Category Archives: Economic News

Exchange Rate Volatility and Alternative Money: The Case of Bitcoin

David Andolfatto has written a very good post on Bitcoin and why it might have positive value. In particular, he provides an excellent overview of what Bitcoin actually is (an electronic record of transactions) and how this relates to the insight that “money is memory.” (On this point, see also, William Luther’s paper, “Bitcoin is Memory.”) Nevertheless, I have some questions about the post regarding David’s discussion of the volatility of Bitcoin and how this impacts the choice of what to use as money. In this post, I hope to address this point and perhaps add some additional substance to the issue.

David ends his post talking about whether Bitcoin would make for a good form of money. This is an interesting question and one that often isn’t given sufficient thought. In David’s own research, however, he has emphasized that the characteristic that determines whether an asset is useful as money is whether that asset is information-sensitive (this claim is often prevalent in Gary Gorton’s work as well). The basic idea is that if the value of an asset is sensitive in the short-run to news that has private value, but no social value, then short run fluctuations in the price of the asset will preclude its use as a medium of exchange. Thus, David suggests looking at how the value of Bitcoin has changed over time. In his graph, he plots the price of bitcoins in terms of dollars. As you can see if you read his post (or if you know anything about Bitcoin), the price of bitcoins relative to dollars is quite volatile — especially over the last year.

However, I wonder whether looking at the volatility of the exchange rate between Bitcoin and the dollar is the best way to determine whether Bitcoin would be a good form of money. There are two reasons why I say this.

First, as David points out, this volatility could be the result of the fact that people view the supply of Bitcoin as being fixed (the supply of Bitcoin will eventually be fixed), but the demand for Bitcoin is fluctuating. David notes that this is consistent with the type of behavior we observe under commodity standards. When there is a change in the demand for gold, the purchasing power of gold varies (at times considerably) even though the long run purchasing power is constant.

I have heard others make this argument as well and this seems very plausible. Nevertheless, it is useful to recall the way in which free banking systems operated. For example, in a free banking system in which banks issued notes that were backed by gold, the supply of bank notes fluctuated with demand. Increases in the demand for money caused an increase in the supply of notes. These changes in the supply of notes, however, needn’t imply any change in the purchasing power of gold. Issuing bank notes redeemable in gold was thereby capable of reducing the volatility of the purchasing power of gold. Similarly, a financial intermediary today could issue bank notes redeemable in bitcoins and reduce the volatility of the purchasing power of bitcoins.

[A quick note: It is perhaps true that the U.S. government might decide that they don't want to allow financial intermediaries to issue bank notes, in which case my proposed solution to this source of volatility would not be operable. I would add though that it is not operable because of a legal restriction and not the volatility of the asset price.]

Second, and perhaps much more importantly, in models with competing money supplies the exchange rate does not factor in to the choice of allocation or welfare analysis. This is true even of David’s own research. For example, in quoting the price of bitcoins in terms of dollars, David is citing an exchange rate. However, in his research, the price volatility that matters for an asset is the own rate of return volatility. I think that this distinction matters.

To illustrate why I think that this distinction matters, let’s consider a simple overlapping generations model. There are two types of agents, young and old. Each lives for two periods. At any point in time, there is a generation of young and a generation of old. The population is assumed to be constant. There is one good to trade and it is non-storable. The young receive an endowment, y, of the consumption good. The old do not receive an endowment of goods. Thus, money is essential. There are two assets that can be used as a possible medium of exchange. The first is fiat currency. The second is bitcoins. The initial old carry both currency and bitcoins into the first period. The aggregate supply of bitcoins is fixed. The aggregate supply of currency, N_t, is assumed to grow at the gross rate x (i.e. N_{t + 1} = x N_t).

Let’s consider the first and second period budget constraints for future generations in our model (i.e. everybody except the initial old). In the first period, future generations can use their endowment for consumption or they can sell some of this endowment for money and/or bitcoins. Thus, the first-period budget constraint is:

c_{1,t} + m_t + b_t \leq y

where c_{1,t} denotes the consumption when young in period t, m is real currency balances, and b denotes real balances of bitcoins.

Denote v_t as the price of currency in terms of goods at time t. Similarly, denote the price of bitcoins in terms of goods as u_t. Thus, the rate of return on currency is v_{t + 1} / v_t. Now let’s assume that there is some cost, \tau that individuals have to pay when they use bitcoin to make a purchase. The rate of return on bitcoins is then given as (1-\tau){{u_{t+1}}\over{u_t}}. Thus, the second-period budget constraint can be written as

c_{2,t+1} = {{v_{t+1}}\over{v_t}} m_t + (1 - \tau){{u_{t+1}}\over{u_t}} b_t

But we can derive a precise definition of the rate of return on money. It follows from our first period budget constraint that we have:

m_t = v_t n_t = (y - b_t - c_{1,t})

where n_t denotes nominal currency balances. Define the total nominal currency stock as N_t and the size of the population, which as assumed to be constant as P. This implies an aggregate demand function for currency:

v_t N_t = P(y - b_t - c_{1,t})

Thus, the rate of return on money is

{{v_{t+1}}\over{v_t}} = {{P(y - b_{t+1} - c_{1,t+1})}\over{P(y - b_t - c_{1,t})}}{{N_t}\over{N_{t + 1}}}

From above, we know that the currency supply grows at a gross rate x. This implies that in a stationary allocation (i.e. where consumption paths a constant across generations), the rate of return on currency is

{{v_{t+1}}\over{v_t}} = {{1}\over{x}}

By similar logic, it is straightforward to show that in a stationary allocation {{u_{t+1}}\over{u_t}} = 1 because the supply of bitcoins was assumed to be fixed.

Thus, our stationary allocation budget constraints are:

c_1 + m + b \leq y

c_2 = {{1}\over{x}}m + (1 - \tau) b

In the present model, money and bitcoins are perfect substitutes (i.e. there only purpose is to serve as proof of a previous transaction when trading with future young generations). Thus, the real rates of return on money and bitcoins must be equal for both to exist in equilibrium. In other words, it must be true that {{1}\over{x}} = (1 - \tau). We can re-write the second-period constraint as

c_2 = {{1}\over{x}}(m + b)

Combining these budget constraints, we have a lifetime budget constraint:

c_1 + x c_2 \leq y

Now let’s consider the basic implications of the model. First, the conditions under which both currency and bitcoins would be held in equilibrium is dependent on their relative rates of return. If these rates of return are equal, then both assets are held. This condition is independent of the exchange rate. Second, lifetime budget constraint outlines the feasible set of allocations available given the agents’ budget. Assume that utility is a function of consumption in both periods. The allocation decision in this case is dependent on the rate of return on currency, which is the same as the rate of return on bitcoins. The allocation decision is therefore contingent on the equilibrium rate of return. The exchange rate between currency and bitcoins plays no role in the allocation decision. In addition, one can show that this is the identical lifetime budget constraint that would exist in a currency economy (i.e. one in which Bitcoin doesn’t circulate). This last characteristic implies that neither the existence of bitcoins nor the exchange rate between bitcoins and currency have any effect on welfare.

So what does this mean? Basically what all of this means is that the exchange rate between currency and bitcoins is irrelevant to the decision to hold bitcoins, to the allocation decision, and to welfare. [Note: This isn't new, Neil Wallace taught us this type of thing over 30 years ago.]

The analysis above is a bit unfair to David for two reasons. First, the framework above skirts David’s main point, which is that Bitcoin is information sensitive whereas currency is not. Second, David doesn’t necessarily mean that the exchange rate between the dollar and bitcoins is relevant for the type of analysis above. Rather, what he means is that since the dollar is relatively stable, the exchange rate serves as a proxy for the own price of bitcoins in terms of goods.

What I would like to do now is to amend the framework above to make bitcoins information sensitive. The results regarding the exchange rate of bitcoins into dollars remain. However, an interesting result emerges. In particular, one can show that it is the risk premium associated with bitcoins that can help us to understand the choice of whether to hold bitcoins or dollar-denominated currency as well as factor into the allocation decision. I will then speculate as to whether this risk premium is sufficient to explain the differences in rates of return between bitcoins and dollar-denominated currency.

For simplicity, let’s now denote the rate of return on bitcoins as r. In addition, we will assume that r is stochastic. In particular the assumption is that the rate of return is entirely determined by random news events. Thus, we can re-write our first- and second-period budget constraints, respectively, as

c_{1,t} + m_t + b_t \leq y

c_{2,t+1} = {{1}\over{x}} m_t + r_{t+1} b_t

The objective of future generations is to maximize u(c_{1,t}) + v(c_{2,t+1}) subject to the two constraints above. Combining the first-order conditions with respect to m and b and using the definition of covariance, we have the following equilibrium condition:

E_t r_{t+1} = {{1}\over{x}} - {{cov[r_{t+1},v'(c_{2,t+1})]}\over{v'(c_{2,t+1})}}

where the second term on the right-hand side measures the risk premium associated with bitcoins (note that this is in fact a risk premium since the covariance between the rate of return on bitcoins and the marginal utility of consumption is negative). If both assets are to be held in equilibrium, then the equibrium condition must hold. If the risk premium is too high, it is possible that nobody would hold bitcoins and they would only hold currency. This confirms David’s view that information sensitivity could affect the decision to hold bitcoins. However, this does not show up in the exchange rate, but rather in the relative rates of return. The risk premium similarly affect the allocation decision. Consider, for example, that the lifetime budget constraint can now be written as

c_{1,t} + x c_{2,t+1} + x \omega \leq y

where \omega is used to simplify notation and denote the risk premium and the aggregate supply of bitcoins has been normalized to one. It is straightforward to see that when the risk premium is zero (i.e. bitcoins are not information sensitive) then the lifetime budget constraint is the same as that outlined above. The existence of a positive risk premium alters the budget set.

So what does all of this mean?

Essentially what it means is that looking at the exchange rate between bitcoins and the dollar is not a useful indicator about whether or not bitcoins would actually make for a good money. Even if we view the exchange rate between bitcoins and dollars as a useful proxy of the price of bitcoins in terms of goods, the exchange rate is not the correct measure for analysis. Rather, to evaluate whether bitcoins are a viable alternative/substitute for dollars, we need to know the relative rates of return on bitcoins and dollars and the risk premium associated with the fact that bitcoins are information sensitive.

This might all seem like semantics, after all, if we think the exchange rate is a good proxy of the price of bitcoins in terms of goods, then the rate of return could just be measured as the rate of change in the exchange rate. Nonetheless, this distinction seems especially important given the nature of the exchange rate between bitcoins and dollars. In particular, just looking at David’s graph of the exchange rate, it is plausible that the time series follows a random walk with a drift (I had trouble acquire actual data rather than ready-made graphs on this so if anybody has the data please send it along). This is important because if this is correct, the variance of the exchange rate is time-dependent. However, in terms of rates of change, the data would be stationary and therefore have some constant, finite variance. Thus, in this hypothetical example, looking at the exchange rate using David’s criteria about information sensitivity would indicate that bitcoin is a very bad money because the variance of the exchange rate is time dependent. In contrast, if the rate of return on bitcoin is stationary, then it is not immediately clear from the data whether or not bitcoin is a good money. This is why we need the model as it helps us to understand what properties the rate of return must possess to make a good money.

Monetarism, Debt, and Observational Equivalence

I have heard a number of people say over the years that one of the best things about reading Adam Smith and Henry Thornton and other classical economists is that they argued their points fairly. In particular, Smith and Thornton argued in favor of their own views and against opposing views while taking these opposing views at face value. They did not attack straw men. They did not caricature their intellectual adversaries (in fact, Thornton and Smith were intellectual adversaries to some extent in their views on the role of bank notes, bills of exchange, and the operation of the monetary system).

This characteristic is, at times, missing from contemporary discourse. This doesn’t mean that modern disagreements are fraught with malice. However, sometimes ideas are not given the proper understanding sufficient for critique. Franco Modigliani, for example, once joked that what we would now call real business cycle theory blamed recessions on mass outbreaks of laziness. Similarly, when Casey Mulligan published his most recent book on the recession in which he argued that expansions of the social safety net can explain a significant fraction of the increase in unemployment, others shrugged this off by saying that this was akin to saying that soup lines caused the Great Depression.

My point is not to defend Casey Mulligan or the real business cycle theorists. It is perfectly reasonable to view real business cycle theory as unconvincing without referencing mass outbreaks of laziness. Rather my point is that more care needs to be taken to understand opposing theories and views of business cycles, growth, etc. so that one can adequately articulate criticisms and rebuttals to such views.

The fact that there is little understanding of (or perhaps just little credit given to) opposing viewpoints is never more apparent than when predictions of two different theories are observationally equivalent. To give an example, consider two explanations of the cause of the most recent recession. Please note that these are not the only two explanations and that the explanations that I give are sufficiently broad to encapsulate a number of more nuanced views.

The first explanation of the recession is what I will refer to as the Debt Theory. According to this view, the expansion that preceded the recession was fueled by an unsustainable accumulation of debt. There are many varieties of this theory that emphasize different factors that caused the run-up of debt, such as monetary policy, policies that subsidize housing, etc. Regardless of the reason that “too much” debt was accumulated, the debt eventually reached a point (most often argued as the beginning of the collapse in housing prices) that was unsustainable and hence the beginning of a recession. The recession is largely the result of de-leveraging.

The second explanation is what I will refer to as the Money Theory. According to this view, it is a deviation between the supply and demand of money (broadly defined) that ultimately results in reduced spending and, as a result, a lower level of real economic activity. As a result, when the large haircuts became apparent in the market for mortgage-backed securities, this reduced the supply of transaction assets thereby causing a deviation between the supply and demand for money. The Federal Reserve, in its failure to provide a sufficient quantity of transactions assets, thereby allowed this deviation to persist and resulted in decline in nominal, and ultimately, real spending.

As these brief descriptions imply, there doesn’t appear to be much overlap between the two views. However, they actually produce a number of observationally equivalent implications. For example, advocates of the Money Theory point to the negative rates of money growth in broad measures of the money supply as evidence that the Federal Reserve failed to provide adequate liquidity. Nonetheless, this observation is consistent with the Debt Theory. According to this view, de-leveraging reduces the demand for credit and therefore reduces the need of financial intermediaries to create new debt instruments that are used as transaction assets. Thus, we would expect a decline in money growth in both cases.

On the other hand, advocates of the Debt Theory point out that there is a strong relationship between counties that had higher levels of debt prior to the recession and the reductions in consumption during the recession. Nonetheless, this observation is also consistent with the Money Theory. Most advocates of the Money Theory are intellectual descendants of Milton Friedman. In Friedman’s theory of money demand, money is considered similar to a durable good in that individuals hold a stock of money to get the flow of services that come from holding money. Thus, contra the transactions view of money demand, individuals do not draw down money balances during a recession. Instead individuals make adjustments to different parts of their portfolio, most notably consumer debt. In other words, we would observe de-leveraging under both frameworks.

To distinguish between the two views it is not sufficient to point to characteristics that they have in common (although those observations are still important). It is also necessary to find areas in which the theories differ so that one is able to develop an empirical approach to assess each framework’s validity.

The examples given above are obviously simplifications, but this is what makes being an economist difficult. It is not enough to use inductive reasoning to support one’s theory. One must be able to differentiate between other theories that would produce observationally equivalent results. Admittedly, this is a problem that exists to a greater extent in the blogosphere than it does in academic journals. The reason is obvious. If one submits a paper to an academic journal, a good reviewer is able to spot the ambiguities between testing the predictions of a particular theory and contrasting the predictions of theories with observationally equivalent predictions. In the blogosphere, the “reviewers” are commenters and colleagues. However, the differences don’t often get resolved. Perhaps this is because there is no gatekeeper that prevents the blog post from being published. (Ironically, the lack of a gatekeeper is perhaps the best quality of the blogosphere because it allows discourse to take place in public view.) Nonetheless, given the degree to which blog posts and debates in the blogosphere ultimately spill over into the popular financial press and public debate, it is important to be careful and considerate regarding opposing views.

[Note: For an example of someone who tries to disentangle the issues surrounding the Debt View and the Money View, see Robert Hetzel's The Great Recession: Market Failure or Policy Failure?]

How Much Capital?

Recently, it has become very popular to argue that the best means of financial reform is to require banks to hold more capital. Put differently, banks should finance using more equity relative to debt. This idea is certainly not without merit. In a Modigliani-Miller world, banks should be indifferent between debt and equity. I would like to take a step back from the policy response and ask why banks overwhelmingly finance their activities with debt. It is my hope that the answer to this question will provide some way to focus the debate.

It is clear that when banks finance primarily using equity, adverse shocks to the asset side of a bank’s balance sheet primarily affect shareholders. This seems at least to be socially desirable if not privately desirable. The imposition of capital requirements would therefore seem to imply that there is some market failure (i.e. the private benefit from holding more capital is less than the social benefit). Even if this is true, however, one needs to consider what makes it so.

One hypothesis for why banks hold too little capital is because they don’t internalize the total cost of a bank failure. For example, banks are limited liability corporations and covered by federal deposit insurance. Thus, if the bank takes on too much risk and becomes insolvent, shareholders lose their initial investment. Depositors are made whole through deposit insurance. It is this latter characteristic that is key. If bank shareholders were responsible not only for their initial level of investment, but also for the losses to depositors, banks would have different incentives. In fact, this was the case under the U.S. system of double liability that lasted from just after the Civil War until the Banking Act of 1933. (I have written about this previous here.) Under that system bank shareholders had a stronger incentive to finance using equity. In fact, evidence shows that banks with double liability took on less leverage and less risk than their limited liability counterparts.

Along similar lines the existence of Too Big Too Fail similarly creates greater incentives toward risk-taking and leverage because in the event that the bank becomes insolvent, it will be rescued by the government. Finally, the U.S. tax system treats debt finance more favorable than equity finance.

Of course, a first-best policy solution to these incentive problems would be to eliminate deposit insurance, Too Big to Fail, and the favorable tax treatment of debt finance. However, such reform is either politically infeasible or, in the case of eliminating Too Big to Fail, relies on a strong commitment mechanism by the government. Thus, a second-best policy prescription is to impose higher capital requirements.

This second-best policy solution, however, is contingent upon the characteristics above being the only source of the socially inefficient level of capital. I would argue that even in the absence of these characteristics banks might still be biased toward debt finance and that imposing capital requirements could actually result in a loss in efficiency along a different dimension of welfare.

The reason that capital requirements could be welfare-reducing has to do with the unique nature of bank liabilities. Banks issue debt in the form of deposits (and, historically, bank notes), which circulate as a medium of exchange. Thus, bank debt serves a social purpose over and above the private purpose of debt finance. This social function is important. In a world that consists entirely of base money, for example, individuals will economize on money balances because money does not earn a pecuniary yield. As a result, the equilibrium quantity of consumption and production will not equal the socially optimum quantity. Bank money, or inside money, has the potential to be welfare improving. In fact, the main result of Cavalcanti and Wallace was that feasible allocations with outside (or base) money are a strict subset of those with inside money. Imposing strict capital requirements would reduce the set of feasible allocations and thereby reduce welfare along this dimension.

Now some might be quick to dismiss this particular welfare criteria. After all, greater stability of the financial system would seem to be more important than whether the equilibrium quantity of production is the socially optimum quantity. However, this ignores the potential interaction between the two. Caballero, for example, has argued that there is a shortage of safe assets. This claim is consistent with what I argued above. If the supply of media of exchange is not sufficient to allow for the socially optimum quantity of output then there is a transaction asset shortage. As a result, there is a strong incentive for banks to create more transaction assets. This can explain while interest rates were low in early part of the decade and can similarly explain the expansion in the use of highly-rated tranches of MBS in repurchase agreements prior to the financial crisis.

In other words, the shortage of transaction assets described above creates an incentive for banks to create new such assets in the form of new debt finance. Thus, it is possible that banks have a bias toward debt finance that would exist even independent of Too Big To Fail, deposit insurance, limited liability, and the tax system. In addition, one could argue that the desire to create such transaction assets played an important role in the subsequent financial crisis as some of the assets that were previously considered safe become information-sensitive and thereby less useful in this role.

To the extent that one believes that the transaction asset shortage is significant, policymakers face a difficult decision with respect to capital requirements. While imposing stronger capital requirements might lead to greater financial stability by imposing greater losses on shareholders, this requirement can also exacerbate the shortage of transaction assets. Banks and other financial institutions will then have a strong incentive to attempt to mitigate this shortage and will likely try to do so through off-balance sheet activities.

This is not meant to be a critique of capital requirements in general. However, in my view, it is not obvious that they are sufficient to produce the desired result. One must be mindful of the role that banks play in the creation of transaction assets. It would be nice to have an explicit framework in which to examine these issues more carefully. In the meantime, hopefully this provides some food for thought.

P.S. Miles Kimball has suggested to me that capital requirements coupled with a sovereign wealth fund could assist in financial stability and fill the gap in transaction assets. I am still thinking this over. I hope to have some thoughts on this soon.

Armen Alchian, 1914 – 2013

Armen Alchian passed away today at the age of 98. Others have chimed in with their thoughts on Alchian and his work (see here and here, for example) and I thought that I would as well. As many others have noted, Alchian was insightful and clever. He had a unique ability to communicate clever, unique, and insightful ideas in a way that suggested that these ideas were obvious. In fact, these ideas were often profound in both clarifying topics and in inspiring the work of fellow economists.

The aspect of Alchian’s work that I have found most insightful and most challenging is thinking about the economy as a coordination problem. There are few, if any, economists who have done as much in terms of thinking about economics in this light as Alchian did and the profession is much better for his insights.

No doubt, in the next couple of days, there will be excellent discussions of his great works as a scholar and a teacher, but what is perhaps the best biographical information about Alchian is found in his “Principles of Professional Advancement”, in which he provides a light-hearted guide to success in academia and also discusses some of his important papers. I think that this excerpt in which Alchian details an experience during his time as a consultant at RAND does a lot to summarize the inquisitive nature of Alchian’s mind and his astute ability to use the economic way of thinking to analyze the problems at hand:

I like to brag that I did the first “event study” in corporate finance, bank in the 1950s and 1960s. The year before the H-bomb was successfully created, we in the economics division at RAND were curious as to what the essential metal was — lithium, beryllium, thorium, or some other. The engineers and physicists wouldn’t tell us economists, quite properly, given the security restrictions. So I told them I would find out. I read the U.S. Department of Commerce Year Book to see which firms made which of the possible ingredients. For the last six months of the year prior to the successful test of the bomb, I traced the stock prices of those firms. I used no inside information. Lo and behold! One firm’s stock prices rose, as best I can recall, from about $2 or $3 per share in August to about $13 per share in December. It was the Lithium Corp. of America. In January, I wrote and circulated a memorandum titled “The Stock Market Speaks.” Two days later I was told to withdraw it. The bomb was tested successfully in February, and thereafter the stock price stabilized.

That entire speech is filled with similar anecdotes that demonstrate the way in which Alchian thought and how that influenced his research.

Today is a day to sit down with Economic Forces at Work and appreciate the brilliance of Armen Alchian.

Re-Thinking Financial Reform

Over at National Review Online I advocate reviving double liability for banks. Here is an excerpt:

The banking system in the U.S. hasn’t always been like this. Between the Civil War and the Great Depression, banks did not have limited liability. Instead, they had double liability. When a bank became insolvent, shareholders lost their initial investment (just as they do under limited liability today). But in addition, a receiver would assess the value of the asset holdings of the bank to determine the par value of the outstanding shares. Shareholders had to pay an amount that could be as high as the current value of their shares in compensation to depositors and creditors.

Shareholders and bank managers (who were often shareholders themselves) thus had a stronger incentive than they do today to assess the risk of investments accurately, because they were risking not just their initial investment but the total value of the banks’ assets. Shareholders also had an incentive to better monitor bank managers and the bank balance sheet.

Monetary Theory and the Platinum Coin

Yesterday I argued that the platinum coin is a bad idea. In doing so I received a substantial amount of pushback. Some have argued that while the platinum coin might be a dumb idea, it is preferable to being held hostage by recalcitrant Republicans. Others argued that my claims about the potential inflationary effect of the platinum coin were overblown. With regards to the first claim, I have very little to add other than the fact that I don’t subscribe to the “two wrongs make a right” theory of public policy. The second claim, however, is more substantive. It is also something about which economic theory has something to say.

In many contemporary models, money is either excluded completely or is introduced using a reduced form approach, such as including real money balances in the utility function. These models are ill-equipped to tackle the effects of the introduction of the platinum coin because they either assume that money always has value (it generates utility) or that it has no value whatsoever. An analysis of the effects of the platinum coin should be backed by an understanding of what gives money value in a world of fiat money and the conditions necessary to insure a unique equilibrium in which money has value. In doing so, one can show that having the Fed conduct open market sales to offset the increase in the monetary base from the minting of the platinum coin (i.e. holding the money supply constant) might not be sufficient to prevent a significant inflation.

To illustrate the properties of money, I am going to employ the monetary search model of Lagos and Wright. (If you’re allergic to math, scroll down a bit.) The reason that I am employing this approach is because it is built on first principles, its explicit about the conditions under which a monetary equilibrium exists, and can be used to derive a dynamic equilibrium condition that can shed light on the value of money.

The basic setup is as follows. Time is discrete and continues forever. There are two types of agents, buyers and sellers. Each time period is divided into two subperiods. In the first subperiod, buyers and sellers are matched pairwise and anonymously to trade (we will call this the decentralized market, or DM). In the second subperiod, buyers and sellers all meet in a centralized (Walrasian) market (we will call this the centralized market, or CM). What makes buyers and sellers different are their preferences. Buyers want to purchase goods in the DM, but cannot produce in that subperiod. Sellers want to purchase goods in the CM, but cannot produce in that subperiod. Thus, there is a basic absence of double-coincidence of wants problem. The anonymity of buyers and sellers in the DM means that money is essential for trade. Given this basic setup, we can examine the conditions under which money has value and this will allow us to discuss the implications of the platinum coin. (Note that we can confine our analysis to buyers since sellers will never carry money into the DM since they never consume in the DM.)

Suppose that buyers have preferences:

E_0 \sum_{t = 0}^{\infty} \beta^t [u(q_t) - x_t]

where \beta is the discount factor, q is the quantity of goods purchased in the DM, and x is the quantity of goods produced by the buyer in the CM. Consumption of the DM good provides utility to the buyer and production of the CM good generates disutility of production. Here, the utility function satisfies u'>0 ; u''<0.

The evolution of money balances for the buyer is given by:

\phi_t m' = \phi_t m + x_t

where \phi denotes the price of money in terms of goods, m denotes money balances, and the apostrophe denotes an end of period value. Now let's denote the value function for buyers in the DM as V_t(m) and the value function for buyers entering the CM as W_t(m).

Thus, entering the CM, the buyer's value function satisfies:

W_t(m) = \max_{x,m'} [-x_t + \beta V_{t + 1}(m')]

Using the evolution of money balances equation, we can re-write this as

W_t(m) = \phi_t m + \max_{m'} [-\phi_t m' + \beta V_{t + 1}(m')]

In the DM, buyers and sellers are matched pairwise. Once matched, the buyers offer money in exchange for goods. For simplicity, we assume that buyers make take-it-or-leave-it offers to sellers such that \phi_t d = c(q_t) where d \in [0,m] represents the quantity of money balances offered for trade and c(q_t) represents the disutility generated by sellers from producing the DM good. The value function for buyers in the DM is given as

V_t(m) = u(q_t) + W_t(m - d)

Using the linearity of W and the conditions of the buyers' offer, this can be re-written as:

V_t(m) = u(q_t) - c(q_t) + \phi_t m

Iterating this expression forward and substituting into $W$, we can then write the buyer's problem as:

max_{m} \bigg[-\bigg({{\phi_t/\phi_{t + 1}}\over{\beta}} - 1\bigg)\phi_{t + 1} m + u(q_{t+1}) - c(q_{t+1}) \bigg]

[If you're trying to skip the math, pick things up here.]

From this last expression, we can now place conditions on whether anyone will actually hold fiat money. It follows from the maximization problem above that the necessary condition for a monetary equilibrium is that \phi_t \geq \beta \phi_{t + 1}. Intuitively, this means that the value of holding fiat money today is greater than or equal to the discounted value of holding money tomorrow. If this condition is violated, everyone would be better off holding their money until tomorrow indefinitely. No monetary equilibrium could exist.

Thus, let's suppose that this condition is satisfied. If so, this also means that money is costly to hold (i.e. there is an opportunity cost of holding money). As a result, buyers will only hold an amount of money necessary to finance consumption (in mathematical terms, this means d = m). This means that the buyers' offer can now be written \phi_t m = c(q_t). This gives us the necessary envelope conditions to solve the maximization problem above. Doing so, yields our equilibrium difference equation that will allow us to talk about the effects of the platinum coin. The difference equation is given as

\phi_t = \beta \phi_{t + 1}\bigg[ \bigg(u'(q_{t + 1})/c'(q_{t + 1}) - 1 \bigg) + 1 \bigg]

Since money is neutral in our framework, we can assume that there is a steady state solution such that q_t = q \forall t. Thus, the difference equation can be written:

\phi_t = \beta \phi_{t + 1}\bigg[ \bigg(u'(q)/c'(q) - 1 \bigg) + 1 \bigg]

This difference equation now governs the dynamics of the price of money. We can now use this assess claims that the platinum coin would not have any inflationary effect.

Suppose that u and c have standard functional forms. Specifically, assume that u(q) = {{q^{1 - \gamma}}\over{1 - \gamma}} and c(q) = q. [I should note that the conclusions here are robust to more general functional forms as well.] If this is the case, then the difference equation is a convex function up to a certain point at which the difference equation becomes linear. The convex portion is what is important for our purposes. The fact that the difference equation is convex implies that the difference equation intersects the 45-degree line used to plot the steady-state equilibrium in two different places. This means that there are multiple equilibria. One equilibrium, which we will call \phi_{ss} is the equilibrium that is assumed to be the case by advocates of the platinum coin. They assume that if we begin in this equilibrium, the Federal Reserve can simply hold the money supply constant through open market operations and in so doing prevent the price of money (i.e. the inverse of the price level) from fluctuating.

However, what this suggestion ignores is that the difference equation also intersects the 45-degree line at the origin. Coupled with the range of convexity of the difference equation, this implies that there are multiple equilibria that converge to an equilibrium in which money does not have value (i.e. \phi = 0). Put in economic terms, there are multiple equilibria that are decreasing in \phi, which means that they increasing in the price level. It is therefore possible to have inflation even with a constant money supply. The beliefs of economic agents are self-fulfilling.

In terms of the platinum coin, this implies that the explicit monetization of the debt by minting the platinum coin can potentially have disastrous effects even if the president states that the infusion is temporary and even if the Federal Reserve conducts open market operations to offset the increase in the monetary base caused by the deposit of the coin by the Treasury. In short, if the debt monetization were to have a significant impact on inflation expectations, it is possible that the United States could experience significant inflation even if the Federal Reserve tried to hold the money supply constant. The very idea that this represents a possible outcome should render the platinum coin to be a bad idea.

The Debt Ceiling, Platinum Coins, and Other Nonsense

In the coming months, it is very likely that the president and Congressional Republicans will once again go to battle over the debt ceiling. Like many others, I am already lamenting the idea of more “negotiations” between the president and Congress. However, unlike others I see this as a problem with the debt ceiling itself, not the Congressional Republicans. So long as it is within their power to use the debt ceiling as a bargaining chip, they should be free to do so if they wish. (They should recognize, of course, that this is not as strong a bargaining chip as they realize, however. A refusal to raise the debt ceiling without spending concessions from the president is simply a game of chicken. Anti-coordination games are unlikely to be the best strategy for achieving one’s objective.)

Nonetheless, a growing subset of individuals who believe that the Congressional Republicans are recalcitrant have suggested that the president authorize the Treasury department to mint a $1 trillion platinum coin (because this is within constitutional authority) and deposit it with the Federal Reserve to enable the payment of the federal government debt. The argument is that in doing so the president can circumvent the debt ceiling within constitutional limits. In addition, advocates argue that, since the coin will never circulate, the minting of the coin will not be inflationary.

If this idea sounds ludicrous, that is because it is.

Minting a platinum coin sufficient to pay off the deficit is what is traditionally known as monetizing the debt. To put it bluntly, large-scale debt monetization is bad. This is traditionally how hyperinflations start. Nonetheless, we are told that we needn’t be concerned because the coin won’t circulate. This would seem to ignore two factors: (1) the point of the coin is to pay for the debt, and (2) money is fungible. Thus, if the Treasury minted a $1 trillion platinum coin and deposited it at the Federal Reserve, the entire point of doing so would be to allow the Federal Reserve to make payments on behalf of the Treasury for government spending that exceeds tax revenue. Even if the coin itself doesn’t circulate (how could it?), the money supply can still increase substantially as the Treasury writes checks out of its account at the Federal Reserve.

Advocates, however, dismiss this possibility. Josh Barro, for example, argues:

[Inflation] is a more serious objection, and it gets at what the platinum coin strategy really is — financing the federal government’s operations by printing money instead of borrowing it. The trillion- dollar coin will never circulate, but it will be used to back cash payments coming from the Treasury that would have otherwise been financed by bond purchases.

If the government financed itself this way in general, that would absolutely be inflationary. But the president can hold inflation expectations steady by making absolutely clear that the policy will not lead to a net change in the money supply over the long term. Obama should pledge that once Congress authorizes additional borrowing, he will direct the Treasury to issue bonds to cover the government’s coin-backed spending and then to melt the coin.

I similarly believe that expectations are important. However, Barro seems to fall into the growing category of folks who think that expectations are all that matters and that policymakers can perfectly affect expectations. An announcement from the president that the increase in the money supply isn’t permanent does not guarantee that the minting of the coin is seen as such. In order to believe that the money supply would not increase, we would not only have to believe that the Treasury would commit to borrowing money in the future once the debt ceiling was lifted, but also that the Treasury would borrow enough money to finance the previously financed cash payments necessary to enable them to withdraw the $1 trillion coin. In other words, we would have to believe that the Treasury could perfectly commit itself to actions it would prefer not to take. Or we would have to assume that the Federal Reserve would conduct large scale asset sales to prevent increases in the money supply. Put differently, in the midst of conducting large scale asset purchases, the Fed must commit to large scale asset sales to prevent the money supply from growing by more than they wish as a result of the minting of the coin. The policy would not only tie the hands of monetary policymakers, but forcing the Federal Reserve to conduct such policy is a threat to its independence. And if inflation expectations became unanchored, this could exasperate the effects of the increased money supply and the coin could be particularly harmful.

Advocates think that it gives the president an upper hand in debt ceiling negotiations. However, all it does is increase the stakes of the chicken game. The platinum coin is a bad idea.

QE3 and the Optimality of Nominal GDP Targeting

The Fed’s announcement last week that they intend to conduct open-ended open market purchases has been seen as a victory for advocates of nominal GDP level targeting, especially market monetarists. Scott Sumner has received praise from a number of publications for leading the charge (see here and here). Scott has long advocated nominal GDP level targeting and was criticizing tight monetary policy from the beginning of the recession. The shift toward open-ended open market purchases is therefore certainly a change in the direction of policy and one that is much more in line with a level target. Nonetheless, I don’t think that this is as much of a victory for level targeters as is being claimed. Thus, I would like to take this post to describe my differing view and also the recent discussion of optimal monetary policy.

The intuition of a level target runs as follows. The purpose of the level target is to anchor long run expectations. Thus, suppose that the central bank announces that their objective is to target 5% trend growth in nominal GDP consistent with the trend from essentially 1983 – 2008. This policy announcement suggests that the central bank would like to create nominal GDP growth in the short term that is higher than 5% (since we have been below that trend since 2008), but once nominal GDP returns to trend, growth will return to 5%. So long as the central bank has a good degree of credibility in committing to these actions, this should help to anchor expectations.

Thus, if nominal GDP is significantly below the long run trend, the policy suggested by this intuition is for the central bank to announce its intention to conduct open market purchases sufficient to achieve its target. In other words, the central bank announces a plan to conduct open-ended open market purchases (i.e. whatever it takes to hit its target).

The recent Fed statement represents a stark change from previous policies specifically as it pertains to its efforts at quantitative easing. Specifically, rather than announcing particular dollar values of assets that they intends to purchase, the Fed has changed their statement to reflect their desire to “increase policy accommodation by purchasing additional agency mortgage-backed securities at a pace of $40 billion per month.” That’s clearly open-ended. However, advocates of a nominal GDP level target and similar objectives should NOT see this a clear victory.

As the description of the intuition behind level targeting makes clear, the use of open-ended open market purchases should be coupled with an explicit objective for policy. There is no such objective in the Fed’s statement. The duration of policy is not defined in terms of objectives, but rather time:

To support continued progress toward maximum employment and price stability, the Committee expects that a highly accommodative stance of monetary policy will remain appropriate for a considerable time after the economic recovery strengthens. In particular, the Committee also decided today to keep the target range for the federal funds rate at 0 to 1/4 percent and currently anticipates that exceptionally low level ofs for the federal funds rate are likely to be warranted at least through mid-2015.

The federal funds rate is not the objective of monetary policy, it is the intermediate target. In addition, and perhaps more importantly, we need the Fed to define what they mean by “after the economic recovery strengthens.”

The closest the FOMC statement comes to an objective is the following statement:

The Committee will closely monitor incoming information on economic and financial developments in coming months. If the outlook for the labor market does not improve substantially, the Committee will continue its purchases of agency mortgage-backed securities, undertake additional asset purchases, and employ its other policy tools as appropriate until such improvement is achieved in a context of price stability. In determining the size, pace, and composition of its asset purchases, the Committee will, as always, take appropriate account of the likely efficacy and costs of such purchases. [Emphasis added.]

This is hardly an explicit objective for policy. In addition, not only does the statement leave out an explicit objective, its one mention of a criteria for adjusting policy is a reference to the labor market. Does the Fed now believe that they can target employment? So some less skeptical of the Fed, this question might seem facetious. However, the Fed explicitly put in the statement that they will judge policy in accordance with fluctuations in the labor market. What is an acceptable amount of unemployment to the Fed? To what extent do they think that they can reduce unemployment?

Note here the important difference between the nominal GDP targeting example given above and the actual policy that is being implemented. The adoption of a nominal GDP level target would lead to higher nominal GDP growth in the short run which, given non-neutralities, would lead to a corresponding short run increase in real GDP thereby reducing unemployment. Thus, the objective of the policy would be to increase nominal GDP growth. The result of the policy (assuming that it is successful) would be to reduce unemployment. The actual policy of the Fed, however, seems to be to use unemployment as their objective. This is not the same thing.

This brings me to my final point. Throughout the discussion above, I was comparing the difference between actual Fed policy and a hypothetical nominal GDP target. This latter type of policy has become substantially more popular in the public conversation thanks to Scott Sumner. Its popularity in the economic literature has been somewhat lagging, but once had the support of Ben McCallum, Greg Mankiw, and others. More recently, Michael Woodford quasi-embraced nominal GDP targeting in his recent talk in Jackson Hole. However, Woodford also stated that he doesn’t see nominal GDP targeting as optimal policy. Rather, flexible inflation targeting in which the central bank targets inflation, but gives some weight to the output gap is optimal within the New Keynesian framework.

On this last point, Woodford is clearly correct — he wrote the book on optimal monetary policy in New Keynesian models, literally. Nominal GDP targeting can be consistent with optimal monetary policy in these models, but it depends on the particular characteristics of the model and the value of the parameters. Nonetheless, it is in the New Keynesian framework that nominal GDP targeting should find much of its support. Optimal monetary policy within these frameworks is defined as the policy that minimizes fluctuations in utility around the steady state. By performing a second-order Taylor series expansion of the utility function around the steady state and some mathematical manipulation, it can be shown that the optimal monetary policy is one that minimizes the weighted average of deviations of inflation from its target and output from its “natural” level. (This, by the way, is contrary to the assertions by Scott Sumner and George Selgin that the welfare criteria in these models is ad hoc.) Woodford is obviously correct that in this context that flexible inflation targeting is the optimal monetary policy. However, how should one use this criteria to practically guide monetary policy? I would argue that New Keynesians should advocate nominal GDP targeting because flexible inflation targeting places a large knowledge burden on central bankers as it requires that they know what natural (or potential) output is an any given point in time. In fact, we have very poor estimates of the output gap in real time — a point highlighted in work by Athanasios Orphanides.

Regardless of what policy is optimal, however, recent Fed policy is only a minor step in the direction of the desired policy of advocates of more expansionary monetary policy.

Question of the Day

If it was so obvious that this recovery would be slow, then the Administration’s forecasts should have reflected it. Were they saying at the time, “normally, the economy bounces back quickly after deep recessions, but it’s destined to be slow this time, because recoveries from housing “bubbles” and financial crises are always slow?”

That is John Cochrane. His answer by the way is: “No, as it turns out.” The whole post is worth reading.

Is Monetary Policy Only About Expectations?

I have argued in the past that an explicit target for monetary policy is necessary for the central bank to accomplish its goals. For example, suppose that the central bank wants to increase the inflation rate by two percentage points. We know that they can do this by increasing money growth. But how much would they have to increase money growth in able to achieve their target? Well, one answer is that they can get out (I wish I could say dust off) one of their Old Keynesian forecasting models and recursively figure out the answer. In a lot of ways, it seems like this is what the Fed is doing. Whenever they announce asset purchases, they announce the nominal quantity of assets that they are going to purchase. An alternative strategy is to announce a target and to an intention to purchase as many assets as necessary to achieve the goal.

Now, of course, this doesn’t guarantee anything. If the Fed is targeting something that it cannot control or if policy doesn’t work in the way that the Fed believes, we might not get intended results.

But is announcing a strategy sufficient? According to what some in the blogosphere have referred to as the Chuck Norris strategy the answer is yes. And believe it or not, this is not the view that originated in the blogosphere. According to Benjamin Friedman and Kenneth Kuttner, for example:

Central banks no longer set the short-term interest rates that they use for monetary policy purposes by manipulating the supply of banking system reserves, as in conventional economics textbooks; today this process involves little or no variation in the supply of central bank liabilities. In effect, the announcement effect has displaced the liquidity effect as the fulcrum of monetary policy implementation.

The problem with the Chuck Norris strategy is that of commitment and credibility. The strong version of this Chuck Norris hypothesis is that an announcement is sufficient. The reference to Chuck Norris is due to (a version of) the following analogy. Suppose that Chuck Norris walks into a bar. He announces that he is going to beat everyone up if they don’t leave. Since he is Chuck Norris and everybody else is not, nobody bothers to fight him. They all leave. He doesn’t have to take action. Ironically, there is a flaw in this analogy that actually lends support to those of us who are skeptical about the Chuck Norris effect. Anybody who has ever been to a bar knows that not everybody will leave just because Chuck Norris makes the announcement. There will be somebody who challenges Chuck Norris — even if that challenge is futile. In other words, Chuck Norris cannot get by on credibility alone. He must follow up that strategy with commitment, i.e. he is going to have to beat a few people up.

Why do I bring this up? I bring this up because of the case of Switzerland. In order to prevent appreciation due to a flight to quality, the Swiss National Bank announced last year that they were pegging the Swiss franc at 1.20 per Euro. This is important because it seems to satisfy all the conditions for a Chuck Norris type policy. For example, a central bank has the resources and the means to buy and sell its own currency in foreign exchange markets to affect the exchange rate. Thus, it is targeting something that it can directly control and it is announcing its intended target. After announcing its intended target, this represents an explicit test as to whether or not the Chuck Norris effect is operational. Alas, Evan Soltas finds evidence that it is not:

I had implied in both posts that the floor was so credible that it did not require an active defense. Indeed, for several months after its establishment, the SNB did not have to conduct any trades. That is no longer true; I realize now that the correct conclusion to make was not that the Swiss currency floor would not require any currency purchases. Rather, the floor’s credibility eliminates the need for foreign currency purchases to the extent that those seeking to buy Swiss francs are speculating on exchange rates. To the extent, however, that Swiss franc buyers are seeking to park money in Swiss assets or deposit accounts, the SNB will have to purchase foreign currency to maintain the floor.

In other words, credibility is not enough. Central banks also need commitment. This is consistent with the view I described in the first paragraph. It is not consistent with the strong version of the Chuck Norris effect.