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

Tuesday, June 14, 2016

DSGE Theory

This post is for my students, and whoever else is interested in what DSGE theory is and why I find it useful.

Dynamic Stochastic General Equilibrium (DSGE) theory refers to a methodology employed by macroeconomists to build DSGE models -- mathematical representations of the macroeconomy. DSGE models, like all models, are used for a variety of purposes. They are used to help organize thinking. They are used to interpret data. They are used to help make conditional forecasts. They are used to predict and evaluate the possible consequences of government policies (especially useful for policies that have never been tried before). They are used to help make policy recommendations.

The use of DSGE theory is often criticized in ways that reflect what I view as a deep misunderstanding of the research program, how it fits in with the evolution of macroeconomic theory over time, and how it is actually applied by (say) central bank policy makers. This is, I think, to some extent the fault of DSGE practitioners who, accustomed to speaking in their specialized trade language, find it difficult to translate core ideas and findings in the vernacular. (This is an issue with most trade associations, of course, but is especially acute in economics because so many non-specialists take an interest in the subject.)

Let me first provide some context for my views. We are all scientists trying to understand the world around us. We use our eyes, ears and other senses to collect data, both qualitative and quantitative. We need some way to interpret/explain this data and, for this purpose, we construct theories (or hypotheses, or models, or whatever term you prefer). Mostly, these theories exist in our brains as informal "half-baked" constructs. This is not meant to be a criticism (as long as we recognize the half-baked nature of our ideas and why some humility is always in order). Often it seems we are not even aware of the implicit assumptions that are necessary to render our views valid. Ideally, we may possess a degree of higher-order awareness--e.g., as when we're aware that we may not be aware of all the assumptions we are making. It's a tricky business. Things are not always a simple as they seem. And to help organize our thinking, it is often useful to construct mathematical representations of our theories--not as a substitute, but as a complement to the other tools in our tool kit (like basic intuition). This is a useful exercise if for no other reason than it forces us to make our assumptions explicit, at least, for a particular thought experiment. We want to make the theory transparent (at least, for those who speak the trade language) and therefore easy to criticize. Constructive criticism is the fuel that fires the furnace of new ideas in academia. [ End of philosophical rant :) ]

Now let me turn back to DSGE theory. I think it will be useful to break the acronym into its parts and discuss each component separately.

The "D" stands for dynamic--as in--the phenomena in question involve a time element. The opposite of dynamic is static. While static models have their uses, who's going to argue that a dynamic element isn't desirable? Almost all decisions like consumption and saving, deficit-finance, human capital investments, have a time dimension to them. No controversy here, I hope.

The "S" stands for stochastic--as in--societies appear subject to random events, like unforeseen technological breakthroughs, unexpected changes in government policy regimes, or just random acts of nature. Again, I don't think there's much controversy with this idea. Note, however, many DSGE models do not have the S, in which case we might instead employ the acronym DGE. (For a history of the evolution of these acronyms, see here.)

The "G" stands for general--as in--well, it's not entirely clear. There is a traditional distinction in economics between partial and general equilibrium theory. The partial equilibrium approach (associated with Alfred Marshall) refers to the supply-demand curve analysis that most people are familiar with. The analysis is "partial" in the sense that it typically restricts attention to a particular market--like the market for motor vehicles, taking the price of other goods as given. In contrast, the general equilibrium approach (associated with Leon Walras) strives to model the economy as a closed system, paying particular attention to how markets interact with each other and how prices are determined jointly. Importantly, the "G" insists on giving an explicit account of the government budget constraint (i.e., a government is not to be modeled as Jesus feeding the multitude.) Another way to think about "G" is that it means to capture the possibility of "feedback effects." The notion of feedback effects in macroeconomic systems is not, I do not think, controversial.

This leaves us with the "E," which stands for equilibrium. Here lies the controversy. But why? For all sorts of reasons, some of which are based on legitimate concerns, and some of which are based on simple misunderstanding.

Let me first address the misunderstanding. The concept of "equilibrium" in economics has evolved to mean something quite specific and something quite different from the notion of a "system at rest" (which is closer to what economists label a steady-state). Technically, an equilibrium is simply a set of conditions imposed by the theorist to help determine the outcome of an hypothetical social interaction. In this sense, an equilibrium is probably better thought of as a solution concept. There is no unique way to specify an equilibrium solution concept. In the game theory, there is plethora of alternatives, beginning with the Nash equilibrium. The classical theory of Walras uses the concept of a competitive equilibrium. In my own view (probably not representative), I even think of general disequilibrium as just another type of equilibrium concept. Every theorist has to have a solution concept in mind when deducing the likely outcome of an hypothetical social interaction. There is no right or wrong way to specify an equilibrium concept--there are just more or less useful ways in doing so.

Another misunderstanding is that insisting on equilibrium analysis necessarily implies that one assumes markets always "clear" in the sense prices adjust to ensure supply equals demand at all times. This is understandable because many DSGE models (especially the RBC variety) do in fact make this assumption. But, of course, there's a large class of DSGE models that do not (e.g., the NK variety). More to the point, it's important to understand that the concept of equilibrium is not wedded to the concept of competitive market-clearing models. In DSGE models that replace centralized Walrasian markets with decentralized search markets, conventional "supply and demand" curves do not even exist. In search models, prices are determined through bilateral negotiations and the "clearing" mechanism operates through quantity variables, like labor-market tightness (the ratio of vacancies to unemployment).

A more legitimate concern relates to the equilibrium concept of "rational expectations." Because of the "D" element, the theorist must take a stand on how expectations are formed and updated over time. Macroeconomic theorists have grappled with this question for over a century, if not longer (see Laider, 1999). There is little controversy that people are forward-looking. But exactly how are they forward-looking? John Muth (1961) suggested that, in the context of a model, we might begin by assuming that our modeled agents (somehow) form model-consistent expectations (i.e., "rational" expectations). Intuitively, the idea is that we should not model people as forming expectations that are wildly at odds with the reality unfolding around them and, that as a limiting case, we might even begin by assuming that expectations are formed in a manner that is perfectly consistent with the surrounding reality. Among other things, model agents are assumed to possess common knowledge (see, Geanakoplos, 1992).

Now, if all of this sounds like a bit of a stretch, it no doubt is. The relevant criticism and response is recorded in section 6.4 Stationary Models and the Neglect of Learning in Lucas and Sargent (1979). I'm not going to get into it here, but suffice it to say that there's been a large and vibrant literature on non-rational-expectations "learning" models since Lucas and Sargent wrote that piece. And you'd be very wrong to think it hasn't had any influence in the way policymakers, central bankers in particular, think about policy and its effects. St. Louis Fed president James Bullard, for example, is among those who have made significant academic contributions in this area (you can view his works here).

In terms of their use in policy making, DSGE models are no different than their predecessors. Some applications entail large scale quantitative models to make conditional forecasts. But their main value is the manner in which they (along with other models) are used to organize thinking in policy deliberations. I think I disagree with Narayana Kocherlakota here when he suggests that DSGE models are built purposely not be useful for day-to-day policy making--for example, in helping to answer the question of whether the interest rate should be changed in the upcoming FOMC meeting. Instead, he views DSGE models as useful for thinking about policy rules (which I agree with). But his view here seems inconsistent with a view he has expressed elsewhere, namely, that isolated changes in the policy rate are largely irrelevant--that what is important is how the path of interest rates is expected to evolve over time (I agree with this too). I think that the decision of whether to move rates today has to be made in the context of what the policymaker views as wise policy principles based on some combination of theory, evidence, and experience. These principles should no doubt make allowances for the necessity of discretionary and ad hoc policy actions. But this allowance does not mean that reference to a DSGE model (or any other model) cannot be useful for thinking through the likely consequences of a contemporaneous policy action. [Note: I may have misunderstood the point NK was trying to make.]

In terms of a defense of the use of DSGE theory for policy, I can do no better than Chris Sims here (video, highly recommended). See also this interview with Tom Sargent, who defends modern macro theory. Finally, I have my own related post: In Defense of Modern Macro Theory.

Sunday, May 29, 2016

Some questions concerning equity-financed banking

John Cochrane has another fun and provocative post making his pitch for equity-financed banking. He makes a lot of great points. But I'm still left feeling a little uneasy. In particular, I wonder whether some of his sweeping claims have any firm theoretical backing. It could be I just haven't thought hard enough or long enough about it. In any case, in the spirit of promoting discussion, let me describe some of the things that bother me.

Actually, before I start, I should preface my concerns with a couple of observations. Policies directed toward stabilizing the banking sector target both the asset and liability side of bank balance sheets. The "narrow banking" proposal of 100% reserves, for example, is a policy designed to make bank assets safe. The "100% equity-financed banking" proposal on the other hand is a policy designed to render bank liabilities safe (run-proof). According to Cochrane, " assets aren’t risky! A diversified, mostly marketable portfolio of loans and mortgage backed securities is far safer than the profit stream of any company." The problem evidently lies on the liability side. Moreover, the issue here is not simply one of ascertaining whether banks are "over-levered" (I'm willing to agree that they probably are). The issue is whether debt (fixed-value promises), especially demandable debt, has a role to play in the business of banking at all.
The main question I have is: where's the theory? In the benchmark neoclassical model, some version of the Modigliani-Miller theorem typically holds. The theorem states that under a very specific set of assumptions, the liability structure of a firm does not matter. We know that these assumptions (e.g., symmetric information) do not literally hold in reality. When information is asymmetric, debt can be superior way to fund assets relative to equity (see here and here, for example). Demandable debt may have socially desirable properties when liquidity demands are private information; see here. In a world where exchange media (including collateral assets) are valued, it could matter very much how the "pizza" is sliced into tranches designed to serve special uses.

What explains the widespread use of the debt contract and the prevalence of fractional reserve banking? The explanation is unlikely (in my view) to be "government distortions" or "greedy bankers." It seems to me that asymmetric information in financial markets is a pertinent real-world friction. Could it be that debt represents a sort of "second-best" solution to the problem of efficient (low-cost) financing in a world of asymmetric information? Might the same not be true of demandable debt? Implicitly, Cochrane must be thinking that these benefits are quantitatively small. Maybe so, but senior liability tranches do seem rather highly valued in the market place, especially as exchange media. Private monetary instruments have always been in the form of debt, not equity. Why has this been the case?

Cochrane begins his post with the statement "My premise is that, at its core, our financial crisis was a systemic run. The mechanism is familiar from Diamond and Dybvig."  The Diamond and Dybvig (1983) model can indeed be interpreted as a theory of bank sector fragility. But we should keep in mind it's also a theory that explains the benefits of an illiquid bank sector (a point stressed by Wallace, 1996). Moreover, it's also a theory that explains the desirability of demandable debt. We want demandable liabilities (according to this theory) because, well, imagine going to an ATM wanting to withdraw cash and then having the blasted thing make you fill out an insurance claim attempting to verify whether you do indeed have a pressing need for liquidity. (In fact, banks were known to do this during the banking panics of the 20th century.)

Now, I suspect that Cochrane may reply that while demandable debt in its traditional form once had a useful role to play, markets and communication technologies are now developed to the point that renders the demand deposit liability superfluous. Call me a hopeful skeptic. Cochrane claims that "unlevered bank equity would have 1/10 less the volatility it has today, so we're talking about 2% volatility on an annual basis." I'm not sure where he gets these numbers, though I do agree with him qualitatively. (On the other hand, how do we know that banks will not hold riskier assets if they are equity financed?)

In any case, just how much volatility is "too much" for depositors wanting transactions balances with a steady value to ensure that payment obligations can be met in all circumstances on a timely basis? Evidently, depositors value the fact that they can redeem their bank money at par for cash quite a bit. What Cochrane advocates is the replacement our present ATMs with one-armed bandits spitting out random returns whenever we want to redeem our bank equity shares for cash. That sounds like a lot of fun, but it may not be very practical. Perhaps the volatility of these returns will not be so great (how do we know?). Maybe we'll be able to withdraw only 98 cents on the dollar more often than not "by chance" (as the Gorton-Pennacchi insiders skim us outsiders while claiming "bad equity returns" as the culprit. Again, how do we know?)

I want to be clear here. I am not suggesting that Cochrane's proposals are a bad idea when all considerations are factored in. I'm just questioning whether it's the open-and-shut case he makes it out to be. If it is such a great idea, I wonder why banks have not offered the product on their own? (I am sure there is no shortage of explanations here, but still, it's worth having them spelled out.)
There is one final thing I want to touch on before I sign off here. The main reason Cochrane preferes equity over debt is because equity is evidently "run-proof." I don't know, he may have his own special definition of "run." There are macroeconomic models of multiple equilibria (see Roger Farmer) where shareholders might be compelled to "run" on equity, driving its price lower, leading to all sorts of negative pecuniary externalities and self-fulfilling crises. Getting rid of debt will not necessarily get rid of financial crises.

Of course, getting rid of debt will get rid of bankruptcy. But I am sometimes led to question whether bankruptcy is quantitatively relevant for causing or exacerbating recessions. As Cochrane points out:
Our crisis and recession were not the result of specific business operations failing. Failure is failure to pay creditors, not a black hole where there once was a business. Operations keep going in bankruptcy. The ATMs did not go dark.
Absolutely. I can recall several times when an airline went bankrupt with no noticeable side-effects (passengers were treated terribly, but that was normal even outside of bankruptcy). Bruce Smith (2002) reports evidence suggesting that bank panics are not always associated with output losses. If so, then what's the big deal? As Cochrane explains, when equity takes a plunge, we all pull out our hair, but the firm is under no obligation to do anything on our behalf. But with debt--demandable debt in particular--we can demand--demand--our money back. And the firm has to ... has to what? I'm not really sure. The firm can just continue to operate as usual and restructure its debt, no? After all, bankruptcy is just a rearrangement of claims against a firm's assets (well, I suppose in some cases senior management gets the ax, but not always). In the old days, banks were permitted to temporarily suspend withdrawals without legal repercussion. As well, bank clearinghouses might issue currency substitutes in lieu of specie, etc.

These considerations lead me to wonder whether interventions on the asset side of bank balance sheets might not be a better way to promote a run-free banking system. Alternatively, as Cochrane suggests, we might consider opening up the central bank's balance sheet to the public. As I've mentioned before, the U.S. treasury does permit the public to hold online UST accounts at While the system is not set up for making payments, there is no reason why, in principle, it could not be. I'm not suggesting this as a panacea, of course. But I think the idea, or some variant of it, deserves serious consideration.

Thursday, May 5, 2016

Why the Blockchain should be familiar to you

From L2R: Michael Casey (MIT Media Lab), David Andolfatto (FRB SL),
Simon Johnson (MIT) and John Schindler (FSB)
I'm freshly returned from Consensus 2016: Making Blockchain Real where I participated in a panel on "Digital Cash for Central Bankers." Michael Casey did a stellar job in crafting the session. It was fun and informative to have Simon Johnson and John Schindler as co-panelists. As we didn't get booed off the stage, I think maybe the audience enjoyed what we had to say as well. (I left the session with almost a kilogram of business cards--odd that paper is still so widely used in this capacity. By the way, some of what I had to say can be found in my blog post here.)

Today's post is more about marketing the idea of blockchain. The word sounds intimidating to many people. That's probably because attempts to explain it often make use of a highly technical trade language that few people understand. My goal here is to think of ways to communicate the idea of blockchain in a manner that will make people feel like the concept is familiar to them. Indeed, I believe that the broad conceptual idea of blockchain should be familiar to us all.

Renowned Bitcoin expert Andreas Antonopoulos writes here:
It will take time for the idea of decentralized trust through computation to become a part of mainstream consciousness, and until then, the idea creates cognitive dissonance for those accustomed to centralized trust systems. With thousands of years of practical use, centralized systems of trust are accepted unconditionally and without much thought as the only model of trust.
It's an excellent article and I highly recommend you read it. What I want to do here is push back a little on the notion that decentralized trust systems should necessarily create cognitive dissonance. In particular, I should like to point out that we've had tens of thousands of years of experience with decentralized trust systems. Alright, so let's get started.

Consider the following scenario. You are attending a cocktail party with dozens of people present and you are asked by your hostess to deliver a short speech. Now suppose you utter something outrageous, e.g., "I think the Fed should buy the existing stock of bitcoin and store it as a foreign currency reserve!" The audience will stare at you, mouths agape (especially if you're a central banker, or a renowned Bitcoin enthusiast). You wake up the next day and regret your rash public remark. You wish you could take back what you said, but how? The only way this could be done is if you could somehow persuade the group to forget what you said. But just think about how difficult it would be to do that. Especially if the number of people in attendance was large.

What has just been demonstrated (I hope) is the power of a distributed database validated through a communal consensus algorithm. The database here is your silly statement above together with the time you made it (a timestamp). The information in this database is shared on a distributed network of brains (what you said and when you said it is imprinted forever in the memories of all who witnessed the event). The consensus algorithm here is "let's all agree to remember what was actually said (as opposed to some alternative, fabricated statement)."

A database in this form is extremely secure. It will survive intact even if some brains holding the database are destroyed. The database can be communicated to other brains (who can confirm the validity of the statement by seeing how it squares with the memories of others). If one or more people tried to fabricate an alternative history, the attempt would almost surely fail (we cannot rule out the possibility entirely, however). If your remark instead lived only as an electronic recording in a central databank, the task of re-writing history would be much easier.

Now imagine living in a primitive village. Relevant elements of the database would include observations like: [1] John had his wound tended to by Bob at date t, [2] John killed a wild pig and shared it with the village at date t-1, etc. The database in this case can be organized in a sequence of time-dated blocks X(t) = {x(t), x(t-1),...}, where x(t) is the database (block) at date t, and X(t) is the "blockchain." So, the blockchain is just a communal databank recording some relevant aspects of villagers' activities. In village economies, this communal memory typically exists in a virtual state (written records are a much more modern invention).

Notice how the blockchain described above could serve a very useful economic purpose. In particular, note that the act of consumption (medical services) in [1], John is effectively using [2] as currency. At least, this is how things work in what anthropologists describe as "gift-giving societies." And if you think about it for a while, you'll notice that the same principle is at work in the various groups you interact with on a daily basis (your friends, your family, coworkers, etc.). Much, quite possibly most, economic exchange occurs via such localized trust networks.

The problem with this ancient blockchain technology is that it doesn't scale very well. There's only so much data we can fit in our brains.  So as populations grew and as people started forming large communities, a new type of record-keeping system was needed. The model that came to dominate is one in which databases are collected and maintained by trusted third parties. Much effort is expended in keeping these private databases secure (not always successfully). It is often difficult for these agencies to communicate and reconcile their databases (as in when you try to send money from your bank account to your friend's foreign bank account overseas).

And so enter the "new" technology, blockchain. I hope I have convinced you what is new here is not the principle of the blockchain. The new technological developments are: [1] bigger brains (increased capacity for data storage and processing via computers); [2] better communications (the Internet); and [3] computer-based algorithms to serve as communal consensus mechanisms (e.g., proof-of-work).

These innovations will permit a revolution in the truest sense of the word: we are traveling back to where we began--but with planet earth as our village.


PS. Please let me know if this was helpful or how it could be improved. After writing this post, I came across this short video: Blockchain for Dummies. Some of the comments are critical of it, but I thought it communicated the idea in a nice way.

Monday, May 2, 2016

On Cochrane's dream of equity-financing banking

John Cochrane has a dream where the banking sector is financed entirely with equity. The dream is premised on the notion that debt-financed endeavors--especially those using short-term debt--are prone to runs. Run-prone structures can cause, or contribute to, financial crises. The possibility of crisis invites government regulation. Government regulation leads to regulatory arbitrage, much of which occurs in the shadows of the financial market. Which leads to more (now harder-to-monitor activities), leading to ... well, you get the picture. Why not just structure a regulatory framework that permits equity-financed banking ventures, like SoFi, to weave their (run free) magic? It's a good question. I'm not sure what the answer is. But I wonder if it's all as easy and straightforward as Cochrane makes it out to be.

I don't want to nitpick here but, I don't think I'd classify SoFi as a "bank" in the legal or economic sense. True, SoFi is acting as a financial intermediary. But insurance companies and pension funds are also financial intermediaries, and we do not think of them as banks. SoFi is more like a venture capital fund. It sounds like it's doing a wonderful job matching savers to borrowers. But matching savers to borrowers is not (the main) business of banking. Even a simple bond market matches savers to borrowers. We do not need banks to do that.

So what do banks do? We can get a grasp of their business model by comparing the structure of their balance sheets to other financial intermediaries. In many respects, the asset side of these balance sheets looks broadly similar: they consist of cash reserves, bonds (government and corporate) and other securities. Retail banks also hold personal and small business loans, which they typically originate as a part of their business. The differences on the liability side of financial intermediaries are much more striking. Pension funds issue time-dependent liabilities. Insurance companies issue state-contingent liabilities. Banks issue demandable liabilities. In all three cases, one wouldn't be so far off in forming the impression that financial intermediaries are fundamentally just "asset-transformers" (they transform a set of assets into structured liability products that people find useful).

Banks, in other words, are in the business of supplying a particular structured liability product: the demand deposit liability (DDL). It is Cochrane's worst nightmare. That's because the DDL is a "fixed-value promise." Specifically, a DDL promises redemption at (or close to) par for cash. But it's even worse than this because the promise is to redeem on demand (rendering the DDL a form of short-term debt). Worse still, the banking system does not possess enough cash in reserve to honor these short-term obligations in the event that all DDLs are presented for redemption at once (this is what it means to be a fractional reserve banking system). And as if things could not get any worse, they actually do. These bank-created DDL products -- they're used widely as payment instruments. That's right, banks are in the business of creating money (out of their assets).

Before I go on, I want to say something about the manner in which "deposits" is used in discussions of banking. It is sometimes said that "banks take deposits." But what does this mean? Even a Las Vegas slot machine takes deposits (and issues a very unattractive state-contingent liability in exchange, I might add). Well, yes, I can make a deposit of cash at my local bank. And my employer "deposits" my paycheck in my bank account (in reality, just a debit-credit operation on a ledger). But this is probably not the best way to think about "deposits." I sometimes like to say that banks don't take deposits--they create deposit liabilities. Related to this notion, the banking system does not "lend out cash." The banking system funds its assets (including loan creation/acquisitions) by creating DDLs. (At the individual level, banks need to acquire cash to fund their operations only to the extent they want or need to meet some reserve requirement). Cash finds its way into circulation whenever the owners of DDLs exercise the redemption option embedded in the DDL contract. Alright, with this out of the way, let me continue.

It's not been easy to discover the fundamental economic (or social) rationale for banks (defined here as intermediaries that fund their assets, including their loans, through DDLs). Economists have struggled to understand debt, never mind demandable debt. Probably the best theory of bank debt we have is still the Diamond and Dybvig (1983) model. Like any model of debt, certain "financial market frictions" need to be present; else, the Modigliani-Miller theorem holds, in which case we should all be living in Cochrane's dream world (assuming no bad government fairy, of course).

The root frictions appear to be what economists label "private information" and "limited commitment." Among other things, limited commitment renders all sorts of assets, like our human capital, illiquid. In a frictionless world, there is no reason why I shouldn't be able to buy my Starbuck's latte by peeling off a slice of my house or my future earnings. It just doesn't work. That's what banks are for. They measure the value of my house, my future earnings, and they create DDLs that are backed by their assessed value of the collateral I have to offer. They would be performing an equivalent service by acting as licensing agents whose job is to verify the quality of the promises I issue (imagine an Andolfatto-IOU stamped as "BoA approved.") What's not entirely clear is why banks couldn't just get me the money I need by the way SoFi does--by first acquiring state-created money from willing lenders?

To put things another way, if banks are primarily in the business of payment services, why are they not limited to that business? Why are banks permitted to create money? (Why should banks help render my illiquid assets liquid?) Why not make banks hold 100% cash reserves? And then let the financial market handle matching lenders with borrowers, a la SoFi? This is the line taken by those who favor "narrow banking" proposals (see, e.g., Musgrave, 2014).

I have yet to digest all the arguments made by Musgrave and others. But they make enough sense to be taken seriously (so I plan to continue reading). I have a lot of questions. I am not bought into Cochrane's claim that equity is a run-proof security. The equity traded on junior exchanges, for example, does not appear run-proof (one can "run" to your stock broker and scream "sell, sell, sell!" just as easily as you can "run" to your bank to ask for your money). Moreover, there's a lot of evidence to suggest that equity makes lousy money. Gorton and Pennacchi, 1990 claim this is the case because equity is "informationally sensitive," and (senior tranches of) debt is not. Like it or not, most contracts are drawn up in nominal terms. In such a world, it would be terribly inconvenient, I think, to have floating NAV MMMF shares used as an exchange medium. People seem to like fixed-exchange rate systems (which is what DDLs are, after all).

What I would really like to see is how their claims stack up in a formal model. After all, the Diamond and Dybvig model does suggest the possibility of a trade-off. Maturity transformation enhances risk-sharing (when conventional markets are absent or too costly to operate), but potentially exposes the bank sector to self-fulfilling bank runs. A narrow banking regime kills risk-sharing but enhances financial stability. So in some jurisdictions, the switch to narrow banking might be worth making (although, there may be other ways to enhance the stability of fractional reserve banks, like central bank lender-of-last resort facilities, etc.).

I suspect that narrow banks might work relatively well in low-inflation environments, but possibly not so well in high-inflation regimes. The reason is because high inflation imposes a big tax on cash reserves (unless they pay interest, I guess). In such an environment, fractional reserve banks may be preferred as a way to escape the inflation tax by offering a higher rate of return on their DDLs. (Of course, it would be better to encourage a low-inflation regime, but that's not always possible).

So, these are just a few of the thoughts that came to mind after reading about Cochrane's dream. It's an interesting debate and I look forward to reading a lot more about it.

Sunday, May 1, 2016

Monetary policy implications of blockchain technology

As I'll be at Consensus 2016 event speaking in a session on "Digital Cash for Central Banks" (agenda available here), I thought this might be a good time to gather my thoughts on what central bankers should be thinking about as a new wave of financial innovation comes crashing on our shore. (Warning: the views I hold presently are subject to change. And, of course, my personal views do not necessarily represent the official views of any central bank anywhere!)

Before talking about policy, what is a "blockchain technology?" Like a lot of new terms that are bandied about, it means different things to different people. But for my purpose, I'm just going to think about it as a different way to keep account of information. The Bitcoin blockchain, for example, is a distributed public ledger that records the entire history of bitcoin transactions (the movement of BTC credits from account to account), where the ledger is updated, maintained, and kept secure by profit-seeking accountants (miners) who are incentivized through a clever algorithm to act in the interests of the Bitcoin community (their actions are also publicly observable so any shenanigans, should they occur, are likely to be short-lived.) There are many possible variations of this basic idea.
Now, it just so happens that money is just a type of ledger, as I explain here: Money and Payments, or How We Move Marbles. The notion of money as a record-keeping device goes back at least to Ostroy (1973). We worry about record-keeping systems because people are opportunistic and cannot be trusted. This is what Kiyotaki and Moore (2001) meant when they quipped that Evil is the Root of All Money. A well-designed record-keeping system constitutes a solution to a social problem (the existence of people willing and able to fabricate information for their private benefit at the expense of the community). Similarly, money should be viewed as a solution to a social problem.

Needless to say, none the solutions that have emerged over time have been perfect although, a Darwinian might claim that there is a time and a place for every species (see also: The Byrds). And now, as the technological environment evolves, a mutation threatens the prevailing order. What are the implications for monetary policy?

In what follows, when I speak of cryptocurrencies, I'll I focus on Bitcoin, first, because of its relative popularity, and second, because it's designed to compete directly with central bank money and payment systems. But what I have to say pertains more broadly to all innovations in this space. I'll also sometimes refer to the Fed but, of course, feel free to substitute in your favorite central bank.

1. Currency competition. To a domestic central bank, Bitcoin looks just like a foreign currency which, of course, it is (since its monetary policy is governed by an entity that is outside the domestic government's jurisdiction). Viewed from this perspective, Bitcoin presents central banks with an old and familiar threat: currency competition. Americans traveling abroad are familiar with the phenomenon--one is often presented an opportunity to exchange USD for local currency at unofficial exchange rates. People in these countries are often just trying to avoid a very high inflation tax. 

Annual Inflation Rate
The willingness and ability of domestics to substitute into a competing currency with a more stable value will put limits on the ability of a government to use the inflation tax as a revenue device. Governments sometimes go to great length to restrict the use of currency substitutes. The new threat poised by Bitcoin is that it's likely going to be much more difficult to enforce domestic currency controls. Anyone with a phone and access to the Internet will have access to an alternative digital bearer asset to use as an exchange medium. Bitcoin, or even just the threat of Bitcoin, will put much stricter limits on the amount of revenue governments can extract through the inflation tax. 

2. Maturity transformation using a foreign currency. While Bitcoin is unlikely to displace a major world currency any time soon, it's likely to play a prominent role in certain niches. I am reminded of the role the USD plays in some countries. An issue that arises in those jurisdictions is the creation of USD denominated bank deposit liabilities by foreign-based banks. Fractional reserve banking can be problematic in the best of times, but could you imagine U.S. banks offering loans denominated in BTC and, more importantly, redeemable on demand for BTC? This type of arrangement is not fantasy--it happens all the time in the so-called Eurodollar market and elsewhere. How should regulators respond to such an activity? How can a central bank act as a lender-of-last resort when, in a crisis, people are wanting their BTC bank deposits and not USD? What role, if any, might the treasury in these circumstances? Lender-of-last resort interventions are not limited to central banks, after all.

3. The safe asset phenomenon. A safe asset is not a risk-free asset--it's an asset that people flock to in times of crisis. (They are more accurately described as "flight-to-safety" assets.) In the 1970s, real estate was a safe asset, and investors ran away from the USD/UST (hence, inflation and high interest rates). In the late 2000s, the USD/UST was a safe asset (hence low inflation and low interest rates), and people ran away from real estate. The set of assets that investors perceive to be "safe" evidently varies over time. Could BTC be the next great safe asset? Maybe yes, maybe no. But monetary policy is all about formulating contingency plans. What if BTC denominated deposit liabilities are a significant source of financing, like CUF denominated mortgage loans in Hungary prior to European crisis? And what if BTC is regarded a safe asset in our next crisis, the way CUF is perceived to be in Europe? If this happened in the U.S., it would mean a large depreciation in the USD/BTC exchange rate, price inflation (measured in USD), price deflation (measured in BTC) and, of course, all of the other wonderful things that accompany financial crises. Except that the Fed would have no direct control over the supply of BTC (i.e., for the purpose of expanding its supply to accommodate the elevated demand for BTC, thereby alleviating the BTC deflation). To the extent that the UST is not a safe asset in this event, the Treasury's powers would also be greatly diminished. 

4. Securities exchange. The standard macroeconomic model typically assumes that securities are exchanged in frictionless financial markets, where trade is instantaneous and property rights are enforced at zero cost. Needless to say, this abstraction is ill-suited for the purpose of understanding monetary policy. Most bonds are thinly-traded on over-the-counter (OTC) markets and so, are highly illiquid. Even the most liquid of bonds, like the 10-year on-the-run U.S. treasury, is prone to unsettling "liquidity events" (e.g., Oct 15, 2015). Despite improvements over time, it can still take days to settle and clear securities transactions. This delay, along with other frictions, generates a huge demand for collateral, largely in the form of USTs to guard against counterparty risk. Improvements in securities exchange brought about by the application of blockchain (or other) technologies has the potential to release billions (or more) of dollars in collateral assets into the market place. The effect of this is likely to lower the liquidity premia on USTs, leading to higher interest rates. The implication for the treasury is obvious, but clearly any force that is likely to impinge on the structure of interest rates is also relevant for monetary policy.

5. Financial stability. There are some who claim that blockchain applications will one day render fractional reserve banking (or maturity transformation in general) obsolete. Maybe. But I am not so sure. One way this might happen is if every asset, our homes, our human capital, can be somehow transformed into perfectly liquid bearer instruments. This won't be happening any time soon. Proponents of blockchain technology point out that it has the potential to remove opacity in financial markets, something that would surely lead to a more stable financial system. However, it's worth pointing out that the leading economic theory of bank sector fragility, the Diamond and Dybvig model, does not rely on the existence of opacity in the financial market. In that model, the portfolios of banks are perfectly transparent. A bank run may nevertheless be triggered by the expectation of a mass redemption event, which subsequently becomes a self-fulfilling prophecy. It is also interesting to note that (in the same model) bank-runs can be eliminated if banks adopt a credible policy of suspending redemptions once they run out of cash (this commits the bank not to firesale assets to meet short-term debt obligations). The perception of perfect credibility is essential for the result and, needless to say, the degree of credibility needed here is frequently lacking. If the suspension clause could somehow be made to trigger automatically and mechanically--perhaps a smart contract could be employed--then depositors would never have an incentive to run a bank and the contract would never be exercised. Of course, this solution relies on the common knowledge assumption required in MAD (see footnote 1 below). I'm not sure what implications for policy this has, but it's fun to think about and, well, who knows where all this might lead. 

6. Central bank digital cash. The existing structure of money and payments (including central bank design) was built for the pre-Internet world. The world is now changed and we must deal with it. Among other things, there is no reason why, in principle, central banks could not offer online digital money accounts for the public. I'm thinking here of a basic utility account, a place to keep your money safe and pay bills. (Private banks could still compete by offering full service accounts). There is a sort of precedent for this: the U.S. Treasury, for example, offers online digital bond accounts. And while that system is not specifically designed to make payments, it could be (again, in principle). There are a number of advantages to consider. First, there would be no need for deposit insurance since the central bank accounts have no default risk (they can just print the money, after all). Second, cash managers at large corporations could simply park their money overnight at the central bank, rather than seek collateralized lending arrangements (repo) in the shadow banking sector. Third, the cost of maintaining the paper money supply can be eliminated. Fourth, it is easy to pay interest (possibly, negative) on digital money accounts, leaving central banks with an additional monetary policy tool. There is the issue of how such an arrangement may impact the funding of private banks. But such an object, if it was to exist, could I think, compete favorably with Bitcoin and other cryptocurrencies, assuming that monetary policy is conducted responsibly, of course. (I discuss a more radical form of central bank digital cash--one designed to compete more directly with Bitcoin--in this blogpost: Fedcoin.)

There are so many more things to discuss, but I think I'm at my limit for blog post length. If you have ideas to share, or papers to link to, please feel free to comment below. Thanks!


Footnote 1: Naturally, one would never want anything to trigger a mutually-assured-destruction clause in a contract. And such an event would never occur, theoretically at least, if everyone is perfectly rational. Few people need to be convinced that this assumption is rather extreme. However, if the collective punishment cost is not too large (well, at least finite), then one might be able to live with the occasional "mistake" and subsequent punishment. I am reminded of the "contract" that governed Roman legions. Good behavior was rewarded (after 20 or so years of service) with land to retire on. While bad behavior in battle was easy to identify collectively, it was sometimes hard to identify individually (a legion consisted of thousands of men). To discipline group effort, a credible threat of group punishment is needed (Holmstrom 1982). Credibility (the ability to commit) seems to have posed no problem for the Romans (how they ever became Italians, I have no idea). A legion deemed to have performed in a cowardly manner was punished by having each soldier draw lots, with a 1 in 10 chance of winning the lottery. The "winners" were then summarily clubbed to death by their colleagues. (Incidentally, this is where we get the word decimation--to reduce in number by one-tenth.) The punishment was not carried out very often, suggesting that the credible threat of the punishment worked reasonably well.

Thursday, April 28, 2016

On the want of U.S. government debt

In a recent article, Narayana Kocherlakota lays out the case for why, under present conditions, the U.S. government should be issuing more debt, using the proceeds to cut taxes, finance infrastructure spending, or both. It's a policy that many economists, including yours truly, have been advocating for some time. And while I generally support the policy, I thought it would be useful, nevertheless, to reflect on some possible counterarguments. It's not a slam dunk case, one way or the other, I think.
Kocherlakota does a good job explaining why a deficit-financed tax cut, or deficit-finance infrastructure spending is a good idea. I want to make it clear that the argument in favor of the policy hinges critically on the presumption that we can rely on Congress to manage the public debt over time in a responsible manner. Let's accept this assumption, provisionally at least, in order to understand the economic argument. I will come back to the political argument later.

While the debt-to-GDP ratio (D/Y) is presently high by historical standards, it's not unmanageable. The key is not the D/Y itself, but its trajectory over time. Clearly, D/Y cannot grow forever. And fortunately, market signals are available to monitor how the public perceives the likely path for D/Y over time. These market signals are: (1) the yields on U.S. treasury debt (at various maturities), and (2) inflation and inflation expectations. So what are these market signals telling us? The yield on U.S. treasuries is presently very low. Both inflation and inflation expectations are presently running below the Fed's 2% target and have done so for years now. So far, so good.

The large increase in D/Y since 2008 together with plummeting yields and low inflation may seem puzzling, but it's not really. Usually, a bad event that triggers a large increase in the public debt also triggers higher bond yields and the prospect of inflation. We can expect this to be the case in any experiment where the supply of debt increases in the face of a stable (or diminished) demand for the debt that is being issued. Think Zimbabwe or Venezuela.

But the U.S. is not Zimbabwe or Venezuela, or the Weimar Republic, for that matter. Rightly or wrongly, the U.S. treasury security is viewed by investors around the world as a safe haven asset. So when the financial crises hit in the U.S. and Europe 2008-10, investors moved en masse into U.S. treasuries (and other sovereign debt instruments viewed to be relatively safe). In short, while the supply of U.S. debt spiked up, the demand for U.S. debt increased by even more. We can infer this from the behavior of bond yields, which went down (the price of debt went up) at the time.

So the economic argument is simple. The U.S. government can presently borrow at essentially zero interest (more or less) even 10 years out and more. This effectively gives the fiscal authority the ability to print money (low-interest debt), so there's no need to rely on the Fed. To the extent that domestic real economic activity is still not firing on all cylinders, why not offer temporary tax cuts to stimulate demand? Why not re-build that crumbling infrastructure, putting people to work, all financed at zero-interest? It sounds like a no-brainer.

Alright, now for a couple of counterarguments, one economic and one political.

An economic argument against temporarily increasing the public debt further (and indeed, taking measures to reduce it) could be made on the basis of the Triffin Dilemma. The economist Robert Triffin noted back in the early 1960s that world reserve currency/debt status is a double-edged sword. On the one hand, it's great that the U.S. can just print paper that is coveted around the globe. If foreigners are willing to export their goods and services to us, expecting only paper in return, then we are extracting wealth from the rest of the world (in exchange for what ever financial service our paper is providing them).

One implication this power, if exercised, is that the world reserve currency issuer is likely to run persistent trade deficits. Triffin worried that the huge amount of U.S. currency held by foreigners exposed the U.S. to foreign risks. What might happen, for example, if foreigners suddenly decided they no longer wanted to hold USD or USTs? This could result in a sudden and dramatic change in the exchange rate, leading to domestic inflation and sharply higher bond yields.

There is also the trade-related argument that persistent trade deficits kill domestic industries and domestic employment. After all, if we can make the rest of the world work for us in exchange for paper, where is the need for us to work at all? The implied boom in domestic leisure consumption sounds good theoretically. But of course, in reality, the gains are not evenly shared. The rich gain by purchasing cheaper foreign goods. The poor are out of their jobs.

A political argument against more government debt could be made by challenging the assumption that it will be managed responsibly. This "we can't trust future politicians to do the right thing" argument is (sadly) not without empirical merit. I am reminded of the following quip by P.J. O'Rourke,
"The Democrats are the party that says government will make you smarter, taller, richer, and remove the crabgrass on your lawn. The Republicans are the party that says government doesn't work and then they get elected and prove it."
I can't help but note a certain irony here. There seems to be a strong presumption among people (Americans in particular) that the government should run its finances in the manner of a household. Economic theory is quite clear that this sentiment, however noble, is just plain wrong. The irony is that to the extent that this sentiment finds its way to being represented in Congress, it proves to be a very valuable "anchoring" device for the fiscal authority.

That is, I sometimes wonder whether US treasury debt is valued around the world the way it is precisely because it is known that Congress is impregnated with a large number of genetic "debt-ceiling" algorithms. It may not be an ideal situation from the perspective of pure economic theory, but then again, it's not hard to think of worse scenarios.

Friday, April 22, 2016

Interest Rates and Aggregate Demand Revisited

Nick Rowe has a nice post (written some time ago) that frames an old macroeconomic issue in a very nice (teachable) way.

In macro policy discussions, one often hears something like "lower interest rates stimulate aggregate demand.'' Many people view such a statement as self-evident. It's only when you think about it for a long time that you realize it's not self-evident at all (few things are when we are left to ponder them long enough, it seems).

The purpose of this post is to add a bit of formalism to Nick's discussion. (Sorry for the wonkish display, but I think it's necessary at this point to make things clear.) To this end, let's begin with an off-the-shelf bare-bones macro model. There is a representative agent (this is not necessary, but makes things easy) with additively-separable log preferences defined over consumption sequences {c(t), t = 0,1,...,∞}, with discount factor 0 < β < 1. Let R(t) denote the gross real rate of interest (risk-free) earned on a bond held from date t to date t+1. Assume that all individuals can borrow/lend freely at the risk-free rate.

Now, consider the cost-benefit calculation associated with the consumption-savings choice. Suppose an individual refrains from consuming one unit of consumption today. The marginal utility cost of this sacrifice is given by 1/c(t). This one extra unit of saving delivers R(t) units of extra consumption tomorrow. The marginal utility benefit of this extra consumption is R(t)β/c(t+1). Individual optimization requires equating marginal cost to marginal benefit:

[1] 1/c(t) = R(t)β/c(t+1) for t = 0,1,...,∞

Condition [1] is sometimes called the consumption-Euler equation, or just the Euler equation, for short. (Noah Smith has a nice post on the Euler equation here.)

One can do a lot with the Euler equation. Here is how it is used to derive "aggregate demand." First, assume that all output is (for simplicity) in the form of nonstorable consumer goods and services. Let N denote population size. Then C(t) = Nc(t) denotes aggregate consumption or GDE (gross domestic expenditure). Now rearrange [1] as follows,

[2] c(t) = [ 1/(R(t)β) ]c(t+1)

Thus, if we hold c(t+1) fixed, then equation [2] traces out a negative relationship between c(t) and R(t). That is, an increase in R(t) results in a decrease in planned present day consumer spending (aggregate demand). This negatively related locus of consumption and interest rate pairs is sometimes called an IS curve (IS = "investment-saving" where investment is fixed at zero in this model). The economic intuition is simple: raising R(t) makes it more attractive to save (lower current consumption). [Never mind for now that any extra saving is likely to boost c(t+1).]

Let me consider an endowment economy where each individual is endowed with a deterministic sequence {y(t), t = 0,1,...,∞}. Usually, y(t) is thought of as an individual's output or income at date t, so that Y(t) = Ny(t) represents GDP (gross domestic product) or GDI (gross domestic income). But more generally (and this is what the General refers to in the General Theory) we can think of y(t) as a maximum production capacity. "Full employment" refers to the special case where Y(t) is the GDP.

The standard neoclassical assumption is that the economy is always at full employment. Maybe calling this property an assumption is not quite accurate. We can derive the property as a result of some deeper assumptions relating to the ability of individuals in an economy to coordinate their activities in an efficient and socially desirable manner (this is the force behind Says' Law, that "supply creates its own demand.") In any case, the upshot is that Y(t) represents the GDP. And since GDE = GDP, we have C(t) = Y(t), or c(t) = y(t), at every date t. Each person consumes his value-added, the economy consumes what it produces.

Suppose that real income grows at rate α, so that, y(t+1) = αy(t). Since c(t) = y(t) for all t, condition [2] can be used to deduce the equilibrium real rate of interest:

[3] R*(t) = α/β

The real interest rate is predicted to be high when growth (α) is high. The real rate of interest is low when growth is low. The intuition here is as follows. An increase in α means that people are expecting higher levels of future income. People will want to bring some of that future income forward in time. They will try to do so by borrowing, or saving less. Either way, the effect is to put upward pressure on the interest rate.

Alright, it's time to do some "textbook" aggregate demand analysis. Actually, I don't like the way textbooks usually do this. The usual assumption is a "sticky wage" that mucks up the labor market (here is my critique on that idea). This idea is certainly not Keynesian:
"There is, therefore, no ground for the belief that a flexible wage policy is capable of maintaining a state of continuous full employment..." [General Theory, 1936 Chp. 19]
Indeed, Keynes (1936) wrote that flexible wages could make things worse, not better (consistent with my Figure 2.12 here.) The best representation of "what Keynes actually meant" is, in my view, expressed formally in the game theoretic notion of multiple Bayes-Nash equilibria (a tool that was not available to Keynes in his lifetime). See Cooper and John (1988), Howitt and McAfee (1990) and Roger Farmer for example.

How to proceed? There are many ways, but I don't want to get bogged down in the details here (although I should stress that the details are critical for other questions). One way to proceed is to embed my static high/low equilibrium model into the model above. In that model, aggregate demand C(t) can be either high or low, and the equilibrium level of output can correspond to the high or low level of demand as a self-fulfilling prophecy.

Here's another way to think about it. Peter Howitt would explain it to me this way. Imagine that the people in our model do not like the smell of their output (any reason to motivate intratemporal trade here will do). So they will want to swap their goods with others. If everything works well here (the neoclassical assumption), then all goods will be traded at par. The real GDP is Y(t).

Now, suppose that trading is costly. Suppose that it is prohibitively costly to sell any output beyond some level k(C), where C is aggregate demand. Assume that k(C) is increasing in C. The idea here is that it is easier to sell larger quantities of output when demand is high. In fact, we could just assume k(C) = C/N. Next, consider an arbitrary 0 < C/N < y. Then the most anyone can expect to sell (and buy) at a given date is c = C/N. In this model, there is a continuum of equilibria, each indexed by an expectation defined over C/N. If everyone expects a thickly traded market, it is individually rational to trade a large volume and, collectively, this is what transpires. "Animal spirits" determine which of these equilibria actually prevail.

Alright, back to Nick's point. Assume that in the "long run," the economy returns to full employment forever. For simplicity, assume that the long-run is expected to occur tomorrow. In this case, c(t+1) = y(t+1) and R(t+1) = α/β for every date t going forward. Now let's take a look at today, t = 0, using condition [2].

[2a] c(0) = [ 1/(R(0)β) ]y(1)

Assume that c(0) is determined by an animal spirit (as described above) such that c(0) < y(0). Then condition [2a] can be used to solve for the equilibrium interest rate,

[4] R(0) = (1/β)y(1)/c(0) > R*(0) = (1/β)y(1)/y(0)

That is, the economy is presently in recession and the interest rate is too high. And if the interest rate is too high, well, then, why not take policy actions designed to lower it? The recession is like diabetes and low interest rate policy is like insulin, as Kocherlokota argues here.

And the argument makes sense IF full employment lives somewhere in the foreseeable future. Lowering the interest rate in this model has the effect of stimulating consumer demand as people try to bring future output closer to the present. But future output here is fixed at full employment. So, to the extent that lowering the real rate of interest increases C(0), the effect is felt entirely in the contemporaneous depressed period in the form of higher real GDP.

But what justifies the assumption that the economy will somehow find its way back to full employment? This is the missing piece in our conventional models.

This leads Nick to ask: what if people do not expect a return to full employment in the near future? Indeed, what if? As it turns out, there are many, many other equilibria in the model above. One such equilibrium path satisfies

[5] C(t+1) = R*βC(t)  where C(t) < Y(t)  for all  t = 0,1,...,∞

That is, the economy can be permanently stuck in a "secular stagnation." Moreover, the equilibrium interest rate is exactly where it should be: it is neither too high  nor too low. Consumption and GDP are growing at rate α. It's just that the level of GDP is permanently below its full employment level.

The real interest rate measures the relative price of output across time. In the equilibrium described by [5], the relative scarcity of output across time is just right. Its the contemporaneous level of output that's off at each date. How is a change in the interest rate supposed to fix this problem?

The short answer is that it can't. In fact, it's easy to construct examples where attempting to lower the interest rate could make things worse (perhaps this is an overdose of insulin, in Kocherlakota's example).

Suppose we're in a situation described by condition [2a], for example. In that exercise, I assumed that y(1) is fixed at full employment and that c(0) is depressed. This is what justified lowering R(0) to stimulate contemporaneous consumer demand. But suppose that animal spirits keep contemporaneous consumer demand fixed, and that the effect of lowering R(0) is to reduce future consumer demand to c(1) < y(1)? There is no a priori reason to expect c(0) to do all the "equilibrating" here. And so, in this manner, the effect of low interest policy could be to cause future recessions, possibly a secular stagnation.


I think most of what I said above can be shown in a conventional 2-period economy (a current and future period). Here are some diagrams.

Consider first the neoclassical general equilibrium (full employment at both dates). Condition [1] states that the slope of the indifference curve is the same as the slope of the intertemporal budget constraint (the real rate of interest). The full employment assumption means that the equilibrium lies on the budget constraint. This is point A in the following diagram.

Suppose now that the economy is expected to be at full employment in the future; i.e., fix c(2) = y(2), but that the economy is presently depressed; i.e., c(1) < y(1). The interest rate is too high, R' > R*. This is point B in the following diagram.

Lowering the interest rate in the diagram above (making the budget line flatter) moves the economy from B back to A. But suppose we instead forecast a future recession, so that c(2) < y(2). Then condition [5] prevails, and the economy moves to point S (secular stagnation) in the diagram below.

And finally, here's how to depict a future recession caused by an artificially low interest rate  policy (point F).