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

Monday, September 24, 2018

What is the yield curve forecasting?

It's well-known that in the United States, recessions are often preceded by an inversion of the yield curve. Is there any economic rationale for why this should be the case? 

Most yield curve analysis makes reference to nominal interest rates. Economic theory, however, stresses the relevance of real (inflation-adjusted) interest rates. (The distinction does not matter much for the U.S in recent decades, as inflation has remained low and stable). According to standard asset-pricing theory (which, unfortunately for present purposes, abstracts from liquidity premia), the real interest rate measures the rate at which consumption (a broad measure of material living standards) is expected to grow over a given horizon. A high 1-year yield signals that growth is expected to be high over a one-year horizon. A high 10-year yield signals that annual growth is expected, on average, to be high over a ten-year horizon. If the difference in the 10-year and 1-year yield is positive, then growth is expected to accelerate. If the difference is negative--i.e., if the real yield curve inverts--then growth is expected to decelerate.

What is the economic intuition for these claims? One way to think about this is in terms of Friedman’s Permanent Income Hypothesis, which states that an individual’s desired consumption expenditure today should depend not only on current income, but the likely path of his/her income over the foreseeable future. The logic of this argument follows from the assumption that people are willing and able to smooth their consumption over time, given their expectations over how their incomes are likely to evolve over time. For example, if people expect their income to be higher in the future, then they will want to consume more today in order to smooth out their consumption. They can attempt to do so by saving less (or borrowing more). If a community is collectively “bullish” in this sense, desired consumer spending should rise in the aggregate, and desired saving should fall, leading to upward pressure on the real interest rate.

Alternatively, suppose that firms suddenly turn bullish on the likely returns to capital spending. Then the resulting increase in the demand for investment financing should drive real interest rates upward. In this case as well, a higher real interest rate signals the expectation of a higher rate of economic growth. If individual expectations over future prospects are correct more often they are incorrect, then higher real interest rates today should be correlated with higher future growth rates.


So, in theory at least, an inverted yield curve does not forecast recessions--it forecasts growth slowdowns. Nevertheless, there is a sense in which an inverted (or even flat) yield curve can, in some circumstances, suggest that recession is more likely. Here's the basic idea.

Consider an economy that grows over time, but where growth occurs unevenly (i.e., the economy alternates between high- and low-growth regimes). Imagine, as well, that the economy is occasionally buffeted by negative “shocks”—adverse events that occur at unpredictable moments in time (an oil price spike, a stock market collapse, etc.). It seems clear enough that in such an economy, recessions are more likely to occur when a shock of a given size occurs in a low-growth state as opposed to a high-growth state.

Now, as explained above, suppose that an inverted yield curve forecasts a deceleration in growth. Then the deceleration will entail moving from a higher growth state to lower growth state. Suppose this lower growth state is near zero. In this state, growth is now more likely to turn negative in the event of a shock. In this way, an inverted yield curve does not forecast recession; instead, it forecasts the economic conditions that make recession more likely.

How does this idea match up the data? Here is a plot of the 10-1 real yield spread in the United States from 1985-2018 (blue line) along with the year-over-year growth rate of real per capita consumption--nondurables plus services (orange line).
Well, it's not perfect, but as is clear from the figure, the real yield curve flattened and inverted prior to each of the past three recessions. Consistent with the theory, note that consumption growth tends to decelerate as the yield curve flattens. This is true even in non-recessionary episodes. In particular, the consumption growth deceleration of 1985-85, 1988-89, and 2006-07 were each associated or preceded by a flattening or inverted yield curve. Each of the three recessions occurred when consumption was growing at a moderate to low pace.

Were the recessions that occurred following yield curve inversion forecastable? The proximate cause of the 1990 recession was the Iraqi invasion of Kuwait and the associated spike in world oil prices. Is it plausible to believe that bond market participants knew well in advance Saddam Hussein’s plans of invasion? The proximate cause of the two most recent recessions were asset price collapses (some blame Fed tightening, but theoretically gradual tightening should only cause a slowdown in growth, not a sharp collapse). While many people may have had a sense of impending doom, it seems unlikely that anyone knew years in advance the exact date of collapse. According to the interpretation here, the severity of the Great Recession was in part due to the fact that the economy was already growing slowly at the time of the collapse in real estate prices. While consumption growth did slow prior to the collapse of the “dot com” asset price bubble in 2000, it grew at a moderate rate entering that recession. Accordingly, the recession of 2000-2001 is one of the mildest ever recorded.

Does the recent flattening of the yield curve portend recession? Not necessarily. The flattening of the real yield curve may simply reflect the fact that real consumption growth is not expected to accelerate or decelerate from the present growth rate of about 1% per annum. On the other hand, a 1% growth rate is substantially lower than the historical average of 2% in the United States. Because of this, the risk that a negative shock (of comparable magnitude to past shocks) sends the economy into technical recession is increased. While the exact date at which the shock arrives is itself is unpredictable, the likelihood of recession is higher relative to a high real interest rate, high growth economy.

Saturday, July 7, 2018

The Trust Machine: The Story of Bitcoin

I came across a Bitcoin explainer the other day called The Trust Machine: The Story of Bitcoin.  I thought it was very thoughtful presentation and I encourage anyone who's interested in Bitcoin to view it (less than 25 minutes). What I offer below are questions and comments that came to my mind as I listened to the narrative. I'd recommend listening to the entire presentation first and then reading my comments below. The bold numbers represent the corresponding time in the video to which the remark pertains.
1:04 Before Bitcoin, the only way to make electronic payments over the Internet was via your bank. However, over 2 billion people in the world do not have access to a bank account.  
Sure, but why is Bitcoin the best solution for this problem? Nobody was connected to their bank accounts electronically prior to the Internet. The solution was to get people connected. Most people are now connected. Why is the solution not to remove the barriers that prevent the rest from getting connected?
1:35 And even those who do have a bank account aren't exactly free to send money to anyone anywhere online (Fidel Castro graphic). If two governments don't get along, money simply doesn't flow across their borders. Digital cash would connect people economically in a way never before possible.
First, just to be clear, electronic money does not "flow" across borders. Electronic money lives in a ledger. The question is who gets to use the ledger. Not being able to "send money" from the U.S. to Cuba means that Cubans (living in Cuba) are not permitted access to the ledgers created by U.S. banks and Americans are not permitted access to the ledgers created by Cuban banks. There is a communication barrier.

Second, given such a communication barrier, it's hard to see how digital cash would help connect people economically--by which I mean that if money is "flowing" in one direction, goods are flowing in the other. How does digital money help lift a trade embargo? It does not. Digital money could be used, however, to facilitate international remittances.
1.59 Antonopolous remarks that Bitcoin can do for banking and finance what cellphone technology did for communications and empower billions of people around the world. Brito remarks that Bitcoin for the first time makes possible P2P transactions without the aid of intermediary.
I have a lot of respect for both these guys. But I'm still not sure how Bitcoin (or blockchain technology more generally) is supposed to facilitate banking and finance (I elaborate here). As for the contention that Bitcoin does not need a third party to clear transactions, this is, strictly speaking, not true. The third party in Bitcoin consists of the miners--no P2P transaction can be cleared without their help. So, no, Bitcoin is not "just like cash" (which truly does not depend on any 3rd party).
5.16 Within a small trusted group like a family, you really don't need money. Money actually starts as a shared memory.
I'm really happy to see this key insight--known to anthropologists and economists for a long time--is starting to catch on. See: Why the blockchain should be familiar to you.
5.40 But this kind of written money works only if we trust the people we are making promises with. 
Well, this is not exactly correct. In fact, memory (e.g., credit histories) are a part of the solution to the lack of trust problem. Reputations rely on memory. And we expect cooperative play from noncooperative agents concerned about protecting their reputations. The need for conventional money arises because memory (the shared communal ledger) does not scale given the limitations of a network of human brains communicating verbally. Money permits anonymous agents to transact and can therefore scale beyond local confines.  An anonymous person is someone for which we have no personal history. But we're still willing to grant them a favor if they show us the money. Money is a substitute for the missing record-keeping technology. (For more detailed and technical explanation, see here.)
11.50 This leads us back to the problem we face online. The Internet connects people globally, yet people are largely restricted to using local currencies. Who is going to make the digital "tickets" for the Internet? And who will we trust to be in charge of them? 
This is clearly leading up to the suggestion that Bitcoin is a natural global currency. The idea of a single global currency has a lot of appeal. The closest thing to this we have today is the U.S. dollar. But because not everyone has USD accounts, there are the usual inconveniences and inefficiencies associated with uncertain nominal exchange rates. How big of a deal is this? I do not know, but I suspect that among all the factors that contribute to the advancement of material living standards, having a common currency is not at the top of the list. We might get some handle on this issue by asking how much better off are the people of the EMU since the adoption of the Euro? (See: How Much Does the EMU Benefit Trade?)
12.22 The key to Bitcoin is the way Satoshi flips the traditional model of trust on its head. Instead of letting a bank control the ledger, you share it with everyone. 
This is subtly (and importantly) misleading. Control of a ledger does not map simply into whether it is shared or not. For any ledger, read and write privileges need to be separately specified. It is true that in today's banking system, banks possess both read and write privileges and that they limit the read privilege severely (you can only look at the account balances in your account and no one else's). Note that there is no technological reason for why conventional bank ledgers cannot be made open for public viewing. Doing so would effectively make the ledger "shared" and "distributed" (if it could be freely copied). That this does not happen reflects the preferences of bank customers. We don't want the world having full viewing privileges over our personal bank accounts. But there is nothing right now with current technology that prevents people from publishing their diary online (rendering is shared and distributed).
12.45 This shared file model is more secure than any bank ledger could ever hope to be.
If every student in a classroom can see what the school teacher scribbles on the blackboard, then it'll be very hard for the teacher to later claim she did not write it. Say something stupid in public and you'll never erase the public record. This is the power of a shared ledger. But banks already have the power to share their ledgers. Their bank customers do not want them to. Perhaps bank customers wouldn't mind so much if their accounts were anonymous (like the old Swiss bank accounts). I'm sure that Paypal would love to offer Swiss-style bank accounts. If it was legal. Which it is not. But if this is what people truly want, then why not have them lobby their respective governments to reinstate the anonymous bank account? Bitcoin is a "solution" in this regard only insofar it circumvents the law (which it's very good at doing, since it's a decentralized autonomous organization).
12.50 Bitcoin is a piece of shared software that everyone runs together instead of having one trusted computer do it (Graphic shows bank with one copy of ledger and Bitcoin with multiple copies). 
First, there is nothing that prevents a bank from keeping multiple backup copies of its ledger (Fedwire has multiple back up computers, for example).  Second, I'm not sure what it means for "everyone to run a shared software together." I presume it means that the agents or agencies that have volunteered to operate as miners collectively agree to follow the protocols laid out in a particular version of the software. Sure, and banks within the banking system collectively agree to abide by banking regulations. The software evolves over time in accordance with the wishes of the broader community--miners can "vote" on which version of the software to use--code patches that benefit the community are adopted. Banking regulations also evolve over time in accordance with the wishes of the broader community via choices made by elected representatives.
13.57 There is no center to the network, no central authority, no concentration of power. It's exactly how ant and bee colonies function.
To say that there's absolutely no concentration of power is overstating things. The core developers likely have more say than others. Those agencies that have invested heavily in mining equipment have more say than others. Concentration of mining power is a concern. (Miners themselves have avoided overly concentrating power for fear of destroying the franchise value. This is, ironically, the same force we expect to discipline conventional banks.) And as for ant and bee colonies, they have hierarchical structures, including a queen. From outer space, humanity looks like an ant colony. So yes, Bitcoin functions just like an ant colony--governed by protocols--as does everything else.
14.44 Description of blockchain. 
This is done very nicely. There is something beautiful about the blockchain, to be sure. And while I have some quibbles with what is said in this section, let me step back and comment on the broader picture.

The key innovation of blockchain is in terms of how the write privilege is governed (in particular, the read privilege is not the innovative part; see my discussion above). The conventional solution to the scaling problem is to delegate the write privilege to a reputable agency (which itself is governed by the laws of society). Judging by the way world commerce has expanded over the centuries, the conventional model has been a huge success.

Of course, the conventional model is not perfect. It has been and continues to be a work in progress. Why not concentrate our efforts on continuing to improve this conventional and successful model? As far as I can tell, this is what corporate "blockchain" solutions are offering (as part of the broader effort to improve information management systems more generally). They are not offering (again, as far as I can tell) bona fide "blockchain" solutions--they are offering "blockchain inspired" innovations in data management (for example, increased transparency and more extensive sharing of the ledger).

The spirit of Bitcoin is based on the more ancient model of collective recording-keeping via a communal consensus protocol. That this is now possible on a global scale is the work of genius (much the same way double-entry book-keeping was a stroke of genius).

But extending the write privilege communally comes at a cost. This is because individuals will always find it in their interest to rewrite history in a manner that benefits themselves at the expense of the broader community. How to guard against this? People somehow have to earn the right to write history, so to speak. The Bitcoin consensus protocol uses a Sybil control mechanism called Proof-of-Work (PoW) that dictates who earns the right to "vote" (i.e., who gets to add a given paragraph of script to an ever-growing novel).

Essentially, the write-privilege in consensus protocols have to be gamed. The question is whether the game in question generates good outcomes (where "good" is to be judged by network members). Bitcoin has shown us that consensus-based record-keeping on a large scale is feasible. But it is also terribly inefficient along many dimensions (note: I say this as a matter of fact, not as a matter of passing judgment since conventional banking systems are also terribly inefficient along many dimensions). There is the hope, however, that advances in the design of consensus algorithms will render consensus-based record-keeping more efficient. But the same hope exists for database management systems more generally.

And so, in true Darwinian fashion, we are witnessing a struggle between competing species. Will there be a clear winner in the end? Or, as is more likely in my view, will there be a peaceful (but still competitive and ever-evolving) coexistence?

Related Reading: Blockchain: What it is, What it does, and Why you probably don't need one.
My other musings on the subject available here in case you're interested.

Thursday, March 29, 2018

Inflation and Unemployment (Part 2)

In my previous post (Inflation and Unemployment), I reviewed what I thought was a fair characterization of the way the Federal Reserve Board staff organize their thinking about inflation and unemployment, as well as how this view of the world was at least partly responsible for the "hawkish" overtone of current Fed policy. I also suggested that the inflation and unemployment dynamic might be better understood through the lens of an alternative theory that emphasized the supply and demand for money (broadly defined to include U.S. treasury debt).

I want to thank Paul Krugman for taking the time to critique my post and draw attention to an important issue that concerns U.S. monetary policy makers today (see: Immaculate Inflation Strikes Again). I was only a little disappointed to learn that I agreed with almost all of what he wrote in his column. But if this is the case, then what are we debating? And more importantly, how does it matter, if at all, for monetary policy?

The amount of disagreement in macroeconomics is often exaggerated and I think this has definitely been the case here. While we may disagree on some things, we seem to agree on the most important part, namely, on the present conduct of U.S. monetary policy.

Krugman begins his piece by stating three questions. Let me state the questions, followed by my own answers and comparisons.

1. Does the Fed know how low the unemployment rate can go? I have quipped before that this is one case in which the Fed can definitely count on a zero-lower-bound being in effect (and this is not just in theory, Switzerland had virtually zero unemployment throughout the 1960s, with low inflation I might add). But what this question is really asking is how low can the "natural" rate of unemployment go? I agree with Krugman: we don't know. But I'll further add: we don't even know if a "natural" rate of unemployment exists in the first place. It's just a theory, after all (which is not to say it shouldn't be taken seriously, only that we need to keep that important caveat in mind).

2. Should the Fed begin tightening now, even though inflation is still low? This is legitimately debatable--and the FOMC is presently debating it. My own view, on balance, seems presently more aligned with the "doves" on the committee. And so I also agree with Krugman on this score, namely, that the Fed could be tightening too aggressively. Krugman suggests that there are several reasons supporting his view and he mentions a few of them. They are all legitimate reasons, in my view. But I could add more reasons, based on my own preferred theory of inflation. The demand for money (broadly defined to include U.S. treasuries) appears to remain elevated. This disinflationary force has been in place for a long time and could, as I explain here, account for the lowflation phenomenon (see also here). If you follow that link, you'll note that I quote Krugman approvingly in regard to his view about monetary policy in a liquidity trap. Perhaps I am wrong, but I read Krugman here as not recommending that the Japanese lower their unemployment rate to raise inflation. Instead, he appeals to the model I alluded to in my post: a monetary-fiscal theory of inflation. If the Japanese want inflation, just cut taxes and finance social security spending by printing JGBs (as I recommended here). I'm not sure what this has to do with "immaculate" inflation. (I did learn from Nick Rowe that "maculate" is indeed a word.)

3. Is there any relationship between inflation and unemployment? I think it would be odd for any macroeconomist schooled in general equilibrium to suggest that the answer to this question is unequivocally no. The answer is yes. The real question is what type of relationship? In labor market search theories of unemployment, where firms and workers bargain over a joint surplus, a low unemployment rate can result in a higher real wage because workers have greater bargaining power. If a decrease in the unemployment rate leads to a rise in the real wage, it could, ceteris paribus, have an effect on the price-level (and, if prices are temporarily sticky, the adjustment could come along other margins). But an increase in the price-level is not the same thing as an increase in the inflation rate (though short-run price-adjustment costs can transform a price-level effect as a short-term rise in measured inflation). For workers to afford buying goods in the presence of ever-rising prices, their bank accounts are going to have to grow accordingly. Ultimately, this can only happen in aggregate if the aggregate quantity of money is growing, either through the banking sector or through the increase in the supply of outside money (including treasury debt). This is the sense in which I think inflation has to be a monetary phenomenon and that, moreover, the actual rate of inflation is ultimately not governed by whether unemployment is living above or below its "natural" rate, whatever that is.

So perhaps there's some room for debate on point 3. But we should be careful not portray the question as an "either/or" issue. We could just be two blind men, feeling different parts of the elephant--the two interpretations are not necessarily inconsistent with each other. We should try to work this out. On the plus side, it seems we are led to the same policy recommendation. This is something worth noting. (I plead guilty on the score of needlessly antagonizing people who "believe in" the Phillips curve. Rather than suggesting we abandon the theory, I could instead have suggested we supplement it with the monetary view.)

Does the debate over question 3 matter? Yes, it could, because different interpretations of how the world works usually--though not always---implies something different about optimal policy. The Phillips curve theory of inflation suffers from a free parameter problem: the natural rate is unobservable and hence, one can always appeal to a shift in the natural rate to explain away discrepancies with the data. However, the monetary theory I prefer also suffers from a free parameter problem: money demand is not directly observable either. I can always appeal to some unobserved shift in money demand to explain away discrepancies with the data. For this reason, it would be useful for economists to identify "robust" policies--policies that can be expected to deliver good results regardless of which theory best describes the world we are living in.

Is the Phillips curve view of inflation contributing to a policy mistake? I wanted to suggest in my post that it is, although this is not necessarily a fault of the theory as much as how it is applied. That is, there may be no policy mistake in the making if the FOMC simply lets its estimate of the natural rate fall freely as evidence of impending inflation fails to materialize. However, this is not what is happening. As Jim Bullard explained to me, he believes that Phillips curve proponents have a (strictly positive) lower bound on their estimate of the natural rate. The unemployment rate is so low now -- how can it possibly go any lower -- this has to lead to inflation in the near future -- it just has to. We'd better start raising now, before we find ourselves behind the curve.

Here is where the "monetarist" view could temper such resolve. Granted, the global outlook is looking relatively rosy, and fiscal policy seems expansionary--these are both inflation risks from a monetarist perspective. On the other hand, there is considerable uncertainty in this outlook, not the least of which is presently being fueled by talk of a global trade war. In uncertain times, consumers and investors are likely to lower their demand for goods and services--increasing their demand for safe assets, like U.S. dollars and U.S. treasuries. We can see these concerns weigh on long-bond yields. Market-based inflation expectations (like the 5yr-5yr forward) seem well-anchored. Current inflation is running below target. All of this suggests that the Fed can afford not to move aggressively at this time (to be fair, the FOMC regularly emphasizes the "data dependent" nature of its policy path). And yes, this is consistent with PC advocates that are willing to let their estimate of the NRU decline in line with the evidence.

This post is already getting too long and so I wouldn't blame you if you stopped reading here: the main points I wanted to make have been made. Still, I have a bit more to say, so in case you are interested...

Krugman presents the following data for Spain. He writes "Consider, for example, the case of Spain. Inflation in Spain is definitely not driven by monetary factors, since Spain hasn’t even had its own money since it joined the euro. Nonetheless, there have been big moves in both Spanish inflation and Spanish unemployment:"


Krugman asserts because Spain doesn't have its own monetary policy, that monetary factors were not responsible for swings in Spanish inflation and unemployment. But my interpretation of the great crash and subsequent rise in unemployment is that it was caused by a large positive money demand shock (where again, I stress, by money I include safe government debt). This positive money demand shock (flight to safety) is just the opposite side of what Krugman and others would label a negative aggregate demand shock. So once again, I think Krugman is digging moats (perhaps unintentionally) where he could be building bridges.

The other thing I should like to point out about the Spanish data is whether it suggests that low unemployment forecasts future inflation (which is really what my post was about). A naive reading of the data above suggests that low unemployment actually seems to forecast low inflation. Again, this suggests caution in using the unemployment rate to forecast inflation.

Finally, on Krugman's broader point: "economics is about what people do, and stories about macrobehavior should always include an explanation of the micromotives that make people change what they do. This isn’t the same thing as saying that we must have “microfoundations” in the sense that everyone is maximizing; often people don’t, and a lot of sensible economics involves just accepting some limits to maximization. But incentives and motives are still key."

I wholeheartedly agree.



Monday, March 26, 2018

Inflation and unemployment

The FOMC decided on March 21 to increase the target band for the federal funds rate by 25 basis points, to a range of 1.50-1.75%. This despite inflation running persistently below the Fed's 2% target, only moderate wage growth, and inflation expectations firmly anchored.
What is the FOMC thinking here? To be more precise, what is the dominant view within the FOMC that is driving the present tightening cycle? Remember, the FOMC is made up of 12 regional bank presidents plus 7 board of governors (at full strength) possessing a variety of views which are somehow aggregated into a policy rate decision. I think it's fair to say that the dominant view, especially among Board members, is heavily influenced by the Board's staff economists. So, maybe what I'm really asking is: what is the Board staff thinking?

Perhaps they're thinking along the following lines. Thanks in part to a recent change in U.S. fiscal policy and in part to a relatively robust world economy, the U.S. economy seems poised for a growth spurt of unknown duration. As the economy expands, so too does the demand for investment and credit which, in turn, puts upward pressure on market interest rates. If the Fed does not follow this pressure upward (by raising its policy rate) then it risks inefficiently "subsidizing" investment spending and credit creation (leading to excess credit and spending). There might even be some justification for raising the policy rate more aggressively than what the market would dictate on its own, if it is judged that the imminent growth spurt was due to an "irrational" exuberance or if it is otherwise judged to be unsustainable (and subject to a sharp correction).

The view above may constitute an element of the way a few hawks on the committee are thinking when they cite financial stability concerns. But economists at the Board are probably not thinking exactly in this way because it offers no direct link to the Fed's dual mandate of promoting price stability and full employment. Price stability is interpreted by the FOMC as a long-run PCE inflation rate of 2% per annum. And while there's no official measure of "full employment," for all practical purposes it is defined as a situation in which the unemployment rate is at its "natural" rate.

What is the "natural" rate of unemployment? The Board defines the term here. According to this statement, it corresponds to the lowest sustainable level of unemployment in the U.S. economy. How do we know what this lowest sustainable level is? The statement implicitly answers this question by mapping "lowest sustainable level" into some notion of a "long-run normal level" of the unemployment rate. In short, take a look at the average unemployment rate over long stretches of time and assume that it roughly corresponds to what is sustainable. In his recent press conference, Fed Chair Jay Powell explicitly mentioned that any such estimate will a have large confidence interval--that is, we don't know what the natural rate is and we suspect it may change over time. (He might have mentioned that we're not even sure this theoretical object exists in reality but, of course, we could say this of any theoretical construct in economics, including supply and demand curves.)

In any case, here is a plot of the U.S. civilian unemployment rate since 1948, along with the Congressional Budget Office's estimate of the "natural" rate of unemployment:
The unemployment rate does appear to be a relatively stationary time-series. What's interesting about the U.S. data is that the unemployment rate only appears to rise in periods of economic recession (when GDP growth is negative). Moreover, there's evidence of a cyclical asymmetry: when it rises, it rises sharply, but when it declines, it does so relatively gradually (these patterns are not so evident in other countries).

The Board's concern, at present, is the fact that the unemployment rate fell to its (estimated) natural rate of 4.7% early in 2017 and has since declined steadily to 4.1% today. Given a relatively robust global economy, and given the recent fiscal stimulus in the U.S., the unemployment rate is projected to decline even further in the foreseeable future. This, evidently, is bad news. Why? Because it's unsustainable (read: likely to end badly). The economy is presently operating above its long-run potential level.

What does any of this have to do with inflation? Inflation is the rate of change of the price level (the "cost of living" measured in dollars). Sometimes people speak of wage inflation--the rate of change of the average nominal wage rate. Way back in the day, William Phillips noted an apparent inverse relationship between the rate of wage inflation and the unemployment rate. Others noticed a similar inverse relationship between the rate of price-level inflation and the unemployment rate. This statistical relationship became known as the Phillips curve.

The standard interpretation of the Phillips curve, a version of which is used by the Board staff today, goes something like this: To the extent that business cycles are caused by movements in aggregate demand (e.g., bouts of optimism or pessimism) then one would expect the general level of prices to rise when aggregate demand is high and to decline when aggregate demand is low. Moreover, one would expect firms to recruit workers more intensively when aggregate demand is high than when it is low, so that the unemployment rate should decline in a boom and rise in a recession.  In this way, aggregate demand shocks cause unemployment and the price-level to move in opposite directions. One would expect the inflation-unemployment relationship to reverse if a recession was instead triggered by a supply disruption (e.g., an oil price shock).

Importantly, the consensus view is that there's no long-run trade-off between inflation and unemployment (or, if there is, it seems to go in the opposite direction). Here's the relationship between inflation and unemployment in the U.S.
Apart from the oil supply shock episodes, inflation and unemployment do tend to move in opposite directions in recessions. But recessions are short-lived, and the relationship between these two variables during economic expansions is much less clear. For example, inflation and unemployment both fell from December 1982 to January 1987, from June 1992 to March 1995, and from August 2011 to October 2015.

It's hard to tell from this data alone whether low rates of unemployment portend higher inflation because in the background we have the Fed raising interest rates when there are signs of inflationary pressure. On the other hand, it's probably just as reasonable to expect the opposite. That is, in a deep demand-driven recession that drives the unemployment rate up and the inflation rate down, the high rate of unemployment at the trough should forecast higher future inflation (assuming that inflation is expected to return to target).

Is there any evidence that a low unemployment rate during an expansion forecasts higher future inflation? My feeling is that the empirical evidence is weak on this score. If so, then it is odd that so many people seem to believe that "low unemployment causes higher inflation." One can see this idea manifest itself in headlines like this: Fed's Mission Improbable: Lift Unemployment--But Avoid Recession (by Greg Ip of the WSJ). I reproduce a few of the opening paragraphs here for convenience:
Massive tax cuts, robust federal spending and a synchronized global upswing are expected to push annual growth in economic output to 2.7% this year and 2.5% next—past what Fed officials consider its long-run sustainable rate of 1.8%—according to projections Fed officials released after their meeting Wednesday
To sustain such growth, the Fed projects employers will have to dig deep into a diminishing supply of workers. That will cause unemployment, already at a 17-year low of 4.1%, to sink to 3.6% by the fourth quarter of 2019, a level last seen in the 1960s. That’s well below the “natural rate” of 4.5%, which is the rate Fed officials and many economists think the economy can sustain without eventually producing inflation. 
But it faces a problem: In theory, unemployment will eventually have to go back to 4.5%, or inflation will head even higher. Yet since records begin in 1948, unemployment has never risen by 0.9 points, except in a recession.
This almost makes it sound like the Fed is trying to increase the unemployment rate.  Of course, this is not how Fed officials would describe their intent. The goal is to ensure that the economy does not embark on an "unsustainable" (bound-to-end-badly) growth path. To hedge against this event, the Fed will have to raise its policy rate to keep aggregate demand and inflation in check. The collateral damage in this hedging strategy is for the unemployment rate to rise (hopefully in a smooth manner and to more sustainable levels).

I think it's time for economists to stop relying so heavily on the Phillips curve as their theory of inflation.There are two good reasons to do so. First, it's bad PR to (unintentionally) suggest that workers are somehow responsible for inflation. Second, and more importantly, it would help avoid policy mistakes like raising the federal funds rate too aggressively against low unemployment rate data.

To see the potential for policy mistakes, recall how in December of 2012 the FOMC adopted the so-called "Evans rule" (named after Chicago Fed president Charlie Evans):
In particular, the Committee decided to keep the target range for the federal funds rate at 0 to 1/4 percent and currently anticipates that this exceptionally low range for the federal funds rate will be appropriate at least as long as the unemployment rate remains above 6-1/2 percent, inflation between one and two years ahead is projected to be no more than a half percentage point above the Committee’s 2 percent longer-run goal, and longer-term inflation expectations continue to be well anchored.
I pointed out  here at the time that while the Evans rule was meant to signal a more Dovish policy, it was inadvertently signalling a more Hawkish policy. As it so happened, the Fed did not raise its policy rate when the unemployment rate broke below 6.5% in April 2014. But it might have, and markets likely hedged against this possibility, resulting in a tighter than desired monetary policy.

In any case, back to the current tightening cycle and the factors influencing it. A few FOMC members are asking what the apparent rush to raise rates is all about. Jim Bullard, president of the St. Louis Fed has long been a vocal advocate for data-dependent policy. Inflation remains below target and long-term inflation expectations are on the low side as well. According to Bullard, the Fed can afford to be patient (and to move rapidly as conditions dictate).

One counterpoint to this view is the idea that the Fed needs to "get ahead of the curve." Again, the notion is that while inflation remains below target, we are confident that it will soon return to target and we can see inflationary pressures building up in the horizon (as evidenced by the very low rate of unemployment, among other things). I saw Charlie Evans push back against this idea pretty effectively on a recent CNBC interview. According to Evans, the "getting ahead of the curve" idea is largely a byproduct of an era where inflation was almost always above target. In the past six years, however, we've been operating in an environment where inflation has been persistently below target. Getting ahead of the curve is perhaps not as pressing an issue as it once was. A doubling of the inflation rate from 1.5% to 3% is not as disconcerting as a doubling from 4% to 8%.

I think that Minneapolis Fed president Neel Kashkari has a pragmatic approach to the problem (see the reasons he gives here for why he dissented for the 3rd time against raising the policy rate).  Suppose we subscribe to the notion that a below-natural-rate of unemployment portends future inflation. Suppose further we admit that we do not know where the natural rate of unemployment resides (as mentioned above, Fed Chair Jay Powell alluded to the uncertainty surrounding this estimate). Well, then why not just assume that the natural rate is declining as long as we see no evidence of price or wage inflation pressure?

If we abandon the traditional Phillips curve view of inflation, what do we replace it with? I think that the traditional money supply/demand approach provides a firmer foundation for understanding inflation (see here, here and here). In particular, we can expect the price-level to rise as households and firms attempt to dispose of excess nominal wealth balances (as when government debt is issued too rapidly when an economy is near full employment--a situation much like today). Conversely, we can expect the price-level to decline (or inflation to slow down) as the demand for safe nominal wealth rises (as in times of crisis). The framework is perfectly consistent with the Phillips curve, but with the direction of causality mainly reversed. That is, we can "blame" unexpected swings in inflation/deflation (emanating from deeper forces) for influencing the unemployment rate, and not the other way around.








Monday, March 19, 2018

What anchors inflation?

Conventional wisdom is that a central bank can anchor the long-run rate of inflation to a target of its own choosing. This belief is evident where ever a government has charged its central bank with a "price stability" mandate (commonly interpreted nowadays as keeping a consumer price index growing on average at around 2% per annum over long periods of time).

What exactly is the mechanism by which a central bank is supposed to control the long-run rate of inflation (the growth rate of the price-level)? And is it really the case that a central bank can defend its preferred inflation target without any degree of fiscal support?

Asking these questions reminds me of the old joke of an economist as someone who sees something work in practice and then asks whether it might also work in theory. In the present context one might point to the success that central banks have experienced with inflation-targeting. It works! And remember how the Fed under Paul Volcker (Chair from 1979-87) slew the 1970s inflation dragon with its Draconian anti-inflation policy? What else do we need to know?

Well, how did Volcker  do it exactly? The conventional view is that Volcker tightened monetary policy sharply by contracting the rate of growth of the monetary base (which paid zero interest at the time). The unexpected shortfall in bank reserves led to a sharp increase in short-term interest rates and a severe recession (1981.2-1982.4). As is typically the case in a recession, the rate of inflation fell, a phenomenon commonly attributed to the decline in aggregate demand for goods and services as unemployment rises and as incomes fall. 


But what kept the inflation low after the recession ended? Why did the inflation rate continue to decline as the economy grew (and as the unemployment rate fell)?
 
It's hard to argue that inflation expectations were declining. While inflation expectations fell with inflation from 1980-82, the median one-year-ahead inflation forecast from the University of Michigan survey remained flat at around 3% for the rest of Volcker's tenure. Although we have no direct market measure of long-term inflation expectations for that period, the 10-year treasury yield is probably not a bad proxy. And while the 10-year yield does decline in the 1981-82 recession, it remains elevated relative to historical (low inflation) norms and begins to rise in 1983 from just over 10% to 13.5% in 1984.


One could argue, I suppose, that the Volcker Fed kept inflation in check by raising its policy rate aggressively against signs of rising inflation expectations (the Fed had by this time abandoned targeting monetary aggregates).  Thus, despite a growing economy, the Fed's interest rate policy kept realized inflation in check, even as expected inflation remained elevated. 

Then, in the second half of 1984, long-term yields (long-term inflation expectations) began to decline. Shortly after, the Fed's policy rate declined as well. Inflation continued to decline modestly. All the while, the economy continued to grow (the unemployment rate continued to decline). Why did inflation remain low and why did inflation expectations decline?

One could argue, I suppose, that the aggressive action taken by the Fed in the first half of 1984 (not to mention the even more aggressive actions taken earlier in Volcker's tenure) finally convinced markets that the Fed was committed to keeping inflation low. This had the effect of keeping short-term inflation expectations low, which motivated wage and price setters to factor in lower cost increases. And it had the effect of lowering long-term inflation expectations, driving long-bond yields lower (as bondholders require less compensation against the loss of purchasing power of money due far in the future). The decline in longer-term inflation expectations c. 1984-85  also evident in the median 5-10 year forecast of inflation from the University of Michigan survey.


So that's the basic story. A central bank that credibly promises to snuff out any hint of rising inflation (and inflation expectations) can keep inflation anchored at a preferred long-run target of its choosing. Ironically, the threat of raising the short-term interest rate against inflationary pressure is what keeps nominal interest rates low. Moreover, if a central bank can credibly commit to a long-run inflation target, the effect is to keep longer-term bond yields low as well. The fact that things didn't work out so smoothly for Volcker early in his regime was because the Fed lost credibility in the 1970s and this credibility took time to rebuild.

I think there's a lot of merit to this view. But I still have a nagging doubt that U.S. fiscal policy had little or anything to do with Volcker's success at keeping inflation low. What exactly am I talking about--didn't Volcker accomplish his goal despite the Reagan deficits? 

People tend to remember the famous Reagan tax cut (the Economic Recovery Act of 1981). The deficit grew very rapidly soon after because of the tax cut, but also because of the severe recession and also to some extent because of the Fed's high interest rate policy (which increased the interest expense of government debt). But as Justin Fox points out here, people frequently forget about the tax increases that came steadily throughout the Reagan administration (and into the Clinton years.)


As the diagram above shows, the year-over-year growth rate of nominal debt in April 1983 hit a peak of about 22%. The growth rate of debt turned around sharply after that, dropping to 14% in July 1984. After popping briefly to 17.5% in October of 1984, it started to decline, slowly at first, and then more sharply in 1986.

The ups and downs in the picture probably do not matter as much as the underlying trends. What matters is whether people generally believe fiscal policy to be anchored in the sense of keeping the long-run rate of nominal debt growth low. (Note: another notion of "anchored" fiscal policy corresponds to keeping the debt-to-GDP ratio stable, even though stability of this ratio is consistent with any inflation rate). If the claim is that the Volcker Fed could have lowered inflation permanently without fiscal accommodation, then it could have done so with debt continuing to grow indefinitely at (say) 20% per annum. There would have been no reason to reverse the Reagan tax cuts!

So, the thought experiment is this: suppose that the political pressure to reduce the Reagan deficits was absent. Could Volcker have kept inflation low?

Who knows what would have happened to economic growth. It may have gone up, down, or roughly followed the path it took. Let's take the middle ground and assume that growth would have remained unaffected. Let us further assume that the U.S. government is never going to default on its debt. (There is, of course, no reason for why a sovereign government issuing debt constituting claims against the currency it issues need ever default. If default does occur, it is a political decision and not an economic one.)

Alright, so now we have nominal debt growing at 20%. Suppose inflation does not change and suppose inflation expectations remain anchored. Then the Fed will have no reason to raise its short-term interest rate. And bondholders will have no reason to demand higher long-term yields.  But lo, then there's a free lunch at hand.  The government can simply use its paper to finance its expenditures without resorting to taxes. At best this might hold for a highly depressed economy, but it seems unlikely to hold for the case we are considering (robust economic growth and low average unemployment).
 
Something has to give. But what? If inflation and interest rates don't budge, then the public is being asked to hold an ever-increasing quantity of debt at the same real (inflation-adjusted) rate of interest. Assuming that the foreign sector doesn't fully absorb it, the increasing level of debt must crowd out domestic investment at some point. The private sector will attempt, at this point, to attract funding by offering higher returns on its debt-offerings. How does the real yield on government bonds rise if the nominal interest rate and inflation remain fixed? Is the Fed supposed to increase its policy rate in the face of declining investment (crowding out)?

One thing to keep in mind is that the permanent tax cuts will have made the private sector wealthier. It seems likely that at some point, they will want to spend this wealth. Of course, in aggregate, the public cannot dispose of the government bonds it holds--the bonds can only pass hand-to-hand. But this smells like a classic "hot potato" effect -- people will try to spend their wealth, driving the price-level higher (reducing the real value of the outstanding government debt).

So, suppose that inflation starts to rise (along with expectations of inflation). In response, the Volcker Fed increases its policy rate sharply and restates its commitment to keeping inflation anchored. The effect of the rate increase might be to slow economic growth and keep inflation in check for a while. But remember, the fiscal authority doesn't care in this thought experiment--it just keeps printing debt as rapidly as ever. The inflationary pressure has to return. So the Volcker Fed raises its policy rate again. And again. And again. And again. This is not going to work.

It is of some interest to note that Volcker himself did not appear to believe that the Fed could unilaterally keep inflation low. At least, I say this judging by the way he often criticized the Reagan administration for its loose fiscal policies. According to Volcker 1982 (see here), huge government deficits were responsible for high interest rates (the Fed's high-interest policy). In other words, fiscal policy was responsible for the price-level pressure that necessitated the Fed's high-interest rate policy.

The clash between the Fed and the administration at that time makes for some interesting reading (see also here). In light of the recent shift in fiscal policy, one wonders whether a similar conflict might be in the works in the not too-distant future.



Thursday, February 22, 2018

The recession of 2012-13 and the taper tantrum

I admit this is a rather strange title for a post, but bear with me. Every once in a while I reflect back on the so-called "taper tantrum" event in the summer of 2013 when Fed Chair Ben Bernanke made an off-the-cuff remark that the FOMC was thinking of maybe slowing down the pace QE3 asset purchases (see here). The stock market had a temporary sell-off, which turned out to be no big deal. What I find more interesting is how long bond yields rose sharply and persistently. Even more interesting, real bond yields behaved in this manner--see the figure below.


OK, so maybe the initial sell-off of bonds could be interpreted as the market being surprised that QE3 (an open-ended program) might terminate earlier than expected. But I just can't believe that QE programs can have such persistent effects on real interest rates. If that's the case, then what explains the broad pattern on display above, including the decline in real yields over 2011-2013?

I attribute it largely to the recession of 2012-2013. Wait, what recession, you say? Well, let's take a look. Contrary to standard practice, I'm going to look at per capita consumption (of nondurables and services). Here is what the data looks like. 
Consumption growth per capita was negative from 2012.1-2013.3. The taper tantrum occurred in 2013.3.  As you can see by this measure, the economy weakened considerably over the period 2011-2013. Over the same time, real bond yields declined. This is most easily explained as the consequence of an increasingly bearish outlook manifesting itself as an increase in the demand for safety (bonds).

Consumption growth turned positive in 2013.4, and continued to climb well into 2015. So while the tantrum may have contributed to the spike up in yields, the reason they stayed higher is because of an increasingly bullish outlook for the economy.

Does this interpretation make sense? What events were leading to the bearish outlook beginning in 2011. Certainly the events in Europe had something to do with it. I also think that domestic factors had a role to play, in particular, fiscal policy. Consider the following diagram.

What would the consumption and GDP dynamic have looked like if government purchases (per capita) had instead remain constant?

Monday, February 19, 2018

U.S. GDP Expenditure Components

One way to decompose the GDP is in terms of its expenditure components, Y ≡ C + I + G + NX. I like to write "≡" instead of "=" to remind myself that this decomposition is measurement, not theory.
 
In what follows, consumption is measured in terms of nondurables and services only--I add consumer durables with private investment. The data is inflation-adjusted, quarterly, and I report year-over-year percent changes. I'll start with recent history (since 2010) and then later look at a longer sample (beginning in 1960).
 
Let me begin with GDP and consumption. I like to study consumption dynamics because I have some notion of Milton Friedman's "permanent income hypothesis" in the back of my mind. The idea is that individuals base their expenditures on nondurable goods and services more on their wealth (a stock) rather on income (a flow)--at least, to the extent they can draw on savings and/or access credit markets. To a first approximation then, one could interpret consumption as the trend for GDP. According to the theory, consumption should respond less strongly to perceived transitory changes in income (GDP) and more strongly to perceive permanent changes in income (GDP). In any case, here's what the data looks like for the U.S. since 2010. 
GDP growth since the end of the Great Recession has averaged about 2%, consumption growth somewhat less. Two things stand out for me. The first is the anemic consumption growth from 2011-early 2014 and in particular 2012-2013. Why were American households so bearish? (Note that the unemployment rate is declining throughout this sample period.) Things seemed to turn around in 2014, but then tailed off somewhat in 2015. Coincidentally (or not), that was the year in which the Fed talked out loud about "lift off" -- raising its policy rate for the first time from 25bp where it had remained since 2009. The second is where we're at now. Yes, GDP growth has rebounded somewhat since early 2016, but we're still well within the bounds of recent history (so, no sign of some impending boom). The tale is told by consumption growth, which has remained steady at about 2%. 
 
The following diagram plots private investment spending, decomposed into residential, non-residential, and consumer durables spending (note that the scales vary across figures).  
The growth rate in consumer durables spending is relatively stable in this sample period, averaging between 5-10%. Residential investment, which collapsed during the Great Recession, did not turn around until late 2011. It has grown as rapidly as 15% in 2012-2013 (the years of anemic consumption growth cited above), but has slowed down markedly since 2016. In terms of non-residential investment, it was surprising (to me) the weakness it displayed, especially in 2016 (this may have been due, at least in part, to the collapse in oil prices, which held back investment in the energy sector.)
Well, here's a picture for you. Government purchases of goods and services actually declined for most of this sample period. (Government investment consists mainly of structures and computer hardware/software (see here) and accounts for about 20% of government purchases.) I've been reflecting a lot on this picture lately because it looks different from what many may think, and also, it looks different from historical behavior (as we'll see below).  
 
For completeness, I include export and import growth. Nothing too interesting here. 
 
What does this same data look like from a longer time perspective? I reproduce the four figures above starting in 1960. 
This is really a striking figure, in my view. There are so many things that catch my eye. The first and most obvious is the decline in volatility beginning around 1985 (this is the so-called Great Moderation). Less obvious, but something worth noting is an apparent growing asymmetry associated with the Great Moderation. In particular, growth recessions seem roughly as severe as they've always been. What's missing are the sharp growth booms. Third, it seems to me that consumption growth was much less volatile than GDP growth prior to 1985. Andrew Spewak and I discuss this here. One possible explanation is that business cycle downturns are generally expected to be much more persistent than in the past (why this might be so would be an interesting question to investigate). Finally, and perhaps most important, economic growth since 2000 has slowed down significantly. St. Louis Fed President Jim Bullard argues we are in a low-growth regime (see here). Is this a recurring phenomenon, as suggested by Schumpeter (see here)? How much of the slowdown is explained by a post WW2 transition dynamic? 
 
Here is private investment spending across categories, 
Again, the Great Moderation is evident, apart from the monumental collapse of residential investment spending in the Great Recession. 
Like private investment, government investment is relatively volatile (though one wonders why this should be the case for government). The most striking aspect of this diagram is the collapse government spending in the immediate aftermath of the Great Recession. One can't help but wonder about the wisdom of such policy during such a period of economic weakness. For those in favor of reducing (G/Y), a more gradual policy would almost surely have been better (e.g., by letting Y grow into G, not by cutting G). 
 
Finally, for completeness, here is export and import growth. 
It's interesting that the Great Moderation shows up along this dimension as well.
 
If you have an economic theory that explains all these patterns, I'd be very interested to hear about it below.  

Thursday, February 8, 2018

Fiscal theories of the price-level

This post is me thinking out loud about how fiscal considerations may influence the price-level.  The question of what determines the price-level is an old one. It's a question that economists struggle with to this day.

To begin, what do we mean by the price-level? Loosely, the price-level refers to the "cost-of-living," where cost is measured in units of money. Living refers to the flow of services consumed (destroyed) for the purpose of survival/enjoyment. (Note that the cost-of-living might alternatively be measured as the amount of labor one must expend per unit of consumption, but this would require a separate discussion.)

Measuring aggregate material living standards is challenging for two reasons. First, people consume a variety of goods and services. Suppose that the price of food goes up and the price of shelter goes down. Does the cost-of-living go up or down? Second, different people have different material needs/wants (and individual wants and needs change over time too). Statisticians do the best they can to address these complications by constructing "average consumption bundles" as done in the calculation of the Consumer Price Index (CPI). The following diagram plots the change in the price-level (the inflation rate) for several categories of goods and services:




In what follows, I'm going to abstract from inflation and focus only on the theory of the price-level (inflation is the rate of change in the price-level over an extended period of time). To this end, think of a very simple world where the real GDP (y) is fixed and determined exogenously (independent of monetary policy). Assume that the expected rate of inflation is zero. Then, by the Fisher equation, the nominal interest rate corresponds to the real interest rate. I want to think of this interest rate as being potentially influenced by monetary policy (I like to think of r as representing the real yield on treasury debt, where treasury debt possesses a liquidity premium.)

Perhaps the oldest theory of the price-level is the so-called Quantity Theory of Money (QTM). It seems clear enough that people and agencies are willing to accept and hold money because money facilitates transactions--it provides liquidity services. In the simplest version of the QTM, the demand for real money balances takes the form L(y), where L is increasing in y. The idea here is that the demand for liquidity is increasing in the level of aggregate economic activity (as indexed by y).

Next, the QTM assumes that the supply of money (M) is determined by the central bank. Let P denote the price-level. Then (M/P) denotes the supply of real money balances. The QTM asserts that the price-level is determined by an equilibrium condition which equates the supply of real money balances with the demand for real money balances. Mathematically,

[1] M/P = L(y)

Condition [1] can be explained as the consequence of the "hot potato" effect. The idea is that someone must be willing to hold the extant money supply. If M/P > L, then the money supply exceeds money demand. In this case, people will presumably try to dispose of their money holdings (by spending them on goods and services). People accepting money for payment will be thinking the same thing--they are willing to accept the money, but only selling their goods at a higher price. The "hot potato" effect ceases only when condition [1] holds. The same logic applies in reverse when M/P < L (with everyone wanting to get their hands on the potato).

Now, suppose that y varies over time. Then the QTM suggests that a central bank can keep the price-level stable at P0 by letting the money supply move in proportion to money demand; i.e., M = L(y)*P0. This is what is meant by "furbishing an elastic currency." This reminds us as well that interpreting money-price correlations in the data are tricky if money demand is "unstable."

O.K., so now let's see where fiscal policy fits in here. Let D denote the outstanding stock of government debt. If a central bank is restricted to create money only out of government debt, then we can write M = θD, where 0 < θ < 1 is the fraction of the debt monetized by the central bank. If the central bank wants to increase the money supply, it would conduct an "open market operation" in which it buys bonds for newly-issued money, resulting in an increase in θ. Note that the money supply may increase through changes in D for a constant θ.

Let B denote the bonds held by the private sector (i.e., not including the bonds held by the central bank). That is, B = (1 - θ)D. The interest expense of the public debt is given by rB. Note, while the treasury actually pays an interest expense rD, the interest payments to the central bank rM are remitted to the treasury, leaving a net cost equal to rB = r(D-M). Thus, the central bank is in a position to lower the interest expense of the public debt by monetizing a larger fraction of it (I discuss this in more detail here and here.) To the extent that the central bank influences r, it is also in a position to lower the interest expense by lowering r.

Now let's write down the government "budget constraint." Let T denote tax revenue (net of transfers) and let G denote government purchases (of goods and services). Then, assuming that default is not an option, the government budget constraint is given by,

[2] = G + rB

The difference T - G is called the primary budget surplus (deficit, if negative). So another way to read [2] is that the interest expense of the government debt must be financed with a primary surplus. Note that if r < 0, then the government is in a position to run a perpetual primary deficit. (The more general condition is r < g, where g is the growth rate of the economy, which I've normalized here to be zero.)
  
In most monetary models, the fiscal policy plays no role in determining the price-level. The reason for this lies in the implicit assumption that taxes are non-distortionary (e.g., lump-sum) and that the fiscal authority passively adjusts T to ensure that condition [2] holds.  This latter assumption is sometimes labeled a Ricardian fiscal regime. In a Ricardian regime, fiscal policy does not matter for the price-level. To see this, suppose that the central bank increases r. Then the fiscal authority increases T (or decreases G) with no change in the money supply or price-level. Or, imagine that the fiscal authority increases D. In this case, the central bank can keep the money supply constant by lowering θ, the fraction of debt it chooses to monetize. If so, then B will increase. In a Ricardian regime, the fiscal authority will again either increase T (or decrease G), leaving the price-level unchanged. 

But suppose fiscal policy does not behave in the Ricardian manner described above. To take an example, suppose that the fiscal authority instead targets T, or T-G, or (T-G)/P, etc. For concreteness, suppose it targets the real primary surplus τ = (T-G)/P.  In this case, condition [2] can be written as, 

[3] τ = r(B/P)

Condition [3] forms the basis of what is known as the fiscal theory of the price-level (FTPL); see Cochrane (1998). The idea is as follows. Imagine a world where there is no need for money (a cashless economy), so that condition [1] is irrelevant. Imagine too that the real rate of interest is determined by market-forces, so that r > 0 represents the "natural" rate of interest. Finally, imagine that the outstanding stock of debt D = B is nominal. Then the price-level is determined by condition [3] which, while resembling a government budget constraint, is in fact a standard stock-valuation equation. To see this, rewrite [3] as follows,

[4] (B/P) = τ/r

The right-hand-side of [4] represents the present value of a perpetual flow of primary government budget surpluses τ. The left-hand-side of [4] measures the real value of the government's debt. The equation [4] asserts that the real value of government debt is equal to the present value of the stream of primary surpluses. This is analogous to the way one might value the equity of a company that generates a stream of profits τ. 

Note that condition [4] looks a lot like condition [1]. We can use the same "hot potato" analogy to describe the determination of the price-level in this case. For example, suppose that (B/P) > τ/r. Then people and agencies will presumably want to sell the over-valued government debt (for goods and services). People are willing to accept these nominal claims, but only if they are sold more cheaply--that is, if the goods sold to acquire the bonds can be sold at a higher price. As before, this hot potato effect ceases only when condition [4] holds. 

I'm still not sure what to think about the FTPL. While I lean more toward the QTM view, I do believe that fiscal considerations can have an important influence on the price-level. The way I'm inclined to think about this, however, is as follows. 

Since nominal government debt represent claims against government money, it's not surprising that such debt inherits a degree of "moneyness." To the extent this is true, the measure of money M used in equation [1] should be expanded to include the liquid component of government debt. Let X < B denote the liquid component of government debt. There are a few ways to think about this. One obvious way is to imagine that the banking sector creates deposit liabilities out of X. Or we could imagine that X is accepted directly as payment for goods and services, at least, for a subset of agencies (China, for example, effectively exports goods and services for X). In any case, the appropriate measure of money is given by M + X. In the limiting case where X = B, the relevant money supply becomes the entire government debt D = M + B, so that condition [1] becomes, 

[5] D/P = L(y)

In a world where government debt becomes increasingly more relevant as an exchange medium than central bank money, control over the money supply is effectively transferred to the fiscal authority.  This is another sense, distinct from the FTPL, in which fiscal policy might influence the price-level. The difference boils down to the source of money demand -- is it primarily liquidity-preference, or is it because money/debt instruments are viewed as tax-backed liabilities?

There is, of course, much that I've left out here.  While the assumed invariance of real economic activity to monetary and fiscal policy is not a bad place to start for the question at hand, it is clearly not a good place to end. As well, the model should be extended to permit sustained inflation. All of this can be easily done and I'll try to come back to it later. 

Something I do not think is critical for the issue at hand is modeling private money creation (beyond the monetization of government debt modeled above). To the extent that banks monetize positive NPV projects, the money they create out of private assets (in the act of lending) creates value that is commensurate with additional liabilities created. In short, accretive share issuances (good bank loans) are not likely to  be dilutive (inflationary). Of course, the same is true of newly-issued government money if the new money is used to finance positive NPV projects (including the employment of labor in cases of severe underemployment). 

Sunday, January 21, 2018

Blockchain: what it is, what it does, and why you probably don't need one


Dilbert - by Scott Adams
Interest in blockchain is at a fever pitch lately. This is in large part due to the eye-popping price dynamics of Bitcoin--the original bad-boy cryptocurrency--which everyone knows is powered by blockchain...whatever that is. But no matter. Given that even big players like Goldman Sachs are getting into the act (check out their super slick presentation here: Blockchain--The New Technology of Trust) maybe it's time to figure out what all the fuss is about. What follows is based on my slide deck which I recently presented at the Olin School of Business at a Blockchain Panel (I will link up to video as soon as it becomes available) 

Things are a little confusing out there I think in part because not enough care is taken in defining terms before assessing pros and cons. And when terms are defined, they sometimes include desired outcomes as a part of their definition. For example, blockchain is often described as consisting of (among other things) an immutable ledger. This is like defining a titanic to be an unsinkable ship. 

So what do people mean when they bandy about the term blockchain? I recently had a chance to learn about the project from a corporate perspective as represented by Ed Corno of IBM (see IBM Blockchain), the other member of the panel I mentioned above. From Ed's slide deck we have the following definition:
Blockchain: a shared, replicated, permissioned ledger with consensus, provenance, immutability and finality. 
Well, if this is what blockchain is, then maybe I want one too! The issue I have with this definition (apart from the fact that it confounds descriptive elements with desired outcomes) is that it glosses over what I consider to be an important defining characteristic of blockchain: the consensus mechanism. Loosely speaking, there are two ways to achieve consensus. One is reputation-based (trust) and the other is game-based (trustless). 

I'm not 100% sure, but I believe the corporate versions of blockchain are likely to stick to the standard model of reputation-based accounting. In this case, the efficiency gains of "blockchain" boil down to the gains associated with making databases more synchronized across trading partners, more cryptographically secure, more visible,  more complete, etc. In short, there is nothing revolutionary or radical going on here -- it's just the usual advancement of the technology and methods associated with the on-going problem of database management. Labeling the endeavor blockchain is alright, I guess. It certainly makes for good marketing!

On the other hand, game-based blockchains--like the one that power Bitcoin--are, in my view, potentially more revolutionary. But before I explain why I think this, I want to step back a bit and describe my bird's eye view of what's happening in this space. 
  
A Database of Individual Action Histories

The type of information that concerns us here is not what one might label "knowledge," say, as in the recipe for a nuclear bomb. The information in question relates more to a set of events that have happened in the past, in particular, events relating to individual actions. Consider, for example, "David washed your car two days ago." This type of information is intrinsically useless in the sense that it is not usable in any productive manner. In addition to work histories like this, the same is true of customer service histories, delivery/receipt histories, credit histories, or any performance-related history. And yet, people value such information. It forms the bedrock of reputation and perhaps even of identity. As such, it is frequently used as a form of currency. 

Why is intrinsically useless history of this form valued? A monetary theorist may tell you it's because of a lack of commitment or a lack of trust (see Evil is the Root of All Money). If people could be relied upon to make good on their promises a priori, their track records would largely be irrelevant from an economic perspective. A good reputation is a form of capital. It is valued because it persuades creditors (believers) that more reputable agencies are more likely to make good on their promises. We keep our money in a bank not because we think bankers are angels, but because we believe the long-term franchise value of banking exceeds the short-run benefit a bank would derive from appropriating our funds. (Well, that's the theory, at least. Admittedly, it doesn't work perfectly.) 

Note something important here. Because histories are just information, they can be created "out of thin air." And, indeed, this is the fundamental source of the problem: people have an incentive to fabricate or counterfeit individual histories (their own and perhaps those of others) for a personal gain that comes at the expense of the community. No society can thrive, let alone survive, if its members have to worry excessively about others taking credit for their own personal contributions to the broader community. I'm writing this blog post in part (well, perhaps mainly) because I'm hoping to get credit for it. 

Since humans (like bankers) are not angels, what is wanted is an honest and immutable database of histories (defined over a set of actions that are relevant for the community in question). Its purpose is to eliminate false claims of sociable behavior (acts which are tantamount to counterfeiting currency). Imagine too eliminating the frustration of discordant records. How much time is wasted in trying to settle "he said/she said" claims inside and outside of law courts? The ultimate goal, of course, is to promote fair and efficient outcomes. We may not want something like this creepy Santa Claus technology, but something similar defined over a restricted domain for a given application would be nice. 

Organizing History

Let e(t) denote a set of events, or actions (relevant to the community in question), performed by an individual at date t = 1,2,3,... An individual history at date t is denoted 

h(t-1) = { e(t-1), e(t-2), ..., e(0) }, t = 1,2,3,... 

Aggregating over individual events, we can let E(t) denote the set of individual actions at date t, and let H(t-1) denote the communal history, that is, the set of individual histories of people belonging to the community in question:

H(t-1) = { E(t-1), E(t-2), ... , E(0) }, t = 1,2,3,...

Observe that E(t) can be thought of as a "block" of information (relating to a set of actions taken by members of the community at date t). If this is so, then H(t-1) consists of time-stamped blocks of information connected in sequence to form a chain of blocks. In this sense, any database consisting of a complete history of (community-relevant) events can be thought of as a "blockchain." 

Note that there are other ways of organizing history. For example, consider a cash-based economy where people are anonymous and let e(t) denote acquisitions of cash (if positive) or expenditures of cash (if negative). Then an individual's cash balances at the beginning of date t is given by h(t-1) = e(t-1) + e(t-2) + ... + e(0). This is the sense in which "money is memory." Measuring a person's worth by how much money they have serves as a crude summary statistic of the net contributions they've made to society in the past (assuming they did not steal or counterfeit the money, of course). Another way to organize history is to specify h(t-1) = { e(t-1) }. This is the "what have you done for me lately?" model of remembering favors. The possibilities are endless. But an essential component of blockchain is that it contains a complete history of all community-relevant events. (We could perhaps generalize to truncated histories if data storage is a problem.)

Database Management Systems (DBMS) and the Read/Write Privilege

Alright then, suppose that a given community (consisting of people, different divisions within a firm, different firms in a supply chain, etc.) wants to manage a chained-block of histories H(t-1) over time. How is this to be done? 

Along with a specification of what is to constitute the relevant information to be contained in the database, any DBMS will have to specify parameters restricting:

  1. The Read Privilege (who, what, and how);
  2. The Write Privilege (who, what, and how). 

That is, who gets to gets to read and write history? Is the database to be completely open, like a public library? Or will some information be held in locked vaults, accessible only with permission? And if by permission, how is this to be granted? By a trusted person, by algorithm, or some other manner? Even more important is the question of who gets to write history. As I explained earlier, the possibility for manipulation along this dimension is immense. How to guard against to attempts to fabricate history?

Historically, in "small" communities (think traditional hunter-gatherer societies) this was accomplished more or less automatically. There are no strangers in a small, isolated village and communal monitoring is relatively easy. Brave deeds and foul acts alike, unobserved by some or even most, rapidly become common knowledge. This is true even of the small communities we belong to today (at work, in clubs, families, friends, etc.). Kocherlakota (1996) labels H(t-1) in this scenario "societal memory." I like to think of it as a virtual database of individual histories living in a distributed ledger of brains talking to each other in a P2P fashion, with additions to, and maintenance of, the shared history determined through a consensus mechanism. In this primitive DBMS, read and write privileges are largely open, the latter being subject to consensus. It all sounds so...blockchainy. 

While the primitive "blockchain" described above works well enough for small societies, it doesn't scale very well. Today, the traditional local networks of human brains have been augmented (and to some extent replaced) by a local and global networks of computers capable of communicating over the Internet. Achieving rapid consensus in a large heterogeneous community characterized by a vast flows of information is a rather daunting task. 

The "solution" to this problem has largely taken the form of proprietary databases with highly restricted read privileges managed by trusted entities who are delegated the write privilege. The double-spend problem for digital money, for example, is solved by delegating the record-keeping task to a bank, located within a banking system, performing debit/credit operations on a set of proprietary ledgers connected to a central hub (a clearing agency) typically managed by a central bank.


The Problem and the Blockchain Solution

Depending on your perspective, the system that has evolved to date is either (if you are born before 1980) a great improvement over how things operated when we were young, or (if you are born post 1980) a hopelessly tangled hodgepodge of networks that have trouble communicating with each other and are intolerably vulnerable to data breaches (see figure below, courtesy Ed Corno of IBM). 



The solution to this present state of affairs is presented as blockchain (defined earlier) which Ed depicts in the following way,
Well sure, this looks like a more organized way to keep the books and clear up communication channels, though the details concerning how consensus is achieved in this system remain a little hazy to me. As I mentioned earlier, I'm guessing that it'll be based on some reputation-based mechanism. But if this is the case, then why can't we depict the solution in the following way? 


That is, gather all the agents and agencies interacting with each other, forming them into a more organized community, but keep it based on the traditional client-server (or hub-and-spoke) model. In the center, we have the set of trusted "historians" (bankers, accountants, auditors, database managers, etc.) who are granted the write-privilege. Communications between members may be intermediated either by historians or take place in a P2P manner with the historians listening in. The database can consist of the chain-blocked sets of information (blockchain) H(t-1) described above. The parameters governing the read-privilege can be determined beforehand by the needs of the community. The database could be made completely open--which is equivalent to rendering it shared. And, of course, multiple copies of the database can be made as often as is deemed necessary. 

The point I'm making is, if we're ultimately going to depend on reputation-based consensus mechanisms, then we need no new innovation (like blockchain) to organize a database. While I'm no expert in the field of database management, it seems to me that standard protocols, for example, in the form of SQL Server 2017, can accommodate what is needed technologically and operationally (if anyone disagrees with me on this matter, please comment below).

Extending the Write Privilege: Game-Based Consensus


As explained above, extending the read-privilege is not a problem technologically. We are all free to publish our diaries online, creating a shared-distributed ledger of our innermost thoughts. Extending the write-privilege to unknown or untrusted parties, however, is an entirely different matter. Of course, this depends in part on the nature of the information to be stored. Wikipedia seems to work tolerably well. But its hard to use Wikipedia as currency. This is not the case with personal action histories. You don't want other people writing your diary! 


Well, fine, so you don't trust "the Man." What then? One alternative is to game the write privilege. The idea is to replace the trusted historian with a set of delegates drawn from the community (a set potentially consisting of the entire community). Next, have these delegates play a validation/consensus game designed in such a way that the equilibrium (say, Nash or some other solution concept) strategy profile chosen by each delegate at every date t = 1,2,3,... entails: (1) No tampering with recorded history H(t-1); and (2) Only true blocks E(t) are validated and appended to the ledger H(t-1).

What we have done here is replace one type of faith for another. Instead of having faith in mechanisms that rely on personal reputations, we must now trust that the mechanism governing non-cooperative play in the validation/consensus game will deliver a unique equilibrium outcome with the desired properties. I think this is in part what people mean when I hear them say "trust the math." 

Well, trusting the math is one thing. Trusting in the outcome of a non-cooperative game is quite another matter. The relevant field in economics is called mechanism design. I'm not going to get into details here, but suffice it to say, it's not so straightforward designing mechanisms with sure-fire good properties. Ironically, mechanisms like Bitcoin will have to build up trust the old-fashioned way--through positive user experience (much the same way most of us trust our vehicles to function, even if we have little idea how an internal combustion engine works). 

Of course, the same holds true for games based on reputational mechanisms. The difference is, I think, that non-cooperative consensus games are intrinsically more costly to operate than their reputational counterparts. The proof-of-work game played by Bitcoin miners, for example, is made intentionally costly (to prevent DDoS attacks) even though validating the relevant transaction information is virtually costless if left in the hands of a trusted validator. And if a lack of transparency is the problem for trusted systems, this conceptually separate issue can be dealt with by extending the read-privilege communally.  


Having said this, I think that depending on the circumstances and the application, the cost associated with a game-based consensus mechanism may be worth incurring. I think we have to remain agnostic on this matter for now and see how future developments unfold. 

Blockchain: Powering DAOs
  
If Blockchain (with non-cooperative consensus) has a comparative advantage, where might it be? To me, the clear application is in supporting Decentralized Autonomous Organizations (DAOs).  A DAO is basically a set of rules written as a computer program. Because it possesses no central authority or node, it can offer tailor-made "legal" systems unencumbered by prevailing laws and regulations, at least, insofar as transactions are limited to virtual fulfillments (e.g., debit/credit operations on a ledger). 

Bitcoin is an example of a DAO, though the intermediaries that are associated with Bitcoin obviously are not. Ethereum is a platform that permits the construction of more sophisticated DAOs via the use of smart contracts. The comparative advantages of DAOs are that they permit: (1) a higher degree of anonymity;  (2) permissionless access and use; and (3) commitment to contractual terms (smart contracts). 

It's not immediately clear to me what value these comparative advantages have for registered businesses. There may be a role for legally compliant smart contracts (a tricky business for international transactions). But perhaps the potential is much more than I can presently imagine. Time will tell.

Link to my past posts on the subject of Bitcoin and Blockchain.