science of Remembering Everything, explaining deliberate practice. Here it is, from pages 169-175:

When people first learn to use a keyboard, they improve very quickly from sloppy single-finger pecking to careful two-handed typing, until eventually the fingers move so effortlessly across the keys that the whole process becomes unconscious and the fingers seem to take on a mind of their own. At this point, most people’s typing skills stop progressing. They reach a plateau. If you think about it, it’s a strange phenomenon. After all, we’ve always been told that practice makes perfect, and many people sit behind a keyboard for at least several hours a day in essence practicing their typing. Why don’t they just keep getting better and better. 

In the 1960’s, the psychologists Paul Fitts and Michael Posner attempted to answer this question by describing the three stages that anyone goes through when acquiring a new skill. During the first phase, known as the “cognitive stage,” you’re intellectualizing the task and discovering new strategies to accomplish it more proficiently. During the second, “associative stage,” you’re concentrating less, making fewer major errors, and generally becoming more efficient. Finally you reach what Fitts called the “autonomous stage,” when you figure that you’ve gotten as good as you need to get at the task and you’re basically running on autopilot….

What separates the experts from the rest of us is that they tend to engage in a very directed, highly focused routine, which Ericsson has labeled “deliberate practice.” Having studied the best of the best in many different fields, he has found that top achievers tend to follow the same general pattern of development. They develop strategies for consciously keeping out of the autonomous stage while they practice by doing three things: focusing on their technique, staying goal-oriented, and getting constant and immediate feedback on their performance. 

Amateur musicians, for example, are more likely to spend their practice time playing music, whereas pros are more likely to work through tedious exercises or focus on specific, difficult parts of pieces. The best ice skaters spend more of their practice time trying jumps that they land less often, while lesser skaters work more on jumps they’ve already mastered. Deliberate practice, by its nature, must be hard….

The best way to get out of the autonomous stage and off the OK plateau, Ericsson has found, is to actually practice failing. One way to do that is to put yourself in the mind of someone far more competent at the task that you’re trying to master, and try to figure out how that person works through problems. Benjamin Franklin was apparently an early practitioner  of this technique. In his autobiography, he describes how he used to read essays by the great thinkers and try to reconstruct the the author’s arguments according to Franklin’s own logic. He’d then open up the essay and compare his reconstruction to the original words to see how his own chain of thinking stacked up against the master’s. The best chess players follow a similar strategy. They will often spend several hours a day replaying the games of grand masters one move at a time, tryhing to understand the expert’s thinking at each step. Indeed, the single best predictor of an individual’s chess skill is not the amount of chess he’s played against opponents, but rather the amount of time he’s spent sitting alone working through old games.

The secret to improving at a skill is to retain some degree of conscious control over it while practicing—to force oneself to stay out of autopilot. With typing, it’s relatively easy to get past the OK plateau. Psychologists have discovered that the most efficient method is to force yourself to type faster than feels comfortable, and to allow yourself to make mistakes. In one noted experiment, typists were repeatedly flashed words 10 to 15 percent faster than their fingers were able to translate them onto the keyboard. At first they weren’t able to keep up, but over a period of days they figured out the obstacles that were slowing them down, and overcame them, and then continued to type at the faster speed. By bringing typing out of the autonomous stage and back under their conscious control, they had conquered the OK plateau….

This, more than anything, is what differentiates the top memorizers from the second tier: they approach memorization like a science. They develop hypotheses about their limitations; they conduct experiments and track data. “It’s like you’re developing a piece of technology, or working on a scientific theory,” the two-time world champ Andi Bell once told me. “You have to analyze what you’re doing.” 

Beginning with “How Subordinating Paper Currency to Electronic Money Can End Recessions and End Inflation,” I have often written of how a crawling-peg exchange rate between paper currency and electronic money can eliminate the zero lower bound. In this post, I want to give more detail about how to determine the appropriate exchange rate.  Also, in “A Minimalist Implementation of Electronic Money,” I wrote of a “deposit charge” for paper currency deposited with the central bank. One minus the deposit charge is the effective exchange rate there. That is, $1 of paper currency would, in effect, be worth $(1-deposit charge) of electronic money, since that is what it would become once deposited. So determining the appropriate exchange rate at which paper currency can be exchanged for electronic money also determines the “deposit charge” (and ideally, the equal withdrawal discount) in the minimalist implementation of electronic money. 

The way to determine the appropriate exchange rate between paper currency and electronic money is to first decide what the effective interest rate on paper currency should be. The current paper currency policies all around the world amount to the choice to have the nominal interest rate on paper currency be equal to zero all the time. (In this post, I will always be talking about the effective interest rate on paper currency before storage costs.) This policy decision (or non-decision) to keep the interest rate on paper currency equal to zero is what creates the zero lower bound. 

In order to eliminate the zero lower bound as a lower bound, the interest rate on paper currency needs to be chosen somewhere below the desired policy interest rate (the fed funds rate in the US, the bank rate in the UK, the repo rate in Sweden, etc.) In an electronic money system, the monetary policy committee would decide on a paper currency interest rate at the same time it chose the policy interest rate. Once the paper currency interest rate is decided upon, that paper currency interest determines how the exchange rate between paper currency and electronic money evolves. 

The math is exactly the math needed to see what $1 turns in to if it earns at each moment the variable interest rate in the graph. Of course the graph above is only an example. What matters is the paper currency interest rate the central bank decides on.

I will give the math for compound interest with a variable interest rate below, but in this context, the basic idea is that to make the paper currency interest rate negative, the exchange rate between paper currency and electronic money has to make a paper dollar worth gradually less and less compared to an electronic dollar. On the other hand, to make the paper currency interest rate positive, the exchange rate between paper currency and electronic money has to make a paper dollar worth gradually more and more compared to an electronic dollar.  

To give the technical description of how the exchange rate is determined from the math of compound interest with a variable interest rate, start from a moment when the paper dollar (or euro, or yen or pound, …) is at par relative to the electronic dollar. An obvious moment when paper currency is at par is the moment electronic money is introduced. Draw the graph of the desired paper currency interest rate as in the graph above. Figure out the area between the x-axis and the curve of the desired paper currency interest rate, with area below the axis counting as negative and area above the axis counting as positive. In calculus, this area is called an integral. (This integral needs to be calculated with 1% per year being represented as .01/year, 2% and .02/year, and so on; or if not you will need to divide the integral by 100 to get the right number. Also, notice that -3% per year is only -0.25% per month, or -0.75% per quarter. I like to think of the % sign as just another name for .01, with a hint that some sort of proportion and maybe some kind of compounding is going on.) The integral of the paper currency interest rate from when electronic money is introduced is then the natural logarithm of the appropriate exchange rate—the value of a paper dollar in terms of electronic dollars. (I give an introduction to natural logarithms in my post  “The Logarithmic Harmony of Percent Changes and Growth Rates.”) Equivalently, if you calculate the integral (with 1% treated as another name for .01) and then use the exp key (or e to the x power key) on a calculator on that number, you will get the appropriate exchange rate. 

Another way to describe things is that, to a good approximation, for exchange rates not too far from par, the integral gives the size of the deposit charge in the minimalist implementation of electronic money that determines the effective exchange rate, except that a negative integral corresponds to a positive deposit charge. 

In the graph above, the integral is shown shaded in over a period of time when the intended interest rate on paper currency is always negative. That will yield an exchange rate in which a paper dollar is worth less than an electronic dollar. 

In the graph below, the integral is shown shaded in over a longer period of time over which the intended interest rate on paper currency is first negative, then positive. With the area below the axis counted as negative and the area above the axis counted as positive, the overall integral is getting close to zero again, so the exchange rate is quickly coming back up towards par. (The earlier moment in time when the paper currency hit zero on its way from negative territory to positive territory was the moment when the value of a paper dollar relative to an electronic dollar was the lowest. After that the exchange rate is going up again.)  

The most important point is this: the zero lower bound is a policy choice. From the perspective I am taking, the zero lower bound arises when governments choose to have a paper currency interest rate equal to zero all the time, in order to keep paper currency at par. The world has suffered a great deal in the past few years from paper currency interest rates too high to allow full economic recovery. In our current environment, a paper currency interest rate of zero is too high in many countries. In countries that are still below the natural level of output, let’s lower paper currency interest rates, along with policy interest rates, the interest rate on reserves, and the discount rate at which central banks lend. 

A Minimalist Painting by Piet Mondrian

The Politics of Negative Nominal Interest Rates. Concerns about political reactions are an issue for negative nominal interest rates and electronic money. First, even without moving to electronic money, negative nominal interest rates raise political issues. To get a sense of how negative nominal interest rates might play, take a look at this very nice 81 second BBC clip in which reporter Giles Dilnot explains negative nominal interest rates (in the context of the BOE Deputy Governor Paul Tucker saying the Bank of England is considering them). Giles is good at emphasizing the benefits for borrowers and for the economy, as well as the blow to savers from lower interest rates. He also alludes to the fact that, once the economy recovers, interest rates naturally go up. This increase in interest rates with economic recovery means that a short period of negative nominal interest rates to kickstart the economy could be better for savers than the likely alternative of a long period of zero interest rates.  

The Politics of Electronic Money. I want to argue that once a central bank has incurred whatever political hit there is from crossing the Rubicon into negative interest rate territory (to, say 0.25% or -0.5% per year), that the additional political hit from doing what is needed prevent massive paper currency storage can be effectively managed. That is, it is possible to implement a paper currency policy that will allow interest rates as low as, say, -2%, -5% per year or below, that is not too far from the way we currently handle paper money. In this post, I will lay out my latest thinking about a minimalist approach to preventing massive paper currency storage. I think what I say here is an advance over what I say in “Getting Leeway on the Zero Lower Bound for Interest Rates by Giving the Central Bank Standby Authority Over Paper Currency Policy,” though it is very much in the same spirit.

The Downside of Penalizing or Limiting Paper Currency Withdrawals. In order to make nominal interest rates as low as -2% per year possible, the key activity that must be prevented is withdrawing paper currency from the bank, storing it for a few months or a few years and then depositing back in the bank at par with no penalty. A policy-maker might be tempted to try to prevent this by limiting or penalizing withdrawals, but that approach has the drawback of penalizing two very different types of paper currency withdrawals:

1. withdrawals of paper currency in order to spend the money—which a country needing aggregate demand stimulus would want to encourage, and
2. withdrawals of paper currency for the purpose of storage—which a country needing aggregate demand stimulus would want to discourage, since that interferes with lowering nominal interest rates below, say, -0.5% per year.

Moreover, in many countries, almost everyone is in the habit of regularly withdrawing paper currency from banks and ATM’s, so any penalty to paper currency withdrawals would be highly visible. And even relatively high limits on withdrawals would be a highly salient policy. People who have never in their whole lives taken out the equivalent of $1000 in paper currency within a single month’s time could reasonably worry that they might someday need to do so because of some emergency.

The Alternative of Penalizing Deposits of Paper Currency (Deposit Charges). An important insight is that returns from (a) withdrawing paper currency, (b) storing it, and then (c) depositing it again at par can be attacked at any of these three stages. I discussed the problems with penalizing or limiting withdrawals above. Storage can be made more expensive, but not easily: paper currency storage is so easy that individuals can do it without any outside help, and is easy to do secretly. So let me argue for the following three measures as a minimalist implementation of electronic money:  

• an appropriate penalty to deposits of paper currency or coins with the central bank (a proportional “deposit charge”), 
• a corresponding discount applied to vault cash that is being used to satisfy reserve requirements, and 
• a right for any individual or business, any government agency, and any creditor, to refuse payment in paper currency—that is, paper currency would no longer be legal tender. 

The way in which this is an implementation of the electronic money policy I proposed in “How Subordinating Paper Currency to Electronic Money Can End Recessions and End Inflation” is that the penalty for depositing paper currency with the central bank would, at first, gradually increase from zero to a higher penalty over time in order to make the effective interest rate on paper currency withdrawn and then later deposited by banks negative. When economic recovery allowed other nominal interest rates to turned positive, then the penalty for deposits at the central bank could start gradually shrinking, until the penalty became zero.

Equilibrium Effects of Deposit Charges for Paper Currency. Presumably, the deposit charge for paper currency that banks face would be passed on to bank customers depositing paper currency. From the perspective of a regular household, an important aspect of this policy is that anyone who holds on to paper currency for long enough will ultimately be able to deposit it without penalty. And indeed, if the deposit penalty is structured so that the effective interest rate on paper currency is kept very close to the target interest rate (e.g., the fed funds rate for the US), then over the period of time the penalty applied for, anyone who saved in paper currency would not be disadvantaged relative to someone who saved in the bank.         

At the grocery store or other shops, it might be a while before merchants discouraged customers from using paper currency. As it is now, merchants accept credit cards despite the fact that must pay to accept credit-card payment. For example, in the UK, Barclay Card currently advertises that it charges businesses 1.5% on credit card transactions. 

So currently, getting paid by credit card is something like 1.5% less attractive than getting paid in paper currency. If, in order to avoid alienating customers, businesses were willing to continue accepting paper currency at par even if it was 1.5% less attractive to themthan credit card payments, that might allow a 3% swing before things changed for retail customers: retail customers might be able to pay with paper currency at par even if banks had to pay a 3% penalty to the central bank for paper currency deposits. Note, however, that as the penalty for deposit of paper currency with the central bank grew, retailers might encourage customers to use their credit and debit cards more in more subtle ways than charging them more for using paper currency. (Based on self-interest, credit card companies might be very supportive of the electronic money program for this reason.)  

Withdrawal Discounts. At a point where banks faced, say, a 3% charge to deposit paper currency with the central bank, and an effective interest rate on paper currency somewhat below other safe interest rates, banks would be likely to offer paper currency to bank customers at, say, a 2% discount. (This means, for example, that withdrawing 100 paper dollars would result in only a $98 subtraction from the bank account.) There is a reasonable hope that some level of withdrawal discount would arise by the time grocery stores and other retailers began refusing to accept paper currency at par. The central bank could encourage such withdrawal discounts by levying the deposit charge on net deposits of paper currency by banks (even if net deposits are negative), thereby effectively giving banks a withdrawal discount on paper currency. But economic theory predicts that if any banks at all are depositing paper currency with the central bank, a withdrawal discount for paper currency should arise in the market even if the central bank gives no withdrawal discount.  

Removing Legal Tender Status from Paper Currency. A key advantage of a minimalist implementation of electronic money is that many independent central banks might have the legal authority for at least two of the three elements of the minimalist implementation: charging for deposits of paper currency with the central bank and discounting the contribution of vault cash to fulfilling reserve requirements. Any country that has already abolished legal tender status for paper currency is ahead of the game. Note that any ability of individuals, firms and creditors to legally refuse payment in paper currency represents a partial elimination of legal tender status for paper currency. So the details of statutory law, case law and administrative law might be important in determining the degree to which a country has economically effective legal tender status for paper currency. Some countries may have legal tender status for paper currency in name only.

For any country that currently has firm legal tender status for paper currency, other issues arise. If done in advance of the institution of a deposit charge, giving everyone, including creditors, the right to refuse payment in paper currency would not immediately change people’s lives much at all. Any country considering an electronic money program would be well-advised to remove legal tender status from paper currency well in advance of the actual decision to implement the complete minimalist program for electronic money. Indeed, if the relevant arms of the government can cooperate, it would make sense to remove legal tender status from paper currency at the moment when target interest rates are first pushed into negative territory, since then any political objection to removing legal tender status to paper currency would probably be drowned out by the much greater political furor over negative interest rates themselves—negative nominal interest rates that have immediate practical consequences. By contrast, as long as the central bank continues to accept paper currency at par (with no deposit charge), there would be little immediate effect of removing legal tender status from paper currency. Any effect from removing legal tender status should be because of an interaction with expected future deposit charges and reserve requirement discounts for paper currency. While removing legal tender status combined with an expected future deposit charge would affect medium-term interest rates, it should not immediately affect the value of paper currency relative to electronic money.     

A Legal-Tender-Work-Around Implementation of Electronic Money. If a central bank decides to implement electronic money, but cannot depend on other arms of the government to remove legal tender status for paper currency, there is a work-around that might do the job in certain legal environments. The central bank might be able to switch over relatively quickly from giving out traditional paper currency in exchange for  electronic money to giving out demandable bearer bonds that paid a variable interest rate that could go negative. These bearer bonds would function in all respects like the non-legal-tender paper currency discussed above, and could be printed in similar denominations and patterns. 

If what was effectively non-legal-tender paper currency coexisted with legal-tender paper currency, by Gresham’s Law that worse money drives out better money, most transactions would soon take place in the non-legal-tender paper currency, while people might hold on to the legal-tender paper money until the moment of the maximum deposit charge, using it at that point to discharge debts that can be paid off in paper currency. In effect, while the “bearer bonds with a variable interest rate” took on the role of paper currency, the old legal-tender paper currency would become, in effect infinitely-lived bonds (that is consols) with a guaranteed zero interest rate that can be used to discharge debts at face value at any time. Except to the extent there were some chance its legal tender status would be eliminated in the future, the old legal-tender paper currency should be worth at least its face value, and could easily be worth a premium in periods when negative interest rates were expected, with the premium gradually declining as the period of negative nominal interest rates drew to a close. After the initial appreciation, that declining premium would make the expected rate of return of the old legal-tender paper currency negative, like other safe assets under the negative nominal interest rate regime with the minimal implementation of electronic money. The uncertainty in the movements of the premium would make the old legal-tender paper currency quite inconvenient as currency, but as currency they would be driven out by the new, non-legal tender paper currency anyway. The old legal-tender paper currency would become simply one more exotic portfolio asset.  

Note that from the moment people realized that the old legal-tender paper currency might soon run at a premium, it might be necessary to immediately limit withdrawals of the old legal-tender paper currency (at least from the central bank), or institute a temporary withdrawal charge on the old paper currency until the new “variable-interest bearer bonds” (also known as the new, non-legal-tender paper currency notes) were ready. But the reason this would be necessary would be to avoid unfair transfers to people who realized what was going on rather than due to any danger that the old legal-tender paper currency would prevent nominal interest rates from going down as low as needed. The fluctuating, and on average declining, premium on the old paper currency during the negative interest rate period would see to that.    

Policy for Government Banks and Other Government Agencies that Accept Paper Currency. In an electronic money regime, any option there was of paying taxes in paper currency should be discontinued.  Also, it is important that all government-owned banks, such as postal savings in Japan, apply the same penalty to deposits of paper currency as the central bank. Finally, so that their managers can think clearly about their revenues and costs, government agencies that accept paper currency for goods and services should face the same deposit charge in passing along paper currency as privately-owned banks face when they deposit paper currency with the central bank. The overarching principle is that in an electronic money regime, government agencies should, in fact, exercise the right they have to refuse payment in paper currency at par.     

The Time Trend for the Politics of Electronic Money. Although nominal illusion is significant enough that the first brush with negative nominal interest rates (for the target rate, on reserves, and for loans from the central bank) will always cause political waves, the further moves discussed above to avoid massive paper currency storage should become easier and easier for the public to accept as a larger fraction of all the transactions they conduct are conducted electronically, using credit cards, debit cards, and electronic transfers. Over the years to come, the primacy of electronic money over paper currency will come to seem more and more natural. Electronic money is an idea whose time is coming, perhaps sooner than many think.  

“Truth” decal

What John Stuart MIll says on how freedom of speech keeps the truth alive is brilliant. Although he couches his discussion in terms of religious debates, where it clearly applies, it isn’t about religious debates alone. It also applies to scientific, political and philosophical debates.

When you finish reading the passage below, compare the picture of “keeping the truth alive” that you have at that point with what you imagined when you first read the title of the post above.   

From On Liberty, chapter II: 

If, however, the mischievous operation of the absence of free discussion, when the received opinions are true, were confined to leaving men ignorant of the grounds of those opinions, it might be thought that this, if an intellectual, is no moral evil, and does not affect the worth of the opinions, regarded in their influence on the character. The fact, however, is, that not only the grounds of the opinion are forgotten in the absence of discussion, but too often the meaning of the opinion itself. The words which convey it, cease to suggest ideas, or suggest only a small portion of those they were originally employed to communicate. Instead of a vivid conception and a living belief, there remain only a few phrases retained by rote; or, if any part, the shell and husk only of the meaning is retained, the finer essence being lost. The great chapter in human history which this fact occupies and fills, cannot be too earnestly studied and meditated on.

It is illustrated in the experience of almost all ethical doctrines and religious creeds. They are all full of meaning and vitality to those who originate them, and to the direct disciples of the originators. Their meaning continues to be felt in undiminished strength, and is perhaps brought out into even fuller consciousness, so long as the struggle lasts to give the doctrine or creed an ascendancy over other creeds. At last it either prevails, and becomes the general opinion, or its progress stops; it keeps possession of the ground it has gained, but ceases to spread further. When either of these results has become apparent, controversy on the subject flags, and gradually dies away. The doctrine has taken its place, if not as a received opinion, as one of the admitted sects or divisions of opinion: those who hold it have generally inherited, not adopted it; and conversion from one of these doctrines to another, being now an exceptional fact, occupies little place in the thoughts of their professors. Instead of being, as at first, constantly on the alert either to defend themselves against the world, or to bring the world over to them, they have subsided into acquiescence, and neither listen, when they can help it, to arguments against their creed, nor trouble dissentients (if there be such) with arguments in its favour. From this time may usually be dated the decline in the living power of the doctrine. We often hear the teachers of all creeds lamenting the difficulty of keeping up in the minds of believers a lively apprehension of the truth which they nominally recognise, so that it may penetrate the feelings, and acquire a real mastery over the conduct. No such difficulty is complained of while the creed is still fighting for its existence: even the weaker combatants then know and feel what they are fighting for, and the difference between it and other doctrines; and in that period of every creed’s existence, not a few persons may be found, who have realized its fundamental principles in all the forms of thought, have weighed and considered them in all their important bearings, and have experienced the full effect on the character, which belief in that creed ought to produce in a mind thoroughly imbued with it. But when it has come to be an hereditary creed, and to be received passively, not actively—when the mind is no longer compelled, in the same degree as at first, to exercise its vital powers on the questions which its belief presents to it, there is a progressive tendency to forget all of the belief except the formularies, or to give it a dull and torpid assent, as if accepting it on trust dispensed with the necessity of realizing it in consciousness, or testing it by personal experience; until it almost ceases to connect itself at all with the inner life of the human being. Then are seen the cases, so frequent in this age of the world as almost to form the majority, in which the creed remains as it were outside the mind, incrusting and petrifying it against all other influences addressed to the higher parts of our nature; manifesting its power by not suffering any fresh and living conviction to get in, but itself doing nothing for the mind or heart, except standing sentinel over them to keep them vacant.

Link to the Column on Quartz

Here is the full text of my 21st Quartz column, “This economic theory was born in the blogosphere and could save markets from collapse,” now brought home to supplysideliberal.com and given my preferred title. (I am now up-to-date bringing home to supplysideliberal.com all of my columns that are past the 30-day exclusive I give Quartz by contract.)  

Even before I started blogging, Noah Smith told me I should write a post about NGDP targeting. This is that post. And it is also the post on “Optimal Monetary Policy” that I have been promising for some time. It was first published on February 22, 2013. Links to all my other columns can be found here.

If you want to mirror the content of this post on another site, that is possible for a limited time if you read the legal notice at this link and include both a link to the original Quartz column and the following copyright notice:

© February 22, 2013: Miles Kimball, as first published on Quartz. Used by permission according to a temporary nonexclusive license expiring June 30, 2014. All rights reserved.

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The most important equation in economics

Much of the history of economics can be traced by the contents of its best-selling textbooks. In 1848, John Stuart Mill published the blockbuster economics textbook of the 19th century: Principles of Political Economy. A century later, in 1948, Paul Samuelson—the very first American Nobel laureate in economics, who more than anyone else made economics the mathematical subject it is today—popularized Keynesian economics in the best-selling economics textbook of all time,Economics: An Introductory Analysis. This past year, in my classroom, I taught from one of the two best and most popular introductory economics textbooks, Brief Principles of Macroeconomics authored by Greg Mankiw—chair of the economics department at Harvard, former chair of the president’s Council of Economic Advisors, and my graduate school advisor.

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