Some Thoughts on the Fed's CBDC Report

Economists within the Federal Reserve System have been musing about central bank digital currency for a while now. For example, yours truly provided a few thoughts on the possibility way back in 2015 (see here) and most recently here. But the views of individual Fed researchers are simply our own personal views. What people are really interested in is an official view--namely the view of the Board of Governors of the Federal Reserve. At long last, their report is now available here). 

The report makes it clear that the Fed has no immediate plans to issue a CBDC. The main purpose of the report is to provide some background information, discuss the potential costs and benefits of a CBDC, and solicit feedback from the general public. It is a very nice educational piece. There was nothing really new in it for people who have been following the discussion over the past few years, but there was one thing I found interesting (and potentially important). The interesting part, I think, has to do with their definition of CBDC:

For the purpose of this paper,  a CBDC is defined as a digital liability of the Federal Reserve that is widely available to the general public.

I used bold font to highlight the important part in the passage above. Most of the digital money Americans use today consists of dollar credits in transaction accounts that reside in the broader bank sector (which includes non-banks providing digital payment services). This form of digital money is technically a liability of private sector agencies, not the government. Is this an important distinction to make? I'm not sure--I suppose it depends on what one thinks is important. 

For one thing, the Board's adopted definition appears to rule out the "wholesale CBDC" proposal that some have advocated for (including myself). Wholesale CBDC (also referred to as "synthetic CBDC" or "sCBDC") is essentially a narrow-banking proposal (which has a long history in the banking policy debate). 

In my writings, I contrasted "wholesale CBDC" with "retail CBDC," the latter of which I interpreted as a product that is both a liability of the Federal Reserve and a payment service managed by the Federal Reserve. I thought this latter property was a bad idea--the Fed should probably not get involved with the challenges of retail banking. I missed the possibility of separating the legal status of digital money from the agencies responsible for managing digital money accounts. As George Selgin explains well here, the Board's definition of CBDC means a privately-intermediated liability of the Federal Reserve (George calls this iCBDC to distinguish it from sCBDC). 

Speaking for myself, I'd be happy with either an sCBDC or an iCBDC (assuming they are properly designed). My main concern was over the prospect of a government agency operating a large retail business. Both sCBDC and iCBDC are intermediated products--we can let the private sector manage the day-to-day operations of processing payments. George, however, believes that sCBDC should be preferred to iCBDC for reasons that he spells out here (I'm not sure I share his concerns).

My own view is that the distinction between sCBDC and iCBDC will be of interest mainly to lawyers and regulators (John Kiff points me to this IMF report). From an economic perspective, the two products appear to be very close--if not perfect--substitutes (again, assuming their design is optimized). The practical difference between a Federal Reserve liability and a private liability fully-insured by the government seems almost non-existent to me. But I'm willing to be persuaded otherwise. 

On the Necessity and Desirability of CBDC

Remarks prepared for P2PFISY Panel Discussion, December 1, 2021

At a conceptual level, CBDC is a compelling idea. It envisions everyone having an account with the central bank consisting of a direct claim against digital fiat currency that can be used as a safe and efficient form of payment. Since all debiting and crediting of accounts occurs on the central bank’s balance sheet, all the costs and counterparty risks associated with intermediated payments is eliminated. All individuals and businesses would have access to secure, low-cost real-time payment services. Moreover, concerns over data privacy and ownership can be dealt with directly and in a manner consistent with societal preferences.

I have nothing against a retail CBDC per se. Indeed, there may even be some merit to the idea as a basic public option. But is it really something that is essential? What existing problems is a CBDC supposed to solve that cannot be solved through a wholesale-CBDC with supporting legislation?

A wholesale-CBDC is an old idea. It is basically a proposal to permit free-entry into the business of narrow-banking. Let Novi, Square, PayPal and other reputable firms have Fed accounts. Let them issue “stablecoin” liabilities fully-backed by interest-bearing reserves. Consider adopting the U.K.’s open banking legislation. Let the private sector work its magic. What else needs to be done?

Do we really think that consumers would flock to CBDC for reasons of safety? Bank deposits are close to fully-insured for most people, and all deposits would effectively be fully-insured in a narrow bank. Do we think that big banks overcharge for basic payment services? I see many online banks offering free checking accounts and I see service fees generally declining over time—something that would be spurred on with a wholesale-CBDC. I do see interchange fees in the U.S. remaining stubbornly high. But I diagnose this as a by-product of American’s love-affair with the cash-back and rewards programs offered by credit card issuers. I do not see how a CBDC is supposed to discourage consumers from using cards that effectively pay them to spend money. (This seems to be less of a problem outside of North America.)

But more importantly, do we want to rely on the government sector to deliver high-performance customer service at the retail level and to keep up with technological advances in the space? A well-functioning government is essential for a well-functioning private sector (and vice-versa), but these two sectors should probably stick to their knitting. Let the central bank handle monetary policy, bank supervision, lender of last resort operations, and wholesale payments. Let the private sector handle servicing the vast, demanding and rapidly-evolving retail sector. It’s a model that has proven to work best, in my view.

As for financial inclusion, one should keep in mind that the most significant progress along this dimension in recent years has been the outcome of private initiatives, not state initiatives. Consider, for example, the hundreds of millions people who now have access to digital payments thanks to M-Pesa, WeChat and AliPay. Contrast this to the many developing countries that already have CBDC issued by their state banks. If their state banks have not been able to deliver on this score, what makes us think that retail-CBDC is essential?

Run-Proof Stablecoins

A stablecoin (SC) is a financial structure that attempts to peg the value of its liabilities (or a tranched subset of its liabilities) to an object outside its control, like the USD. To do this, the SC must effectively convince its liability holders that SC liabilities can be redeemed on demand (or on short notice) for USD at par (or some fixed exchange rate). 

The purpose of this structure is to render SC liabilities more attractive as a payment instrument. Pegging to the USD is attractive to people living in the U.S. because the USD is the unit of account. Non-U.S. holders may be attracted to the product because the USD is the world's reserve currency. This structure serves to increase the demand for a SC pegged to the USD. 

To a macroeconomist, an SC looks like a unilateral fixed exchange rate regime or a currency board. The structure also resembles a money market fund that pegs the price of its liabilities with the USD at par (presently, government money funds in the United States). It also looks like a bank without deposit insurance (bank deposit liabilities are pegged at par value against cash). 

The history of unilateral fixed exchange rate regimes is mixed. Hong Kong has successfully pegged its currency to the USD for decades. But the experience for many countries seems closer to that of Argentina. Unless a USD-based SC is backed fully by USD reserves (it needs an account at the Fed for this) or by USD bills (maximum denomination is $100, so unlikely), it may be prone to a bank run. Any other security (including USTs, as the events of March 2020 demonstrated) is subject to liquidity risk -- i.e., a risk that the market for the security suddenly freezes, or demand for the security vanishes as investors seek safer havens. If a SC cannot dispose of its assets at "fair" or "normal" prices, it will fail to raise the money it needs to meet its par redemption promise. The SC will turn out to be not so stable. 

 

The theory of bank runs suggests that SCs might be rendered run-proof if their liabilities are properly designed. The famous Diamond and Dybvig (JPE 1983) model of bank runs is, in fact, a paper that demonstrates how banks can be rendered run-proof. In the first part of their paper, the explain how a credible promise to suspend redemptions when redemption activity is abnormally high can serve to discourage runs (redemptions based on belief of failure, rather than a need for liquidity) altogether. There is no need for deposit insurance (the second part of their paper is devoted to explaining why deposit insurance may nevertheless be needed, but their argument is not entirely satisfactory). 

 

In reality, we do see attempts to render run-prone structures less prone to runs. The Dodd-Frank Act, for example, prevented institutional money funds from pricing their liabilities at par with the USD (only government funds can now do this). In addition, the Act required that fund managers implement liquidity fees and redemption gates in the event of heavy redemption activity. These provisions have not been entirely successful. Even banks that suspended redemptions in the old days did not manage to prevent mass redemption events. The theory suggests that what is needed is a *credible* policy. Evidently, when push comes to shove, people cannot always be expected to follow through on their promises. 

 

Back in my teaching days, I used a "crowded movie theatre" as a metaphor to explain the phenomenon. Imagine a movie theatre that seats 500 people. If someone was to yell "fire!" (for legitimate or illegitimate reasons), people can be expected to rush for the exits. Invariably, some people are likely to be trampled and even killed. If people would instead react to the alarm by rising calmly from their seats and proceeding sequentially to the exits, then only the very last few people in the queue are destined not to make it. Losing one or two people relative to (say) is terrible, but it's preferable to losing 50 people in a mad rush for the exits. 

An economist might detect a missing market here. Why not sell tickets with queue positions (in the event of fire)? The tickets with the last few queue positions are likely to sell at a discount (that would depend on the likelihood of the event). This way, if someone yells "fire!", customers will simply show their assigned queue position to the ushers and proceed calmly out of the exits. If the fire does exist, the few people know they are doomed and accept their fate with stoic resignation, knowing that they are dying so that many others may live. (And if it turns out there is no fire, they are saved from the fire and the prospect of death that would have been present had they joined the rush to the exits). 

Except we know that's not what is likely to happen. People cannot be expected to commit in this manner. And there's no obvious way to enforce such contractual stipulations. 

 

But this is where SCs may have an advantage over conventional institutional structures. In particular, their use of "smart contracts" means that commitment is not an issue. The terms of such contracts are executed under the specified contingencies whether you like it or not. You may not like it ex post, but such commitment can be valuable ex ante. In the context of SCs, the credible threat of suspending redemptions in the event of abnormal redemption activity may actually prevent any runs from occurring in the first place. 

There are, of course, limits to what smart contracts can achieve. They wouldn't, for example, solve the movie theatre problem I just described. This is because people do not live "on-chain." (See also my blog post Smart Contracts and Asset Tokenization.) To some extent, the same issue exists for USD SCs because USDs and USTs exist "off-chain." Nevertheless, money accounts are different than people, so I think the principle described above can apply to financial products. 

****

Related work: Preventing Bank Runs (w/ Nosal and Sultanum, TE 2017).

 

EEA-ESEM Panel: Macroeconomic Consequences of the Pandemic

I was recently asked whether I'd like to share my thoughts on monetary policy in a post-pandemic world. Sure, why not? Thanks to Jan Eckhout for thinking of me. The panel was hosted by the European Economic Association last month and moderated by Diane Coyle. I was honored to speak alongside Ricardo Reis and Beata Javorcik, both of whom provided riveting presentations. For what it's worth, I thought I'd provide a transcript of my remarks here. 

Lunch Panel EEA-ESEM Copenhagen
August 25, 2021

I want to focus my discussion on the U.S. economy and from the perspective of a Fed official concerned with the challenges the Fed may face in fulfilling its Congressional mandates in a post-pandemic world.

First, to provide a bit of context, let me offer a bit of history on policy and, in particular, on what I think were some policy mistakes. Let me begin with the 2008-09 financial crisis, which is something I think most people would agree should never have happened. Whether a sufficiently aggressive Fed lender-of-last-resort operation would have averted the crisis remains a open question. Even if it had been successful, such an operation would have had costs. It may, for example, have elicited an even greater political backlash than we saw at the time--and who knows how this may have manifested itself as undesirable changes to the FRA. As well, such an intervention may have just pushed mounting structural problems down the road. In particular, while it’s now clear that some private sector lending practices needed to change, it’s not clear where the incentive to do so would have come from absent a crisis. In any case, the crisis happened. How was it managed?

The ensuing recession was deep and the recovery dynamic very slow. The prime-age employment-to-population ratio did not reach its pre-pandemic level until 2019, a full decade later. Nevertheless, on the whole, I think the Fed followed an appropriate interest rate policy. There were one or two times the FOMC exhibited a little too much enthusiasm for “normalizing” policy, but I think the slow recovery dynamic had more to do with insufficient fiscal stimulus—especially at the state and local level—rather than a consequence of inappropriate monetary policy. The evidence for this can also be seen by the fact that inflation remained below the Fed’s 2% target for most of the time the policy rate was close to its ELB. The Fed has interpreted this low inflation episode as partly a monetary policy mistake, something its new AIT regime is designed to address. But my own view is that persistently low inflation—and the low money market yields that go along with it—have more to do with the supply and demand for U.S. Treasury securities. This is something the Fed does not have very much direct control over.

I know many people are skeptical of fiscal theories of the price-level, but in virtually every economic model I know, a fiscal anchor is necessary to pin down the long-run rate of inflation. Monetary policy—specifically, interest rate policy—can, of course, influence the price-level, so monetary policy can influence inflation dynamics. But it can do so only in the “short run.” Interest rate policy alone cannot, in my view, determine the long-run rate of inflation, at least, not without appropriate fiscal support.

Now, I know many of you may be asking how I can think fiscal policy has very much to do with inflation given how rapidly the debt has risen since the financial crisis and again with the C-19 crisis, all with little apparent pressure on long-run inflation expectations and on long-term bond yields. We should, however, keep in mind that an observed change in the quantity of an object may entail both supply and demand considerations. And one can easily point to several forces that have contributed to increases in the global demand for UST securities in recent decades. For example, the growing use of USTs as collateral in repo and credit derivatives markets beginning in the 1970s and accelerating through the 1980s. The growing demand for USTs as a safe store of value from EMEs. The evaporation of private-label safe assets during the financial crisis that left a gaping hole for USTs to fill. Next, we had a large increase in the regulatory demand for USTs coming out of Dodd-Frank and Basel III. The Fed’s SRF and FIMA facility should further enhance the demand for USTs. On top of all this, we’ve witnessed an emergent class of money funds called “stablecoins” that are further contributing to the demand for USTs. These forces have been disinflationary, leading bond investors to revise down their expectation of the future path of policy interest rates. It is interesting to ponder a counterfactual here. In particular, think of what may have transpired absent an accommodating U.S. fiscal policy. We may very well have experienced the mother of all deflations. If this is correct, then an elevated debt-to-GDP ratio, given a relatively stable inflation and interest rate structure, reflects an elevated real demand for outside assets. The problem is not that the debt-to-GDP ratio is going up. The problem is what disruptions might occur if it goes down owing to a sudden and unexpected inflation.

The recent rise in inflation is concentrated in durable goods, and I think is mostly attributable to ongoing supply-chain issues associated with the pandemic. This effect is likely to reverse itself, the way lumber prices recently have. Some of what I think is temporarily high inflation may not reverse itself, leading to a permanently higher price-level. In this case, households will worry whether their wages will keep pace with the higher the cost of living. There is even the possibility—though I think less likely—that the rate of inflation itself will remain elevated and that inflation expectations will rise well above the Fed’s 2% target. This may happen, for example, if the traditional bipartisan support for fiscal anchoring in the new generation of Congressional representatives is perceived to wane, or if the global demand for safe assets slows. If either or both of these things happen and are persistent, then the Fed may find itself faced with what Sargent and Wallace phrase an “unpleasant monetarist arithmetic.” That paper, which was published exactly 40 years ago, warned how tightening monetary policy without fiscal support might actually make inflation go higher rather than lower.

The implications for U.S. monetary policy are quite interesting should an event like this unfold. A determined Fed may try to fight inflation by raising its policy rate. The result is likely to be a temporary disinflation and recession.  Should fiscal policy remain unaltered, the logic provided by Sargent and Wallace implies that inflation will return even higher than before as the deficit must increase to finance a larger interest expense on the debt. The best the Fed can do in this case is to lower its policy rate, announce a temporarily higher inflation target, and hope that the fiscal authority gets its house in order. The notion that a Volcker-like policy would lower the long-run rate of inflation depends on fiscal capitulation. This capitulation to some extent did happen under Volcker, although keep in mind he had considerable Congressional support from both sides of the aisle. I do not think this type of political support is something one can count on, especially given today’s political climate. So, you may want to buckle up, as we may be in for some interesting times ahead.

Related Readings:

Is it Time for Some Unpleasant Monetarist Arithmetic? Link to blog post. Link to paper.

Labor Force Participation Gaps Between the U.S. and Canada

Am hearing some talk about whether the U.S. labor market can fully recover to its pre-Covid19 levels. Is it possible that a sizeable number of workers with marginal attachment to the workforce decide to remain out of the labor force? For example, this crisis, unlike the one that preceded it, has been associated with large increases in personal wealth. Workers on the cusp of retiring may now choose to do so earlier? (This is just one of the many stories I hear.)

For what it's worth, I thought I'd update my labor market participate blog post from 2013 which compared participation rates across Canada and the U.S., for males and females, and across different age categories. You can find my old post here along with some links to related posts. Below I report the updated data.

Remember, an individual is counted "in the labor force" if they are either employed (working) or unemployed (actively searching for work) in the previous 4 weeks from the time the labor force survey enquires about labor market status. 

First up, prime-age women. 

The increase in female labor participation is well-known. Less well-known is how U.S. female participation rates have diverged from other countries (I think Canada is more similar to Europe, last time I checked).  Let's take a look at prime-age men.

For the U.S., a secular decline throughout the sample, with evidence of a short-lived rebound from 2016-2019. The Canada-U.S. gap emerged during the Great Recession and is now wider than its ever been. This does suggest there's considerable room for an employment rebound for this demographic. But what accounts for the cross-country gap? 

I provide the other diagrams without commentary. 

On the Role and Future of Cryptocurrencies

My former colleague Howard Wall asked me to join Lawrence White yesterday evening to discuss the role and future of cryptocurrencies at an event hosted by the Hammond Institute for Free Enterprise. It was a great honor to share the stage with Larry. 

I've been thinking about cryptocurrencies for a long time; many of my writings and talks on the subject can be found here. My thoughts on the subject are evolving as I learn more about the phenomenon. For what it's worth, I thought I'd share my opening remarks with interested readers below. As usual, any feedback is welcome. 

The Role and Future of Cryptocurrencies

A money and payments system is about managing databases containing the money accounts of individuals and organizations. Any database management system must necessarily define read and write protocols. Read privileges specify who can view what on the database. Write privileges specify who gets to write what to the database.

So, for example, we can read what’s in our bank account. So can the bank and its regulators. But other people cannot see how much money is held in any account apart from their own. While we cannot write directly to our account, we can send our bank instructions to so on our behalf. The bank can also write directly to our account. It may, for example, credit our account with interest, or debit it for service fees.

Note that bank accounts are digital. Moreover, the messages we send to our bank over the Internet are secured with the aid of cryptography. In this sense, one could say that bank deposits are a form of cryptocurrency.

Bank deposits, however, are not typically viewed as cryptocurrencies. Well then, what are the distinguishing characteristics of a cryptocurrency? It’s not so clear-cut, but two things come to my mind. First, the database for a cryptocurrency is typically associated with an open-read privilege. This implies that the database can, in principle, at least, be subject to audits from any person, or any agency, at any time, all the time.  This property offers a degree of financial transparency that is unheard of in conventional money services businesses. Second, the task of managing the database is typically decentralized in some manner to “validator nodes;” or, what one might label more mundanely as “accountants” in the non-crypto world. What is interesting here is how these validators are potentially recruited and compensated. For Bitcoin, anyone can potentially become a validator and compensation arrives in the form of a stochastic reward.

When it comes to keeping track of money balances, an open-write privilege is problematic. This is known as the double-spend problem. In conventional payment systems, the double-spend problem is solved by delegating database management to a trusted third party. A cryptocurrency like Bitcoin or Ethereum must instead rely on a consensus mechanism that somehow ensures that a dispersed write-privilege does not result in garbage being written to the database. To date, the most popular mechanisms are based on PoW (Proof of Work) and PoS (Proof of Stake). But there are others as well, and one should expect innovation along this dimension since, as far as I know, no existing consensus mechanism has yet proven to be entirely satisfactory.

Of course, the same can be said of conventional database management systems. To young eyes, the current system seems a hopelessly tangled mess of databases that have trouble communicating with each other. Moreover, they appear not to be very secure at times. But despite the problems we all encounter with the modern banking system, one should, in fairness, acknowledge the tremendous achievements that have taken place over the last fifty years. For example, we are now able to travel to foreign countries with just a credit card. This is not the way things worked until relatively recently. Anyone who has had the experience of needing traveler’s checks can fill you in on what it was like to travel in the old days.

Well, if there’s been so much progress in money and payments, what accounts for the emergence and proliferation of cryptocurrencies?

As is so often the case, I think the fundamental cause of this development is rapid technological change moving against a relatively slow-moving incumbency that includes banks, money services businesses, and especially their regulators. In saying this, I do not mean to assign blame; the inertial properties of existing institutional arrangements likely has some merit. Institutional inertia can stabilizing, for example. But to benefit the communities they serve, institutions also have to evolve to meet the challenges of new technologies. And I think this is happening today in the sphere of money and payments.

What new technologies are we talking about? Innovations in communications, like the Internet, have been transformational. As well, there have been advances in data storage and cryptography that have played a critical role. All these innovations are, however, within the grasp of incumbent banks and money service businesses. And indeed, incumbents have made use of these technologies. Internet banking and PayPal are real things, after all. I think the important innovation as far as cryptocurrencies are concerned isthe development of database management protocols that permits a degree of decentralization for managing large databases. I say “large” databases because we already have decentralized database management systems for small communities, like gift exchange or the exchange of favors among friends (see: Why the Blockchain Should be Familiar to You). Advances in data storage and communications have, in effect, permitted this ancient form of communal record-keeping to scale.

The decentralized or communal aspect of managing a database is, of course, very much at odds with the notion of delegating the responsibility to a privileged set of institutions. Some people believe that these developments will lead to a revolution—an overthrow of existing institutions—a triumph in democracy over a privileged class. What is much more likely is an evolution of existing institutions to accommodate the threat posed by the potential usurpers in a manner that serves the broader community. In short, what we are likely to witness is the usual pattern of economic development in relatively well-functioning societies.

What do cryptocurrencies offer individuals and society? What are the concerns of regulators and policymakers?

To answer these questions, we need to recognize that there are different classes of cryptocurrencies, each of which cater to a specific constituency. Broadly, they can be categorized as belonging to one of two groups distinguished by their respective exchange rate regimes and governance structures.

In one group, we have the decentralized autonomous organizations, like Bitcoin. From the perspective of domestic policymakers, Bitcoin can be viewed as foreign currency operating under a floating exchange rate regime. Except that there’s no negotiating with Bitcoin (there's no negotiating with some countries either). The intermediaries that deal or broker BTC transactions can, however, be regulated.

In the other group, we have the so-called stablecoins, like USD Coin (sponsored by Circle and Coinbase) and Diem (sponsored by Facebook). To domestic policymakers, stablecoins can be viewed as checkable mutual funds operating under a unilateral fixed exchange rate regime utilizing various forms of collateral. The major innovation here has less to do with technological innovation and more to do with the willingness and ability to process USD payments outside the commercial banking sector.

Viewed in this light, cryptocurrencies do not look so unfamiliar. As a foreign currency operating under a floating exchange rate, they’ll likely never displace the domestic unit of account. They may, however, serve as store-of-value or portfolio hedge. And they may facilitate certain kinds of payments, typically on-chain and large-value. As a stablecoin offering a par exchange rate, they suffer from all the usual problems of uninsured fractional reserve banking—unless they promise to back their currencies fully with USD cash.

The question here is whether these products are offering something fundamentally more cost-effective when it comes to making payments, or whether they owe their existence primarily to regulatory arbitrage. I do not know the answer to this question, but I suspect that much of what they have to offer comes from the latter. Diem, for example, can bypass banking regulations by not becoming a bank. It can leverage Facebook’s huge social network as a payment system connecting 2B+ users around the world. It can potentially offer money-transmitting services for “free” or, rather, in exchange for personal data. My guess is that banks (or even PayPal) are not permitted operate in this manner. Regulatory advantage: Diem. 

Regulators need to keep a close eye on these structures since it is politically impossible to commit to the doctrine of caveat emptor when it comes to money and banking. The temptation, as always, will be to replace “cash” for higher-yielding “cash equivalents” on the balance sheet. The structure slowly evolves into an uninsured fractional reserve bank, but in the shadow bank sector. If something goes wrong, depositors will seek compensation, first from the firm and then from the government. After all, how could a government knowingly permit such an unstable structure to exist in the first place?

To sum up, I think the future of cryptocurrencies like Bitcoin is to serve as an alternative asset class for investors. I doubt that it will ever become a dominant medium of exchange in any large economy. Fractional reserve banks using BTC as reserves are not likely to be tolerated.

The future of stablecoins seems more interesting to me. In the first instance, they seem capable of filling the gaps that remain apparent in modern day payment systems (think correspondent banking here). But the main effect here is likely to spur conventional banks and their regulators to fill these gaps at a faster pace. There is a possibility that a project like Diem might one day abandon its peg to the USD and offer itself as a stand-alone currency. Policymakers would in that case be concerned about a country maintaining monetary policy sovereignty. One manifestation of this concern could be a pre-emptive action on the part of the government, for example, by offering its own universally-accessible CBDC.

 

A Natural Rate of Interest

This post was motivated by a conversation with Eric Lonergan. It began with a simple question: what should be the interest rate paid on reserves? I answered that according to theories I'm familiar with, reserves should earn the "natural" rate of interest, which I defined as the sum of population and productivity growth. So, assuming 2% "real" growth and 2% inflation, reserves (and government debt more generally) should be yielding around 4%. 

I think it's fair to say most people did not find my answer very satisfying. So I thought I'd take a moment to explain how I arrived at it. I want to do so in the context of a model economy. Let me describe the model first. We can discuss its limitations and possible extensions later on. 

Consider an economy where people live for two periods; they are "young" and then become "old." Let N(t) denote the population of young at date t. Assume that the population grows at (gross) rate n; that is, N(t) = nN(t-1). In this "overlapping generations" model, the population at date t is given by N(t)+N(t-1). 

Individuals in this economy generate y units of perishable output (goods and services) when they are young. I'm going to treat y as fixed over time. This implies that the RGDP at date t is given by N(t)y and that the RGDP grows at rate n over time (there is no productivity growth). In what follows, I label n the "natural" rate of interest. 

Suppose that people only value consumption when they are old. This poses an interesting economic problem. The young can produce goods that the old value, but the old have no way of paying for these goods. Private credit markets don't work here. 

The cooperative solution is very simple: the young should "gift" their goods y to the old. If everyone followed this cooperative protocol, then the young of generation t would consume (in their old age) c(t+1) = N(t+1)y/N(t) = ny. 

That is, by following this protocol, it's as if the young "deposit" their income y in a savings account that generates a (gross) real yield equal to n, the "natural" rate of interest. 

Since private competitive markets cannot be expected to implement this socially-desirable outcome, what other mechanisms might be employed? In small communities, reciprocal gift exchange seems to work quite well. In the present context, the young look after their parents, expecting their children to return the favor, and so on. 

Larger communities need to rely on other mechanisms. In the present context, a PAYGO social security system that taxes the young y and pays the old ny would do the trick. 

The same outcome could be achieved through monetary exchange. Suppose the government lets all individuals open a central bank money account. The government creates (out of thin air) M dollars and credit the accounts of the "initial old" with M/N(0) dollars. Assume that M is kept constant over time. The old are expected to spend these dollars on a competitive spot market, where goods exchange for dollars at price p(t). 

The equilibrium price-level is easy to derive in this example. At any date t, we have N(t-1) old people collectively holding M dollars. These M dollars will be spent (the old have no reason not to) on the goods available for sale, N(t)y. The market-clearing condition here is M = p(t)N(t)y at every date t. Because both M and y are constant, and because population N(t) is growing at rate n, it follows that the equilibrium price-level p(t) must be falling at rate n. 

So, if we interpret M as "reserves" in this model economy, then reserves yielding the natural rate of interest would be consistent with economic efficiency. If reserves yield zero nominal interest rate, then efficiency requires some deflation. But the same outcome is possible if reserves were to yield a nominal interest rate n in a zero-inflation rate regime. 

This result continues to hold for more general preferences. Suppose that people care about consumption when young and old. Then the young will only want to consume a fraction of their income. That fraction will depend on (among other things) the real rate of return they expect on their retirement savings. As it turns out, the so-called "Golden Rule" allocation requires that money/bonds yield the natural rate of interest. 

Is this a good place to start thinking about Eric's question? It may be a good place to start, but we don't want to stop here. The analytical framework above is "bare bones." Among other things, my analysis implicitly assumes that there is no difference between reserves and government treasury securities. Does this matter? If it does, the reasons need to be spelled out. What modifications to the simple model above would imply that to meet a given social objective, it is desirable to have reserves yield less than treasury securities? In reality there is duration risk. But why does the Treasury issue bonds with different maturities in the first place? Moreover, why are these bonds purposefully rendered illiquid (for example, by discouraging the Fed from monetizing the entire bond issue or, at least, from setting up standing purchase facilities?). The answers to these questions are not immediately obvious to me. But they may be to you!