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My first post described a few anecdotes about what a warm person Bob Lucas was, and such a great colleague. Here I describe a little bit of his intellectual influence, in a form that is I hope accessible to average people.The "rational expectations" revolution that brought down Keynesianism in the 1970s was really much larger than that. It was really the "general equilibrium" revolution. Macroeconomics until 1970 was sharply different from regular microeconomics. Economics is all about "models," complete toy economies that we construct via equations and in computer programs. You can't keep track of everything in even the most beautiful prose. Microeconomic models, and "general equilibrium" as that term was used at the time, wrote down how people behave — how they decide what to buy, how hard to work, whether to save, etc.. Then it similarly described how companies behave and how government behaves. Set this in motion and see where it all settles down; what prices and quantities result. But for macroeconomic issues, this approach was sterile. I took a lot of general equilibrium classes as a PhD student — Berkeley, home of Gerard Debreu was strong in the field. But it was devoted to proving the existence of equilibrium with more and more general assumptions, and never got around to calculating that equilibrium and what it might say about recessions and government policies. Macroeconomics, exemplified by the ISLM tradition,  inhabited a different planet. One wrote down equations for quantities rather than people, for example that "consumption" depended on "income," and investment on interest rates. Most importantly, macroeconomics treated each year as a completely separate economy. Today's consumption depended on today's income, having nothing to do with whether people expected the future to look better or worse. Economists recognized this weakness, and a vast and now thankfully forgotten literature tried fruitlessly to find "micro foundations" for Keynesian economics. But building foundations under an existing castle doesn't work. The foundations want a different castle. Bob's "islands" paper is famous, yes, for a complete model of how unexpected money might move output in the short run and not just raise inflation. But you can do that with a half a page of simple math, and Bob's paper is hard to read. It's deeper contribution, and the reason for that difficulty, is that Bob wrote out a complete "general equilibrium" model. People, companies and government each follow described rules of behavior. Those rules are derived as being the optimal thing for people and companies to do given their environment. And they are forward-looking. People think about how to make their whole lives as pleasant as possible, companies to maximize the present value of profits. Prices adjust so supply = demand. Bob said, by example, that we should do macroeconomics by writing down general equilibrium models. General equilibrium had also been abandoned by the presumption that it only studies perfect economies. Macroeconomics is really about studying how things go wrong, how "frictions" in the economy, such as the "sticky" wages underlying Keynesian thinking, can produce undesirable and unnecessary recessions. But here too, Bob requires us to write down the frictions explicitly. In his model, people don't see the aggregate price level right away, and do the best they can with local information. That is the real influence of the paper  and Bob's real influence in the profession. (Current macroeconomic modeling reflects the fact that the Fed sets interest rates, and does not control the money supply.) You can see this influence in Tom Sargent's textbooks. The first textbook has an extensive treatment of Keynesian economics. It's about the most comprehensible treatment there is — but it is no insult to Tom to say that in that book you can see how Keynesian economics really doesn't hang together. Tom describes how, the minute he learned from Bob how to to general equilibrium, everything changed instantly. Rational expectations was, like any other advance, a group effort. But what made Bob the leader was that he showed the rest how to do general equilibrium. This is the heart of my characterization that Bob is the most important macroeconomist of the 20th century. Yes, Keynes and Friedman had more policy impact, and Friedman's advocacy of free markets in microeconomic affairs is the most consequential piece of 20th century economics. But within macroeconomics, there is before Lucas and after Lucas.  Everyone today does economics the Lucas way. Even the most new-Keynesian article follows the Lucas rules of how to do economics. Once you see models founded on complete descriptions of people, businesses, government, and frictions, you can see the gaping holes in standard ISLM models. This is some of his stinging critique, such as "after Keynesian macroeconomics." Sure, if people's income goes up they are likely to consume more, as the Keynesians posited. But interest rates, wages, and expectations of the future also affect consumption, which Keynesians leave out. "Cross equations restrictions" and "budget constraints" are missing. Now, the substantive prediction that monetary policy can only move the real economy via unexpected money supply growth did not bear out, and both subsequent real business cycles and new-Keynesianism brought persistent responses. But the how we do macroeconomics part is the enduring contribution. The paper still had enduring practical lessons. Lucas, together with Friedman and Phelps brought down the Phillips curve. This curve, relating inflation to unemployment, had been (and sadly, remains) at the center of macroeconomics. It is a statistical correlation, but like many correlations people got enthused with it and started reading it as stable relationship, and indeed a causal one. Raise inflation and you can have less unemployment. Raise unemployment in order to lower inflation. The Fed still thinks about it in that causal way. But Lucas, Friedman, and Phelps bring a basic theory to it, and thereby realize it is just a correlation, which will vanish if you push on it. Rich guys wear Rolexes. That doesn't mean that giving everyone a Rolex will have a huge "multiplier" effect and make us all rich. This is the essence of the "Lucas critique" which is a second big contribution that lay readers can easily comprehend. If you push on correlations they will vanish. Macroeconomics was dedicated to the idea that policy makers can fool people. Monetary policy might try to boost output in a recession with a surprise bit of money growth. That will wok once or twice. But like the boy who cried wolf, people will catch on, come to expect higher money growth in recessions and the trick won't work anymore. Bob showed here that all the "behavioral" relations of Keynesian models will fall apart if you exploit them for policy, or push on them, though they may well hold as robust correlations in the data. The "consumption function" is the next great example. Keynesians noticed that when income rises people consume more, so write a consumption function relating consumption to income. But, following Friedman's great work   on consumption, we know that correlation isn't always true in the data. The relation between consumption and income is different across countries (about one for one) than it is over time (less than one for one). And we understand that with Friedman's theory: People, trying to do their best over their whole lives don't follow mechanical rules. If they know income will fall in the future, they consume a lot less today, no matter what today's current income. Lucas showed that people who behave this sensible way will follow a Keynesian consumption function, given the properties of income overt the business cycle. You will see a Keynesian consumption function. Econometric estimates and tests will verify a Keynesian consumption function. Yet if you use the model to change policies, the consumption function will evaporate. This paper is devastating. Large scale Keynesian models had already been constructed, and used for forecasting and policy simulation. It's natural. The model says, given a set of policies (money supply, interest rates, taxes, spending) and other shocks, here is where the economy goes. Well, then, try different policies and find ones that lead to better outcomes. Bob shows the models are totally useless for that effort. If the policy changes, the model will change. Bob also showed that this was happening in real time. Supposedly stable parameters drifted around. (This one is also very simple mathematically. You can see the point instantly. Bob always uses the minimum math necessary. If other papers are harder, that's by necessity not bravado.) This devastation is sad in a way. Economics moved to analyzing policies in much simpler, more theoretically grounded, but less realistic models. Washington policy analysis sort of gave up. The big models lumber on, the Fred's FRBUS for example, but nobody takes the policy predictions that seriously. And they don't even forecast very well. For example, in the 2008 stimulus, the CEA was reduced to assuming a back of the envelope 1.5 multiplier, this 40 years after the first large scale policy models were constructed. Bob always praised the effort of the last generation of Keynesians to write explicit quantitative models, to fit them to data, and to make numerical predictions of various policies. He hoped to improve that effort. It didn't work out that way, but not by intention. This affair explains a lot of why economists flocked to the general equilibrium camp. Behavioral relationships, like what fraction of an extra dollar of income you consume, are not stable over time or as policy changes. But one hopes that preferences, — how impatient you are, how much you are willing to save more to get a better rate of return — and technology — how much a firm can produce with given capital and labor — do not change when policy changes. So, write models for policy evaluation at the level of preferences and technology, with people and companies at the base, not from behavioral relationships that are just correlations. Another deep change: Once you start thinking about macroeconomics as intertemporal economics — the economics that results from people who make decisions about how to consume over time, businesses make decisions about how to produce this year and next — and once you see that their expectations of what will happen next year, and what policies will be in place next year are crucial, you have to think of policy in terms of rules, and regimes, not isolated decisions. The Fed often asks economists for advice, "should we raise the funds rate?" Post Lucas macroeconomists answer that this isn't a well posed question. It's like saying "should we cry wolf?" The right question is, should we start to follow a rule, a regime, should we create an institution, that regularly and reliably raises interest rates in a situation like the current one? Decisions do not live in isolation. They create expectations and reputations. Needless to say, this fundamental reality has not soaked in to policy institutions. And that answer (which I have tried at Fed advisory meetings) leads to glazed eyes. John Taylor's rule has been making progress for 30 years trying to bridge that conceptual gap, with some success.  This was, and remains, extraordinarily contentious. 50 years later, Alan Blinder's book, supposedly about policy, is really one long snark about how terrible Lucas and his followers are, and how we should go back to the Keynesian models of the 1960s. Some of that contention comes back to basic philosophy.  The program applies standard microeconomics: derive people's behaviors as the best thing they can do given their circumstances. If people pick the best combination of apples and bananas when they shop, then also describe consumption today vs. tomorrow as the best they can do given interest rates. But a lot of economics doesn't like this "rational actor" assumption. It's not written in stone, but it has been extraordinarily successful. And it imposes a lot of discipline. There are a thousand arbitrary ways to be irrational.  Somehow though, a large set of economists are happy to write down that people pick fruit baskets optimally, but don't apply the same rationality to decisions over time, or in how they think about the future. But "rational expectations" is really just a humility condition. It says, don't write models in which the predictions of the model are different from the expectations in the model. If you do, if your model is right, people will read the model and catch on, and the model won't work anymore. Don't assume you economist (or Fed chair) are so much less behavioral than the people in your model. Don't base policy on an attempt to fool the little peasants over and over again. It does not say that people are big super rational calculating machines. It just says that they eventually catch on. Some of the contentiousness is also understandable by career concerns. Many people had said "we should do macro seriously like general equilibrium." But it isn't easy to do. Bob had to teach himself, and get the rest of us to learn, a range of new mathematical  and modeling tools to be able to write down interesting general equilibrium models. A 1970 Keynesian can live just knowing how to solve simple systems of linear equations, and run regressions.  To follow Bob and the rational expectations crowd, you had to learn linear time-series statistics, dynamic programming, and general equilibrium math. Bob once described how tough the year was that it took him to learn functional analysis and dynamic programming. The models themselves consisted of a mathematically hard set of constructions. The older generation either needed to completely retool, fade away, or fight the revolution. Some good summary words: Bob's economics uses"rational expectations," or at least forward-looking and model-consistent expectations. Economics becomes "intertemporal," not "static" (one year at a time). Economics is "stochastic" as well as "dynamic," we can treat uncertainty over time, not just economies in which everyone knows the future perfectly. It applies "general equilibrium" to macroeconomics. And I've just gotten to the beginning of the 1970s. When I got to Chicago in the 1980s, there was a feeling of "well, you just missed the party." But it wasn't true. The 1980s as well were a golden age. The early rational expectations work was done, and the following real business cycles were the rage in macro. But Bob's dynamic programming, general equilibrium tool kit was on a rampage all over dynamic economics. The money workshop was one creative use of dynamic programs and interetempboral tools after another one, ranging from taxes to Thai villages (Townsend). I'll mention two. Bob's consumption model is at the foundation of modern asset pricing. Bob parachuted in, made the seminal contribution, and then left finance for other pursuits. The issue at the time was how to generalize the capital asset pricing model. Economists understood that some stocks pay higher returns than others, and that they must do so to compensate for risk. The understood that the risk is, in general terms, that the stock falls in some sense of bad times. But how to measure "bad times?" The CAPM uses the market, other models use somewhat nebulous other portfolios. Bob showed us that at least in the purest theory, that stocks must pay higher average returns if they fall when consumption falls. (Breeden also constructed a consumption model in parallel, but without this "endowment economy" aspect of Bob's) This is the purest most general theory, and all the others are (useful) specializations. My asset pricing book follows. The genius here was to turn it all around. Finance had sensibly built up from portfolio theory, like supply and demand: Given returns, what stocks do you buy, and how much to you save vs. consume? Then, markets have to clear find the stock prices, and thus returns, given which people will buy exactly the amount that's for sale and consume what is produced. That's hard. (Technically, finding the vector of prices that clears markets is hard. Yes, N equations in N unknowns, but they're nonlinear and N is big.)  Bob instead imagined that consumption is fixed at each moment in time, like a desert island  in which so many coconuts fall each day and you can't store them or plant them. Then, you can just read prices from people's preferences. This gives the same answer as if the consumption you assume is fixed had derived from a complex production economy. You don't have to solve for prices that equate supply and demand. Brilliantly, though prices cause consumption to individual people, consumption causes prices in aggregate. This is part of Bob's contribution to the hard business of actually computing quantitative models in the stochastic dynamic general equilibrium tradition. Bob, with Nancy Stokey also took the new tools to the theory of taxation. (Bob Barro also was a founder of this effort in the late 1980s.) You can see the opportunity: we just learned how to handle dynamic (overt time, expectations of tomorrow matter to what you do today) stochastic (but there is uncertainty about what will happen tomorrow) economics (people make explicit optimizing decisions) for macro. How about taking that same approach to taxes? The field of dynamic public finance is born. Bob and Nancy, like Barro, show that it's a good idea for governments to borrow and then repay, so as to spread the pain of taxes evenly over time. But not always. When a big crisis comes, it is useful to execute a "state contingent default." The big tension of Lucas-Stokey (and now, all) dynamic public finance: You don't want any capital taxes for the incentive effects. If you tax capital, people invest less, and you just get less capital. But once people have invested, a capital tax grabs revenue for the government with no economic distortion. Well, that is, if you can persuade them you'll never do it again. (Do you see expectations, reputations, rules, regimes, wolves in how we think of policy?) Lucas and Stoney say, do it only very rarely to balance the disincentive of a bad reputation with the need to raise revenue in once a century calamities. Bob went on, of course, to be one of the founders of modern growth theory. I always felt he deserved a second Nobel for this work. He's absolutely right. Once you look at growth, it's hard to think about anything else. The average Indian lives on $2,000 per year. The average American, $60,000. That was $15,000 in 1950. Nothing else comes close. I only work on money and inflation because that's where I think I have answers. For us mortals, good research proceeds where you think you have an answer, not necessarily from working on Big Questions. Bob brilliantly put together basic facts and theory to arrive at the current breakthrough. Once you get out of the way, growth does not come from more capital, or even more efficiency. It comes from more and better ideas. I remember being awed by his first work for cutting through the morass and assembling the facts that only look salient in retrospect. A key one: Interest rates in poor countries are not much higher than they are in rich countries. Poor countries have lots of workers, but little capital. Why isn't the return on scarce capital enormous, with interest rates in the hundreds of percent, to attract more capital to poor countries? Well, you sort of know the answer, that capital is not productive in those countries.  Productivity is low, meaning those countries don't make use of better ideas on how to organize production.  Ideas too are produced by economics, but, as Paul Romer crystallized, they are fundamentally different from other goods. If I produce an idea, you can use it without hurting my use of it. Yes, you might drive down the monopoly profits I gain from my intellectual property. But if you use my Pizza recipe, that's not like using my car. I can still make Pizza, where if you use my car I can't go anywhere. Thus, the usual free market presumption that we will produce enough ideas is false. (Don't jump too quickly to advocate government subsides for ideas. You have to find the right ideas, and governments aren't necessarily good at subsidizing that search.) And the presumption that intellectual property should be preserved forever is also false. Once produced it is socially optimal for everyone to use it. I won't go on. It's enough to say that Bob was as central to the creation of idea-based growth theory, which dominates today, as he was to general equilibrium macro, which also dominates today.Bob is an underrated empiricist. Bob's work on the size distribution of firms (great tweet summary by Luis Garicano) similarly starts from basic facts of the size distribution of firms and the lack of relationship between size and growth rates. It's interesting how we can go on for years with detailed econometric estimates of models that don't get basic facts right. I loved Bob's paper on money demand for the Carnegie Rochester conference series. An immense literature had tried to estimate money demand functions with dynamics, and was pretty confusing. It made a basic mistake, by looking at first differences rather than levels and thereby isolating the noise and drowning out the signal. Bob made a few plots, basically rediscovered cointegration all on his own, and made sense of it all. And don't forget the classic international comparison of inflation-output relations. Countries with volatile inflation have less Phillips curve tradeoff, just as his islands model featuring confusion between relative prices and the price level predicts. One last note to young scholars. There is a tendency today to value people by the number of papers they produce, and how quickly they rise through the ranks. Read Bob's CV. He wrote about one paper a year, starting quite late in life. But, as Aesop said, they were lions. In his Nobel prize speech, Bob also passed on that he and his Nobel-winning generation at Chicago always felt they were in some backwater, where the high prestige stuff was going on at Harvard and MIT. You never know when it might be a golden age. And the AER rejected his islands paper (as well as Akerlof's lemons). If you know it's good, revise and try again. I will miss his brilliant papers as much as his generous personality. Update: See Ivan Werning's excellent "Lucas Miracles" for an appreciation by a real theorist. 

My former colleague Howard Wall asked me to join Lawrence White yesterday evening to discuss the role and future of cryptocurrencies at an event hosted by the Hammond Institute for Free Enterprise. It was a great honor to share the stage with Larry. I've been thinking about cryptocurrencies for a long time; many of my writings and talks on the subject can be found here. My thoughts on the subject are evolving as I learn more about the phenomenon. For what it's worth, I thought I'd share my opening remarks with interested readers below. As usual, any feedback is welcome. The Role and Future of CryptocurrenciesA money and
payments system is about managing databases containing the money accounts of
individuals and organizations. Any database management system must necessarily
define read and write protocols. Read privileges specify who can view what on
the database. Write privileges specify who gets to write what to the database.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 

This post is from a set of comments I gave at the NBER Asset Pricing conference in early November at Stanford.  Conference agenda here. My full slides here. There was video, but sadly I took too long to write this post and the NBER took down the conference video. I was asked to comment on "Downward Nominal Rigidities and Bond Premia" by François Gourio  and Phuong Ngo. It's a very nice clean paper, so all I could think to do as discussant is praise it, then move on to bigger issues. These are really comments about whole literatures, not about one paper. One can admire the play but complain about the game. The paper implements a version of Bob Lucas' 1973 "International evidence" observation. Prices are less sticky in high inflation countries. The Phillips curve more vertical. Output is less affected by inflation. The Calvo fairy visits every night in Argentina. To Lucas, high inflation comes with variable inflation, so people understand that price changes are mostly aggregate not relative prices, and ignore them. Gourio and Ngo use a new-Keynesian model with downwardly sticky prices and wages to express the idea.  When inflation is low, we're more often in the more-sticky regime. They use this idea in a model of bond risk premia. Times of low inflation lead to more correlation of inflation and output, and so a different correlation of nominal bond returns with the discount factor, and a different term premium. I made two points, first about bond premiums and second about new-Keynesian models. Only the latter for this post. This paper, like hundreds before it, adds a few ingredients on top of a standard textbook new-Keynesian model. But that textbook model has deep structural problems. There are known ways to fix the problems. Yet we continually build on the standard model, rather than incorporate known ways or find new ways to fix its underlying problems. Problem 1: The sign is "wrong" or at least unconventional.The basic sign is wrong -- or at least counter to the standard belief of all policy makers. In the model, higher interest rates cause inflation to jump down immediately, and then rise over time. Everyone at the Fed uniformly believes that higher interest rates cause inflation to go nowhere immediately, and then gently decline over time, with "long and variable lags." Larry Ball pointed this out 30 years ago. The behavior comes straight from the forward-looking Phillips curve. Lower output goes with lower inflation, relative to future inflation. I.e. inflation rising over time. To be clear, maybe the model is right and the beliefs are wrong. It's amazing that so much modeling and empirical work has gone in to massaging theory and data to conform to Milton Friedman's 1968 proclamation of how monetary policy works. The "long and variable lags" in particular are a trouble to modern economics. If you know prices are going up tomorrow, you raise prices today. But that's for another day. This model does not behave the way most people think the economy behaves, so if you're going to use it, at least that needs a major asterisk.  Well, we know how to fix this. You can see that sneaking lagged inflation into the Phillips curve is going to be a big part of that.  Christiano Eichenbaum and Evans, 20  years ago, produced a widely cited model that "fixes" this problem. It has a lot of ingredients. Most of all, it assumes that wages and prices are indexed. Firms and workers that don't get tapped by the Calvo fairy to change their price or wage nonetheless raise by observed inflation. This gives a Phillips curve with lagged inflation. Moreover, in preferences, investment, and this Phillips curve, CEE modify the model to put growth rates in place of levels. (More review in a three part series on new-Keynesian models here.) The result: If the funds rate goes down (right panel) unexpectedly, inflation goes down just a bit but then turns around and goes up a year later. (Several other authors get to the same place by abandoning rational expectations. But that has its own problems, and it's going to be hard to incorporate asset pricing that way. Much more in Expectations and the Neutrality of Interest Rates) Great. But notice that neither Gourio and Pho nor pretty much anyone else builds on this model. We cite it, but don't use it. Instead, 20 more years of NK theorizing studies different extensions of the basic model, that don't solve the central conundrum. Problem 2: Fed induced explosionsThe standard new-Keynesian model says that if the Fed holds interest rates constant, inflation is stable -- will go away on its own -- but indeterminate. There are multiple equilibria. The standard new-Keynesian model thus assumes that the Fed deliberately destabilizes the economy. If inflation comes out more than the Fed wishes, the Fed will lead the economy to hyperinflation or hyper deflation. Under that threat, people jump to the inflation that the Fed wishes to see. But the Fed does no such thing.  Central bankers resolutely state that their job is to stabilize the economy, to bring inflation back from wherever it might go. Despite thousands of papers with new-Keynesian equations written at central banks, if anyone were ever to honestly describe those equations in the introduction, "we assume that the central bank is committed to respond to inflation by hyperinflation or deflation in order to select from multiple equilibria" they would be laughed out of a job. This has been clear, I think, since 2000 or so. I figured it out by reading Bob King's "Language and Limits." My  "Determinacy and Identification" in the JPE 2011 was all about this. We've also known at least one way to fix it, as shown: fiscal theory. OK, I'm a broken record on this topic. Instead, we go on with the same model and its underlying widely counterfactual assumption about policy. Problem 3: The fit is terribleA model consists of a set of equations, with the thing you want to determine (say, inflation) on the left, the economic causes described by the model on the right, plus "shocks," which are things your model can't capture. In the explanation part, there are parameters (\(\sigma, \ \beta, \ \kappa, \ \phi\)), that control how much the things on the right affect the things on the left. The fit of new-Keynesian models is usually terrible. In accounting for economic variables (\(x_t,\) \(\pi_t, \) \(i_t \) here), the error terms (\(\varepsilon\)) are much larger than the model's economic mechanisms (the \(x,\) \(\pi\) on the right hand side). Forecasts -- predicting  \(\pi\), \(x\) ahead of time -- is worse. For example, where did inflation come from and why did it go away? Expected inflation hasn't moved much, and the economy just plugged along. Most of the rise and fall of inflation came from inflation shocks.  Related, the fit of the models is about the same amount of terrible for different values of the parameters. That means the parameters are "poorly identified" if identified at all. That means that the mechanisms of the model -- say, how much higher interest rates lower output, and then how much lower output affects inflation -- are weak, and poorly understood. In part this isn't often noticed because we got out of the habit of evaluating models by fit in the 1980s. Most models are evaluated, as I showed above for CEE by matching select "identified" impulse response functions. But as those response functions also explain small variances of output and inflation, it's possible to match response functions well, yet still fit the data badly, i.e. fit the data only by adding big shocks to every equation. I don't know of good fixes here. Old fashioned ISLM models had similar problems (See Sims 1980). But it is a fact that we just ignore and go on. The Phillips curve is a central problem, which has only gotten worse lately. Unemployment was high and declining throughout the 2010s, with stable inflation. Inflation came with high unemployment in 2021. And inflation fell with no high real interest rates, no unemployment, and strong growth in 2022-2023. But what will replace it? So where are we?Macro is surprisingly un-cumulative. We start with a textbook model. People find some shortcomings and suggest a fix. But rather than incorporate that fix, the next paper adds a different fix to the same textbook  model. One would think we would follow the path on the right. We don't. We follow the path on the left. This is common in economics. The real business cycle literature followed much the same path. After the King Plosser Rebelo stochastic growth model became the standard, people spent a decade with one extension after another, each well motivated to fix a stylized fact. But by and large the next paper didn't build on the last one, but instead offered a new variation on the KPR model. Posteriors follow priors according to Bayes' rule, of course. So another way of putting the observation, people seem to put a pretty high prior on the original model, but don't trust the variations at all. I sin too. In Fiscal Theory of the Price Level  I married fiscal theory with the new-Keynsian IS and Phillips curve, exactly as above, despite problems #1 and #3. Well, it makes a lot of sense to change one ingredient at a time to see how a new theory works. I'm unhappy with the result, but I haven't been able to move on to a new and better textbook model, which is what has occasioned several of these related posts.  Wę need a digestion. Which of the new ingredients are reliable, robust, and belong as part of the new "textbook" model? That's not easy. Reliable and robust is very hard to find, and to persuade people. There are so many to choose from -- CEE's smorgasbord, capital, financial frictions, heterogeneous agents, different expectation formation stories, different pricing frictions,  and so on. What's the minimal easy set of these to use? Part of the trouble lies in how publishing works. It's nearly impossible to publish a paper that removes old ingredients, that digests the model down to a new textbook version. The rewards are to publishing papers that add new ingredients. Even if, like CEE, everyone cites them but doesn't use them. I've asked many economists why they build on a model with so many known problems, and why they don't include known fixes. (Not just fiscal theory!) The answer is usually, yes, I know about all these problems, but nobody will bother me about them since every other paper makes the same assumptions, and I need to get papers published.     I went on a bit of a tear here as I referee lots of great papers like this one. Every part of the paper is great, except it builds on a model with big flaws we've known about for 30 years. It feels unfair to complain about the underlying model, since the journal has published and will publish a hundred other papers. But at what point can we, collectively, scream "Stop!" The new-Keynesian model has been the standard model for an astonishing 30 years. None of ISLM, monetarism, rational expectations, or real business cycles lasted that long.  It's even more amazing that it is so unchanged in all this time. It is definitely time for a better textbook version of the model! Maybe this is a plea for Woodford, Gali or one of the other NK textbook authors, which much better command of all the variations than I have, to bless us a new textbook model. Or, perhaps it's time for something totally new. That's not fiscal theory per se. Fiscal theory is an ingredient, not a model.  You can marry it to new-Keynesian models, as I, Leeper, Sims, and others have done. But you can also marry it to old ISLM or anything else you want. Given the above, maybe there isn't an existing modification but a new start. I don't  know what that is. (My comments also have some similar comments about term premiums and how to think about them, but this post is long enough.) Update:Twitter correspondents Stéphane Surprenant and Tom Holden point me to The Transmission of Monetary Policy Shocks by Silvia Miranda-Agrippino Giovanni Ricco in the AEJ Macro, and Inflation, output and markup dynamics with purely forward-looking wage and price setters by Louis Phaneuf, Eric Sims, and Jean Gardy Victor in the European Economic Review. The former is a VAR with high frequency measurement of the monetary policy shock. And.. Source: Miranda-Agrippino and RiccoThe price level as well as the inflation rate can jump down immediately when the interest rate rises! (I think the graph plots the level of CPI, not growth rate.) That's even stronger than the baseline model in which the price level, being sticky, does not move, but the inflation rate jumps on the interest rate rise. The latter is a nice theoretical paper. It adds a lot of the CEE assumptions.  I overstated a great deal that others have not used these ingredients.  They are used in these "medium scale" models, just not in "textbook" models. However, it gets rid of indexed prices and wages with purely forward looking Phillips curves. It adds intermediate goods however. This makes prices changes work through the network of suppliers adding interesting dynamics, which has always struck me as a very important ingredient. And...Source: Phaneuf, Sims ,and VictorThe main estimate is the dark line. Here you see a model with the conventional response: inflation does not move on impact, and increases some time after the interest rate rise.  So, we can switch places! Estimates can replicate the conventional model, with an instant inflation response. Models can replicate the conventional estimates, with a slow inflation response. This one is much prettier than CEEs. 

I've been thinking a bit lately about theories of the business cycle (a lot of time for reflection in these days of COVID-19). At least, the way some of these theories have evolved over my lifetime and from the perspective of my own training in the field. From my (admittedly narrow) perspective as a researcher and advisor at a central bank, the journey beginning c. 1960 seems like it's taken the following steps: (1) Phillips Curve and some Natural Rate Hypothesis; (2) Real Business Cycle (RBC) theory; (3) New Keynesian theory. It seems like we might be ready to take the next step. I'll offer some thoughts on this at the end, for whatever they're worth. There's no easy way to summarize the state of macroeconomic thinking, of course. But it seems clear that, at any given time, some voices and ways of thinking are more dominant than others. By the time the 1960s rolled around, there seemed to be a consensus that monetary and fiscal policy should be used to stabilize the business cycle. The main issue, in this regard, revolved over which set of instruments was better suited for the job. (See, for example, this classic debate between Milton Friedman and Walter Heller). Central to macroeconomic thinking at the time was a concept called the Phillips Curve (PC). There is a subtle, but important, distinction to make here between the PC as a statistical correlation and the PC as a theory of that statistical relationship. In 1958, Phillips noticed an interesting pattern in the data: nominal wage growth seemed negatively correlated with the unemployment rate in the U.K. over the period 1913-48 (see diagram to the right). How to interpret this correlation? One theory is that when the unemployment rate is high, workers are easy to find and their bargaining position is weak, leading to small nominal wage gains. Conversely, when unemployment is low, available workers are scarce and their bargaining position is strong, leading to large nominal wage gains. Then, in 1960, Paul Samuelson and Robert Solow wrote their classic piece "Problem of Achieving and Maintaining a Stable Price-Level: Analytical Aspects of Anti-Inflation Policy." Then, as is the case still now, the authors lamented the lack of consensus on a theory of price inflation. Various cost-push and demand-pull hypotheses were reviewed, problems of identification noted, and calls for micro-data to help settle the issue were made. They also mentioned Phillips' article and noted how the same diagram for the U.S. looked like a shot-gun blast (little correlation, except for some sub-samples). Then they translated the Phillips curve using price inflation instead of wage inflation. No data was sacrificed in this exercise; their "theory" was summarized with the diagram to the left. I put "theory" in quotes in the passage above because the theory (explanation) was never clear to me. In particular, while I could see how an increase in the rate of unemployment might depress the level wage, I could not grasp how it could influence the rate of growth of wages for any prolonged period of time. This logical inconsistency was solved by the Phelps-Friedman natural rate hypothesis; see Farmer (2013) for a summary and critique. The TL;DR version of this hypothesis is that the PC is negatively sloped only in the short-run, but vertical in the long-run. So, while monetary policy (increasing the rate of inflation) could lower the unemployment rate below its natural rate, it could only do so temporarily. Eventually, the unemployment rate would move back to its natural rate at the higher rate of inflation. This hypothesis seemed to provide a compelling interpretation of the stagflation (high inflation and high unemployment) experienced in the 1970s. It also seemed to explain the success of Volcker's disinflation policy in the 1980s. Nevertheless, uneasiness in the state of the theory remained and a new (well, nothing is ever completely new) way of theorizing was on the horizon.By the time I got to grad school in the late 1980s, "real business cycle theory" was in vogue; see Charles Plosser's summary here and Bob King's lecture notes here. There was a lot going on with this program. A central thesis of RBC theory is that the phenomena of economic growth and business cycles are inextricably linked. This is, of course, is an old idea in economics going back at least to Dennis Robertson (see this review by Charles Goodhart) and explored extensively by a number of Austrian economists, like Joseph Schumpeter. The idea that "the business cycle" is to some extent a byproduct of the process of economic development is an attractive hypothesis. Economic growth is driven by technological innovation and diffusion, and perhaps regulatory policies. There is no a priori reason to expect these "real" processes to evolve in a "smooth" manner. In fact, these changes appear to arrive randomly and with little or no mean-reverting properties. It would truly be a marvel if the business cycle did not exist. The notion of "no mean-reverting properties" is important. It basically means that technology/policy shocks are largely permanent (or at least, highly persistent). If macroeconomic variables like the GDP inherit this property, then a "cycle"--the tendency for a variable to return to some long-run trend--does not even exist (and if you think you see it, it's only a figment of your imagination). For this reason, early proponents of RBC theory preferred the label "fluctuations" over "cycle." This view was supported by the fact that econometricians had a hard time rejecting the hypothesis that the real GDP followed a random walk (with drift). For example, here is Canadian GDP plotted against two realizations of a random walk with drift:This perspective fermented at a time when the cost of computing power was falling dramatically. This permitted economists to study models that were too complicated to analyze with conventional "pencil and paper" methods. Inspiration was provided by Lucas (1980), who wrote:Our task, as I see it…is to write a FORTRAN program
that will accept specific economic policy rules as 'input' and will generate as
'output' statistics describing the operating characteristics of time series we
care about, which are predicted to result from these policies."And so that's what people did. But what sort of statistics were model economies supposed to reproduce? Once again, it was Lucas (1976) who provided the needed guidance. The empirical business cycle regularities emphasized by Lucas were "co-movements" between different aggregate time-series. Employment, for example, is "pro-cyclical" (tends to move in the same direction as GDP) around "trend." These types of regularities can be captured by statistics like correlations. But these correlations (and standard deviations) only make sense for stationary time-series, and the data is mostly non-stationary. So, what to do? Transforming the data through first-differencing (i.e., looking at growth rates instead of levels) is one way to render (much of) the data stationary. Another approach was made popular by Prescott (1986), who advocated a method that most people employ: draw a smooth line through the data, label it "trend," and then examine the behavior of "deviations from trend." Something like this, It's important to note that Prescott viewed the trend line in the figure above as "statistical trend," not an "economic trend." To him, there was no deterministic trend, since the data was being generated by a random walk (so, the actual trend is stochastic). Nevertheless, drawing a smooth trend line was a useful way to render the data stationary. The idea was to apply the same de-trending procedure to actual data and simulated data, and then compare statistical properties across model and data.The point of mentioning this is that no one involved in this program was conditioned to interpret the economy as "overheating" or in "depression." Growing economies exhibited fluctuations--sometimes big and persistent fluctuations. The question was how much of these observed fluctuations could be attributed purely to the process of economic development (technological change), without reference to monetary or financial factors? I think it's fair to say that the answer turned out to be "not much, at least, not at business cycle frequencies." The important action seemed to occur at lower frequencies. Lucas (1988) once again provided the lead when he remarked "Once one starts to think about growth, it is hard to think about anything else." And so, the narrow RBC approach turned its attention to low-frequency dynamics; e.g., see my interview with Lee Ohanian here. Of course, many economists never bought into the idea that monetary and financial factors were unimportant for understanding business cycles. Allen and Gale, for example, schooled us on financial fragility; see here. But this branch of the literature never really made much headway in mainstream macro, at least, not before 2008. Financial crises were something that happened in history, or in other parts of the world. Instead, macroeconomists looked back on its roots in the 1960s and embedded a version of the PC into an RBC model to produce what is now known as the New Keynesian framework. Short-run money non-neutrality was achieved by assuming that nominal price-setting behavior was subject to frictions, rendering nominal prices "sticky." In this environment, shocks to the economy are not absorbed efficiently, at least, not in the absence of an appropriate monetary policy. And so, drawing inspiration from John Taylor and Michael Woodford, the framework added an interest rate policy rule now known as the Taylor rule. Today, the basic NK model consists of these three core elements:[1] An IS curve: Relates aggregate demand to the real interest rate and shocks.[2] An Phillips Curve: Relates the rate of inflation (around trend) to the output gap.[3] A Taylor Rule: Describes how interest rate policy reacts to output and inflation gaps.I have to be honest with you. I never took a liking to NK model. I'm more of an Old Keynesian, similar to Roger Farmer (we share the same supervisor, so perhaps this is no accident). In any case, the NK framework became (and continues to be) a core thought-organizing principle for central bank economists around the world. It has become a sort of lingua franca in academic macro circles. And if you don't know how to speak its language, you're going to have a hard time communicating with the orthodoxy. Of the three basic elements of the NK model, I think the NK Phillips Curve (which embeds the natural rate hypothesis) has resulted in the most mischief; at least, from the perspective of advising the conduct of monetary policy. The concept is firmly embedded in the minds of many macroeconomists and policymakers. Consider, for example, Greg Mankiw's recent piece "Yes, There is a Trade-Off Between Inflation and Unemployment."Today, most economists believe there is a trade-off between inflation and unemployment in the sense that actions taken by a central bank push these variables in opposite directions. As a corollary, they also believe there must be a minimum level of unemployment that the economy can sustain without inflation rising too high. But for various reasons, that level fluctuates and is difficult to determine. The Fed's job is to balance the competing risks of rising unemployment and rising inflation. Striking just the right balance is never easy. The first step, however, is to recognize that the Phillips curve is always out there lurking.The Phillips curve is always lurking. The message for a central banker is "sure, inflation and unemployment may be low for now, but if we keep monetary policy where it is and permit the unemployment rate to fall further, we will risk higher inflation in the future." I'm not sure if economists who write in this manner are aware that they're making it sound like workers are somehow responsible for inflation. Central banker to workers: "I'm sorry, but we need to keep some of you unemployed...it's the inflation, you see." There is evidence that this line of thinking influenced the FOMC in 2015 in its decision to "lift off" and return the policy rate to some historically normal level; see my post here explaining the pros and cons in the lift-off debate. By the start of 2014, there was considerable pressure on the Fed to begin "normalizing" its policy rate. By mid 2014, the expectation of "lift off" likely contributed to significant USD appreciation and the economic weakness that followed. If I recall correctly, Vice Chair Stan Fischer started off the year by announcing that four rate hikes for 2015 were in order (as it turned out, the Fed only raised rates once--in December). To some observers, this all seemed very strange. After all, the unemployment rate was still above its estimated "natural" rate (5%) and inflation continued to undershoot its 2% target. What was going on?What was going on was the Phillips curve. Here is Chair Yellen at the March 17-18, 2015 FOMC meeting (transcript available here):If we adopt alternative B, one criterion for an initial tightening is that we need to be reasonably confident that inflation will move back to 2 percent over the medium term. For the remainder of this year, my guess is that it will be hard to point to data demonstrating that inflation is actually moving up toward our objective. Measured on a 12-month basis, both core and headline inflation will very likely be running below 1½ percent all year. That means that if we decide to start tightening later this year, a development that I think is likely, we will have to justify our inflation forecasts using indirect evidence, historical experience, and economic theory.The argument from history and economic theory seems straightforward. Experience here and abroad teaches us that, as resource utilization tightens, eventually inflation will begin to rise. To me, this seems like a simple matter of demand and supply. So the more labor and product markets tighten, the more confident I'll become in the inflation outlook. Because of the lags in monetary policy, the current high degree of monetary accommodation, and the speed at which the unemployment rate is coming down, it would, to my mind, be imprudent to wait until inflation is much closer to 2 percent to begin to normalize policy. I consider this a strong argument for an initial tightening with inflation still at low levels, and it's one that I plan to make. But I also recognize and am concerned that, at least in recent years, the empirical relationship between slack and inflation has been quite weak.Now, I don't want to make too much of this particular episode. Personally, I don't think it had a major impact on the recovery dynamic. But I do think it had an impact; in particular, the pace of improvement in labor market conditions temporarily slowed. It was an unforced error (as I think other members of the Committee sensed as well).  I think the lift-off episode has contributed to a general re-thinking of the Phillips curve and the natural rate hypothesis. The notion of an economy operating at "excess capacity" has always seemed a bit strange to me, let alone the idea that excess capacity as a cause of inflation (as opposed to a force operating on the price-level). Perhaps it is time to re-visit Milton Friedman's "plucking model."  Instead of drawing a smooth line through the center of a time-series, Friedman drew a line that defined a ceiling (a capacity constraint). Shocks to the economy manifest themselves as "downward plucks" (as if plucking on an elastic band). The plucking model is consistent with the observed cyclical asymmetry in unemployment rate fluctuations. And labor market search models are a natural way to model that asymmetry. In case you're interested, I develop a super-simple (and dare I say, elegant) search model here to demonstrate (and test) the idea: Evidence and Theory on the Cyclical Asymmetry in Unemployment Rate Fluctuations, CJE 1997). See also my blog post here as well as some recent work by Ferraro (RED, 2018) and Dupraz, Nakamura and Steinsson (2019). I like where this is going! One attractive feature of search models, in my view, is that they model relationship formation. Relationships provide a very different mechanism for coordinating economic activity relative to the canonical economic view of anonymous spot exchange in centralized markets. In a relationship, spot prices do not matter as much as the dynamic path of these prices (and other important aspects) over the course of a relationship (see my critique of the sticky price hypothesis here). The observation that retailers, in the early days of C-19, voluntarily rationed goods instead of raising prices makes little sense in anonymous spot exchange, but makes perfect sense for a merchant concerned with maintaining a good relationship with his or her customers. And merchant-supplier relationships can handle shortages without price signals (we're out of toilet paper--please send more!). In financial markets too, the amount of time that is spent forming and maintaining credit relationships is hugely underappreciated in economic modeling. Search theory turns out to be useful for interpreting the way money and bond markets work too. These markets are not like the centralized markets we see modeled in textbooks--they operate as decentralized over-the-counter (OTC) markets, where relationships are key. One reason why economies sometimes take so long to recover after a shock is because the shock has destroyed an existing set of relationships. And it takes time to rebuild relationship capital.Notions of "overheating" in this context probably do not apply to labor market variables, although there is still the possibility of an overaccumulation of certain types of physical capital in a boom (what the Austrians label "malinvestment"). Any "overheating" is likely to manifest itself primarily in asset prices. And sudden crashes in asset prices (whether driven by fundamentals or not), can have significant consequences on real economic activity if asset valuations are used to support lines of credit. Finally, we need a good theory of inflation. The NKPC theory of inflation is not, in my view, a completely satisfactory theory in this regard. To begin, it simply assumes that the central bank can target a long-run rate of inflation (implicitly, with the support of a Ricardian fiscal policy, though this is rarely, if ever, mentioned). At best, it is a theory of how inflation can temporarily depart from its long-run target and how interest rate policy can be used to influence transition dynamics. But the really interesting questions, in my view, have to do with monetary and fiscal policy coordination and what this entails for the ability of an "independent" central bank even to determine the long-run rate of inflation (Sargent and Wallace, 1981).  I know what I've described only scratches the surface of this amazingly deep and broad field. Most of you have no doubt lived through your own process of discovery and contemplation in the world of macroeconomic theorizing. Feel free to share your thoughts below. 

I've been reading a lot of macro lately. In part, I'm just catching up from a few years of book writing. In part,  I want to understand inflation dynamics, the quest set forth in "expectations and the neutrality of interest rates," and an  obvious next step in the fiscal theory program. Perhaps blog readers might find interesting some summaries of recent papers, when there is a great idea that can be summarized without a huge amount of math. So, I start a series on cool papers I'm reading. Today: "Tail risk in production networks" by Ian Dew-Becker, a beautiful paper. A "production network" approach recognizes that each firm buys from others, and models this interconnection. It's a hot topic for lots of reasons, below.  I'm interested because prices cascading through production networks might induce a better model of inflation dynamics. (This post uses Mathjax equations. If you're seeing garbage like [\alpha = \beta] then come back to the source  here.) To Ian's paper: Each firm uses other firms' outputs as inputs. Now, hit the economy with a vector of productivity shocks. Some firms get more productive, some get less productive. The more productive ones will expand and lower prices, but that changes everyone's input prices too. Where does it all settle down? This is the fun question of network economics. Ian's central idea: The problem simplifies a lot for large shocks. Usually when problems are complicated we look at first or second order approximations, i.e. for small shocks, obtaining linear or quadratic ("simple") approximations. On the x axis, take a vector of productivity shocks for each firm, and scale it up or down. The x axis represents this overall scale. The y axis is GDP. The right hand graph is Ian's point: for large shocks, log GDP becomes linear in log productivity -- really simple. Why? Because for large enough shocks, all the networky stuff disappears. Each firm's output moves up or down depending only on one critical input. To see this, we have to dig deeper to complements vs. substitutes. Suppose the price of an input goes up 10%. The firm tries to use less of this input. If the best it can do is to cut use 5%, then the firm ends up paying 5% more overall for this input, the "expenditure share" of this input rises. That is the case of "complements." But if the firm can cut use of the input 15%, then it pays 5% less overall for the input, even though the price went up. That is the case of "substitutes." This is the key concept for the whole question: when an input's price goes up, does its share of overall expenditure go up (complements) or down (substitutes)? Suppose inputs are complements. Again, this vector of technology shocks hits the economy. As the size of the shock gets bigger, the expenditure of each firm, and thus the price it charges for its output, becomes more and more dominated by the one input whose price grows the most. In that sense, all the networkiness simplifies enormously. Each firm is only "connected" to one other firm. Turn the shock around. Each firm that was getting a productivity boost now gets a productivity reduction. Each price that was going up now goes down. Again, in the large shock limit, our firm's price becomes dominated by the price of its most expensive input. But it's a different input.  So, naturally, the economy's response to this technology shock is linear, but with a different slope in one direction vs. the other. Suppose instead that inputs are substitutes. Now, as prices change, the firm expands more and more its use of the cheapest input, and its costs and price become dominated by that input instead. Again, the network collapsed to one link.  Ian: "negative productivity shocks propagate downstream through parts of the production process that are complementary (\(\sigma_i < 1\)), while positive productivity shocks propagate through parts that are substitutable (\(\sigma_i > 1\)). ...every sector's behavior ends up driven by a single one of its inputs....there is a tail network, which depends on \(\theta\) and in which each sector has just a single upstream link."Equations: Each firm's production function is (somewhat simplifying Ian's (1)) \[Y_i = Z_i L_i^{1-\alpha} \left( \sum_j A_{ij}^{1/\sigma} X_{ij}^{(\sigma-1)/\sigma} \right)^{\alpha \sigma/(\sigma-1)}.\]Here \(Y_i\) is output, \(Z_i\) is productivity, \(L_i\) is labor input, \(X_{ij}\) is how much good j firm i  uses as an input, and \(A_{ij}\) captures how important each input is in production. \(\sigma>1\) are substitutes, \(\sigma<1\) are complements. Firms are competitive, so price equals marginal cost, and each firm's price is \[ p_i = -z_i + \frac{\alpha}{1-\sigma}\log\left(\sum_j A_{ij}e^{(1-\sigma)p_j}\right).\; \; \; (1)\]Small letters are logs of big letters.  Each price depends on the prices of all the inputs, plus the firm's own productivity.  Log GDP, plotted in the above figure is \[gdp = -\beta'p\] where \(p\) is the vector of prices and \(\beta\) is a vector of how important each good is to the consumer. In the case \(\sigma=1\) (1)  reduces to a linear formula. We can easily solve for prices and then gdp as a function of the technology shocks: \[p_i = - z_i + \sum_j A_{ij} p_j\] and hence \[p=-(I-\alpha A)^{-1}z,\]where the letters represent vectors and matrices across \(i\) and \(j\). This expression shows some of the point of networks, that the pattern of prices and output reflects the whole network of production, not just individual firm productivity. But with \(\sigma \neq 1\) (1) is nonlinear without a known closed form solution. Hence approximations. You can see Ian's central point directly from (1). Take the \(\sigma<1\) case, complements. Parameterize the size of the technology shocks by a fixed vector \(\theta = [\theta_1, \ \theta_2, \ ...\theta_i,...]\) times a scalar \(t>0\), so that \(z_i=\theta_i \times t\). Then let \(t\) grow keeping the pattern of shocks \(\theta\) the same. Now, as the \(\{p_i\}\) get larger in absolute value, the term with the greatest \(p_i\) has the greatest value of \( e^{(1-\sigma)p_j} \). So, for large technology shocks \(z\), only that largest term matters, the log and e cancel, and \[p_i \approx -z_i + \alpha \max_{j} p_j.\] This is linear, so we can also write prices as a pattern \(\phi\) times the scale \(t\), in the large-t limit \(p_i = \phi_i t\),  and  \[\phi_i =  -\theta_i + \alpha \max_{j} \phi_j.\;\;\; (2)\] With substitutes, \(\sigma<1\), the firm's costs, and so its price, will be driven by the smallest (most negative) upstream price, in the same way. \[\phi_i \approx -\theta_i + \alpha \min_{j} \phi_j.\] To express gdp scaling with \(t\), write \(gdp=\lambda t\), or when you want to emphasize the dependence on the vector of technology shocks, \(\lambda(\theta)\). Then we find gdp by \(\lambda =-\beta'\phi\). In this big price limit, the \(A_{ij}\) contribute a constant term, which also washes out. Thus the actual "network" coefficients stop mattering at all so long as they are not zero -- the max and min are taken over all non-zero inputs. Ian: ...the limits for prices, do not depend on the exact values of any \(\sigma_i\) or \(A_{i,j}.\) All that matters is whether the elasticities are above or below 1 and whether the production weights are greater than zero. In the example in Figure 2, changing the exact values of the production parameters (away from \(\sigma_i = 1\) or \(A_{i,j} = 0\)) changes...the levels of the asymptotes, and it can change the curvature of GDP with respect to productivity, but the slopes of the asymptotes are unaffected....when thinking about the supply-chain risks associated with large shocks, what is important is not how large a given supplier is on average, but rather how many sectors it supplies...For a full solution, look at the (more interesting) case of complements, and suppose every firm uses a little bit of every other firm's output, so all the \(A_{ij}>0\). The largest input  price in (2) is the same for each firm \(i\), and you can quickly see then that the biggest price will be the smallest technology shock. Now we can solve the model for prices and GDP as a function of technology shocks: \[\phi_i \approx -\theta_i - \frac{\alpha}{1-\alpha} \theta_{\min},\] \[\lambda \approx  \beta'\theta + \frac{\alpha}{1-\alpha}\theta_{\min}.\] We have solved the large-shock approximation for prices and GDP as a function of technology shocks. (This is Ian's example 1.) The graph is concave when inputs are complements, and convex when they are substitutes. Let's do complements. We do the graph to the left of the kink by changing the sign of \(\theta\).  If the identity of \(\theta_{\min}\) did not change, \(\lambda(-\theta)=-\lambda(\theta)\) and the graph would be linear; it would go down on the left of the kink by the same amount it goes up on the right of the kink. But now a different \(j\) has the largest price and the worst technology shock. Since this must be a worse technology shock than the one driving the previous case, GDP is lower and the graph is concave.  \[-\lambda(-\theta) = \beta'\theta + \frac{\alpha}{1-\alpha}\theta_{\max} \ge\beta'\theta + \frac{\alpha}{1-\alpha}\theta_{\min} = \lambda(\theta).\] Therefore  \(\lambda(-\theta)\le-\lambda(\theta),\) the left side falls by more than the right side rises. Does all of this matter? Well, surely more for questions when there might be a big shock, such as the big shocks we saw in a pandemic, or big shocks we might see in a war. One of the big questions that network theory asks is, how much does GDP change if there is a technology shock in a particular industry? The \(\sigma=1\) case in which expenditure shares are constant gives a standard and fairly reassuring result: the effect on GDP of a shock in industry i is given by the ratio of i's output to total GDP. ("Hulten's theorem.") Industries that are small relative to GDP don't affect GDP that much if they get into trouble. You can intuit that constant expenditure shares are important for this result. If an industry has a negative technology shock, raises its prices, and others can't reduce use of its inputs, then its share of expenditure will rise, and it will all of a sudden be important to GDP. Continuing our example, if one firm has a negative technology shock, then it is the minimum technology, and [(d gdp/dz_i = \beta_i + \frac{\alpha}{1-\alpha}.\] For small firms (industries) the latter term is likely to be the most important.  All the A and \(\sigma\) have disappeared, and basically the whole economy is driven by this one unlucky industry and labor.   Ian: ...what determines tail risk is not whether there is granularity on average, but whether there can ever be granularity – whether a single sector can become pivotal if shocks are large enough.For example, take electricity and restaurants. In normal times, those sectors are of similar size, which in a linear approximation would imply that they have similar effects on GDP. But one lesson of Covid was that shutting down restaurants is not catastrophic for GDP, [Consumer spending on food services and accommodations fell by 40 percent, or $403 billion between 2019Q4 and 2020Q2. Spending at movie theaters fell by 99 percent.] whereas one might expect that a significant reduction in available electricity would have strongly negative effects – and that those effects would be convex in the size of the decline in available power. Electricity is systemically important not because it is important in good times, but because it would be important in bad times. Ben Moll turned out to be right and Germany was able to substitute away from Russian Gas a lot more than people had thought, but even that proves the rule: if it is hard to substitute away from even a small input, then large shocks to that input imply larger expenditure shares and larger impacts on the economy than its small output in normal times would suggest.There is an enormous amount more in the paper and voluminous appendices, but this is enough for a blog review. ****Now, a few limitations, or really thoughts on where we go next. (No more in this paper, please, Ian!) Ian does a nice illustrative computation of the sensitivity to large shocks:Ian assumes \(\sigma>1\), so the main ingredients are how many downstream firms use your products and a bit their labor shares. No surprise, trucks, and energy have big tail impacts. But so do lawyers and insurance. Can we really not do without lawyers? Here I hope the next step looks hard at substitutes vs. complements.That raises a bunch of issues. Substitutes vs. complements surely depends on time horizon and size of shocks. It might be easy to use a little less water or electricity initially, but then really hard to reduce more than, say, 80%. It's usually easier to substitute in the long run than the short run. The analysis in this literature is "static," meaning it describes the economy when everything has settled down.  The responses -- you charge more, I use less, I charge more, you use less of my output, etc. -- all happen instantly, or equivalently the model studies a long run where this has all settled down. But then we talk about responses to shocks, as in the pandemic.  Surely there is a dynamic response here, not just including capital accumulation (which Ian studies). Indeed, my hope was to see prices spreading out through a production network over time, but this structure would have all price adjustments instantly. Mixing production networks with sticky prices is an obvious idea, which some of the papers below are working on. In the theory and data handling, you see a big discontinuity. If a firm uses any inputs at all from another firm,  if \(A_{ij}>0\), that input can take over and drive everything. If it uses no inputs at all, then there is no network link and the upstream firm can't have any effect. There is a big discontinuity at \(A_{ij}=0.\) We would prefer a theory that does not jump from zero to everything when the firm buys one stick of chewing gum. Ian had to drop small but nonzero elements of the input-output matrix to produces sensible results. Perhaps we should regard very small inputs as always substitutes? How important is the network stuff anyway? We tend to use industry categorizations, because we have an industry input-output table. But how much of the US industry input-output is simply vertical: Loggers sell trees to mills who sell wood to lumberyards who sell lumber to Home Depot who sells it to contractors who put up your house? Energy and tools feed each stage, but don't use a whole lot of wood to make those. I haven't looked at an input-output matrix recently, but just how "vertical" is it? ****The literature on networks in macro is vast. One approach is to pick a recent paper like Ian's and work back through the references. I started to summarize, but gave up in the deluge. Have fun. One way to think of a branch of economics is not just "what tools does it use?" but "what questions is it asking?  Long and Plosser "Real Business Cycles," a classic, went after idea that the central defining feature of business cycles (since Burns and Mitchell) is comovement. States and industries all go up and down together to a remarkable degree. That pointed to "aggregate demand" as a key driving force. One would think that "technology shocks" whatever they are would be local or industry specific. Long and Plosser showed that an input output structure led idiosyncratic shocks to produce business cycle common movement in output. Brilliant. Macro went in another way, emphasizing time series -- the idea that recessions are defined, say, by two quarters of aggregate GDP decline, or by the greater decline of investment and durable goods than consumption -- and in the aggregate models of Kydland and Prescott, and the stochastic growth model as pioneered by King, Plosser and Rebelo, driven by a single economy-wide technology shock.  Part of this shift is simply technical: Long and Plosser used analytical tools, and were thereby stuck in a model without capital, plus they did not inaugurate matching to data. Kydland and Prescott brought numerical model solution and calibration to macro, which is what macro has done ever since.  Maybe it's time to add capital, solve numerically, and calibrate Long and Plosser (with up to date frictions and consumer heterogeneity too, maybe). Xavier Gabaix (2011)  had a different Big Question in mind: Why are business cycles so large? Individual firms and industries have large shocks, but \(\sigma/\sqrt{N}\) ought to dampen those at the aggregate level. Again, this was a classic argument for aggregate "demand" as opposed to "supply."  Gabaix notices that the US has a fat-tailed firm distribution with a few large firms, and those firms have large shocks. He amplifies his argument via the Hulten mechanism, a bit of networkyiness, since the impact of a firm on the economy is sales / GDP,  not value added / GDP. The enormous literature since then  has gone after a variety of questions. Dew-Becker's paper is about the effect of big shocks, and obviously not that useful for small shocks. Remember which question you're after.My quest for a new Phillips curve in production networks is better represented by Elisa Rubbo's "Networks, Phillips curves and Monetary Policy," and Jennifer La'o and  Alireza Tahbaz-Salehi's "Optimal Monetary Policy in Production Networks," If I can boil those down for the blog, you'll hear about it eventually.  The "what's the question" question is doubly important for this branch of macro that explicitly models heterogeneous agents and heterogenous firms. Why are we doing this? One can always represent the aggregates with a social welfare function and an aggregate production function. You might be interested in how aggregates affect individuals, but that doesn't change your model of aggregates. Or, you might be interested in seeing what the aggregate production or utility function looks like -- is it consistent with what we know about individual firms and people? Does the size of the aggregate production function shock make sense? But still, you end up with just a better (hopefully) aggregate production and utility function. Or, you might want models that break the aggregation theorems in a significant way; models for which distributions matter for aggregate dynamics, theoretically and (harder) empirically. But don't forget you need a reason to build disaggregated models. Expression (1) is not easy to get to. I started reading Ian's paper in my usual way:  to learn a literature start with the latest paper and work backward. Alas, this literature has evolved to the point that authors plop results down that "everybody knows" and will take you a day or so of head-scratching to reproduce. I complained to Ian, and he said he had the same problem when he was getting in to the literature! Yes, journals now demand such overstuffed papers that it's hard to do, but it would be awfully nice for everyone to start including ground up algebra for major results in one of the endless internet appendices.  I eventually found Jonathan Dingel's notes on Dixit Stiglitz tricks, which were helpful. Update:Chase Abram's University of Chicago Math Camp notes here  are also a fantastic resource. See Appendix B starting p. 94 for  production network math. The rest of the notes are also really good. The first part goes a little deeper into more abstract material than is really necessary for the second part and applied work, but it is a wonderful and concise review of that material as well.