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

Thursday, December 24, 2015

Low interest rate policy and secular stagnation

Nick Rowe's post on upward-sloping IS curves motivates today's musings. I'm sorry, but what follows is a tad on the wonkish side. It's intended mainly to promote a conversation with Nick. (You can look in if you want, but I'm sure most of you have better things to do on Christmas Eve!).

Consider the Solow growth model. Output (the real GDP) is produced with capital (K) and labor (N) according to a neoclassical aggregate production function Y = F(K,N).

Define y = Y/N (output per worker) and k = K/N (capital-labor ratio). Define f(k) = F(K/N,1). Then y = f(k). That is, output per worker is an increasing function of capital per worker.

If capital and labor are exchanged on competitive markets, then factor prices are equated to their respective marginal products. Let (w,r) denote the real wage and the real rental rate, respectively. Let 0 < a < 1 denote capital's share of income. Then,

[1] w = (1 - a)f(k) and r = af(k)/k

That is, the real wage is an increasing function of the capital-labor ratio (since labor becomes relatively scarce). The real rental rate for capital services is a decreasing function of the capital-labor ratio (since capital becomes relatively abundant).

Now, consider an economy populated by two-period-lived overlapping generations. People enter the economy as youngsters, they become old, and then they exit the economy. The population of young people remains fixed at N over time t = 0,1,2,... The young are each endowed with one unit of labor, which they supply inelastically at the going wage. Hence, N represents labor supply. The young save all their income and consume only when they are old. Saving is used to finance investment, which adds to the future stock of productive capital. For simplicity, assume that capital depreciates fully after it is used in production. (None of the results below are sensitive to these simplifying assumptions).

Since a young person saves his entire wage, the capital stock (per worker) evolves over time as follows:

[2] k(t+1) = (1 - a)f(k(t)) for t = 0,1,2,... with k(0) > 0 given (as an initial condition).

The transition dynamics are such that k(t) converges monotonically to a steady-state satisfying k* = (1 - a)f(k*).

The real interest rate at date t in this model is equal to the future (t+1) marginal product of capital (which is proportional to the average product of capital), R(t) = af(k(t+1)) = af((1 -a)y(t) ) / ((1-a)y(t) ).

The IS curve in this model is defined as the locus of real interest rates and output consistent with goods-market-clearing. In the present context:

[3] R(t) = af( (1-a)y(t) )/( (1-a)y(t) ).

Equation [3] describes a conventional downward-sloping IS curve. A higher level of income (because of more abundant capital) increases desired saving, which puts downward pressure on the real interest rate. Conversely, an increase in the real interest rate reduces aggregate demand.

Now, let's consider one of Nick's experiments. Begin in a steady state. Nick considers an exogenous 10% increase in the capital stock. I'll do the opposite experiment and consider a 10% decline.

The capital-labor ratio is now lower. From [1], the effect is to lower the real wage and increase the rental rate. From its depressed level, the real wage increases monotonically back to its steady-state level. From its elevated level, the rental rate declines back to its steady-state level. The real interest rate, in turn, jumps up and then declines back to its steady-state level.

In a competitive economy, these price adjustments reflect the underlying fundamentals. The shock renders capital scarce. Less capital depresses the demand for labor, which is reflected in a lower real wage. Capital scarcity means the the return to rebuilding the capital stock is high. As saving flows into capital spending, the scarcity diminishes, and the real interest rate falls back to normal levels.

Next, to follow Nick's thought experiment in a slightly different way, suppose that a central bank tries to keep the real interest rate low in the face of the shock just described above. In fact, suppose that the central can manage to fix the real rental rate (hence the real interest rate) at its initial steady-state level forever.

If r(t) = r* forever, then by [1] the capital-labor ratio must remain fixed for all t > 1.

An implication of this policy is that the real wage will not fall. It's not that it cannot fall (it would fall if the real interest rate was permitted to rise). The real wage needs to fall, temporarily, to maintain full employment. But because it will not fall, then something else has to give. The level of employment must fall. Since k* = K/N is fixed and since K falls by 10%, it follows that N must fall by 10% as well. The central bank's refusal to permit the real interest rate to rise has led to an increase in unemployment (instead of a decrease in the real wage).

But things are even worse than they seem. While a shock that evaporates a part of the capital stock is eventually replenished when factor prices are market-determined, the same is not true when either the real interest rate or the real wage is fixed. In a post I wrote earlier (here), I considered a fixed real wage. But Nick's column made me realize that the same result holds if we fix the interest rate instead. A "low interest rate policy" in this case leads to "secular stagnation" (the level of output and employment is lower than it should be) as depicted in the following diagram:

One way to read this result is that it vindicates Bill Gross' idea that artificially low interest rate policy constitutes a form of "financial repression" inhibiting the U.S. recovery (I criticize his views here.)

How seriously to take this result? I'm not so sure. A lot depends on the nature of the shock that is imagined to have afflicted the economy. In the experiment considered above, I just wiped out a fraction of the economy's capital stock--like a hurricane, or nuclear bomb. A more generous interpretation is that the shock stands in for an event that evaporates a fraction of the value of existing capital (not necessarily its physical quantity). People do not become any more pessimistic in the model as a result of the shock, which is why the economy transitions back to its initial steady-state when the price-system is left unencumbered. A depressed economic outlook, on the other hand, would serve to reduce real interest rates, not increase them as in the experiment above--and that sort of scenario would provide more justification for low-interest policy.

Merry Christmas, everyone.

Wednesday, December 23, 2015

Schumpeterian growth and secular stagnation

What is secular stagnation? The "secular" part suggests something that's persistent--in the order of decades (as opposed to the 2-5 year frequency usually associated with a business "cycle."). The "stagnation" part suggests a measure of under-performance. But what measure? Are we talking about lower than average growth in employment and incomes? Or are we talking about depressed levels, instead of depressed growth rates? Are we talking about both? Getting this straight makes a difference in how we want to approach thinking about the phenomenon in question.

In what follows, I'll take the view that secular stagnation refers to prolonged episodes in which growth in real per capita income (GDP) is lower than its long-run average.

Most economists agree that long-run growth in material living standards (real per capita income or consumption) is the product of technological progress. Contemporary business cycle models (at least, those used for monetary policy) assume that technological progress occurs more or less in a straight line. This abstraction may be fine for some purposes, but I never much liked it myself. As a PhD student, I was influenced by Schumpeter's 1939 masterpiece Business Cycles.

Schumpeter (1939) emphasized that there is no God-given reason to expect growth to occur in a straight line. Research and development, and the process of learning in general, can be expected to generate innovations of random sizes and at random intervals. Moreover, any given innovation takes time to diffuse. Economy-wide productivity does not jump instantaneously with the arrival of the internet. I like this quote from his book:
 ‘‘Considerations of this type [the difficulty of coping with new with new things] entail the consequence that whenever a new production function has been set up successfully and the trade beholds the new thing done and its major problems solved, it becomes easier for other people to do the same thing and even improve upon it. In fact, they are driven to copying it if they can, and some people will do so forthwith. Hence, it follows w that innovations do not remain isolated events, and are not evenly distributed in time, but that on the contrary they tend to cluster, to come about in bunches, simply because first some, and then most, firms follow in the wake of successful innovation.’’ [p. 100]
It was this passage that led me to think of a model in which technological innovation drove growth but in a manner that was uneven because of diffusion lags. The notion that a new general purpose technology might spread like a contagion to generate the classic S-shaped diffusion pattern in GDP seemed like a very interesting hypothesis to investigate.

I was also influenced by Zvi Griliches' famous empirical investigation of the diffusion of hybrid corn in the United States:

In my paper (actually, the second chapter of my PhD thesis, published in 1998 with Glenn MacDonald) I saw this:

And so Glenn and I built a dynamic general equilibrium model where firms were motivated to innovate and imitate superior technologies. We estimated parameters so that the model reproduced the smooth but undulating path of GDP depicted in the figure above. I think I see these patterns in more recent TFP data as well (source):

According to this interpretation, episodes of secular stagnation are largely an inevitable byproduct of the process of technological development and growth. Accepting such an interpretation does not, in itself, have any implications for the desirability of policy interventions. But it does call into question the efficacy of certain types of interventions. In particular, do we really believe that more QE will spur future economic growth? Or should policy attention be directed elsewhere?

Now, one might object, as Larry Summers does here, that "If the dominant shock were slower productivity one might expect to see an increase in inflation." The type of reasoning that underpins this view is the simple Quantity Theory of Money equation: PY=VM. Ceteris paribus (holding MV fixed) a decrease in real income Y should induce an increase in the price level P. Maybe the 1970s provides the empirical basis for this view.

But there is no theoretical reason to believe that productivity slowdowns, or indeed, expected productivity slowdowns, should be inflationary. It's very easy to demonstrate, in fact, that "bad news" in the form of a slowdown in productivity leading to depressed expectations over the net return to capital spending can cause a "flight to safety" to government debt instruments (including money). The effect of such portfolio substitution is to depress bond yields and the price-level (see here and here for example).  But even apart from these effects, the behavior of inflation depends critically on the nature of monetary and fiscal policy.

Wednesday, December 16, 2015

The Neo-Fisherian Proposition

The Neo-Fisherian proposition is that a persistent policy-induced increase in short-term nominal interest rates will lead to higher inflation in the long-run. John Cochrane, one of the main proponents of this view (along with my colleague, Steve Williamson) discusses the idea here. Visually, the proposition asserts something like this:

Of course, the conventional view is that raising the policy interest rate will cause inflation to go down, not up. The idea that the opposite might be true is evidently something to be ridiculed.

I can't help but think that Pettifor's view on the proposition was formed without first trying to understand it's underlying logic (but I could be wrong). Also note that the proposition is not inconsistent a higher interest rate leading to lower inflation in the short-run.

Why do people generally feel uncomfortable with the Neo-Fisherian proposition? I think that fellow Canuck Grep Ip of the WSJ gets at one reason here where he writes:
Neo-Fisherism has theoretical elegance but lacks intuitive logic. At its heart, neo-Fisherism says there is, somewhere, a fixed real rate that drives what the public expects inflation to be. Yet few people–even those who know what real rates are–have a firm view of what they should be. Their expectations of inflation are more likely to depend on past inflation, central bank or private forecasts, and the state of the economy. These expectations of inflation will then drive the returns they expect on saving and investment, not vice-versa.
The uncomfortable part is that despite this apparent lack of intuition underlying the proposition, it appears consistent with recent experience:

However, in a recent column, David Beckworth questions whether the proposition is consistent with what is happening in Japan. This led me to ask him:

Now, it might seem strange to some of you that I asked him which Neo-Fisherian theory he was referring to, but I did so because there seem to be two different strains. But before I get to that, it's worth emphasizing that the proposition does not state that raising interest rates is necessary to raise inflation. (I stated the proposition above, go read it again if you have to.)

The first strain of the theory seems to rely entirely on rational expectations and the Fisher equation (without any reference to central bank balance sheets or the conduct of fiscal policy). The way this thinking goes is that the Fisher equation is just a no-arbitrage-condition. (No-arbitrage-conditions are compelling economic restrictions because if they did not hold, traders could make infinite riskless profits.) If a central bank raises the nominal interest rate, then for a given real rate of interest, the expected inflation rate must rise (else traders will be making infinite profits). This seems to be the interpretation favored by Stephanie Schmitt-Grohe and Martin Uribe (see my discussion here).

Personally, I am not sold on this interpretation. I prefer the second strain of the theory, which is related more to the fiscal theory of the price-level (as the name suggests, the theory emphasizes the role of fiscal policy in helping to determine inflation).  According to this interpretation, the proposition that "a persistent policy-induced increase in short-term nominal interest rates will lead to higher inflation in the long-run" must be qualified with the condition that the fiscal authority passively accommodate the monetary authority's policy decision (see my column here: A Dirty Little Secret.)

Intuitively, think of the following thought experiment. The Fed raises its policy rate and its widely expected to remain at this elevated level for the foreseeable future. The effect of this policy is to increase the carrying cost of debt for the government. Assume that the government services this higher debt burden not by cutting expenditures or increasing taxes, but by increasing the rate of growth of its nominal debt. Essentially, the government is printing "money" to finance interest payments on its debt. Then (assuming a constant long-run money-to-debt ratio) the money supply must start growing at this higher rate. Suppose that people generally understand this (a big supposition, I know). Then, people should revise their inflation expectations upward (and actual inflation should result, not because of inflation expectations, but because the monetary and fiscal authorities are printing nominal liabilities at a more rapid pace to finance the higher interest cost).

I'm pretty sure that David and others understand the proposition when it is framed in this manner. Whether this is what actually transpires is, of course, anybody's guess (consider this case study for Brazil 1975-1985). It's really  hard to forecast precisely how the fiscal authority (Congress) might react to higher interest rates. I do find it interesting, however, that fellow Twitterer Matt Yglesias noticed the following:

Impressive indeed. But if interest rates on U.S. treasury debt continue to rise, the debt-service problem will make the headlines soon enough. The debate will then turn to whether the U.S. should cut G and increase T (austerity) or permit more rapid debt expansion (and inflation). 

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.

Saturday, October 31, 2015

NeoFisherism without rational expectations

Is the Fed's "zero-interest-rate policy" (ZIRP) inflationary or deflationary? You'd think that macroeconomists would have a straight answer for such a simple question. But we don't. As usual, the answer seems to depend on things.

Someone once joked that an economist is someone who sees something work in practice and then asks whether it might work in theory. Well, appealing to the evidence is not much help here either. We have examples like that of Volcker temporarily raising rates (by lowering the money supply growth rate) to lower inflation in the early 1980s. But then we have the present counterexample of ZIRP, which seems to be having little effect in raising inflation. Indeed, the Fed has consistently missed its 2% inflation target from below for years now (see Understanding Lowflation).

Some economists suggest that there are theoretical reasons to support the notion that ZIRP is deflationary. The proposition that targeting a nominal interest rate at a low (high) level results in low (high) inflation is known as "NeoFisherism." The idea goes back at least to Benhabib, Schmitt-Grohe and Uribe (2001) in their The Perils of Taylor Rules. The idea has been taken seriously in policy circles. My boss, St. Louis Fed president Jim Bullard wrote about it here in 2010. You can read all about the recent controversy here: Understanding the NeoFisherite Rebellion.

The basic idea behind NeoFisherism is the Fisher equation:

FE1: Nominal interest rate = real interest rate + expected inflation.

One interpretation of the Fisher equation is that it is a no-arbitrage-condition that equates the real rate of return on a nominal bond with the real rate of return on a real (e.g., TIPS) bond. FE1 implicitly assumes that the risk and liquidity characteristics of the nominal and real bond are identical. Steve Williamson and I consider a model where the nominal bond (potentially) carries a liquidity premium, in which case FE1 becomes:

FE2: Nominal interest rate + liquidity premium = real interest rate + expected inflation.

I'm not aware of any economist that disputes the logic underlying (some version of) the Fisher equation. The controversy lies elsewhere. But before going there, let me describe the way things are supposed to work in neoclassical theory.

Start in a steady-state equilibrium where FE1 holds. Now consider a surprise permanent increase in the nominal interest rate. What happens? Well, a higher nominal interest rate increases the opportunity cost of holding money, so people want to economize on their money balances. However, because someone must hold the outstanding stock of money, a "hot potato effect" implies that the equilibrium inflation rate must rise (the real rate of return on money must fall). In the new steady-state equilibrium, real money balances are lower (the price-level and the inflation rate are higher than they would have been prior to the policy shock). If people have rational expectations, then absent any friction, inflation expectations jump up along with actual inflation. If there are nominal rigidities, then inflation may (or may not) decline for a while following the shock, but in the long-run, higher interest rate policy leads to higher inflation. [Aside: my own view is that a supporting fiscal policy is needed for this result to transpire; see here: A Dirty Little Secret.]

The conventional wisdom, however, is that pegging the nominal interest rate is unstable. Suppose we begin, by some fluke, in a steady-state where FE1 holds. Now consider the same experiment but assume that people form their expectations of inflation through some adaptive process; see Howitt (1992). For example, suppose that today's inflation expectation is simply yesterday's inflation rate. Then an increase in the nominal rate must, by FE1, lead to an increase in the real interest rate. An increase in the real interest rate depresses aggregate demand today (consumer and investment goods). The surprise drop in demand leads to a surprise decline in the price-level--the inflation rate turns out to be lower than expected. Going forward, people adapt their inflation forecasts downward. But given FE1, this implies yet another increase in the real interest rate. And so on. A deflationary spiral ensues.

For those interested, refer to this more detailed discussion by John Cochrane: The Neo-Fisherian Question.

Now, the thought occurred to me: what if we replace the assumption of rational expectations in my model with Williamson (cited above) with a form of adaptive expectations? What would happen if we performed the same experiment but, beginning in a steady-state where there is an "asset shortage" so that the FE2 version of the Fisher equation holds. My back-of-the-envelope calculations suggest the following.

First, because expected inflation is fixed in the period the nominal interest rate is raised, FE2 suggests that either the real interest rate rises, or the liquidity premium falls, or both. In our model, there is substitution out of the cash good into the credit good. But because there is a cash-in-advance constraint on the cash good, i.e., p(t)c(t) = M(t), it follows that a decline in the demand for c(t) corresponds to a decline in the demand for real money balances--that is, the price-level p(t) must jump up unexpectedly (for a given money supply M(t)).

Now, given the surprise jump in the price-level, an adaptive expectations rule will adjust the expected rate of inflation upward. What happens next depends critically on the properties of the assumed learning rule, the policy rule, etc. For my purpose here, I make the following assumptions. Suppose that the economy remains in the "asset shortage" scenario and assume that the government fixes the money growth rate at exactly the new, higher, adaptively-formed, inflation expectation. In this case, the economy reaches a new steady-state with a higher interest rate, an arbitrarily higher inflation rate, and an arbitrarily lower liquidity premium (conditional on the liquidity premium remaining strictly positive). [Note: by arbitrary what I mean is that the new inflation rate is determined, under my maintained assumptions, by the initial surprise increase in inflation, which may lie anywhere within a range such that the liquidity premium remains positive. In the absence of a liquidity premium, the inflation rate would rise one-for-one with the nominal interest rate.]

I hope I made my point clear enough. The claim that increasing the nominal interest rate leads to higher inflation does not depend on rational expectations as is commonly claimed. A simple adaptive rule could lead to higher inflation expectations. The key is whether the price-level impact of increasing the nominal interest rate is positive or negative. If it's positive, then people will revise their adaptive expectations upward and, depending on the learning rule and policy reaction, the ensuing inflation dynamic could play itself out in the form of permanently higher inflation. The NeoFisherite proposition is possible even if people do not have rational expectations.

Postscript Nov. 01, 2015
Tony Yates suggests the cost channel in Ravenna and Walsh (2006)  together with least-squares learning might deliver the same result. It's a good idea. Somebody should try to work it out!