## On Prediction

Suppose that you are a parent of a young child. Every night you give your child a glass of milk with their dinner. When your child is very young, they have a lid on their cup to prevent it from spilling. However, there comes a time when you let them drink without the lid. The absence of a lid presents a possible problem: spilled milk. Initially there is not much you can do to prevent milk from being spilled. However, over time, you begin to notice things that predict when the milk is going to be spilled. For example, certain placements of the cup on the table might make it more likely that the milk is spilled. Similarly, when your child reaches across the table, this also increases the likelihood of spilled milk. The fact that you are able to notice these “risk factors” means that, over time, you will be able to limit the number of times milk is spilled. You begin to move the cup away from troublesome spots before the spill. You institute a rule that the child is not allowed to reach across the table to get something they want. By doing so, the spills become less frequent. You might even get so good at predicting when the milk will spill and preventing it from happening that when it does happen, you and your spouse might argue about it. In fact, with the benefit of hindsight, one of you might say to the other “how did you not see that the milk was going to spill?”

Now suppose that there was an outside observer who studied the spilling of milk at your house. They are tasked with difficult questions: How good are you at successfully predicting when milk is spilled? Were any of your methods to prevent spilling actually successful?

In theory these don’t sound like hard questions. For example, if the observer notices that you are taking preemptive action and the spilling is becoming less frequent, then isn’t this evidence that you are doing a good job at both predicting and preventing spills? Not necessarily. Your child might be maturing and gaining more experience with drinking out of a cup with no lid and therefore less likely to spill their milk. In addition, we would need to know the counterfactual of what would have happened if you had not taken action or created a particular dinner rule for your child. In other words, we need to know whether your child would have spilled the milk if you had not taken the action that you did.

Now, let’s imagine a scenario in which the observer studying your dinner table is naive and just records what happens. Based on their observations, the observer then has to explain why the milk spills. Since the naive observer sees you take action (perhaps even frequently), but also records instances where the milk spills, the observer might come away with the conclusion that you know how to prevent spills (they see you taking such actions), but that you don’t do a good job predicting spills. Their recommendation would be that you need to get better at predicting spills.

As you have certainly realized by now, this post is not meant to be about milk or the weird person observing your dinner habits. It is really about business cycles and countercyclical policy. Naive critics of macroeconomics often point to recessions (especially severe recessions) and say “why didn’t macroeconomists see this coming?” This is an incredibly naive and silly critique in the same way that concluding that you could prevent all of your child’s spills if you were just better at prediction. This view is naive for several reasons. First, we do not have the counterfactual. What would have happened if we had done things differently? It is possible that it might have prevented what we observed, but we need to have a model of how things would have played out differently. It is also possible that there was nothing that we could do or that our actions could have made things even worse. Second, even if we live in a world in which there is some Pareto-improving policy that would have prevented the recession and everyone knows it, this doesn’t mean that we would never have recessions. In fact, in a world of a commonly known Pareto-improving policy, recessions would only occur when they were not predicted. In other words, virtually by definition, recessions would be unpredictable events in that world. To the naive observer, however, they only see the data. They do not have the counterfactuals. Thus, they are likely to conclude that macroeconomists are terrible at their jobs because they never see the recession coming. Put differently, their criticism of macroeconomics would be that macroeconomists fail to predict unpredictable events. That critique is as silly as crying over spilled milk.

## Allan Meltzer

Earlier this month, I had the privilege of speaking at a conference in honor of Allan Meltzer. It was a great conference with a number of excellent speakers (how I got on the list is anyone’s guess). Meltzer had an incredible influence on the profession through his work on monetary policy and the history of the Federal Reserve.

I was on a panel discussing Meltzer’s views on the monetary transmission mechanism. Anyone who is familiar with Meltzer’s work knows that this was a topic that he thought was of the utmost significance. For those not familiar with economic jargon, this line of research examines the various possible channels through which monetary policy affects economic activity. On the one hand, this research has been pretty influential in the sense that Ben Bernanke often sounded quite Meltzer-esque in his discussion of monetary transmission when justifying the Federal Reserve’s large scale asset purchases. On the other hand, much of the current literature on monetary policy fails to take into account many of Meltzer’s insights because this recent literature focuses too narrowly on the short term nominal interest rate.

I understand that they are putting together a book that collects the contributions of each of the speakers, but some of the material is already available online. I know of 3 papers that have been posted online, including my own (I’ll update this if I hear of others before the book comes out). These papers are linked below. I hope that those interested will take the time to wrestle with Meltzer’s arguments.

and my paper:

Monetary Policy and the Interest Rate: Reflections on Allan Meltzer’s Contributions to Monetary Economics

## The Quantity Theory of Money: Lessons from Sweden’s Age of Freedom

Throughout the 17th and early 18th century, Sweden had a significant empire in northern Europe. In 1700, an alliance of Denmark-Norway, Russia, and others attacked the Swedes. While Charles XII, then the king of Sweden, had initial success against this alliance, he was eventually wounded and the Swedes never really recovered. Charles died in 1718. Charles had taken power at the age of 15 and spent virtually his entire adult life at war. He never married nor did he have children. When he died, there was uncertainty about who had the rightful claim to the throne. Charles’s sister Ulrika claimed that she was the rightful heiress since she was the closest living relative. Ultimately, the Swedish Riksdag agreed to recognize Ulrika in exchange for eliminating the absolute monarchy and setting up a parliamentary system. In this new system, the political power was concentrated in the Riksdag. The period from 1721 – 1772 is therefore known as “Frihetstiden”, or the Age of Freedom.

During the Age of Freedom, the Riksdag was dominated by two political parties that were referred to as the Hats and the Caps. The Hats controlled power for nearly 30 years beginning in 1738 and were mercantilists (their motto was “Svensker man i svensk drakt”, or “Swedish men in Swedish clothes”). In 1739, The Hats used the Swedish central bank, the Riksens Standers Bank (what is now known as the Riksbank), to give loans to private industry. These loans were funded with the creation of bank notes. In addition, the Hats started an ill-fated war with the Russians over parts of Finland. During this time, Sweden was effectively on a copper standard, but the expansion of bank notes for the provision of private lending and the use of the bank to finance the war ultimately led to the suspension of convertibility into copper in 1745. The increase in the provision of private credit by the central bank continued. In the 1750s, Sweden entered the Seven Years War to fight alongside their French allies. Sweden was particularly involved in the Pomeranian War with Prussia over land that they had lost in the Great Northern War under Charles XII (discussed above). The Hats were hesitant to levy any new taxes to pay for the war because to do so would require calling the Riksdag and therefore divulging the state’s budget. As a result, loans to the Crown increased substantially during the war and the supply of bank notes increased correspondingly.

The Hats seemed to view the money supply as a limiting factor in development. They thought that an increase in the money supply would increase aggregate demand, which would encourage greater production and entrepreneurship. Increases in the money supply could apparently have a permanent effect on output. The opposition party, the Caps, countered that this increase the supply of bank notes was excessive and that the excess supply of money was causing rising prices and a depreciation of the exchange rate. By 1765, the public voted the Caps into power and the Hats become the main opposition party. Upon taking power the Caps decided to decrease the money supply in order to restore the price level and the exchange rate to what it had been prior to this expansion. What followed was a major decline in the supply of bank notes and a very costly deflation. The deflation was so costly that it pushed the Caps out of power and returned the Hats to power. Ultimately, a coup ended the parliamentary system and restored the monarchy. Shortly thereafter, Sweden adopted a silver standard.

So why give you all of this history? The reason is that this series of events represents a sort of quasi-natural experiment regarding monetary policy. The Hats engaged in a deliberate increase in the money supply to increase economic activity and finance a war. What followed were significantly higher prices and a depreciation of the exchange rate. The increase in the money supply can be considered exogenous in the sense that the change in the money supply was brought about through deliberate policies by the Hats and is therefore immune to claims that higher prices were causing an increase in the supply of bank notes. The subsequent reduction of the money supply by the Caps brought about a significant deflation. Again, this was a deliberate attempt by the Caps to reduce the money supply and is therefore immune to claims of reverse causation. As Johan Myhrman notes “it is almost like a controlled experiment.” Below is a line graph of the monetary base and the price level during the period in question (the source is Riksbank historical statistics). I have also plotted the best linear fit of the data. As shown in the figure, there is a standard quantity theoretic interpretation of the data. Given the quasi-experimental nature of the period, this would seem to provide strong evidence in favor of the quantity theory of money under an inconvertible paper money.

## The Phillips Curve, Again

The Phillips Curve is back. In saying so, I do not mean to imply that being “back” refers to a sudden reappearance of a stable empirical relationship between unemployment (or the output gap) and inflation. The Phillips Curve is back in the same way that conspiracy theories about the assassination of JFK are back after the recent release of government documents. In other words, the Phillips Curve is something that people desperately want to believe in, despite the lack of evidence.

The Phillips Curve is all the rage among central bankers. Since the Federal Reserve embarked on quantitative easing, they have been ensuring the public that QE would not be inflationary because of the slack in the economy. Until labor market conditions tighten, there would be little threat of inflation. Then, as the labor market tightened, the Federal Reserve warned that they might have to start raising interest rates to prevent these tightening conditions from creating inflation.

What is remarkable about this period is that the Federal Reserve has undershot its target rate of inflation throughout this entire period — and continues to do so today. So what does this tell us about the Phillips Curve and what can we learn about monetary policy?

If one looks at the data on unemployment and inflation (or even the output gap and inflation), you could more easily draw Orion the Hunter as you could a stable Phillips Curve. Fear not, sophisticated advocates of the Phillips Curve will say. This is simply the Lucas Critique at play here. If a Phillips Curve exists, and if the central bank tries to exploit it, then it will not be evident in the data. In fact, if you take a really basic 3-equation-version of the New Keynesian model, there is a New Keynesian Phillips Curve in the model. However, when you solve for the equilibrium conditions, you find that inflation is a function of demand shocks, technology shocks, and unexpected changes in interest rates. The output gap doesn’t appear in the solution. But fear not, this simply means that monetary policy is working properly. The Phillips Curve is apparently like the observer effect in quantum mechanics in that when we try to observe the Phillips Curve, we change the actual result (this is a joke, please do not leave comments about why I’ve misunderstood the observer effect).

However, I would like to submit that even this interpretation is problematic for thinking about monetary policy and defending the Phillips Curve. In the New Keynesian model, we get an equation that looks like this:

$\pi_t = \beta E_t \pi_{t+1} + \kappa y_t$

where $\pi$ is the rate of inflation, $y_t$ is the output gap, and $\kappa$ and $\beta$ are parameters. This equation is an equilibrium condition of the model. Since it is an equilibrium condition, it always holds. This equilibrium condition can be derived by (1) having a monopolistically competitive firm solve a profit-maximization problem with a Rotemberg-esque quadratic adjustment cost associated with prices, (2) solving for a symmetric equilibrium, and (3) log-linearizing around the steady state. So this is an equilibrium condition for the aggregate economy. When you look at this equation, you would think that you can use this equation for some intuition about the evolution of inflation. To demonstrate how silly it would be to do so, let’s assume that people in the economy are sufficiently patient that we can re-write this equation as:

$\pi_t = E_t \pi_{t+1} + \kappa y_t$

So you look at this equilibrium condition and you get a very New Keynesian interpretation of the world. It looks as though inflation is explained by changes in expected inflation and changes in the output gap. However, this interpretation is wrong. This equation is an equilibrium relationship. Thus, I could just as easily re-write this equation as

$y_t = \frac{1}{\kappa} (\pi_t - E_t \pi_{t+1})$

Hmm. Now we have something that looks like an expectations augmented Phillips Curve with the direction of causation moving in the opposite direction. Now, it looks as though unexpected changes in inflation are causing changes in the output gap.

So what is a central bank to do?

Actually, using this equation alone, we can’t say anything at all! This equation is just an equilibrium relationship. Without knowing anything else about the economy, this tells us nothing. We have one equilibrium equation with two unknowns. In addition, we have a rational expectation about inflation, which implies that the expectation is model-consistent. In order to know what a model consistent expectation is, we need to have a model from which we can form expectations. In other words, this equation tells us absolutely nothing in isolation from a bigger model.

For example, suppose that we are in a world with the gold standard. Let $p_t$ be the log of the price level. A reasonable assumption would be that $p_t$ follows a random walk:

$p_t = p_{t-1} + e_t$

or

$\pi_t = e_t$

Combining this with our Phillips Curve would give us

$y_t = \frac{1}{\kappa} \pi_t = \frac{1}{\kappa} e_t$

So output and inflation are driven by shocks to the price level. There is no exploitable relationship between inflation and the output gap, despite the fact that (a) regressing the output gap on inflation would yield a positive coefficient, and (b) the model features a New Keynesian Phillips Curve. This is important because the best evidence that we have when it comes to the Phillips Curve is from the gold standard era.

In addition, if the quantity theory holds, then the rate of inflation and the expected rate of inflation would be determined by the path of money supply. Output would then adjust to fit the equilibrium condition that looks like a Phillips Curve. This was the view of Fisher and Friedman, for example.

What all of this means is that even given the fact that the New Keynesian model features an equation that resembles the Phillips curve, this does not imply that there is some predictive power that comes from thinking about this equation in isolation. In addition, it certainly does not imply that changes in the output gap cause changes in the rate of inflation. There is no direction of causation implied by this one equilibrium condition.

## The Law of Reflux Returns

One could make the case, quite convincingly, that all of the major monetary debates are between those whose arguments are based on classical monetary theory and those whose arguments are based on the quantity theory of money. This would be fine if one theory or the other was always correct. However, the model that is appropriate for any given debate depends on the particular monetary institutions in place. For example, if money is convertible into some commodity, such as gold, then classical monetary theory is appropriate. If we have a system of inconvertible paper money, then the quantity theory is appropriate. Thus, to put my original point differently, the history of thought in monetary economics essentially consists of one side using the appropriate model and the other side mis-applying the lessons of the other model.

The quantity theory is perhaps sufficiently well-known that it does not require a long summary. The basic idea is that with a system of inconvertible paper money, the value of that money is determined by the interaction between the supply and demand. An excess supply of money leads to inflation. An excess demand for money leads to deflation. In contrast, under classical monetary theory, the price level is pinned down by the price of gold through arbitrage. The money supply then varies directly with money demand. If banks (or a central bank) issues too many bank notes, then they will experience a wave of redemptions (people start converting their bank notes to gold). This causes a drain of gold reserves and the banks (or central bank) will have to restrict bank note issuance to ensure that they do not lose all of their reserves. (This is known as the Law of Reflux. I will return to this idea later.)

So, if we can summarize this concisely, the quantity theory implies that there can be deviations between the supply of and demand for money that cause price level fluctuations. The classical theory implies that the money supply will move in conjunction with money demand and have no effect on prices.

As I said, a great many of the debates in monetary history involve misapplications of one theory or the other. During the Bullionist Controversy, the British suspended the convertibility of bank notes into gold at the Bank of England. One group, the Bullionists, argued that the subsequent inflation was caused by excess note issuance. The other group, the Anti-Bullionists, argued that this could not be true. In fact, some of the Anti-Bullionists cited Adam Smith as the authority on the topic and argued that it was impossible for an excess supply of money to cause inflation because the money supply only fluctuated with money demand. The Bullionists were essentially applying the quantity theory of money. The Anti-Bullionists were applying the classical theory. As my forthcoming paper in the JMCB shows, the Bullionists were correct. And they were correct because they were applying the correct theory given the circumstances. In fact, if the Anti-Bullionists had read Adam Smith carefully, they would have realized that Adam Smith had assumed a convertible money. They failed to realized that the Law of Reflux does not apply when there is an inconvertible paper money.

The subsequent debate between the Banking School and the Currency School in the U.K. was similarly plagued by misapplications. The Currency School wanted limits on the quantity of notes the Bank of England could issue. The Banking School argued that this was unnecessary, that the Law of Reflux applied. If the Bank of England issued too many notes, they would be converted into gold and the Bank would have to reduce its note issuance. An excess supply of money would not cause inflation. This time it was the Banking School that was correct. Under the gold standard, the quantity theory is not the appropriate framework to apply.

Critics of monetary explanations of the Great Depression like to point to the monetary base and argue that the Fed “did all it could.” However, this mis-applies the Quantity Theory of Money. Economists like Earl Thompson, David Glasner, and Scott Sumner explain that it is more appropriate to look at the gold market for the monetary explanation. Changes in the relative price of gold were the important source of fluctuations in the economy during the early stage of the Depression, 1929 – 1933. In other words, the classical theory is the appropriate framework. (This is complicated by the fact that while the Law of Reflux applies, it is still possible to have an excess demand for money because the central bank has a monopoly over currency issuance and if they fail to increase the money supply, this can cause disruptions in the economy as well. So I view the Thompson-Glasner-Sumner view as the appropriate way to look at the Depression with Friedman and Schwartz as a complement.)

In the 1970s, macroeconomists debated the causes of inflation. On the one side, the Keynesians pointed to the Phillips Curve, which appeared to be a stable negative relationship between the unemployment rate and the inflation rate for an explanation. Specifically, they argued that as labor markets tighten this puts upward pressure on wages, increasing firms costs, and causing higher prices. On the other side of the debate were the Monetarists who argued that the growth rate of the money supply was the source of inflation. The Monetarists were applying the Quantity Theory of Money. The Keynesians meanwhile made a crucial error. What they failed to consider is the data generating process that produced the Phillips Curve. The negative relationship between inflation and unemployment was identified during periods in which money was convertible into gold. Thus, the appropriate model to use to explain these fluctuations is Classical Monetary Theory. According to this view, fluctuations in the gold market were the source of fluctuations in the price level. Such fluctuations were often unexpected. In addition, since prices were relatively constant over long horizons, so were nominal wages. Thus, unexpected fluctuations in the gold market would result in unexpected fluctuations in the price level. With stable nominal wages, this meant that unexpected increases in the price level led to unexpected decreases in real wages and therefore lower unemployment rates. The Keynesian explanation of inflation therefore failed on two fronts: (1) they failed to realize that the relationship might not be robust across monetary regimes, and (2) they reversed the direction of causation in the Phillips Curve. This latter point being an under-appreciated aspect of both Friedman’s and Lucas’s critique of the Phillips Curve.

I bring all of this up because there is once again a debate in monetary economics in which one side is misapplying one of the two theories. This time, it is the Classical Theory that is being misapplied. Specifically, the Law of Reflux is back in vogue. When I discuss paying interest on excess reserves (IOER) and why IOER is contractionary, I am regularly met with the following critique: “the central bank determines the supply of reserves. Individuals banks can try to reduce their reserve balances, but collectively the banking system must hold this supply of reserves.” This is just a modern version of the Law of Reflux. Allow me to explain. The relevant question is not why banks are holding this quantity of reserves. The relevant question is why banks are holding this quantity of excess reserves. It is true that the central bank determines the aggregate quantity supplied of reserves. However, the banking system determines whether these reserves are held as required reserves or as excess reserves. For example, if the bank lends out some of these reserves, they also create a new deposit liability. This new deposit liability increases the amount of required reserves that the bank must hold. If the banking system creates enough new deposits then all of these reserves will be required reserves and banks will not be holding excess reserves (despite the fact that the aggregate supply of reserves is still the same). So when someone says that the banks have no choice but to hold the quantity of reserves the Fed supplies, they must either be (a) confused as to this distinction between aggregate reserves and aggregate excess reserves, or (b) invoking some modern version of the Law of Reflux in which the banking system is unable to convert excess reserves into required reserves.

A better explanation for why banks are holding such a large quantity of excess reserves is not that they have no choice, but rather that they have been given an incentive to do so. In particular, Dutkowsky and VanHoose provide perhaps the most compelling explanation. What they argue is that a good rule of thumb is to compare the interest rate paid on excess reserves to the federal funds rate. If the interest paid on excess reserves is higher than the federal funds rate, then the wholesale market for loans between banks just breaks down. In other words, we should expect to end up in either one or two different corner solutions. In one corner solution, banks hold no excess reserves and engage in wholesale lending. In the other corner solution, banks hold a lot of excess reserves and do not engage in wholesale lending. (It is possible to end up in an interior solution, but only in rare cases.)

As I have written elsewhere, whether or not this matters for monetary policy depends on the monetary transmission mechanism. If you think that monetary policy works solely through the short term nominal rate, then the interest rate paid on excess reserves just replaces the federal funds rate as the relevant policy rate. However, if you think that monetary policy works by altering portfolio composition, including those of banks, then paying IOER actually hinders the monetary transmission mechanism and makes it harder for the central bank to hits its target. (This is incidentally the mechanism Bernanke cited over and over again during rounds of QE.) Regardless, this isn’t the time to revive the Law of Reflux and the implications thereof.

## Economists Say the Darndest Things, Gold Standard Edition

When I hear economists say that the majority of their colleagues oppose the gold standard, what they are typically referencing is a critique of the international gold standard that existed during the interwar period. In fact, in my experience, I have found that there are few economists outside of the field of monetary economics who actually know much about the gold standard beyond the interwar experience. This is problematic. If I ask an economist if the gold standard is bad, I would expect them to answer based on carefully thinking through the costs and benefits of the gold standard relative to alternative monetary institutions. One should not expect that they simply point to a very negative experience and conclude that it was bad. This is not good economics. One must consider the counterfactual.

With regards to the interwar experience, people often point to the role that the gold standard played in the Great Depression and conclude that the gold standard is bad. For example, Earl Thompson and Scott Sumner have argued that the Great Depression can be explained by fluctuations in the real price of gold. Barry Eichengreen (and others) have discussed how the recovery of a particular country from the Great Depression can be predicted by the timing of their decision to leave the gold standard. Milton Friedman and Anna Schwartz argued that China avoided the worst of the Great Depression because it was on a silver standard.

If this is all you knew about the gold standard, you might naturally conclude that it was a terrible monetary system. However, it is important to understand the particular details of the monetary system during the interwar period. For example, an important characteristic of the interwar period was the fact that the gold standard was managed by central banks. Why is this important? Well, one reason is that the functioning of any monetary system depends on participants following particular rules of the game. As Doug Irwin has shown, the Bank of France did not follow the rules of the game for the gold standard. Instead the French hoarded gold, creating an artificial shortage of gold reserves that, in turn, created significant, exogenous deflationary pressure amongst those countries on the gold standard.

So, if one wanted to judge the gold standard based on the interwar experience, the correct conclusion would be that the gold standard can produce massive costs when mismanaged by central banks. Based on the magnitude of the costs it would therefore not be unreasonable to say that “the gold standard can be terrible when managed by central banks.” In fact, I have made this argument many times! However, note that I have qualified the statement that the gold standard is terrible by placing it in a particular institutional context. This is a much weaker statement than concluding that the gold standard is always and everywhere bad.

The qualification that I outlined in the previous paragraph is important. A number of economists, such as Larry White, George Selgin, and others have written about competitive note issuance under a commodity standard. If one is to conclude that the gold standard is always and everywhere terrible, then one must not only assess the performance of the gold standard in the presence of central banks, but also in the absence of central banks. Larry White’s pioneering work demonstrated that a free banking system actually worked quite well.

Another problem is that economists often compare the actual performance of the gold standard to the theoretical possibilities of central banking under a fiat standard. If a country maintains the gold standard, then fluctuations in the real price of gold can have real effects on economic activity. Thus, dispensing with the gold standard eliminates these sorts of effects. Not only that, but in theory a central bank under a fiat standard can adjust the money supply to maintain relative price stability while also potentially minimizing fluctuations in real economic activity. However, it is unfair to compare the experience of the gold standard with the theoretical possibilities of central banking. For example, Jurg Niehans (1979: 140) writes:

Commodity money does not exist today. It is also not ideal in the sense that it is relatively easy to imagine noncommodity systems that are intellectually more satisfying than commodity money. In fact, a noncommodity system, since it gives monetary policy more freedom, can, if it is ideally managed, always do at least as well as any commodity money system and probably better.

The emphasis is my own. It is easy to argue that, in theory, a fiat money managed by a central bank is preferable to the gold standard. However, the question is whether central banking in a fiat regime actually produces better outcomes than a gold standard. This is a much more complicated question than people think. We cannot look to the interwar period and conclude that the gold standard is bad any more than we can look at the 1970s in the U.S. or the hyperinflation in Zimbabwe and conclude that fiat regimes are bad — yet this is precisely what people on both sides of this debate often do! Similarly, we cannot look at idealized versions of the gold standard or central banking under a fiat regime to draw our conclusions.

To assess whether the gold standard, or any monetary system, is “good” or “bad” requires careful consideration of the institutional characteristics of the system. A gold standard can work quite well within the right institutional structure. But the same could be said for a fiat regime. To argue that one or the other is inherently bad — or worse, claim that everyone agrees with you — is to do a disservice to those who want to learn about monetary economics.

## Free Banking and the Friedman Rule

Imagine that there are two types of people in the world — recognizable and unrecognizable. Recognizable people can develop reputations, which can have either positive or negative effects. If a recognizable person develops a reputation for being trustworthy, then he or she will likely be able to issue debt to finance the purchase of goods and services. If the person is not trustworthy, but is easily recognized, then he or she will not be able to issue debt. All else equal, people who are recognizable will have an incentive to be trustworthy so that they can issue IOUs to pay for stuff. People who are not recognizable don’t have the same incentives. Since nobody can recognize them, they will never be able to issue IOUs.

Let’s think about this in the context of general equilibrium theory (without a Walrasian auctioneer and without any exogenously specified thing called “money”). In the absence of some auctioneer to price and distribute goods and in the absence of money, people must meet with every other person in the market to determine whether trade is possible. Recognizable people will be able to issue IOUs in order to trade as long as they are trustworthy and there is a mechanism to punish them if they do not repay their debts (e.g., exclude them to a world of autarky if they don’t repay their debts). But how can the non-recognizable people trade? Well, they could sell their goods to recognizable people in exchange for an IOU, but then all they have is an IOU. And what exactly does the IOU provide?

Assuming that each recognizable person can produce some good, the IOU would represent a promise to produce some quantity of the good in the future. A non-recognizable person could then present the IOU for this good at some future date or the person could turn around and use this IOU to purchase some other good. The seller in this circumstance would be willing to accept a third party IOU if (a) they want the good that IOU promises, or (b) they think they can pass on the IOU to someone else. Whether or not condition (b) is satisfied depends on the good the IOU-issuer is promising. Ultimately, what happens in this scenario is that certain goods will be found to satisfy condition (b) and those IOUs will start to circulate as a medium of exchange.

What this example resembles is a sort of free banking regime. People with good reputations are able to issue IOUs that can end up circulating like bank notes — these are banks. Eventually an IOU can be redeemed by whoever is holding it for some fixed quantity of a good that the IOU-issuer promised.

This implies that there is a key feature of free banking regimes. In actual free banking regimes, bank notes could be redeemed for one particular good, gold. The value of one bank note, consistent with our example, was defined as a particular quantity of gold. This implies that the price of gold in terms of bank notes is necessarily fixed. However, the relative price of gold to an index of all other prices is not fixed. In a growing economy, under these conditions, prices would decline on average with increases in productivity. As a result, the promise to pay a fixed amount of gold at a future date would actually entail a positive rate of return.

Thus, under a free banking regime, if (1) productivity is growing, (2) the decline in prices due to rising productivity completely offset the real interest rate, then a free banking regime naturally reproduces the Friedman rule.