Believe those who are seeking the truth. Doubt those who find it. Andre Gide

Wednesday, November 25, 2015

Lift off in a world of excess reserves

Back in the good ol' days, U.S. depository institutions (mostly banks) held just enough cash reserves (deposits they held at the Fed) to meet their settlement needs. At the end of the day, a bank short of reserves could borrow them from a bank with excess reserves. These trades would occur on the so-called federal funds market and the interest rate agreed upon on these (unsecured) overnight loans is called the federal funds rate (FFR). In fact, there was (and is) no such thing as "the" FFR because these trades did not (and do not) occur in a centralized market at a single price. Trades in the FF market occur in decentralized over-the-counter markets, with the terms of trade (interest rates) varying widely across transactions (see figure 12 here). "The" FFR we see reported is sometimes called the effective FFR. The effective FFR is just a weighted average of reported interest rates negotiated in the federal funds market.

For better or worse, the FFR was (and still remains) the Fed's target interest rate. Prior to 2008, the Fed (actually, the FOMC) would choose a FFR target rate and then instruct the open markets trading desk at the New York Fed to engage in open market operations (purchases and sales of short-term Treasury debt) to hit the target. To raise the FFR, the trading desk would sell bonds, to lower it, they would buy bonds. (Evidently, even the mere "threat" of buying and selling bonds following an FOMC policy rate announcement often seemed sufficient to move the market FFR close to target.) The way this worked was as follows. A sale of bonds would drain reserves from the banking system, compelling banks short of cash in the FFR market to bid up the FFR rate. A purchase of bonds would induce the opposite effect. The system worked because banks were compelled to economize as much as they prudently could on their reserve balances. Prior to 2008, the Fed was legally prohibited from paying interest on reserves (IOR).

But the world is now changed. In 2008, the Fed started paying a positive IOR (25 basis points). And it started buying large quantities of U.S. treasury and agency debt. The Fed funded these purchases with interest-bearing reserves. It may seem like a strange thing to do, but from a banker's perspective it looks brilliant. Imagine buying a risk-free asset yielding 2-3% and funding the purchase by borrowing at 1/4%. The profit the Fed makes on this spread is mostly remitted to the U.S. treasury (i.e., the taxpayer). In 2014, the Fed remitted close to $100B.

The U.S. banking system is now flush with reserves--most depository institutions (DIs) hold "excess" reserves. (Incidentally, there is no way for the banking system collectively to "get rid" of these excess reserves. In particular, the banking system as a whole cannot "lend out reserves.") And since most DIs have excess reserves, the FFR market is essentially dead.

Well, not quite dead. There are still a few trades, motivated  primarily by the fact that some key participants in the FF market (GSEs) are legally prohibited from earning IOR. The Federal Home Loan Banks, in particular, have a large supply of funds that, if they could, would happily hold these deposits at the Fed earning 25bp. Instead, they must hold these funds with DIs, who are able to earn IOR (see here). Because short-term treasury debt is yielding close to zero, the effective FFR negotiated between DIs and non-DIs lies somewhere between zero and IOR (see following graph). According to Afonso and Lagos (2014),  the volume of trade in the FF market has dropped to about $40B per day from its peak of $150B per day prior to 2008 (see their figure 4).

Alright, so where are we at? Since 2008, the Fed has congressional authority to pay IOR (to DIs only). The Fed can clearly set IOR where ever it wants (within limits). So when lift off date arrives, raising IOR by (say) 25bp will pose no problem from an operational viewpoint.

The Fed, however, has elected to keep the FFR--not the IOR--as "the" policy rate. Given this choice, there is the question of how the Fed expects to influence the FFR when there is no (or very little) FF market left in this world of excess reserves. Theoretically, IOR should serve as a floor for the FFR. But evidently there are "balance sheet costs" and other frictions that prevent arbitrage from working its magic. So the problem (for the Fed) is how to guarantee that its policy rate--the FFR--will lift off along with an increase in IOR.

Enter the Fed's new policy tool -- the overnight reverse repo (ON RRP) facility, overseen by Simon Potter of the NY Fed. Actually, the tool is not exactly new. The Fed has historically used repos and reverse repos for a long time; see the following graph.

In a repo exchange, the Fed buys (borrows) a security from a DI in exchange for reserves. In this case, the DI is borrowing reserves from the Fed. The value of the Fed's repo holdings is plotted in red above. Since the advent of QE, the repo facility has remained dormant. In a reverse repo, the Fed sells (lends) a security to a DI in exchange for reserves. In this case, the DI is lending reserves to the Fed--that is, reverse repo is just a way for the Fed to pay interest on reserves. The blue line above plots the value of reverse repo holdings.

What's new about the ON RRP facility is that it is open to an expanded set of counterparties (beyond the regular set of DIs). The NY Fed publishes a list of these counterparties here. It is notable that GSEs and MMMFs are including in this list.

Lift-off (an announced increase in the FFR target rate or band) will then be accompanied by an increase in the IOR to (say) 50bp together with an ON RRP rate of (say) 25bp. The hope is for the effective FFR to trade somewhere within this interest rate band. Theoretically, the ON RRP rate should provide an effective floor for the FFR--assuming that the facility is conducted on a full allotment basis (i.e., assuming that the facility is not capped in some manner). If the facility is capped, and if the cap binds, then we may observe trades in the FF market occurring at rates lower than the ON RRP rate. This latter scenario is obviously one that the Fed would like to avoid.

There is also the question of whether other market interest rates will follow the FFR upward in the present environment. Some economists, like Manmohan Singh of the IMF worry that the Fed is using the wrong tool for lift off (see his piece in the Financial Times here). Singh would prefer outright asset sales because the treasuries released in the market can then be left to circulate (via re-use and rehypothecation) to relieve an ongoing asset shortage. (The securities released by the Fed in its ON RRP facility are evidently not expected to circulate.) It is conceivable, though perhaps unlikely, that the yield on short-term treasuries remains close to zero (reflecting a stubborn liquidity premium) even as the FFR is increased. As always, it will be interesting to see what actually transpires.

Thursday, November 12, 2015

Bitcoin and central banking

Economic exchange depends critically on secure and trustworthy payment systems. Because payment systems are fundamentally about recording and communicating information, it should come as no surprise that payment systems have evolved in tandem with advancements in electronic data storage and communications. One exciting development of late is Bitcoin--an algorithmic-based, communally-operated money and payment system. I thought I'd take some time to gather my thoughts on Bitcoin and to ponder how central banks might respond to this innovation.

Bitcoin is open-source software designed to govern a money and payment system without the aid of conventional intermediaries like chartered and central banks. The role of chartered banks as payment processors is replaced by a communal consensus protocol (mining), where transaction histories are recorded on an open ledger (the blockchain). The role of a central bank is replaced by a "fixed" money supply rule (Note: nothing is truly "fixed" in Bitcoin since the community could, in principle, "vote" to change program parameters at subsequent dates. This is true, of course, for any system of governance.)
Bitcoin is about as close as we have come to digital cash. And because the bitcoin is in relatively fixed supply (or so we think), people sometimes refer to Bitcoin as managing a digital-gold system.

Let's think about cash for a minute.  Cash is a bearer instrument (ownership is equated with possession). Cash payments are made in a P2P manner, without the aid of an intermediary. When I buy my morning coffee, I debit my wallet of cash and the merchant credits her register by the same amount. There is a finality to the transaction (unless my coffee is cold and the merchant values my future business). To the extent that cash is difficult to counterfeit, it solves the double-spend problem. The use of a cash-based payment system is "permissionless" (no application process is needed to open a cash wallet, no personal information needs to be relinquished to open an account). Relatedly, cash is "censorship-resistant," meaning that you can basically spend it as you see fit. Finally, cash is distributed on an invisible ledger, permitting a degree of anonymity. Cash transactions need not leave a paper trail.
The digital money issued by banks is different from cash in several respects. One main difference is that transactions between any two traders must be intermediated by a bank. Transactors implicitly trust the bank to do the proper book-keeping and it is this trust that "solves" the double-spend problem for digital bank money. Bank money is not permissionless. One has to make an application for a bank account and, in the process, relinquish a great deal of personal information that one trusts the bank to keep secure. People who are unable to properly identity themselves are denied conventional banking services (up to 1/4 of American households are estimated to be unbanked or underbanked). Bank money is not censorship resistant--banks may not process certain types of payment requests on your behalf. Of course, bank money leaves a digital trail (albeit on a system of closed ledgers) with your identity clearly attached to a particular transaction history.

So what are the benefits of Bitcoin? The benefits are likely to vary from person to person, but in general, I'd say the following. First, it's monetary policy reduces the "hot potato" motive of economizing on money balances--that is, it offers the prospect of being a decent long-run store of value. Second, anyone with access to the internet can access an account (a public/private key pair) for free--like cash, no permission is needed. The public key is like an account number and the private key is like a password. Account balances remain secure as long as the private key remains secure. Third, like cash, no personal information is necessary to open an account, so no need to worry about securing private information. Fourth, like cash, bitcoin is censorship resistant--no one can prevent you from spending/receiving bitcoin from whomever you like. Fifth, bitcoin can offer a greater degree of anonymity than bank deposit money, but less so than cash (unlike cash, the blockchain ledger is visible and public). Sixth, the entire money supply (blockchain) lives on a replicated distributed ledger--it lives simultaneously everywhere--so that "sending money somewhere" means updating the ledger on all computers everywhere. There are no banks, there are no borders. Seventh, the user cost of transferring value is relatively low.

As I said, the extent to which consumers value these benefits likely depends on a host of factors. I see potentially large benefits to relatively poor individuals who have limited access to conventional banking services. It is estimated that up to one in four U.S. households are unbanked or underbanked--people who must rely on high-cost bill-pay, prepaid debit cards, check cashing services, and payday loans. The benefits are likely to be greater for poor individuals living in high inflation regimes that do not have access to interest-bearing (inflation protected) accounts.

What are the costs of Bitcoin? First, it is not a unit of account. Because of its monetary policy and its unstable demand, its value is quite volatile over short periods of time, making it inconvenient as a payment instrument (even if it is a good long-run store of value). Second, it has the same security properties as cash--losing or forgetting your private key is like losing your wallet. One could employ the services of a third-party in this regard, but if so, then why not just use a bank? Third, although the user cost of Bitcoin is presently low, the social cost (primarily in the form of electricity) is high relative to the cost of operating trusted ledgers. Fourth, because of its cash-like properties, bitcoin can also help facilitate illicit trade. (Of course, the same is true of cash.)

How might the advent of Bitcoin influence central bank thinking?

First, the threat of Bitcoin (and of currency substitutes in general) places constraints on monetary policy. In jurisdictions that finance large amounts government spending through the inflation tax, such a constraint may become binding.

Second, to the extent that bitcoin becomes a significant payment instrument (or even the unit of account), it might open the door to financial instability. Experience demonstrates the private sector's desire for maturity transformation or, more generally, the willingness to act on incentives that make funding illiquid assets with short-term debt a preferred balance sheet structure. The same incentives would presumably be in place in a Bitcoin economy. In principle, demand-like liabilities should trade at a risk premium. But in practice, they may not. Especially in times of economic complacency, they are likely to be viewed as close to perfect substitutes in terms of their money properties, just like bank money and cash today (and the way U.S. treasury debt and senior tranches of private-label MBS were viewed as close collateral substitutes in the repo market prior to 2008). The question is what happens if and when there is a "bank-run" or "roll-over crisis" on such a system? The situation is exacerbated if bitcoin is not the unit of account (think of European banks issuing loans denominated in USD). Since federal deposit insurance may not be available and since no LOLR can issue BTC, a classic bank panic is possible. Central banks and fiscal authorities would have to think about what, if anything, to do in such circumstances. One solution may be to impose narrow banking restrictions for banks (and other entities) engaged in bitcoin-denominated maturity transformation.

My own recommendation is for central banks to consider offering digital money services (possibly even a cryptocurrency) at the retail and wholesale level. There is no reason why, in principle, a central bank could not offer online accounts, the same way the U.S. Treasury presently does ( These accounts would obviously not have to be insured. They would provide firms with a safe place to manage their cash without resorting to the banking or shadow banking sector. They would give monetary policy an additional instrument--the ability to pay interest on low-denomination money (possibly at a negative rate). To the extent paper money is displaced, there would be large cost savings as well.

It's hard (for me) to see what the downsides are in having a central bank supply digital money. Critics might argue that it leaves people exposed to potentially poor monetary policy. This may be true and, for these people, currency substitutes should be available (including Bitcoin). In terms of payments, critics might argue that central bank accounts will be permissioned accounts, requiring the release of personal information, application efforts, that KYC restrictions will apply (so not censorship resistant) and so on. To address these concerns, a central bank could go one step further and issue a cryptocurrency (Fedcoin) offered at a fixed exchange rate where payments are cleared using a Bitcoin-inspired anonymous communal consensus algorithm. I don't think we can expect anything like this in the near future, but it is technologically possible. Of course, people will complain that Fedcoin will inspire illicit trade, etc. But again, the same is true of regular central bank issued cash.

There is the question of how such an innovation might impact traditional banking models. I'll leave this question for another post. 

Friday, November 6, 2015

Fisher without Euler

The Neo-Fisherian proposition is that raising the nominal interest rate (and keeping it elevated) will eventually cause inflation to rise (see Steve Williamson's explanation here.)

The basic idea revolves around the so-called Fisher equation:

R = r + E[p]

where R is the nominal interest rate, r is the real interest rate, and E[p] is the expected rate of inflation. If bond buyers expect inflation to increase then they'll ask for more compensation in the form of a higher nominal interest rate (a lower bond price).

The conventional idea is that monetary and fiscal policies (in particular, the expectation of how these policies will unfold over time) largely determined inflation expectations E[p]. In conventional (modern) macro economic theories, expectations are assumed to be formed "rationally" (i.e., in a manner that is consistent with the stochastic processes that actually govern the economy).

Neo-Fisherians reverse this conventional direction of causality. They argue that increasing R leads people to revise their inflation expectations upward. And because people have rational expectations, for these expectations to be consistent with reality, actual inflation will (somehow) have to increase.

As far as I can tell, this Neo-Fisherian proposition comes in two stripes. The first stripe is of the "cashless economy with Ricardian equivalence" variety--the models that Michael Woodford likes to use. In this class of models, "balance sheets don't matter." And because central bank money and government bonds are just ways of labeling the liabilities of the consolidated government sector, they don't matter for determining (among other things) the price-level. In this class of models, inflation expectations are somehow assumed to adjust to satisfy the Fisher equation. And then the price-setting behavior of firms (who set prices in an abstract unit of account but do not actually accept payment in any monetary object) adjusts in a manner that is consistent with higher expected inflations. Personally, I find this view implausible. Moreover, it's frustrating that no one promoting this view seems willing or able to explain how/why all this is supposed to happen (beyond repeating the phrase "the Fisher equation must hold" or "it's a rational expectations equilibrium").

The second stripe of this proposition, however, seems more plausible (at least, in principle) to me. In this world, balance sheets matter. The supply and composition of the government's assets and liabilities matter. And in particular, the time-path of the total nominal government debt (and its composition) matters for determining the price-level. The idea here is that when the central bank announces a higher R, there is a corresponding passive accommodation of central bank policy on the part of the fiscal policy to increase the rate of growth of total government debt (i.e., cut taxes, or engage in "helicopter drops"). If the fiscal authority behaves "passively" in this sense, then people will rationally expect higher inflation--and the higher inflation will actually transpire not because people expected it, but because the fiscal authority delivered it. I think this is an interpretation that even Nick Rowe agrees with (see here).

Both versions of the Neo-Fisherian proposition above seem to rely heavily on the notion of rational expectations. In my previous post, I speculated that the proposition might hold even if people had non-rational "adaptive" expectations. The idea I had there was that if a sudden increase in R caused to the price-level to jump up (instead of down, which is the usual presumption), then people with adaptive expectations will revise their inflation expectations upward (not downward).  An initial increase in the price-level might happen if, for example, the higher interest rate led to higher operating expenditures on the part of firms. Following this initial impulse, the actual path of inflation would be determined either by (stripe 1) the nature of learning dynamics or (stripe 2) the manner in which policy accommodates itself to the price shock (e.g., see Christiano and Gust, 1999).

In response to my post, Erzo Luttmer alerted me to his paper Fisher without Euler, in which he claims that the Neo-Fisherian proposition pops out of a model in which people are not forward-looking at all. The argument, as far as I can tell, relies heavily on how the government debt-service cost is financed. Let me try to explain (you can refer to Erzo's paper and short note to see whether I have it right).

Let's start with the government budget constraint,

G(t) - T(t) = q*B(t) - B(t-1)

where T(t) denotes tax revenue, G(t) government purchases, and B(t-1) denotes bonds maturing to cash at date t. Let 0 < q < 1 denote the price of a bond (1/q is the gross nominal interest rate, set by the Fed). For simplicity, I think we can set G(t) = 0 for all t, so that

T(t) = B(t-1) - q*B(t)

This makes it clear how a lower q (higher interest rate) means either  higher taxes and/or higher debt level. Now, let p(t) denote the price-level and define τ = T(t)/p(t). Assume that nominal debt grows at a constant rate, B(t) = μB(t-1). Now use this notation to rewrite the government budget constraint above as
τ = (1 - q*μ)*B(t-1)/p(t)

To close the model, we need a theory of the price-level. The simplest theory I can think of is the Quantity Theory: p(t) = B(t-1)/y(t), where y(t) is real income (and velocity is held constant), so that B(t-1)/p(t) = y(t). If we treat y(t) as exogenous, then it follows immediately that lowering the interest rate (increasing q) necessitates a decline in inflation (μ). So lowering the interest rate lowers the debt-service cost of debt which (for given real spending and taxation levels) means that the supply of nominal debt need not grow as quickly -- as the growth rate in the supply of "money" declines, so does inflation. The Neo-Fisherian result follows even without forward-looking behavior.

Erzo does not use the simple version of the Quantity Theory as I did here. Instead, he assumes that individuals adopt a simple behavioral rule (consumption function):

c(t) = α(y(t) - τ) + βB(t-1)/p(t)

where α is the propensity to consume out of disposable income and β is the propensity to consume out of wealth (here in the form of real bond holdings). If we let g(t) denote real government purchases, then goods-market-clearing requires:

c(t) = y(t) - g(t)

Erzo then combines these latter two equations to determine the price-level p(t), treating y(t) and g(t) as exogenous (as did I).

At the end of the day, it's a simple point. Still, I think it's an important one to keep in mind since I am reading in more than one place that the Neo-Fisherian proposition depends on rational expectations. Evidently, it does not.