Basil Halperin

Essays — Basil Halperin


Monetary policy in 2050: evidence from Metaculus
April 26, 2022

I have created a new set of questions on the forecasting platform Metaculus to help predict what monetary policy will look like over the next three decades. These questions accompany a “fortified essay” located here which offers context on the importance of these questions, which I expand on below.

You, yes you, can go forecast on these questions right now – or even go submit your own questions if you’re dissatisfied with mine.

My hope is that these forecasts will be, at the least, marginally useful for those thinking about how to design policy – but also useful to researchers (e.g.: me!) in determining which research will be most relevant in coming decades.

Below I give some background on Metaculus for those not already familiar, and I offer some thoughts on my choice of questions and their design.

I. Brief background on Metaculus

The background on Metaculus is that the website allows anyone to register an account and forecast on a huge variety of questions: from will Trump win the 2024 election (27%) to Chinese annexation of Taiwan by 2050 (55%) to nanotech FDA approval by 2031 (62%). Interestingly, the questions need not be binary yes/no and instead can be date-based – e.g. year AGI developed (2045); or nonbinary – e.g. number of nuclear weapons used offensively by 2050 (1.10).

Metaculus is not a prediction market: you do not need to bet real money to participate, and conversely there is no monetary incentive for accuracy.

This is an important shortcoming! THE reason markets are good at aggregating dispersed information and varying beliefs is the possibility of arbitrage. Arbitrage is not possible here.

II. Metaculus is surprisingly accurate

Nonetheless, Metaculus has both a surprisingly active userbase and, as far as I can tell, a surprisingly good track record? Their track record page has some summary statistics.

For binary yes/no questions, taking the Metaculus forecast at 25% of the way through the question lifetime, the calibration chart looks like this:

The way to read this chart is that, for questions where Metaculus predicts a (for example) 70% probability of a “YES” outcome, it happens 67.5% of the time on average.

For comparison, here is FiveThirtyEight’s calibration chart:

And here is an actual prediction market, PredictIt, using 9 months’ worth of data collected by Jake Koenig on 567 markets:

(See also: Arpit Gupta’s great analysis of prediction markets vs. FiveThirtyEight on 2020 US elections. If you want to be a real nerd about this stuff, Scott Alexander’s “Mantic Monday” posts and Nuño Sempere’s Forecasting Newsletter have good regular discussions of new developments in the space.)

A potentially very important caveat is that these calibration charts only score the accuracy of yes-versus-no types of questions. For date-based questions (e.g. “AGI when?”) or questions with continuous outcomes, scoring accuracy is more complicated. I don’t know of a great way to score, let alone visualize, the accuracy of date-based questions; send suggestions. Metaculus’ track record page offers the log score, which is one particular accuracy statistic, for all questions:

As far as I’m aware, the only way to interpret this is: ‘higher is gooder’. I also do not have any reference forecasters to which this can be compared, unlike for the binary questions above – again, making things hard to interpret. The log score also does not capture all of the information contained in the entirety of the CDF of a forecast; only the forecasted probability at the resolution date.

Last, given that Metaculus launched in 2017, it’s not yet possible to analyze the accuracy of long-run forecasts.

III. Metaculus for forecasting monetary policy design

For macroeconomics, we already have some forecasts directly from financial markets for short- or medium-term variables, e.g. predictions for the Fed’s policy interest rate.

I think forecasts for longer-term questions and for questions not available on financial markets could be useful for researchers and practitioners. To make this argument, I’ll walk through the questions I wrote up for Metaculus, listed in the intro above.

The first set of questions is about the zero lower bound and negative interest rates: when is the next time the US will get stuck at the ZLB; how many times between now and 2050 will we end up stuck there; and will the Fed push interest rates below zero if so.

This is of extreme practical importance. The ZLB is conventionally believed to be an important constraint on monetary policy and consequently a justification for fiscal intervention (“stimmies”). If we will hit the ZLB frequently in coming decades, then it is even more important than previously considered to (1) develop our understanding of optimal policy at the ZLB, and (2) analyze more out-of-the-Overton-window policy choices, like using negative rates.

A policy even further out of the Overton window would be the abolition of cash, which is another topic I solicit forecasts on for the US as well as for China (where likely this will occur sooner). If cash is abolished, then the ZLB ceases to be a constraint. (This to me implies pretty strongly that we ought to have abolished cash, yesterday.)

Cash abolition would be useful to predict not just so that I can think about how much time to spend analyzing such a policy; but also because abolishing cash would mean that studying “optimal policy constrained by the ZLB” would be less important – there would be no ZLB to worry about!

Finally, I asked about if the Fed will switch from its current practice of focusing on stabilizing inflation (“inflation targeting”/“flexible average inflation targeting”) to nominal GDP or nominal wage targeting. This is a topic especially close to my own research.

IV. Questions I did not ask

There are a lot of other questions, or variations on the above questions, that I could have asked but did not.

Expanding my questions to other countries and regions is one obvious possibility. As just one example, it would also be useful to have a forecast for when cash in the eurozone might be abolished. The US-centrism of my questions pains me, but I didn’t want to spam the Metaculus platform with small variations on questions. You should go create these questions though 😊.

Another possible set of questions would have had conditional forecasts. “Will the US ever implement negative rates”; “conditional on the US ever implementing negative rates, when will it first do so”. This would be useful because the questions I created have to smush together these two questions. For example: if Metaculus forecasts 2049 for the expected date of cash abolition, does that mean forecasters have a high probability on cash being abolished, but not until the late 2040s; or that they expect it may be abolished in the next decade, but otherwise will never be abolished? It’s hard to disentangle when there’s only one question, although forecasters do provide their full CDFs.

A final set of possible questions that I considered were too subjective for the Metaculus platform: for example, “Will the ECB ever adopt a form of level targeting?” The resolution criteria for this question were just too hard to specify precisely. (As an example of the difficulty: does the Fed’s new policy of “flexible average inflation targeting” count as level targeting?) Perhaps I will post these more subjective questions on Manifold Markets, a new Metaculus competitor which allows for more subjectivity (which, of course, comes at some cost).

Thanks to Christian Williams and Alyssa Stevens from the team at Metaculus for support, and to Eric Neyman for useful discussion on scoring forecasts.

March 31, 2022

Confidence level (?): Medium

I want to argue that Newcomb’s problem does not reveal any deep flaw in standard decision theory. There is no need to develop new decision theories to understand the problem.

I’ll explain Newcomb’s problem and expand on these points below, but here’s the punchline up front.


  1. Newcomb’s problem, framed properly, simply highlights the issue of time consistency. If you can, you would beforehand commit to being the type of person who takes 1 box; but in the moment, under discretion, you want to 2-box.
  2. That is: the answer to Newcomb depends on from which point in time the question is being asked. There’s just no right way to answer the question without specifying this.
  3. Confusion about Newcomb’s problem comes when people describing the problem implicitly and accidentally conflate the two different possible temporal perspectives.
  4. Newcomb’s problem is isomorphic to the classic time consistency problem in monetary policy – a problem that is well-understood and which absolutely can be formally analyzed via standard decision theory.

I emphasize that the textbook version of expected utility theory lets us see all this! There’s no need to develop new decision theories. Time consistency is an important but also well-known feature of bog-standard theory.

I. Background on Newcomb

(You can skip this section if you’re already familiar.)

Newcomb’s problem is a favorite thought experiment for philosophers of a certain bent and for philosophically-inclined decision theorists (hi). The problem is the following:

  • Scientists have designed a machine for predicting human decisions: it scans your brain, and predicts on average with very high accuracy your choice in the following problem.
  • I come to you with two different boxes:
    • 1. In one box, I show you there is $100.
    • 2. The second box is a mystery box.
  • I offer to let you choose between taking just the one mystery box, or taking both the mystery box and the $100 box.
  • Here’s the trick: I tell you that the mystery box either contains nothing or it contains a million dollars.
    • If the machine had predicted in advance that you would only take the mystery box, then I had put a million bucks in the mystery box.
    • But if the machine had predicted you would take both boxes, I had put zero in the mystery box.

As Robert Nozick famously put it, “To almost everyone, it is perfectly clear and obvious what should be done. The difficulty is that these people seem to divide almost evenly on the problem, with large numbers thinking that the opposing half is just being silly.”

The argument for taking both boxes goes like, ‘If there’s a million dollars already in the mystery box, well then I’m better off taking both and getting a million plus a hundred. If there’s nothing in the mystery box, I’m better off taking both and at least getting the hundred bucks. So either way I’m better off taking both boxes!’

The argument for “one-boxing” – taking only the one mystery box – goes like, ‘If I only take the mystery box, the prediction machine forecasted I would do this, and so I’ll almost certainly get the million dollars. So I should only take the mystery box!’

II. The critique of expected utility theory

It’s often argued that standard decision theory would have you “two-box”, but that since ‘you win more’ by one-boxing, we ought to develop a new form of decision theory (EDT/UDT/TDT/LDT/FDT/...) that prescribes you should one-box.

My claim is essentially: Newcomb’s problem needs to be specified more precisely, and once done so, standard decision theory correctly implies you could one- or two-box, depending on from which point in time the question is being asked.

III. Newcomb’s problem as a static problem

In the very moment that I have come to you, here is what your payoff table looks like:

You are choosing between the first row and the second row; I’m choosing between the first column and the second column. Notice that if I’ve chosen the first column, you’re better off in the first row; and if I’ve chosen the second column, you’re also better off in the first row. Thus the argument for being in the first row – taking both boxes.

In the very moment that I have come to you, you ARE better off in taking both boxes.

To borrow a trick from Sean Carroll, go to the atomic level: in the very moment I have come to you, the atoms in the mystery box cannot change. Your choice cannot alter the composition of atoms in the box – so you ARE better off “two-boxing” and taking both boxes, since nothing you can do can affect the atoms in the mystery box.

I want to emphasize this is a thought experiment. You need to be sure to decouple your thinking here from possible intuitions that could absolutely make sense in reality but which we need to turn off for the thought experiment. You should envision in your mind’s eye that you have been teleported to some separate plane from reality, floating above the clouds, where your choice is a one-time action, never to be repeated, with no implications for future choices. (Yes, this is hard. Do it anyway!) If you one-box in the very moment, in this hypothetical plane separate from reality where this is a one-time action with no future implications, you are losing – not winning. You are throwing away utils.

IV. Newcomb’s problem as a dynamic problem

But what if this were a dynamic game instead, and you were able to commit beforehand to a choice? Here’s the dynamic game in extensive form:

Here I’ve presented the problem from a different moment in time. Instead of being in the very moment of choice, we’re considering the problem from an ex ante perspective: the time before the game itself.

Your choice now is not simply whether to one-box or to two-box – you can choose to commit to an action before the game. You can either:

  1. Tie your hands and commit to only take one box. In which case the prediction machine would know this, predict your choice, I would put $1M in the mystery box, and so you would get $1M.
  2. or
  3. Don’t commit to anything. In which case you end up back in the same situation as the game table before, in the very moment of choice.

But we both already know that if you take the second option and don’t commit, then in the very moment of choice you’re going to want to two-box. In which case the machine is going to predict this, and I’m going to put nothing in the mystery box, so when you inevitably two-box after not committing you’ll only get the $100.

So the dynamic game can be written simply as:

Obviously, then, if it’s before the game and you’re able to commit to being the type of person who only takes the mystery box, then you want to do so.

You would want to commit to being the type of person who – “irrationally”, quote unquote – only takes the mystery box. You would want to tie your hands, to modify your brain, to edit your DNA – to commit to being a religious one-boxer. You want to be Odysseus on his ship, tied to the mast.

V. It’s essential to be precise about timing

So to summarize, what’s the answer to, “Should you one-box or two-box?”?

The answer is, it depends on from which point in time you are making your decision. In the moment: you should two-box. But if you’re deciding beforehand and able to commit, you should commit to one-boxing.

How does this work out in real life? In real life, you should – right now, literally right now – commit to being the type of person who if ever placed in this situation would only take the 1-box. Impose a moral code on yourself, or something, to serve as a commitment device. So that if anyone ever comes to you with such a prediction machine, you can become a millionaire 😊.

This is of course what’s known as the problem of “time consistency”: what you want to do in the moment of choice is different from what you-five-minutes-ago would have preferred your future self to do. Another example would be that I’d prefer future-me to only eat half a cookie, but if you were to put a cookie in front of me, sorry past-me but I’m going to eat the whole thing.

Thus my claim: Newcomb merely highlights the issue of time consistency.

So why does Newcomb’s problem produce so much confusion? When describing the problem, people typically conflate and confuse the two different points in time from which the problem can be considered. In the way the problem is often described, people are – implicitly, accidentally – jumping between the two different points of view, from the two different points in time. You need to separate the two possibilities and consider them separately. I have some examples in the appendix at the bottom of this type of conflation.

Once they are cleanly separated, expected utility maximization gives the correct answer in each of the two possible – hypothetical – problems.

VI. Time consistency and macroeconomics

I say Newcomb “merely” highlights the issue of time consistency, because the idea of time consistency is both well-known and completely non-paradoxical. No new decision theories needed.

But that is not at all to say the concept is trivial! Kydland and Prescott won a Nobel Prize (in economics) for developing on the insight in a range of economic applications. In particular, they highlighted that time consistency may be an issue for central banks. I don’t want to explain in detail here the problem, but if you’re not familiar here’s one summary. What I do want to draw out is a couple of points.

Frydman, O’Driscoll, and Schotter (1982) have a fairly obscure paper that, to my (very possibly incomplete) knowledge, is the first paper arguing that Newcomb’s problem is really just a time consistency problem. It does so by pointing out that the time consistency problem facing a central bank is, literally, isomorphic to Newcomb’s problem. Broome (1989), which also is nearly uncited, summarizes Frydman-O’Driscoll-Schotter and makes the point more clearly.

Here are the two game tables for the two problems, from Broome:


On the left, Newcomb’s problem; on the right, the Kydland-Prescott central bank problem. You can see that the rankings of the different outcomes are the exact same.

The two decision problems – the two games – are completely equivalent!

In macroeconomics we know how to state, describe, and solve this problem in formal mathematical language using the tools of standard, textbook decision theory. See Kydland and Prescott (1977) for the math if you don’t believe me! It’s just a standard optimization problem, which can be written at two possible points in time, and therefore has two possible answers.

Thus in philosophy, Newcomb’s problem can be solved the exact same way as we do it in macro, using the standard, textbook decision theory. And thus in artificial intelligence research, Newcomb’s problem can be decided by an AI in the same way that the Federal Reserve decides on monetary policy.

Philosophers want to talk about “causal decision theory” versus “evidential decision theory” versus more exotic things, and frankly I cannot figure out what those words mean in contexts I care about, or the meaning of those words when translation to economics is attempted. Why do we need to talk about counterfactual conditionals? Or perhaps equivalently: shouldn‘t we treat the predictor as an agent in the game, rather than as a state of the world to condition on?

(Eliezer Yudkowsky comments briefly on a different connection between Newcomb and monetary policy here. “Backwards causality” and “controlling the past” are just extremely common and totally normal phenomena in dynamic economics!)

(Woodford 1999 section 4 on the ‘timeless perspective’ for optimal monetary policy is another relevant macro paper here. Rather than expand on this point I’ll just say that the timeless perspective is a [very correct] argument for taking a particular perspective on optimal policy problems, in order to avoid the absurdities associated with the ‘period-0 problem’, not an alternative form of decision theory.)

VII. Steelmanning the opposing view

Some very smart people insist that Newcomb-like problems are a Big Deal. If you stuck a gun to my head and forced me to describe the most charitable interpretation of their work, here’s how I would describe that effort:

“We want to come up with a form of decision theory which is immune to time consistency problems.”

I have not seen any researchers working in this area describe their objective that way. I think it would be extremely helpful and clarifying if they described their objective that way – explicitly in terms of time consistency problems. Everyone knows what time consistency is, and using this language would make it clear to other researchers what the objective is.

I think such an objective is totally a fool’s errand. I don’t have an impossibility proof – if you have ideas, let me know – but time consistency problems are just a ubiquitous and completely, utterly normal feature in applied theory.

You can ensure an agent never faces a time consistency problem by restricting her preferences and the set of possible environments she faces. But coming up with a decision theory that guarantees she never faces time consistency problems for any preference ordering or for any environment?

It’s like asking for a decision theory that never ever results in an agent facing multiple equilibria, only a unique equilibrium. I can ensure there is a unique equilibrium by putting restrictions on the agent’s preferences and/or environment. But coming up with a decision theory that rules out multiple equilibria always and everywhere?

No, like come on, that’s just a thing that happens in the universe that we live in, you’re not going to get rid of it.

(Phrasing this directly in terms of AI safety. The goal should not be to build an AI that has a decision algorithm which never is time inconsistent, and always cooperates in the prisoners‘ dilemma, and never generates negative externalities, and always contributes in the public goods game, and et cetera. The goal should be to build up a broader economic system with a set of rules and incentives such that, in each of these situations, the socially optimal action is privately optimal – for all agents both carbon-based and silicon, not just for one particular AI agent.)

VIII. Meta comment: the importance of staying tethered to reality

For me and for Frydman-O’Driscoll-Schotter, analyzing Newcomb as a time consistency problem was possible because of our backgrounds in macroeconomics. I think there’s a meta-level lesson here on how to make progress on answering big philosophical questions.

Answering big questions is best done by staying tethered to reality: having a concrete problem to work on lets you make progress on the big picture questions. Dissolving Newcomb’s problem via analogy to macroeconomics is an example of that.

As Cameron Harwick beautifully puts it, “Big questions can only be competently approached from a specialized research program”. More on that from him here as applied to monetary economics – the field which, again, not coincidentally has been at the heart of my own research. This is also why my last post, while nominally about monetary policy, was really about ‘what is causality’ (TLDR: causality is a property of the map, not of the territory).

Scott Aaronson has made a similar point: “A crucial thing humans learned, starting around Galileo’s time, is that even if you’re interested in the biggest questions, usually the only way to make progress on them is to pick off smaller subquestions: ideally, subquestions that you can attack using math, empirical observation, or both”. He goes on to say:

For again and again, you find that the subquestions aren’t nearly as small as they originally looked! Much like with zooming in to the Mandelbrot set, each subquestion has its own twists and tendrils that could occupy you for a lifetime, and each one gives you a new perspective on the big questions. And best of all, you can actually answer a few of the subquestions, and be the first person to do so: you can permanently move the needle of human knowledge, even if only by a minuscule amount. As I once put it, progress in math and science – think of natural selection, Godel’s and Turing’s theorems, relativity and quantum mechanics – has repeatedly altered the terms of philosophical discussion, as philosophical discussion itself has rarely altered them!

Another framing for this point is on the importance of feedback loops, e.g. as discussed by Holden Karnofsky here. Without feedback loops tethering you to reality, it’s too easy to find yourself floating off into space and confused on what’s real and what’s important.

(Choosing the right strength of that tether is an art, of course. Microeconomics friends would probably tell me that monetary economics is still too detached from reality – because experiments are too difficult to run, etc. – to make progress on understanding the world!)

A somewhat narrower, but related, lesson: formal game theory is useful and in fact essential for thinking about many key ideas in philosophy, as Tyler Cowen argued in his review of Parfit’s On What Matters: “By the end of his lengthy and indeed exhausting discussions, I do not feel I am up to where game theory was in 1990”. (A recent nice example of this, among many, is Itai Sher on John Roemer“s notion of Kantian equilibrium.)

IX. Dissolving the question, dissolving confusion

Let me just restate the thesis to double down: The answer to Newcomb’s problem depends on from which point in time the question is being asked. There’s no right way to answer the question without specifying this. When the problem is properly specified, there is a time inconsistency problem: in the moment, you should two-box; but if you’re deciding beforehand and able to commit, you should commit to one-boxing.

Thanks to Ying Gao, Philipp Schoenegger, Trevor Chow, and Andrew Koh for useful discussions.

Appendix A: On “program equilibria” and “contractible contracts”

Some decision theory papers in this space (e.g. 1, 2) use the Tennenholz (2003) notion of a “program equilibrium” when discussing these types of issues. This equilibrium concept is potentially quite interesting, and I’d be interested in thinking about applications to other econ-CS domains. (See e.g. recent work on collusion in algorithmic pricing by Brown and MacKay.)

What I want to highlight is that: the definition of program equilibrium sort of smuggles in an assumption of commitment power!

The fact that your choice consists of “writing a computer program” means that after you’ve sent off your program to the interpreter, you can no longer alter your choice. Imagine instead that you could send in your program to the interpreter; your source code would be read by the other player; and then you would have the opportunity to rewrite your code. This would bring the issue of discretion vs. commitment back into the problem.

Thus the reason that program equilibria can give the “intuitive” type of result: it implicitly assumes a type of commitment power.

This very well might be the most useful equilibrium concept for understanding some situations, e.g. interaction between DAOs. But it’s clearly not the right equilibrium concept for every situation of this sort – sometimes agents don’t have commitment power.

The work of Peters and Szentes (2012) on “contractible contracts” is similar – where players can condition their actions on the contracts of other players – and they do explicitly note the role of commitment from the very first sentence of the paper.

Appendix B: Examples of conflating points in time

One example of the conflation is Nate Soares’ fantastically clear exposition here, where he writes, “You (yesterday) is the algorithm implementing you yesterday. In this simplified setting, we assume that its value determines the contents of You (today)”. This second sentence, clearly, brings in an assumption of commitment power.

Another is on this Arbital page. Are you in the moment in an ultimatum game, deciding what to do? Or are you ex ante deciding how to write the source code for your DAO, locking in the DAO’s future decisions? The discussion conflates two possible temporal perspectives.

A similar example is here from Eliezer Yudkowsky (who I keep linking to as a foil only because, and despite the fact that, he has deeply influenced me):

I keep trying to say that rationality is the winning-Way, but causal decision theorists insist that taking both boxes is what really wins, because you can’t possibly do better by leaving $1000 on the table... even though the single-boxers leave the experiment with more money.

In a static version of the game, where you’re deciding in the very moment, no! Two-boxers walk away with more money – two-boxers win more. One-boxers only win in the dynamic version of the game; or in a repeated version of the static game; or in a much more complicated version of the game taking place in reality, instead of in our separate hypothetical plane, where there’s the prospect of repeated such interactions in the future.

(My very low-confidence, underinformed read is that Scott Garrabrant’s work on ‘finite factored sets’ and ‘Cartesian frames’ gets closer to thinking about Newcomb this way, by gesturing at the role of time. But I don’t understand why the theory that he has built up is more useful for thinking about this kind of problem than is the standard theory that I describe.)

I‘m not necessarily convinced that the problem is actually well-defined, but the cloned prisoners’ dilemma also seems like a time consistency problem. Before you are cloned, you would like to commit to cooperating. After being cloned, you would like to deviate from your commitment and defect.

A final example is Parfit’s Hitchhiker, which I will only comment extremely briefly on to say: this is just obviously an issue of dynamic inconsistency. The relevant actions take place at two different points in time, and your optimal action changes over time.

Oct 28, 2021

Confidence level (?): Medium


Your home has a thermostat that wants to maintain a temperature of, say, 70 degrees.

One day, while it happens to be slightly cold outside, your thermostat randomly happens to break. Your house gets cold, and it is miserable.

Both of the following statements are true in a sense:

  1. “The cold weather outside caused your house to freeze.”
  2. “The broken thermostat caused your house to freeze.”

You can say both of these statements.

It seems quite plausible, though, that describing your broken thermostat as ‘the’ cause of your cold house is a more useful way of talking about the world. The most useful way of thinking about the world is that your thermostat should, by default, keep a constant internal temperature – but that in this instance it failed.

(Causality is a property of the map, not of the territory; but some maps are more useful than other ones.)

If someone asked you, “Why is your house so cold?”, you would say, “Because my thermostat broke”; you would not say, “Because it’s cold outside.”


Your economy has a central bank that wants to maintain output at potential and inflation on trend.

One day, there is a financial crisis; your central bank “breaks” and screws up. Your economy crashes below potential, and it is miserable.

Both of the following statements are true in a sense:

  1. “The financial crisis caused the economy to crash.”
  2. “The incompetent central bank caused the economy to crash.”

You can say both of these statements.

It seems quite plausible, though, that describing your incompetent central bank as ‘the’ cause of the recession is a more useful way of talking about the world. The most useful way of thinking about the world is that the central bank should, by default, keep an economy out of recession – but that in this instance it failed.

(Causality is a property of the map, not of the territory; but some maps are more useful than other ones.)

If someone asked you, “Why was there a recession?”, you should say it’s because your central bank screwed up; you should not say it’s because there was a financial crisis.


To close, a related syllogism:

  1. Recessions are periods when output is below potential.
  2. Output below potential is, almost by definition, a shortfall in aggregate demand.
  3. Central banks control aggregate demand.

Therefore, all recessions (in the sense of output being below potential) are caused by central banks.


If you are unhappy with the logic above, the syllogism also provides a natural taxonomy of possible counterarguments. Considering each point of the syllogism #1-3 in turn:

  1. Perhaps we should not define recessions as periods when output is below potential. The real business cycle theory that economic fluctuations are due to productivity or other ‘real’ shocks would be one version of this.
  2. Perhaps output can be below potential without “aggregate demand” (whatever this means) falling, as in theories of macroeconomic multiple equilibria.
  3. Perhaps central banks do not have perfect control of aggregate demand.
    1. For example: some argue that central banks cannot control aggregate demand at the zero lower bound.
    2. Alternatively (and, really, a generalization of the ZLB problem): perhaps aggregate demand is not a one-dimensional concept, and it is impossible to simultaneously set all dimensions at the right level. For example, a recession might involve “a shortfall in demand” in one region but “excess demand” in another region. The central bank might not be able to perfectly control demand in each region at the same time, and can only ensure zero shortfall in one region at a time.

The counterargument 3b is how I would frame the mainline New Keynesian view (eg).

It is analogous to the problem of having a single thermostat set the temperature for all of the many rooms in your house, and asking what is to blame when your bedroom is too hot but your kitchen is too cold. To me, if your bedroom is consistently too hot but your kitchen too cold, the most useful way of talking about the world is to say, ‘my thermostat is not working very well’ and to think about ways to make your thermostat work better – not to blame the weather outside.

Likewise, even if central banks cannot perfectly set all dimensions of “aggregate demand” to the right level simultaneously, the most useful way of talking about the world is to say, ‘my central bank is not working very well’ and to think about ways to make it work better (eg, eg).


If it keeps breaking, have you thought about replacing your monetary institutions thermostat with a newer version?

Aug 11, 2021

Plausibly the most shocking graph I’ve ever seen from an economics paper, speaking frankly, is the following graph of suicide rate by month, from Hansen and Lang (2011):

The black line is the suicide rate for 14-18 year olds, versus the dashed line of the 19-25 group. This is US data for 1980 to 2004.

What sticks out is a large decrease in teen suicide rates during the summer vacation months of June/July/August. In contrast, the somewhat older group sees, if anything, an increase in suicide rates in the summer. There’s also a drop in high school suicides in December, around winter vacation.

This is emphatically not causal evidence, but it is enough to make one wonder: is there a causal relationship between school and teenage suicide?

I. Replicating and extending the result

Honestly, when I first saw the Hansen and Lang graph, I figured that it must be just noise. Fortunately, the NBER has nicely organized the NCHS Multiple Cause-of-Death mortality data, which made it pretty straightforward to replicate the graph.

Better (“better”) yet: the original Hansen-Lang paper runs through 2004 but data is now available through 2019, so the replication also allows for an extension with a 60% higher number of years of data.

The pattern remains with the 15 years of new data:

The Hansen and Lang figure has the 14-18 age group and the 19-25 group; this figure also includes a line for those under age 14 and one for those above age 25. The pattern for those under age 14 is even steeper.

Note that suicide rates vary by age – older age groups have higher suicide rates – so I normalize the suicide rate each month by the average over the entire year to make the monthly pattern readable. Here’s the rate by month, not normalized, where you can see the level differences, and the pattern is still evident but harder to see:

II. Interpreting the graph

Here’s a back of the envelope calculation to help interpret the magnitudes:

If US teen suicide rates were as low during the school year as they are during the summer, then there would be ∼2600 fewer teen suicides per year. Eek.

III. Further checks

This replication and extension convinced me, at least, that this seasonal pattern is not a data fluke. Another check that Hansen and Lang do is to look individually at each year of monthly data, by age group, and to regress suicide rate by month on a dummy for is_summer. The coefficient is (depressingly) stable:

(Note that I did this regression in absolute terms, hence why under-14 has a coefficient close to zero – again suicide rates for this group are comparatively low.)

Another thought is that seasonal patterns might be attributable to something related to seasonal affective disorder (SAD). For one thing, you can check out the Hansen and Lang paper where they compare states with differing levels of sunlight to argue that SAD is not the cause. Second, note the comparison with adults: adults have a higher suicide rate during summer months, despite the existence of SAD.

IV. Background: US suicide rates are rising

The background context here is that US suicide rates have risen substantially in the last 15 years, particularly in relative terms for the <14 group, which makes the study of this – and other “public mental health” issues – especially important and underrated, in my opinion.

(This was my motivation when I dug into this data originally a few years ago. As regular readers will know, I spend most of time thinking about macroeconomics: how to abolish recessions and the grave evil of (excess) unemployment. But: some welfare trends are so tangible they’re hard to ignore.)

The optimistic view is that suicide rates for older age groups are to some extent just returning to their early-1990s level. That’s not much optimism, at all, though. (You might also think that this is just a shift in the age distribution within bins – this is not the case. An example.)

That the “summer effect/correlation” seems to have been constant while total suicides have fluctuated around is maybe a point against the idea that ‘increasing school-related stress’ is driving teen suicide rates.

V. Correlation is not causation

I emphasize that this analysis very much IS a correlation, not a strong argument that “school causes teen suicide.”

You could think about identification strategies to tease out the causal effect of school on suicide rates or mental health, and hopefully someone will do that (!). A crucial challenge is that any quasi-randomness which “increases school time” (for example) not only “increases school time” but also necessarily has a bunch of other effects – increasing education being only one of many to consider. The exclusion restriction is not your friend here.

Even setting aside causality (which you should absolutely not!), a big question here in my view is the data itself: could this be driven by reporting differentials? Are school officials during the school year more likely to be willing to classify a death as a suicide, compared perhaps to family members over the summer?

Even if the data is completely correct, the causal mechanism is not at all obvious. School and mental health would certainly be one possible channel, but there are other possibilities. Alcohol is a major risk factor in suicides. Perhaps(?) during the school year, teens are more likely to have access to and consume alcohol – though the same pattern for under-14s perhaps pushes against this.

Alternatively, perhaps schooling affects timing but not the outcome – if forced schooling were abolished, would total suicides fall, or would there be merely a shift in timing?

VI. Policy implications: unclear?

All this said, it’s not even clear what the implications of a causal finding would be – we’re not(?) going to stop sending kids to school.

There are other margins of adjustment, though, as we like to say. School administrators and educational policymakers could think harder (???) about or allocate more resources to mental health programs for students.

“Better school, not less school”? This seems like the most promising avenue for additional research on this topic – research which surely exists – i.e. examining specific policy programs. Besides programs directly related to mental health, you could think about how these outcomes are affected by school start times, school funding cuts, standardized testing rollouts, or school shutdowns, as some off-the-cuff examples.

VII. Covid

The data stops in 2019 since that’s the latest year for which we have full data.

I can’t say it will be telling to see the 2020 data, during the not-at-all-quasirandom remote learning era. But it will certainly be a unique data point, for lack of a better word.

(Here’s evidence on ER visits for suicide attempts since the pandemic showing an increase among girls, particularly in winter/spring 2021. The general seasonal patterns discussed above are also evident in this higher-frequency ER data. See also: a Scott Alexander review of existing evidence on suicide during the pandemic for all ages.)

I do want to use this section as an excuse to force an analogy, though. After the fact, it sure seems like many would argue that the US and other countries underinvested in public health: underinvested in detection of, treatment for, and prevention of macro-scale public health events.

There’s a strong case to be made that, similarly, we are underinvesting in public mental health: detection of, treatment for, and prevention of society-level mental health crises as they already exist and also as they may emerge.

(I am uniformed – please inform me! – but my bias is for bigger-picture policies in the standard utopian and technological directions here: break the licensing cartels; allow telemedicine; allow right to try for apps and/or pharmaceuticals; and, maybe, allocate more research funding to the issue.)

VIII. Outside the US

US data is overrated. What about outside the US?

A 2017 paper from “Economic Analysis of Suicide Prevention” cites a number of studies from other countries in a review, but most don’t zoom in on those of school age in particular and/or have poor data.

Of the more-relevant studies, Singapore data shows little seasonal variation; Finnish data shows an increase in the autumn with the start of school; Chinese data shows no clear seasonal pattern. Most striking, unfortunately, is Japan, where daily data is available:

You can see spikes in teen suicides immediately after each school break (the shaded areas).

VII. Conclusion

This is extremely stomach-twisting stuff if you/I think about it for too long, so let me end things here.

I have little interaction with the mental health research community, and there are probably obvious points here that someone should point out to me. (Please do!)

Code and the cleaned data are here; you should be able to run the Jupyter notebook from top to bottom to download the original raw data (∼50GB) and fully replicate every graph or number here.

Thanks to Charlie Rafkin for useful discussion on this topic.

June 16, 2021

Confidence level (?): High


  1. Intuitively, wage stickiness seems more important than price stickiness
  2. The first microfounded ‘new Keynesian’ models did use wage stickiness, not price stickiness; but in the mid-1980s there was a transition to sticky price models, which dominate today
  3. But that transition was based on a set of arguments which today are regarded as wrong!
  4. The policy implication: Taking wage stickiness seriously implies we should ensure stable nominal wage growth, not stable price inflation


When most people worry about recessions, they’re worried about involuntary unemployment. If we want to think about the role of monetary policy in recessions, then, it feels natural to worry about sticky wages.

In their heart of hearts, I think a lot of macroeconomists – and casual observers of macro – think sticky wages are in fact the most important reason for thinking about the role of monetary policy in recessions.

But in our baseline New Keynesian macroeconomic models, we think about price stickiness and not wage stickiness. In the baseline textbook monetary model, as in e.g. Gali/Woodford/Walsh, we work with a model of sticky prices as our base case; and only teach sticky wages as supplementary material.


Tracing the history of thought on this, going back to the advent of “new Keynesianism” in the 1980s, my takeaway is that:

The preference for sticky price models over sticky wage models is somewhat of a historical accident; in that the original critiques of sticky wage models are now broadly accepted to be incorrect.

I. A distinguishing feature of New Keynesian economics was the use of sticky price, not sticky wage, models

One of the first papers to use the term “new Keynesian” (with a lowercase ‘n’, rather than the uppercase that is now used) was the Rotemberg (1987) Macro Annual paper on “The New Keynesian Microfoundations”. Here’s how he described what made this “new”:

“One might ask in all seriousness what is new about the current generation of Keynesian models. The major difference between the current and previous generations (Fischer 1977, Taylor 1980) is an emphasis on the behavior of product markets.”

As highlighted here by Rotemberg, in the mid-1980s there was a switch from the Fischer and Taylor sticky wage models (focusing on the labor market) to sticky price models (focusing on the product market).

If you think of high involuntary unemployment as being the defining feature of recessions, how do such sticky price models explain unemployment? As Mankiw explains in a comment on Rotemberg’s paper,

“Firms lay off workers in recessions not because labor costs are too high [due to nominal wage stickiness], but because sales are too low [due to goods price stickiness].”

That is: you weren’t fired from your job because you were “too stupid and too stubborn” to lower your wage demand. You were fired because your firm’s sales fell, and so they no longer needed to produce as much, and so didn’t need you. (See also: Barro and Grossman 1971 or the first half of Michaillat and Saez 2015.)

Unemployment, here, is the same phenomenon as a classical model: you chose to be unemployed because you preferred the leisure of Netflix compared to working for a lower real wage. More complicated models can and do add frictions that change this story – labor search frictions; sticky wages on top of sticky prices – but as a baseline, this is the logic and mechanism of these models.

Why was this switch to sticky price models made? With sticky wage models, by contrast, people are genuinely involuntarily unemployed – which again is plausibly the defining characteristic of recessions. Why switch away towards this muddier logic of sticky prices?

II. Two critiques of sticky wages: one empirical, one theoretical

Two critiques of sticky wage models led to the adoption of sticky price models:

  1. The empirical critique that aggregate real wages were basically acyclical, and
  2. The theoretical “Barro(-Hall) critique”

As we’ll get to in a bit, today no one (?) agrees with the empirical critique, and the theoretical critique both does not have real bite and is anyway typically ignored. First, a summary of each critique:

1. Arguably the strongest critique against sticky wage models at the time was the evidence that real wages don’t go up during recessions. After all, if unemployment is caused by real wages being too high – the price level has fallen but nominal wages cannot – then we should see real wages going up during recessions.

In the aggregate US data, this simply did not hold: depending on the time period and the deflator used, real wages could appear countercyclical as predicted, basically acyclical, or even procyclical. To get the general idea (we’ll quibble over measurement later) here’s a graph of a measure of real average hourly earnings I grabbed from the WSJ:

Average real wages are not strikingly obviously “too high” during recessions here – earnings don’t spike upward in the shaded areas – particularly when you look at the 1970s and 1980s.

2. The second, theoretical critique was advanced by Barro (1977) and described by Hall (1980). This argument is usually summarized as: employer-employee relationships could be implicitly long-term contracts, and so observed nominal wage stickiness in the short run need not imply allocative inefficiency.

For example, if I expect to produce $3 of (marginal) value this year and $1 next year, I don’t really care if my boss promises to pay me $2 in each year – even though this year I’m being paid less than my value.

Similarly, even if my nominal wages don’t fall during a recession, perhaps over my entire lifetime my total compensation falls appropriately; or, other margins adjust.


Arguably, price stickiness is not vulnerable to either of the above critiques of wage stickiness, and hence the appeal over wage stickiness:

  1. The apparent acyclicality of real wages is not a problem for a theory based on price stickiness
  2. Goods prices are plausibly spot prices, not part of implicit long-term relationships unlike labor (though: even this isn’t always clear, e.g. considering the importance of intermediaries and supply chain relationships!)

Hence, the transition from sticky wage models to the dominance of sticky price models starting in the 1980s. Yun (1996) builds the full dynamic model with Calvo sticky pricing at the heart of the New Keynesian framework; Woodford, Gali, and Walsh organize NK thought into textbook format.

But – these critiques are at best incomplete and at worst conceptually incorrect. Here’s why:

III. The acyclicality of aggregate real wages does not in any way invalidate the wage stickiness hypothesis

“Observed real wages are not constant over the cycle, but neither do they exhibit consistent pro- or countercyclical tendencies. This suggests that any attempt to assign systematic real wage movements a central role in an explanation of business cycles is doomed to failure.”
Lucas (1977)
Mankiw (1991) – another comment on a later Rotemberg Macro Annual paper coauthored with Woodford – writes: “As far as I know, there are six ways to explain the failure of real wages to move countercyclically over the business cycle... None of these explanations commands a consensus among macroeconomists, and none leaves me completely satisfied.” He offered this list of possible explanations:

I don’t want to go through each of these in detail – see Mankiw’s comment; and note some of these suggestions are pretty esoteric. Most of these are immediately unsatisfactory; on #2, implicit contracts, we’ll come back to.

The problem I want to highlight is that: the late-80s/early-90s understanding summarized in this table leaves out the three most compelling – and now widely-recognized – reasons that the cyclicality of the aggregate real wage is not diagnostic of the sticky wage model.

1. Identification: the source of the shock matters!

Recessions caused by tight monetary policy should cause real wages to increase and be too high, leading to involuntary unemployment. Recessions caused by real supply-side shocks should cause real wages to fall and nonemployment to rise.

If the economy experiences a mix of both, then on average the correlation of real wages and recessions could be anything.

Maybe in 1973 there’s an oil shock, which is a real supply-side shock: real wages fall and nonemployment rises (as in the data). Maybe in 2008 monetary policy is too tight: real wages spike and unemployment rises (as in the data). Averaging over the two, the relationship between real wages and unemployment is maybe approximately zero.

This view was around as early as Sumner and Silver (1989) JPE, where they take a proto-“sign restrictions” approach with US data and find procyclical real wages during the real shocks of the 1970s and countercyclical real wages during other recessions.

But: while Sumner-Silver was published in the JPE and racked up some citations, it seems clear that, for too long a time, this view did not penetrate enough skulls. Macroeconomists, I think it’s fair to say, were too careless for too long regarding the challenge of identification.

My sense is that this view is taken seriously now: e.g. in my second-year grad macro course, this was one of the main explanations given. At the risk of overclaiming, I would say that for anyone who has been trained post-credibility revolution, this view is simply obviously correct.

2. Composition bias: the measured real wage can be deceptive

Solon, Barsky, and Parker (1994) QJE make another vitally important point.

  1. The measured aggregate real wage only includes workers who are actually working – not the unemployed.
  2. Low wage workers have historically been more likely to lose their jobs during recessions than high wage workers. (Why is this? Good question.)

The combination of (1) and (2) implies that a measurement of aggregate real wages of employed workers will be biased upwards during recessions. (This happened in 2020, too; source)

Thus adjusting for this composition bias – as long as (2) continues to hold – causes you to realize that the more conceptually correct “shadow aggregate average real wage” is even lower, not higher, during recessions. It does point out, however, that the measured aggregate real wage is simply not the right object to look at!

(For the most comprehensive analysis of this general topic and evidence that the importance of this composition bias has grown over time, see John Grigsby’s job market paper.)

3. New hire wages, not aggregate wages, is what matters anyway

The third important point is that: conceptually, the average real wage of the incumbent employed – which is what we usually have data on – is not what matters anyway!

As Pissarides (2009) ECMA pointed out, it doesn’t really matter if the wages of incumbent employed workers are sticky. What matters is that the wages of new hires are sticky.

Why is this? Suppose that the wages of everyone working at your firm are completely fixed, but that when you hire new people, their wages can be whatever you and they want. Then there’s simply no reason for involuntary unemployment: unemployed workers will always be able to be hired by you at a sufficiently low real wage (or to drop out of the labor force voluntarily and efficiently). If new hire wages were sticky on the other hand, that’s when the unemployed can’t find such a job.

That is: it is potential new-hire wages that are the relevant marginal cost for the firm.

(For potential caveats on the importance of incumbent wages, see Masao Fukui’s job market paper; for related empirics, see Joe Hazell’s job market paper with Bledi Taska.)


Putting it all together, we have three reasons to think that the data which informed the move from sticky wage to sticky price models were misleading:

  1. Identification: looking at the real wage averaged over different shocks is misleading
  2. Composition bias: looking at the measured real wage is misleading
  3. Conceptually, looking at the real wage among the incumbent employed is not the right object

Now, maybe correcting for these, we would still find that (new-hire) real wages are not “too high” after a contractionary monetary policy shock. But this is an open question. And the best evidence from Hazell and Taska does argue for sticky wages for new hires from 2010-2016 – in particular, sticky downwards.

With that discussion of the empirical critique of sticky wage models, on to the theoretical critique.

IV. The Barro(-Hall) critique is “utterly unpersuasive”

Brief reminder: the Barro (1977) critique says that merely observing sticky nominal wages in the data does not necessarily imply that sticky wages are distortionary, because it’s possible that wages are determined as part of long-term implicit contracts.

1. So what?

But! This also does not rule out the possibility that observed nominal wage stickiness is distortionary!

We observe unresponsive nominal wages in the data. This is consistent either with the model of implicit contracts or with the distortionary sticky wage hypothesis. Based on this alone there is an observational equivalence, and thus of course this cannot be used to reject the hypothesis that sticky wages are distortionary.

Moreover, it’s unclear that we observe contracts of the type described in Barro (1977) – where the quantity of labor is highly state-dependent – in the real world, at all.

2. Circa 2021, this critique is most typically ignored anyway

The other thing to note here is: despite the concern in the 1980s about this critique of sticky wage models... we’ve ended up using these models anyway!

Erceg, Henderson, and Levin (2000) applied the Calvo assumption that a (completely random) fraction of wage-setters are (randomly) unable to adjust their wages each period. This modeling device is now completely standard – though as emphasized above only as an appendage to the baseline New Keynesian framework.

Moreover, the ascendant heterogeneous agent New Keynesian (HANK) literature often does, in fact, takes sticky wages as the baseline rather than sticky prices. See the sequence of Auclert-Rognlie-Straub papers; as well as Broer, Hansen, Krusell, and Oberg (2020) for an argument that sticky wage HANK models have a more realistic transmission mechanism than sticky price ones (cf Werning 2015).

Now maybe you think that large swathes of the macroeconomic literature are garbage (this is not, in general, unreasonable).

But this certainly does reveal that most macroeconomists today reject, at least for some purposes, the critique. Hall (2005) for example writes of, “Barro’s critique, which I have long found utterly unpersuasive.”

V. Put sticky wage models back at the center of New Keynesian thought and pedagogy?

The history of thought here and how it has changed over time is interesting on its own, but it also suggests a natural conclusion: if you think of involuntary unemployment as being at the heart of recessions, you should start from a sticky wage framework, not a sticky price framework. The original empirical and conceptual critiques of such a framework were misguided.

VI. Stabilize nominal wage growth, not inflation

More importantly, this should affect your view on normative policy recommendations:

  1. Sticky prices – when modeled via Calvo – prescribe inflation targeting: in the simplest setup, stabilize aggregate inflation so that the stickiness of prices need never affect anything. (This provides an intellectual foundation for the policy of inflation targeting used by most developed central banks today.)
  2. Sticky wages on the other hand prescribe stabilizing nominal wages: in the simplest setup, stabilize an index of aggregate nominal wages, so that the stickiness of wages need never affect anything.

We don’t want to stabilize P; we want to stabilize W!

These can be quite different. Let’s cheat and note that in a model without labor force fluctuations, stabilizing nominal wages W is the same as stabilizing nominal labor income WN. Then, for example, observe in the critical period of 2007 through late 2008 – before the Fed hit the zero lower bound – nominal labor income growth (blue) was steadily declining even though inflation (red) was rising due to spiking oil and food prices.

The accelerating inflation is why we had the FOMC meeting on September 16, 2008 – the day after Lehman Brothers declared bankruptcy (!!) – and stating, “The downside risks to growth and the upside risks to inflation are both of significant concern to the Committee” and unanimously refusing (!!) to cut its policy rate from 2%.

If the Fed had been targeting nominal wages or nominal income, instead of inflation, it would have acted sooner and the Great Recession would have been, at the least, less great.


Finally, while I just wrote that sticky prices prescribe inflation targeting as optimal monetary policy, in fact this is not generically true. It is true in the textbook New Keynesian model, where price stickiness is due to exogenously-specified Calvo pricing: a perfectly random fraction of firms is allowed to adjust price each period while all others remain stuck.

Daniele Caratelli and I have a new paper (almost ready to post!), though, showing that if price stickiness instead arises endogenously due to menu costs, then optimal policy is to stabilize nominal wages. Under menu costs, even if wages are completely flexible, then ensuring stable nominal wage growth – not stable inflation – is optimal, just as in the basic sticky wage model.

Thanks to Marc de la Barrera, Daniele Caratelli, Trevor Chow, and Laura Nicolae for useful discussions around this topic.

Dec 16, 2020

Confidence level (?): High

TLDR: “GDP percentage growth is slowing down” emphatically does not mean that “the rate at which human lives are improving” is slowing down, even under the assumption that GDP is all that matters for human wellbeing. Percentage growth slowdowns are even consistent with wellbeing growth accelerating.

I. Percentage growth is slowing down, dollar growth is speeding up

1. Here’s one perspective. The average percentage growth rate of GDP per capita in the US has fallen nearly monotonically by decade: From 2.8% in the 1960s to 0.8% in the 2000s, before rebounding to 2.5% in the recovery years of the 2010s. Pretty depressing! The growth rate is mostly slowing down.

2. Here’s another perspective. The average dollar growth rate of GDP per capita in the US has risen nearly monotonically by decade, excepting the depression years of the 2000s: From $592 in growth per year in the 1960s to $852 in the 2010s. Pretty good! The growth rate is speeding up.

3. Why should we privilege the percentage growth rate metric over the dollar metric? In contemporary discussions of our “productivity slowdown” and “great stagnation”, or debates on “how to speed up growth”, inevitably the first chart with percentage growth is shown.

I can’t eat 3 percent GDP growth; but 850 dollars in cash, I certainly know what to do with that. Does that mean that we should say “growth”, quote unquote, is not slowing down?

II. The translation into welfare growth is what matters

This isn’t a trick question: we should not in fact attach so much importance and status to percentage growth rates. But dollar terms isn’t the right metric either.

Ultimately, what we care about is welfare: how happy are people. And in that case, the relevant comparison has to use a cardinal measure of utility: how fast is utility growing?

III. Log utility is the dividing line

We’re going to need to do a bit of math to go further.

Say that – just to make the point as clear as possible – utility is only a function of GDP: higher GDP means more happiness. (Thinking of utility as depending on other factors – which it definitely does! – only strengthens the point.)

Also suppose that GDP is growing at a constant rate g:

y(t+1) = y(t) * exp(g)

If utility is log of GDP, U(t)=ln[y(t)], then percentage change in GDP exactly equals growth in welfare:

U(t+1) - U(t)
= ln[y(t+1)] - ln[y(t)] = ln[y(t+1)/y(t)] = ln[exp(g)]
= g

Thus, under log utility, we have a direct justification for caring about percentage growth: it is exactly informative of how fast welfare is growing.

Log utility is a very specific, knife-edge functional form, though!

More generally, think of the graph of ln(y): it’s upward sloping, at a diminishing rate – it’s curved. That is: there is diminishing marginal utility from higher GDP. (Diminishing marginal utility rules everything.)

Here’s the key question for any non-log utility function: How quickly does marginal utility diminish? Or graphically, how curved is the function (in GDP space)? More curved than log, or less curved than log?

For example, consider the frequently-used CRRA utility function. If the CRRA coefficient is less than 1, then the utility function is less curved than log – marginal utility diminishes slowly. Vice versa for a coefficient greater than 1. (With a coefficient equal to 1 the function becomes log).

You can see visually what I mean by more-or-less curved here: where “more curved” is CRRA with coefficient of 2, and “less curved” with a coefficient of 0.5.

The gray line – a “less curved” utility function – is closer to being linear than the other two “more curved” lines.

IV. More-or-less curved determines how we should care about percentage growth slowdowns

Here’s the resulting kernel of insight from thinking about more vs. less curved:

1. If the utility function is “more curved” than log – and marginal utility thus diminishes faster – then welfare grows slower than g. That is: if utility is more curved than log, then we need accelerating percentage growth in GDP just to maintain the same growth rate in well-being.

2. If the utility function is “less curved” than log – and marginal utility thus diminishes slower – then welfare grows faster than g. That is: if utility is less curved than log, then decelerating percentage growth in GDP can even be consistent with accelerating levels of welfare.

(In the extreme case when utility is not curved at all – when utility is linear – that is precisely when the dollar metric for growth is the right metric.)

The intuition for these points comes exactly from diminishing marginal utility: with log utility and constant percentage GDP growth, we saw that welfare growth is constant. If marginal utility diminishes faster than log, then the level of utility is of course growing slower; and vice versa.

The next figure shows this. Constant GDP growth leads to constant welfare gains under log, as time passes; accelerating welfare gains under “less curved”; and decelerating gains under “more curved”.

V. Conclusion

TLDR: “GDP percentage growth is slowing down” emphatically does not mean that “the rate at which human lives are improving” is slowing down, even under the assumption that GDP is all that matters for human wellbeing. Percentage growth slowdowns are even consistent with wellbeing growth accelerating.

Finally, to translate all this to academic-ese: even a balanced growth path model, like the semi-endogenous growth model, can have ever-accelerating welfare growth; it just depends on the utility function.

(PS: The vast majority of models of economic growth are built around functional forms that result in constant percentage growth in key variables in the long run. Thus from a modeling perspective, you may also be interested in GDP percentage growth as a test of how well these assumptions fit the data: is it constant in the long run, or not.)

Thanks to Alexey Guzey and Bharat Chandar for useful discussions around this topic; and see also Phil Trammell’s note on growth accelerations.

March 15, 2020

Confidence level (?): thinking out loud

(Ex post update: After this post was published, the FOMC met for an emergency meeting, in which it cut the policy interest rate to zero and began a new round of quantitative easing, among other measures!)

If I closed my eyes and completely wiped from my mind the fact of the coronavirus pandemic, here's what I would see in the last week:

1. Real interest rates are rising: 5 year TIPS rates are up 80bps (!!) in the last 1.5 weeks

2. Inflation expectations are collapsing: 5-year breakeven inflation is down to 0.50%

3. In the last week, even nominal interest rates are rising: 2-year treasuries rose in the past few days, including even on Thursday when equity markets were down 10%

4. Equity prices, of course, cratering

The data are not 100% clear, but this looks like a massive contractionary monetary policy shock. Interpreting these data:

1. Real rates are rising: this could be due to
(1) rising growth expectations (...unlikely);
(2) risk premia movements (maybe? Would have to be large);
(3) higher TIPS illiquidity premium (probable – cf Fed action on Thursday); or
(4) changing subjective discount factor (seems unlikely for a five-year horizon?)
(5) tighter monetary policy expectations (seems very possible!)

This reads to me like monetary policy is tightening. Even if much of the movement is due to liquidity issues rather than a change in the expected path of real rates, that illiquidity would also suggest monetary policy is too tight!

2. Inflation expectations are falling: this could be in part due to the positive oil supply shock; but expectations were falling before Saudi Arabia and Russia made their moves on March 9. Moreover, we would ceterus paribus think that the negative supply-side effects of the coronavirus would increase inflation.

3. Nominal rates: It is truly bizarre, in my mind, to see nominal Treasury yields rising in the past few days – and not just on days when the stock market was up, like Friday. That seems suggestive of expectations for tighter-than-previously-expected monetary policy.

It's also possible that liquidity issues in both the nominal and real government bond markets are distorting all of these measures. I don't know, these are some of the most liquid markets in the world.

The data above are for the US, but looking at French government bonds, I also see real rates rising (!!) and inflation expectations falling:

Meanwhile, the ECB on Thursday chose not to cut interest rates, despite widespread expectation for them to cut, which seems frankly insane (and equity markets were subsequently down 10-15%!).

Watching these various indicators – particularly real interest rates rising almost a full percentage point (!) – frankly I feel a little like I'm going crazy. Everyone is talking about the pandemic – rightly – but it seems to me that we have a dual crisis at the moment. The virus, and monetary policy is way too tight.

In the US, we are not at the zero lower bound, so the Fed has no excuse for not acting. And before the FOMC uses the ZLB as an excuse anyway, they could at least attempt forward guidance or actual QE (not the repo liquidity measures that occurred on Thursday).

Obviously, the pandemic is a big crisis with its own set of complicating issues. But central banks shouldn't be making the problem worse than it need be. I.e., even if potential real GDP falls due to the pandemic and associated shutdowns, central banks should still be (approximately) trying to keep GDP on track with potential GDP (modulo perhaps some tradeoff with price dispersion), not implicitly tightening policy and making things even worse.

The supply side, as almost always, is more important; but at the moment central banks seem like they're actively or passively making things worse.

It will be very informative, I think, to watch the market open tonight.

June 5, 2018

Confidence level (?): High

The efficient market hypothesis says that you can't pick out which stocks are undervalued versus which are overvalued. Likewise, I claim that you can't pick out which restaurants are underpriced versus which restaurants are overpriced.

Think you've found a great company, so that their stock will outperform on a risk-adjusted basis? Nope, someone else has already incorporated that information into the stock price and pushed the price up.

Think you've found a great restaurant which offers meals at a decent price? Nope, they've already raised their prices to the point where the extra cost just equals the extra utility you get from their extra delicious cuisine.


A. But, first of all, we need to emphasize that this is on a risk-adjusted basis. A portfolio of stocks might have higher expected returns – but only if it's riskier.

This applies to restaurants as well to stocks – trying a new exotic cuisine could be eye-opening and awesome, or awful. Admittedly, this is quantitatively much less important for restaurants.

(This is the essence of modern asset pricing theory.)

B. Similarly to stocks, fund managers will not consistently deliver alpha to their investors: if any manager can consistently deliver alpha, that manager will simply raise their fees to capture it for themselves. (This is the essence of the "rational model of active management" model of Berk and Green 2004.)


Moreover, second of all, cheap restaurants and cheap managers might exist, but they can have very high search costs.

Truly great cheap restaurants might exist, but you have to pay a lot in time, money, and energy spent searching and reading reviews to pinpoint them. These search costs, this time wasted digging around on Yelp, are real costs: they take time and money that you could otherwise have spent on better food or anything else which gives you utility.

This is likewise true of asset managers. Cheap asset managers that provide alpha might truly exist, but you have to spend so much time and money searching and evaluating potential such managers that these search costs will eat up that alpha. Otherwise, other investors would have already found the manager and grabbed that alpha.

(This is the essence of Garleanu and Pedersen's "Efficiently Inefficient" model.)


Third and finally: the utility of eating out at a restaurant is not just a result of tastiness and search costs. It incorporates every stream of services provided by the restaurant: convenience of location most of all, but also quality of service, ambience, and the social aspect of the other patrons. If a given restaurant achieves higher on these marks – e.g. a restaurant full of beautiful fashion models – then it should be expected that the quality of the food is less.

Similarly, to a lesser extent, with assets or with asset managers. Assets provide more than just a stream of returns: they provide the service of liquidity, or a "convenience yield". We can think of people enjoying the comfort provided by liquid assets, much like they enjoy the ambience of a nice restaurant. And just as a restaurant full of fashion models will – all else equal – have lower quality food, an asset or manager that offers higher liquidity should be expected to provide a lower pecuniary return.

(The idea of a convenience yield has been discussed by Cochrane, Koning, and others. This is also the entirety of the value behind cryptocurrencies.)

[Personal aside: This area is a core component of my own research agenda, as I currently envision it.]


Conclusion: in equilibrium, assets or asset managers should not be undervalued or overvalued, on a risk-adjusted, fee-adjusted, search cost-adjusted, liquidity-adjusted basis. Likewise, in equilibrium, restaurants should not be underpriced or overpriced, once one takes into account their riskiness; the time spent searching for them on Yelp and reading reviews; and the ambience and other "convenience yield" services provided by the restaurant.

Aug 15, 2017

Confidence level (?): Low

Most people are probably somewhat overconfident. Most people – myself surely included – probably typically overestimate their own talents, and they (we) are overly confident in the precision of their estimates, underestimating uncertainty.

This bias has viscerally real, important consequences. Governments are overconfident that they can win wars quickly and easily; overconfident CEOs have a higher tendency to undertake mergers and issue more debt than their peers.

I claim, however, that this bias does not matter for asset pricing in particular. That is, stock prices (and other asset prices) are not affected by overconfident investors.

In fact, I claim that any kind of behavioral bias cannot in and of itself affect stock prices.

The idea that behavioral biases, on their own, can affect asset prices is one of if not the most widely held misconceptions about financial markets. Just because most people (myself included!) are blinded by cognitive biases – overconfidence, status quo bias, confirmation bias, etc. – does not mean that stock prices are at all affected or distorted.

If this seems crazy, let me try putting it another way: just because behavioral biases exist does not mean that you can get rich by playing the stock market and exploiting the existence of these biases.

The trick is that it only takes the existence of one rational unconstrained arbitrageur to keep prices from deviating away from their rational level.

To see this, consider two extremes.

All it takes is one
First, suppose everyone in the world is perfectly rational and unbiased, except for one poor fellow, Joe Smith. Joe is horribly overconfident, and thinks he's smarter than everyone else. He invests all of his money in Apple stock, insisting that everyone else is undervaluing the company, and pushing the Apple share price up.

Of course, since every other investor is perfectly rational and informed, they will notice this and immediately race to go short Apple, betting against it until the price of the Apple stock is pushed back to the rational level.

Now, consider the inverse situation. Everyone in the world is systematically biased and cognitively limited, except for one rational informed Jane Smith. Perhaps more realistically, instead of Jane Smith, the one rational agent is some secretive hedge fund.

Now, billions of irrational investors are pushing prices away from their rational value. However, as long as Rational Hedge Fund LLC has access to enough capital, this one rational agent can always buy an undervalued stock until the price gets pushed up to its rational level, or short an overvalued stock until the price gets pushed down to the rational level. Rational Hedge Fund LLC profits, and prices are kept at their rational levels.

Even more realistically, instead of a single hypervigilant rational hedge fund keeping all stocks at their respective rational levels, there could be many widely dispersed investors each with specialized knowledge in one stock or one industry, collectively working to keep prices in line.

The marginal investor
The real world, of course, is somewhere between these two extremes. Most people have a host of cognitive biases, which leads to "noise traders" randomly buying and selling stocks. However, there is also a small universe of highly active, often lightning fast rational investors who quickly arbitrage away any price distortions for profit.

It is these marginal investors who determine the price of stocks, not the biased investors. This is why I say that "cognitive biases don't matter for stock prices" – the existence of any unconstrained rational investors ensures that biases will not flow through to asset pricing.

The important caveat: the "limits to arbitrage"
There is an extremely important caveat to this story.

Note that I quietly slipped in the requirement that Rational Hedge Fund LLC must have "access to enough capital." If the rational investors cannot raise enough money to bet against the noisy irrational traders, then prices cannot be pushed to their rational equilibrium level.

(The importance of access to capital is more than just the ability to apply price pressure. It's also important for the marginal investor to be able to withstand the riskiness of arbitrage.)

This assumption of frictionless access to leverage clearly does not hold perfectly in the real world: lending markets are troubled by principal-agent problems, moral hazard, and other imperfections.

This (very important) friction is known as the "limits to arbitrage."

Summing up
It is irrationality in conjunction with limits to arbitrage which allow for market prices to diverge from their rational levels. It is important to acknowledge that cognitive biases alone are not a sufficient condition for market inefficiency. Irrationality and limits to arbitrage are both necessary.

More pithily: Peanut butter alone is not enough to make a PB&J sandwich, and behavioral biases alone are not enough to make the stock market inefficient.

July 18, 2017

Confidence level (?): Very high

The Efficient Market Hypothesis (EMH) was famously defined by Fama (1991) as "the simple statement that security prices fully reflect all available information."

That is, you can't open the Wall Street Journal, read a news article from this morning about Google's great earnings numbers that were just released, and make money by buying Google stock. The positive information contained in the earnings numbers would already have been incorporated into Google's share price.

To put it another way, the EMH simply says that there is no such thing as a free lunch for investors.

Does this imply that stock prices (or other asset prices) are unpredictable? No! The EMH unequivocally does not mean that prices or returns are unpredictable.

This fallacy arises all the time. Some author claims to have found a way to predict returns and so declares, "The EMH is dead." Return predictability does not invalidate the EMH. This is important – the empirical evidence shows that returns are indeed eminently predictable.

The key lies with risk premia.

I. What are risk premia?
The price of a stock (or any other asset) can be decomposed into two parts:

  1. The (discounted) expected value of the stock
  2. A "risk premium"

The first part is the standard discounted present-value that you might read about in an accounting textbook. The second is the compensation required by the stock investor in order to bear the risk that the stock might drop in value, known as a risk premium.

To understand risk premia, suppose that I offer you the following deal. You can pay me $x, and then get to flip a coin: heads I give you $100, tails you get nothing. How much would you be willing to pay to have this opportunity?

Although the expected value of this bet is $50, you're probably only going to be willing to pay something like $45 for the chance to flip the coin, if that. The five dollars difference is the compensation you demand in order to bear the risk that you could lose all your money – the risk premium.

II. Return predictability is compensation for risk
The above decomposition suggests that return predictability can either be the result of

  1. The ability to truly predict movements in the underlying value of the stock
  2. The ability to predict risk premia

If the first type of predictability were possible, this would in fact invalidate the EMH. However, the second sort of predictability – predictability of risk premia – allows for stock returns to be predictable, even under the EMH.

This is because, if only risk premia are predictable, then there is still no free lunch.

Sure, you can predict that a stock portfolio will outperform the market over the next year. However, this excess return is simply compensation for the fact that this set of stocks is extra risky – i.e., the portfolio has a high risk premium.

As an extreme example, consider the well-known fact that buying and holding a diverse basket of stocks predictably has higher expected returns than buying and holding short-term Treasury bills.

Is this a free lunch? Does the existence of the stock market invalidate the EMH? No. This return predictability exists only because equities are fundamentally riskier than T-bills.

III. Summing up
This is all to say that while returns may be predictable, it is likely that any profits earned from such predictable strategies are merely compensation for extra risk.

The EMH says that there is no free lunch from investing. Just because returns are predictable does not mean you can eat for free.


Postscript. There is another (outdated) theory, the "random walk hypothesis", defined as the claim that returns are not predictable. This is different from the EMH, which says that asset prices reflect all available information. The random walk hypothesis has been shown to be clearly empirically false, per links above.

Apr 9, 2017

Confidence level (?): Medium

Update: Selgin points out in correspondence and Sumner points out in comments below that, the below discussion is implicitly using variables in per capita terms.

This post continues the discussion from Scott Sumner's thoughtful reply to my critique of NGDP targeting from 2015.

In short:

  1. Some economists see zero inflation as optimal in the long run. NGDP targeting cannot achieve this in the long run, except under discretion, as I discussed in my original post.
  2. On the other hand, as I discuss below, many models prescribe the Friedman rule for the optimal long-run rate of inflation. This can, in fact, be achieved under NGDP targeting, even without discretion!

I. The benefit of NGDP targeting is that inflation can fluctuate in the short run. But can NGDP targeting achieve a long-run optimal inflation rate?

Targeting NGDP rather than targeting inflation allows inflation to fluctuate in the short run. This is the major benefit of NGDP targeting, since it makes sense to have higher inflation in the short run when there is a cyclical growth slowdown and lower inflation when there is a growth boom, (see Selgin, Sumner, Sheedy, myself).

This is an argument about the short or medium run, at the frequency of business cycles (say 2-5 years).

Separately, you could imagine – whether or not inflation is allowed to vary in the short run, as it would be under NGDP targeting – that there is a long-run rate of inflation which is optimal. That is, is there a "best" inflation rate at which the economy should ideally settle, at a 10+ year horizon?

If there is an optimal long-run inflation rate, you would hope that this could be achieved under NGDP targeting in the long-run, even while inflation is allowed to fluctuate in the short run.

II. The optimal long-run inflation rate
Economists have thought a lot about the question of what the long-run optimal inflation rate is. There are two competing answers [1]:

1. No inflation: One strand of literature argues that the optimal long-run inflation rate is precisely zero, based on price stickiness. The argument goes: by keeping the price level stable, sticky prices cannot distort relative prices.

2. Friedman rule: Alternatively, another strand of the literature going back to Milton Friedman argues that the optimal inflation rate is the negative of the short-term risk-free real interest rate (i.e. slight deflation). The argument here is that this would set the nominal risk-free interest rate to zero. In this world, there would be no opportunity cost to holding money, since both cash and risk-free bonds would pay zero interest, and the economy could be flush with liquidity and the optimum quantity of money achieved.

These two schools of thought clearly contradict each other. We will consider each separately.

What we want to know is this: could NGDP targeting achieve the optimal inflation rate in the long run (even while allowing beneficial short-run fluctuations in inflation)?

III. NGDP targeting and zero long-run inflation
In a previous essays post, I critiqued NGDP targeting by pointing out that NGDP targeting could not achieve zero inflation in long-run, unless the central bank could discretionarily change the NGDP target. In other words, I was arguing based on the first strand of literature that NGDP targeting was deficient in this respect.

The accounting is simple: NGDP growth = real growth + inflation. Under NGDP targeting without discretion, the growth rate of NGDP is fixed. But, real growth varies in the long run due to changing productivity growth – for example, real growth was higher in the 1960s than it has been in recent decades. As a result, the long-run inflation rate must vary and thus is unanchored.

Zero inflation can be achieved in the long run, but only at the cost of trusting the central bank to act discretionarily and appropriately modify the long-run NGDP target.

I think that such discretion would be problematic, for reasons I outline in the original post. I'll note, however, that I (now) assess that the benefits of NGDP targeting in preventing short-run recessions outweigh this smaller long-run cost.

IV. NGDP targeting and the Friedman rule
On the other hand – and I haven't seen this result discussed elsewhere before – NGDP targeting can achieve the Friedman rule for the optimal inflation rate in the long run without discretion. That is, under the logic of the second strand of literature, NGDP targeting can achieve the optimum. Here's the accounting logic:

The Friedman rule prescribes that the optimal inflation rate, pi*, be set equal to the negative of the real interest rate r so that the nominal interest rate is zero:
pi* = -r

Here's the kicker: Under a wide class of models (with log utility), the long-run real interest rate equals the rate of technological progress g plus the rate of time preference b. See Baker, DeLong, and Krugman (2005) for a nice overview. As a result, the optimal inflation rate under the Friedman rule can be written:
pi* = -r = -(b+g)

This can be achieved under NGDP targeting without discretion! Here's how.

Suppose that the central bank targets a nominal GDP growth rate of -b, that is, an NGDP path that declines at the rate of time preference. Recall again, under NGDP targeting, NGDP growth = g + pi. Since the central bank is targeting an NGDP growth rate of -b, if we rearrange to solve for inflation, we get that
pi = NGDP growth - g = -b - g

That's the optimal inflation rate implied by the Friedman rule shown above. This result holds even if the long-run rate of productivity growth (g) changes.

Thus, we have shown that if the central bank targets an NGDP path that declines at the rate of time preference, then in the long run the Friedman rule will be achieved.

To summarize, under such a regime, the economy would get the short-run benefits of flexible inflation for which NGDP targeting is rightfully acclaimed; while still achieving the optimal long-run inflation rate.

This is a novel point in support of NGDP targeting, albeit a very specific version of NGDP targeting: an NGDP target of negative the rate of time preference.

V. Summing up
There's still the tricky problem that economists can't even agree on whether the Friedman rule or no-inflation is superior.

So, to sum up once more:

  1. NGDP targeting cannot achieve zero inflation in the long run without discretion, as discussed in my original post. This is unfortunate if zero inflation is long-run optimal.
  2. However, NGDP targeting – if targeting a growth rate of -b – can in fact achieve the Friedman rule in the long run without discretion. This is fortunate if the Friedman rule is the long-run optimal inflation rate.

To close this out, I'll note that an alternative middle ground exists... an NGDP target of 0%. This would see a long-run inflation rate of -g: not as low as -g-b as prescribed by the Friedman rule; but not as high as 0% as prescribed by no-inflationistas.

Such a policy is also known as a "productivity norm," (since long-run inflation is negative of productivity growth), advocated prominently by George Selgin (1997).

[1] I ignore ZLB considerations, which typically imply a higher optimal inflation rate, since many advocates of NGDP targeting do not see the ZLB as a true policy constraint (myself included).

Dec 21, 2016

Confidence level (?): Very high

I. Marx vs. Smith and food banks
When Heinz produces too many Bagel Bites, or Kellogg produces too many Pop-Tarts, or whatever, these mammoth food-processing companies can donate their surplus food to Feeding America, a national food bank. Feeding America then distributes these corporate donations to local food banks throughout the country.

What's the economically optimal way to allocate the donations across the country?

Option one is what you might call "full communism." Under full communism, Feeding America collects the food donations and then top-down tells individual food banks what endowments they will be receiving, based on Feeding America's own calculation of which food banks need what.

Prior to 2005, this was indeed what occurred: food was distributed by centralized assignment. Full communism!

The problem was one of distributed versus centralized knowledge. While Feeding America had very good knowledge of poverty rates around the country, and thus could measure need in different areas, it was not as good at dealing with idiosyncratic local issues.

Food banks in Idaho don't need a truckload of potatoes, for example, and Feeding America might fail to take this into account. Or maybe the Chicago regional food bank just this week received a large direct donation of peanut butter from a local food drive, and then Feeding America comes along and says that it has two tons of peanut butter that it is sending to Chicago.

To an economist, this problem screams of the Hayekian knowledge problem. Even a benevolent central planner will be hard-pressed to efficiently allocate resources in a society since it is simply too difficult for a centralized system to collect information on all local variation in needs, preferences, and abilities.

This knowledge problem leads to option two: market capitalism. Unlike poorly informed central planners, the decentralized price system – i.e., the free market – can (often but not always) do an extremely good job of aggregating local information to efficiently allocate scarce resources. This result is known as the First Welfare Theorem.

Such a system was created for Feeding America with the help of four Chicago Booth economists in 2005. Instead of centralized allocation, food banks were given fake money – with needier food banks being given more – and allowed to bid for different types of food in online auctions. Prices are thus determined by supply and demand.

At midnight each day all of the (fake) money spent that day is redistributed, according to the same formula as the initial allocation. Accordingly, any food bank which does not bid today will have more money to bid with tomorrow.

Under this system, the Chicago food bank does not have to bid on peanut butter if it has just received a large peanut butter donation from another source. The Idaho food bank, in turn, can skip on bidding for potatoes and bid for extra peanut butter at a lower price. It's win-win-win.

By all accounts, the system has worked brilliantly. Food banks are happier with their allocations; donations have gone up as donors have more confidence that their donations will actually be used. Chalk one up for economic theory.

II. MV=PY, information frictions, and food banks
This is all pretty neat, but here's the really interesting question: what is optimal monetary policy for the food bank economy?

Remember that food banks are bidding for peanut butter or cereal or mini pizzas with units of fake money. Feeding America has to decide if and how the fake money supply should grow over time, and how to allocate new units of fake money. That's monetary policy!

Here's the problem for Feeding America when thinking about optimal monetary policy. Feeding America wants to ensure that changes in prices are informative for food banks when they bid. In the words of one of the Booth economists who helped design the system:

"Suppose I am a small food bank; I really want a truckload of cereal. I haven't bid on cereal for, like, a year and a half, so I'm not really sure I should be paying for it. But what you can do on the website, you basically click a link and when you click that link it says: This is what the history of prices is for cereal over the last 5 years. And what we wanted to do is set up a system whereby by observing that history of prices, it gave you a reasonable instinct for what you should be bidding."

That is, food banks face information frictions: individual food banks are not completely aware of economic conditions and only occasionally update their knowledge of the state of the world. This is because obtaining such information is time-consuming and costly.

Relating this to our question of optimal monetary policy for the food bank economy: How should the fake money supply be set, taking into consideration this friction?

Obviously, if Feeding America were to randomly double the supply of (fake) money, then all prices would double, and this would be confusing for food banks. A food bank might go online to bid for peanut butter, see that the price has doubled, and mistakenly think that demand specifically for peanut butter has surged.

This "monetary misperception" would distort decision making: the food bank wants peanut butter, but might bid for a cheaper good like chicken noodle soup, thinking that peanut butter is really scarce at the moment.

Clearly, random variation in the money supply is not a good idea. More generally, how should Feeding America set the money supply?

One natural idea is to copy what real-world central banks do: target inflation.

The Fed targets something like 2% inflation. But, if the price of a box of pasta and other foods were to rise 2% per year, that might be confusing for food banks, so let's suppose a 0% inflation target instead.

It turns out inflation targeting is not a good idea! In the presence of the information frictions described above, inflation targeting will only sow confusion. Here's why.

As I go through this, keep in the back of your mind: if households and firms in the real-world macroeconomy face similar information frictions, then – and this is the punchline of this entire post – perhaps inflation targeting is a bad idea in the real world as well.

III. Monetary misperceptions
I demonstrate the following argument rigorously in a formal mathematical model in a paper, "Monetary Misperceptions: Optimal Monetary Policy under Incomplete Information," using a microfounded Lucas Islands model. The intuition for why inflation targeting is problematic is as follows.

Suppose the total quantity of all donations doubles.

You're a food bank and go to bid on cheerios, and find that there are twice as many boxes of cheerios available today as yesterday. You're going to want to bid at a price something like half as much as yesterday.

Every other food bank looking at every other item will have the same thought. Aggregate inflation thus would be something like -50%, as all prices would drop by half.

As a result, under inflation targeting, the money supply would simultaneously have to double to keep inflation at zero. But this would be confusing: Seeing the quantity of cheerios double but the price remain the same, you won't be able to tell if the price has remained the same because
(a) The central bank has doubled the money supply
(b) Demand specifically for cheerios has jumped up quite a bit

It's a signal extraction problem, and rationally you're going to put some weight on both of these possibilities. However, only the first possibility actually occurred.

This problem leads to all sorts of monetary misperceptions, as money supply growth creates confusions, hence the title of my paper.

Inflation targeting, in this case, is very suboptimal. Price level variation provides useful information to agents.

IV. Optimal monetary policy
As I work out formally in the paper, optimal policy is instead something close to a nominal income (NGDP) target. Under log utility, it is exactly a nominal income target. (I've written about nominal income targeting before more critically here.)

Nominal income targeting in this case means that the money supply should not respond to aggregate supply shocks. In the context of our food banks, this result means that the money supply should not be altered in response to an increase or decrease in aggregate donations.

Instead, if the total quantity of all donations doubles, then the price level should be allowed to fall by (roughly) half. This policy prevents the confusion described above.

Restating, the intuition is this. Under optimal policy, the aggregate price level acts as a coordination mechanism, analogous to the way that relative prices convey useful information to agents about the relative scarcity of different goods. When total donations double, the aggregate price level signals that aggregate output is less scarce by halving.

It turns out that nominal income targeting is only exactly optimal (as opposed to approximately optimal) under some special conditions. I'll save that discussion for another post though.

Feeding America, by the way, does not target constant inflation. They instead target "zero inflation for a given good if demand and supply conditions are unchanged." This alternative is a move in the direction of a nominal income target.

V. Real-world macroeconomic implications
I want to claim that the information frictions facing food banks also apply to the real economy, and as a result, the Federal Reserve and other central banks should consider adopting a nominal income target. Let me tell a story to illustrate the point.

Consider the owner of an isolated bakery. Suppose one day, all of the customers seen by the baker spend twice as much money as the customers from the day before.

The baker has two options. She can interpret this increased demand as customers having come to appreciate the superior quality of her baked goods, and thus increase her production to match the new demand. Alternatively, she could interpret this increased spending as evidence that there is simply more money in the economy as a whole, and that she should merely increase her prices proportionally to account for inflation.

Economic agents confounding these two effects is the source of economic booms and busts, according to this model. This is exactly analogous to the problem faced by food banks trying to decide how much to bid at auction.

To the extent that these frictions are quantitatively important in the real world, central banks like the Fed and ECB should consider moving away from their inflation targeting regimes and toward something like a nominal income target, as Feeding America has.

VI. Summing up
Nominal income targeting has recently enjoyed a surge in popularity among academic monetary economists, so the fact that this result aligns with that intuition is pretty interesting.

To sum up, I'll use a metaphor from Selgin (1997).

Consider listening to a symphony on the radio. Randomly turning the volume knob up and down merely detracts from the musical performance (random variation in the price level is not useful). But, the changing volume of the orchestra players themselves, from quieter to louder and back down again, is an integral part of the performance (the price level should adjust with natural variations in the supply of food donations). The changing volume of the orchestra should not be smoothed out to maintain a constant volume (constant inflation is not optimal).

Central banks may want to consider allowing the orchestra to do its job, and reconsider inflation targeting as a strategy.

Dec 16, 2015

Confidence level (?): High

Behavioral economists have a concept called loss aversion. It's almost always described something like this:

"Loss aversion implies that one who loses $100 will lose more satisfaction than another person will gain satisfaction from a $100 windfall."
Wikipedia, as of December 2015

Sounds eminently reasonable, right? Some might say so reasonable, in fact, that it's crazy that those darn neoclassical economists don't incorporate such an obvious, fundamental fact about human nature in their models.

It is crazy – because it's not true! The pop definition of loss aversion given above – that 'losses hurt more than equivalently sized gains' – is precisely the concept of diminishing marginal utility (DMU) that is boringly standard in standard price theory.

Loss aversion is, in fact, a distinct and (perhaps) useful concept. But somewhat obnoxiously, many behavioral economists, particularly in their popular writings, have a tendency to conflate it with DMU in a way that makes the concept seem far more intuitive than it is, and in the process wrongly makes standard price theory look bad.

I'm not just cherry-picking a bad Wikipedia edit. I name names at the bottom of this post, listing where behavioral economists have (often!) given the same misleading definition. It's wrong! Loss aversion is about reference dependence.

To restate, what I'm claiming is this:

  1. Many behavioral economists use an incorrect definition of loss aversion when writing for popular audiences
  2. This incorrect definition is in fact the property of DMU that is assumed in all of neoclassical economics
  3. DMU is much more intuitive than the real definition of loss aversion, and so by using a false definition of loss aversion, neoclassical economics is made to look unnecessarily bad and behavioral economics misleadingly good

Let me walk through the difference between DMU and loss aversion painstakingly slowly:

Diminishing marginal utility
"Diminishing marginal utility" is the idea that the more you have of something, the less you get out of having a little bit more of it. For example:

If you own nothing but $1,000 and the clothes on your back, and I then give you $100,000, that is going to give you a heck of a lot more extra happiness then if you had $100 million and I gave you $100,000.

An important corollary follows immediately from this: losses hurt more than gains!

I made a super high quality illustration to depict this:

What we have here is a graph of your utility as a function of your wealth under extremely standard (i.e., non-behavioral) assumptions. The fact that the line flattens out as you get to higher wealth levels is the property of DMU.

We can also see that equivalently sized losses hurt more than gains. As you go from 10k wealth to 2k wealth (middle green line to bottom green line), your utility falls by more than the amount your utility rises if you go from 10k wealth to 18k wealth (middle green to top green lines), despite the change in wealth being the same 8k in both directions.

Standard economics will always assume DMU, thus capturing exactly the intuition of the idea described in the above Wikipedia definition of loss aversion.

More mathematically – and I'm going to breeze through this – if your utility is purely a function of your wealth, Utility=U(W), then we assume that U'(W)>0 but U''(W)<0, i.e. your utility function is concave. With these assumptions, the result that U(W+ε)-U(W) < U(W)-U(W-ε) follows from taking a Taylor expansion. See proof attached below.

Loss aversion
Loss aversion is a consequence of reference dependence and is an entirely different beast. The mathematical formulation was first made in Tversky and Kahneman (1991).

In words, loss aversion says this: Suppose you have nothing but the clothes you're wearing and $10,000 in your pocket, and then another $10,000 appears in your pocket out of nowhere. Your level of utility/happiness will now be some quantity given your wealth of $20,000.

Now consider a situation where you only own your clothes and the $30,000 in your pocket. Suppose suddenly $10,000 in your pocket disappears. Your total wealth is $20,000 – that is, exactly the same as the prior situation. Loss aversion predicts that in this situation, your level of utility will be lower than in the first situation, despite the fact that in both situations your wealth is exactly $20,000, because you lost money to get there.

Perhaps this concept of loss aversion is reasonable in some situations. It doesn't seem crazy to think that people don't like to lose things they had before.

But this concept is entirely different from the idea that 'people dislike losses more than they like gains' which some sloppy behavioral economists go around blathering about. It's about reference dependence! Your utility depends on your reference point: did you start with higher or lower wealth than you currently have?

In their academic papers, behavioral economists are very clear on the distinction. The use of math in formal economic models imposes precision. But when writing for a popular audience in the less-precise language of English – see below for examples – the same economists slip into using an incorrect definition of loss aversion.

Behavioral economics has not developed a brilliant newfound qualitative insight that people hate losses more than they like gains. This has been standard in price theory since Alfred Marshall's 1890 Principles of Economics.


Sep 15, 2015

Confidence level (?): Very high

Until very recently – see last month's WSJ survey of economists – the FOMC was widely expected to raise the target federal funds rate this week at their September meeting. Whether or not the Fed should be raising rates is a question that has received much attention from a variety of angles. What I want to do in this post is answer that question from a very specific angle: the perspective of a New Keynesian economist.

Why the New Keynesian perspective? There is certainly a lot to fault in the New Keynesian model (see e.g. Josh Hendrickson). However, the New Keynesian framework dominates the Fed and other central banks across the world. If we take the New Keynesian approach seriously, we can see what policymakers should be doing according to their own preferred framework.

The punch line is that the Fed raising rates now is the exact opposite of what the New Keynesian model of a liquidity trap recommends.

If you're a New Keynesian, this is the critical moment in monetary policy. For New Keynesians, the zero lower bound can cause a recession, but need not result in a deep depression, as long as the central bank credibly promises to create an economic boom after the zero lower bound (ZLB) ceases to be binding.

That promise of future growth is sufficient to prevent a depression. If the central bank instead promises to return to business as normal as soon as the ZLB stops binding, the result is a deep depression while the economy is trapped at the ZLB, like we saw in 2008 and continue to see in Europe today. The Fed appears poised to validate earlier expectations that it would indeed return to business as normal.

If the New Keynesian model is accurate, this is extremely important. By not creating a boom today, the Fed is destroying any credibility it has for the next time we hit the ZLB (which will almost certainly occur during the next recession). It won't credibly be able to promise to create a boom after the recession ends, since everyone will remember that it did not do so after the 2008 recession.

The result, according to New Keynesian theory, will be another depression.

I. The theory: an overview of the New Keynesian liquidity trap

I have attached at the bottom of this post a reference sheet going into more detail on Eggertsson and Woodford (2003), the definitive paper on the New Keynesian liquidity trap. Here, I summarize at a high level –skip to section II if you are familiar with the model.

A. The NK model without a ZLB

Let's start by sketching the standard NK model without a zero lower bound, and then see how including the ZLB changes optimal monetary policy.

The basic canonical New Keynesian model of the economy has no zero lower bound on interest rates and thus no liquidity traps (in the NK context, a liquidity trap is defined as a period when the nominal interest rate is constrained at zero). Households earn income through labor and use that income to buy a variety of consumption goods and consume them to receive utility. Firms, which have some monopoly power, hire labor and sell goods to maximize their profits. Each period, a random selection of firms are not allowed to change their prices (Calvo price stickiness).

With this setup, the optimal monetary policy is to have the central bank manipulate the nominal interest rate such that the real interest rate matches the "natural interest rate," which is the interest rate which would prevail in the absence of economic frictions. The intuition is that by matching the actual interest rate to the "natural" one, the central bank causes the economy to behave as if there are no frictions, which is desirable.

In our basic environment without a ZLB, a policy of targeting zero percent inflation via a Taylor rule for the interest rate exactly achieves the goal of matching the real rate to the natural rate. Thus optimal monetary policy results in no inflation, no recessions, and everyone's the happiest that they could possibly be.

B. The NK liquidity trap

The New Keynesian model of a liquidity trap is exactly the same as the model described above, with one single additional equation: the nominal interest rate must always be greater than or equal to zero.

This small change has significant consequences. Whereas before zero inflation targeting made everyone happy, now such a policy can cause a severe depression.

The problem is that sometimes the interest rate should be less than zero, and the ZLB can prevent it from getting there. As in the canonical model without a ZLB, optimal monetary policy would still have the central bank match the real interest rate to the natural interest rate.

Now that we have a zero lower bound, however, if the central bank targets zero inflation, then the real interest rate won't be able to match the natural interest rate if the natural interest rate ever falls below zero!

And that, in one run-on sentence, is the New Keynesian liquidity trap.

Optimal policy is no longer zero inflation. The new optimal policy rule is considerably more complex and I refer you to the attached reference sheet for full details. But the essence of the idea is quite intuitive:

If the economy ever gets stuck at the ZLB, the central bank must promise that as soon as the ZLB is no longer binding it will create inflation and an economic boom.

The intuition behind this idea is that the promise of a future boom increases the inflation expectations of forward-looking households and firms. These increased inflation expectations reduce the real interest rate today. This in turn encourages consumption today, diminishing the depth of the recession today.

All this effect today despite the fact that the boom won't occur until perhaps far into the future! Expectations are important, indeed they are the essence of monetary policy.

C. An illustration of optimal policy

Eggertsson (2008) illustrates this principle nicely in the following simulation. Suppose the natural rate is below the ZLB for 15 quarters. The dashed line shows the response of the economy to a zero-inflation target, and the solid line the response to the optimal policy described above.

Under optimal policy (solid line), we see in the first panel that the interest rate is kept at zero even after period 15 when the ZLB ceases to bind. As a result, we see in panels two and three that the depth of the recession is reduced to almost zero under policy; there is no massive deflation; and there's a nice juicy boom after the liquidity trap ends.

In contrast, under the dashed line – which you can sort of think of as closer to the Fed's current history independent policy – there is deflation and economic disaster.

II. We're leaving the liquidity trap; where's our boom?

To be completely fair, we cannot yet say that the Fed has failed to follow its own model. We first must show that the ZLB only recently has ceased or will cease to be binding. Otherwise, a defender of the Fed could argue that the lower bound could have ceased to bind years ago, and the Fed has already held rates low for an extended period.

The problem for showing this is that estimating the natural interest rate is extremely challenging, as famously argued by Milton Friedman (1968). That said, several different models using varied estimation methodologies all point to the economy still being on the cusp of the ZLB, and thus the thesis of this post: the Fed is acting in serious error.

Consider, most tellingly, the New York Fed's own model! The NY Fed's medium-scale DSGE model is at its core the exact same as the basic canonical NK model described above, with a lot of bells and whistles grafted on. The calibrated model takes in a whole jumble of data – real GDP, financial market prices, consumption, the kitchen sink, forecast inflation, etc. – and spits outs economic forecasts.

It can also tell us what it thinks the natural interest rate is. From the perspective of the New York Fed DSGE team, the economy is only just exiting the ZLB:

Barsky et al (2014) of the Chicago Fed perform a similar exercise with their own DSGE model and come to the same conclusion:

Instead of using a microfounded DSGE model, John Williams and Thomas Laubach, president of the Federal Reserve Bank of San Francisco and director of monetary affairs of the Board of Governors respectively, use a reduced form model estimated using a Kalman filter. Their model has that the natural rate in fact still below its lower bound (in green):

David Beckworth has a cruder but more transparent regression model here and also finds that the economy remains on the cusp of the ZLB (in blue):

If anyone knows of any alternative estimates, I'd love to hear in the comments.

With this fact established, we have worked through the entire argument. To summarize:

  1. The Fed thinks about the world through a New Keynesian lens
  2. The New Keynesian model of a liquidity trap says that to prevent a depression, the central bank must keep rates low even after the ZLB stops being binding, in order to create an economic boom
  3. The economy is only just now coming off the ZLB
  4. Therefore, a good New Keynesian should support keeping rates at zero.
  5. So: why is the Fed about to raise rates?!

III. What's the strongest possible counterargument?

I intend to conclude all future essays by considering the strongest possible counterarguments to my own. In this case, I see only two interesting critiques:

A. The NK model is junk

This argument is something I have a lot of sympathy for. Nonetheless, it is not a very useful point, for two reasons.

First, the NK model is the preferred model of Fed economists. As mentioned in the introduction, this is a useful exercise as the Fed's actions should be consistent with its method of thought. Or, its method of thought must change.

Second, other models give fairly similar results. Consider the more monetarist model of Auerbach and Obstfeld (2005) where the central bank's instrument is the money supply instead of the interest rate (I again attach my notes on the paper below).

Instead of prescribing that the Fed hold interest rates lower for longer as in Eggertsson and Woodford, Auerbach and Obstfeld's cash-in-advance model shows that to defeat a liquidity trap the Fed should promise a one-time permanent level expansion of the money supply. That is, the expansion must not be temporary: the Fed must continue to be "expansionary" even after the ZLB has ceased to be binding by keeping the money supply expanded.

This is not dissimilar in spirit to Eggertsson and Woodford's recommendation that the Fed continue to be "expansionary" even after the ZLB ceases to bind by keeping the nominal rate at zero.

B. The ZLB ceased to bind a long time ago

The second possible argument against my above indictment of the Fed is the argument that the natural rate has long since crossed the ZLB threshold and therefore the FOMC has targeted a zero interest rate for a sufficiently long time.

This is no doubt the strongest argument a New Keynesian Fed economist could make for raising rates now. That said, I am not convinced, partly because of the model estimations shown above. More convincing to me is the fact that we have not seen the boom that would accompany interest rates being below their natural rate. Inflation has been quite low and growth has certainly not boomed.

Ideally we'd have some sort of market measure of the natural rate (e.g. a prediction market). As a bit of an aside, as David Beckworth forcefully argues, it's a scandal that the Fed Board does not publish its own estimates of the natural rate. Such data would help settle this point.


I'll end things there. The New Keynesian model currently dominates macroeconomics, and its implications for whether or not the Fed should be raising rates in September are a resounding no. If you're an economist who finds value in the New Keynesian perspective, I'd be extremely curious to hear why you support raising rates in September if you do – or, if not, why you're not speaking up more loudly.


Jan 6, 2015

Confidence level (?): Medium

Edit: The critique in this post that NGDP targeting cannot achieve zero inflation in the long run without discretion is somewhat tempered by my 2017 follow-up here: perhaps zero long-run inflation would be inferior to a long-run Friedman rule; which in fact can be naturally implemented with NGDP targeting.


  1. NGDP growth is equal to real GDP growth plus inflation. Thus, under NGDP targeting, if the potential real growth rate of the economy changes, then the full-employment inflation rate changes.
  2. New Keynesians advocate that the Fed adjust the NGDP target one for one with changes in potential GDP. However, this rule would be extremely problematic for market monetarists.
  3. Most importantly, it is simply not possible to estimate potential GDP in real time: an accurate structural model will never be built.
  4. Further: such a policy would give the Fed huge amounts of discretion; unanchor long term expectations, especially under level targeting; and be especially problematic if technological growth rapidly accelerates as some predict.

I want to discuss a problem that I see with nominal GDP targeting: structural growth slowdowns. This problem isn't exactly a novel insight, but it is an issue with which I think the market monetarist community has not grappled enough.

I. A hypothetical example

Remember that nominal GDP growth (in the limit) is equal to inflation plus real GDP growth. Consider a hypothetical economy where market monetarism has triumphed, and the Fed maintains a target path for NGDP growing annually at 5% (perhaps even with the help of a NGDP futures market). The economy has been humming along at 3% RGDP growth, which is the potential growth rate, and 2% inflation for (say) a decade or two. Everything is hunky dory.

But then – the potential growth rate of the economy drops to 2% due to structural (i.e., supply side) factors, and potential growth will be at this rate for the foreseeable future.

Perhaps there has been a large drop in the birth rate, shrinking the labor force. Perhaps a newly elected government has just pushed through a smorgasbord of measures that reduce the incentive to work and to invest in capital. Perhaps, most plausibly (and worrisomely!) of all, the rate of innovation has simply dropped significantly.

In this market monetarist fantasy world, the Fed maintains the 5% NGDP path. But maintaining 5% NGDP growth with potential real GDP growth at 2% means 3% steady state inflation! Not good. And we can imagine even more dramatic cases.

II. Historical examples

Skip this section if you're convinced that the above scenario is plausible

Say a time machine transports Scott Sumner back to 1980 Tokyo: a chance to prevent Japan's Lost Decade! Bank of Japan officials are quickly convinced to adopt an NGDP target of 9.5%, the rationale behind this specific number being that the average real growth in the 1960s and 70s was 7.5%, plus a 2% implicit inflation target.

Thirty years later, trend real GDP in Japan is around 0.0%, by Sumner's (offhand) estimation and I don't doubt it. Had the BOJ maintained the 9.5% NGDP target in this alternate timeline, Japan would be seeing something like 9.5% inflation today.

Counterfactuals are hard: of course much else would have changed had the BOJ been implementing NGDPLT for over 30 years, perhaps including the trend rate of growth. But to a first approximation, the inflation rate would certainly be approaching 10%.

Or, take China today. China saw five years of double digit real growth in the mid-2000s, and not because the economy was overheating. I.e., the 12.5% and 14% growth in real incomes in China in 2006 and 2007 were representative of the true structural growth rate of the Chinese economy at the time. To be conservative, consider the 9.4% growth rate average over the decade, which includes the meltdown in 2008-9 and a slowdown in the earlier part of the decade.

Today, growth is close to 7%, and before the decade is up it very well could have a 5 handle. If the People's Bank had adopted NGDP targeting at the start of the millennium with a 9.4% real growth rate in mind, inflation in China today would be more than 2 percentage points higher than what the PBOC desired when it first set the NGDP target! That's not at all trivial, and would only become a more severe issue as the Chinese economy finishes converging with the developed world and growth slows still further.

This isn't only a problem for countries playing catch-up to the technological frontier. France has had a declining structural growth rate for the past 30 years, at first principally because of declining labor hours/poor labor market policies and then compounded by slowing productivity and population growth. The mess that is Russia has surely had a highly variable structural growth rate since the end of the Cold War. The United States today, very debatably, seems to be undergoing at least some kind of significant structural change in economic growth as well, though perhaps not as drastic.

Source: Margaret Jacobson, "Behind the Slowdown of Potential GDP"

III. Possible solutions to the problem of changing structural growth

There are really only two possible solutions to this problem for a central bank to adopt.

First, you can accept the higher inflation, and pray to the Solow residual gods that the technological growth rate doesn't drop further and push steady state inflation even higher. I find this solution completely unacceptable. Higher long term inflation is simply never a good thing; but even if you don't feel that strongly, you at least should feel extremely nervous about risking the possibility of extremely high steady state inflation.

Second, you can allow the central bank to periodically adjust the NGDP target rate (or target path) to adjust for perceived changes to the structural growth rate. For example, in the original hypothetical, the Fed would simply change its NGDP target path to grow at 4% instead of 5% as previously so that real income grows at 2% and inflation continues at 2%.

IV. This is bad – and particularly bad for market monetarists

This second solution, I think, is probably what Michael Woodford, Brad DeLong, Paul Krugman, and other non-monetarist backers of NGDP targeting would support. Indeed, Woodford writes in his Jackson Hole paper, "It is surely true – and not just in the special model of Eggertsson and Woodford – that if consensus could be reached about the path of potential output, it would be desirable in principle to adjust the target path for nominal GDP to account for variations over time in the growth of potential." (p. 46-7) Miles Kimball notes the same argument: in the New Keynesian framework, an NGDP target rate should be adjusted for changes in potential.

However – here's the kicker – allowing the Fed to change its NGDP target is extremely problematic for some of the core beliefs held by market monetarists. (Market monetarism as a school of thought is about more than merely just NGDP targeting – see Christensen (2011) – contra some.) Let me walk through a list of these issues now; by the end, I hope it will be clear why I think that Scott Sumner and others have not discussed this issue enough.

IVa. The Fed shouldn't need a structural model

For the Fed to be able to change its NGDP target to match the changing structural growth rate of the economy, it needs a structural model that describes how the economy behaves. This is the practical issue facing NGDP targeting (level or rate). However, the quest for an accurate structural model of the macroeconomy is an impossible pipe dream: the economy is simply too complex. There is no reason to think that the Fed's structural model could do a good job predicting technological progress. And under NGDP targeting, the Fed would be entirely dependent on that structural model.

Ironically, two of Scott Sumner's big papers on futures market targeting are titled, "Velocity Futures Markets: Does the Fed Need a Structural Model?" with Aaron Jackson (their answer: no), and "Let a Thousand Models Bloom: The Advantages of Making the FOMC a Truly 'Open Market'".

In these, Sumner makes the case for tying monetary policy to a prediction market, and in this way having the Fed adopt the market consensus model of the economy as its model of the economy, instead of using an internal structural model. Since the price mechanism is, in general, extremely good at aggregating disperse information, this model would outperform anything internally developed by our friends at the Federal Reserve Board.

If the Fed had to rely on an internal structural model adjust the NGDP target to match structural shifts in potential growth, this elegance would be completely lost! But it's more than just a loss in elegance: it's a huge roadblock to effective monetary policymaking, since the accuracy of said model would be highly questionable.

IVb. Rules are better than discretion

Old Monetarists always strongly preferred a monetary policy based on well-defined rules rather than discretion. This is for all the now-familiar reasons: the time-inconsistency problem; preventing political interference; creating accountability for the Fed; etc. Market monetarists are no different in championing rule-based monetary policy.

Giving the Fed the ability to modify its NGDP target is simply an absurd amount of discretionary power. It's one thing to give the FOMC the ability to decide how to best achieve its target, whether than be 2% inflation or 5% NGDP. It's another matter entirely to allow it to change that NGDP target at will. It removes all semblance of accountability, as the Fed could simply move the goalessays whenever it misses; and of course it entirely recreates the time inconsistency problem.

IVc. Expectations need to be anchored

Closely related to the above is the idea that monetary policy needs to anchor nominal expectations, perhaps especially at the zero lower bound. Monetary policy in the current period can never be separated from expectations about future policy. For example, if Janet Yellen is going to mail trillion dollar coins to every American a year from now, I am – and hopefully you are too – going to spend all of my or your dollars ASAP.

Because of this, one of the key necessary conditions for stable monetary policy is the anchoring of expectations for future policy. Giving the Fed the power to discretionarily change its NGDP target wrecks this anchor completely!

Say the Fed tells me today that it's targeting a 5% NGDP level path, and I go take out a 30-year mortgage under the expectation that my nominal income (which remember is equal to NGDP in aggregate) will be 5% higher year after year after year. This is important as my ability to pay my mortgage, which is fixed in nominal terms, is dependent on my nominal income.

But then Janet Yellen turns around and tells me tomorrow, "Joke's on you pal! We're switching to a 4% level target." It's simply harder for risk-averse consumers and firms to plan for the future when there's so much possible variation in future monetary policy.

IVd. Level targeting exacerbates this issue

Further, level targeting exacerbates this entire issue. The push for level targeting over growth rate targeting is at least as important to market monetarism as the push for NGDP targeting over inflation targeting, for precisely the reasoning described above. To keep expectations on track, and thus not hinder firms and households trying to make decisions about the future, the central bank needs to make up for past mistakes, i.e. level target.

However, level targeting has issues even beyond those that rate targeting has, when the central bank has the ability to change the growth rate. In particular: what happens if the Fed misses the level target one year, and decides at the start of the next to change its target growth rate for the level path?

For instance, say the Fed had adopted a 5% NGDP level target in 2005, which it maintained successfully in 2006 and 2007. Then, say, a massive crisis hits in 2008, and the Fed misses its target for say three years running. By 2011, it looks like the structural growth rate of the economy has also slowed. Now, agents in the economy have to wonder: is the Fed going to try to return to its 5% NGDP path? Or is it going to shift down to a 4.5% path and not go back all the way? And will that new path have as a base year 2011? Or will it be 2008?

(Note: I am aware that had the Fed been implementing NGDPLT in 2008 the crisis would have been much less severe, perhaps not even a recession! The above is for illustration.)

(Also, I thank Joe Mihm for this point.)

IVe. This problem for NGDP targeting is analogous to the velocity instability problem for Friedman's k-percent rule

Finally, I want to make an analogy that hopefully emphasizes why I think this issue is so serious. Milton Friedman long advocated that the Fed adopt a rule whereby it would have promised to keep the money supply (M2, for Friedman) growing at a steady rate of perhaps 3%. Recalling the equation of exchange, MV = PY, we can see that when velocity is constant, the k-percent rule is equivalent to NGDP targeting!

In fact, velocity used to be quite stable:

Source: FRED

For the decade and a half or two after 1963 when Friedman and Schwartz published A Monetary History, the rule probably would have worked brilliantly. But between high inflation and financial innovation in the late 70s and 80s, the stable relationship between velocity, income, and interest rates began to break down, and the k-percent rule would have been a disaster. This is because velocity – sort of the inverse of real, income-adjusted money demand – is a structural, real variable that depends on the technology of the economy and household preferences.

The journals of the 1980s are somewhat famously a graveyard of structural velocity models attempting to find a universal model that could accurately explain past movements in velocity and accurately predict future movements. It was a hopeless task: the economy is simply too complex. (I link twice to the same Hayek essay for a reason.) Hence the title of the Sumner and Jackson paper already referenced above.

Today, instead of hopelessly modeling money demand, we have economists engaged in the even more hopeless task of attempting to develop a structural model for the entire economy. Even today, when the supply side of the economy really changes very little year-to-year, we don't do that good of a job at it.

And (this is the kicker) what happens if the predictability of the structural growth rate breaks down to the same extent that the predictability of velocity broke down in the 1980s? What if, instead of the structural growth rate only changing a handful of basis points each year, we have year-to-year swings in the potential growth rate on the order of whole percentage points? I.e., one year the structural growth is 3%, but the next year it's 5%, and the year after that it's 2.5%?

I know that at this point I'm probably losing anybody that has bothered to read this far, but I think this scenario is entirely more likely than most people might expect. Rapidly accelerating technological progress in the next couple of decades as we reach the "back half of the chessboard", or even an intelligence explosion, could very well result in an extremely high structural growth rate that swings violently year to year.

However, it is hard to argue either for or against the techno-utopian vision I describe and link to above, since trying to estimate the future of productivity growth is really not much more than speculation. That said, it does seem to me that there are very persuasive arguments that growth will rapidly accelerate in the next couple of decades. I would point those interested in a more full-throated defense of this position to the work of Robin Hanson, Erik Brynjolfsson and Andrew McAfee, Nick Bostrom, and Eliezer Yudkowsky.

If you accept the possibility that we could indeed see rapidly accelerating technological change, an "adaptable NGDP target" would essentially force the future Janet Yellen to engage in an ultimately hopeless attempt to predict the path of the structural growth rate and to chase after it. I think it's clear why this would be a disaster.

V. An anticipation of some responses

Before I close this out, let me anticipate four possible responses.

1. NGDP variability is more important than inflation variability

Nick Rowe makes this argument here and Sumner also does sort of here. Ultimately, I think this is a good point, because of the problem of incomplete financial markets described by Koenig (2013) and Sheedy (2014): debt is priced in fixed nominal terms, and thus ability to repay is dependent on nominal incomes.

Nevertheless, just because NGDP targeting has other good things going for it does not resolve the fact that if the potential growth rate changes, the long run inflation rate would be higher. This is welfare-reducing for all the standard reasons. Because of this, it seems to me that there's not really a good way of determining whether NGDP level targeting or price level targeting is more optimal, and it's certainly not the case that NGDPLT is the monetary policy regime to end all other monetary policy regimes.

2. Target NGDP per capita instead!

You might argue that if the most significant reason that the structural growth rate could fluctuate is changing population growth, then the Fed should just target NGDP per capita. Indeed, Scott Sumner has often mentioned that he actually would prefer an NGDP per capita target. To be frank, I think this is an even worse idea! This would require the Fed to have a long term structural model of demographics, which is just a terrible prospect to imagine.

3. Target nominal wages/nominal labor compensation/etc. instead!

Sumner has also often suggested that perhaps nominal aggregate wage targeting would be superior to targeting NGDP, but that it would be too politically controversial. Funnily enough, the basic New Keynesian model with wage stickiness instead of price stickiness (and no zero lower bound) would recommend the same thing.

I don't think this solves the issue. Take the neoclassical growth or Solow model with Cobb-Douglas technology and preferences and no population growth. On the balanced growth path, the growth rate of wages = the potential growth rate of the economy = the growth rate of technology. For a more generalized production function and preferences, wages and output still grow at the same rate.

In other words, the growth rate of real wages parallels that of the potential growth rate of the economy. So this doesn't appear to solve anything, as it would still require a structural model.

4. Set up a prediction market for the structural growth rate!

I don't even know if this would work well with Sumner's proposal. But perhaps it would. In that case, my response is... stay tuned for my critique of market monetarism, part two: why handing policymaking over to prediction markets is a terrible idea.

VI. In conclusion

The concerns I outline above have driven me from an evangelist for NGDP level targeting to someone extremely skeptical that any central banking policy can maintain monetary equilibrium. The idea of optimal policy under NGDP targeting necessitating a structural model of the economy disturbs me, for a successful such model – as Sumner persuasively argues – will never be built. The prospect that NGDP targeting might collapse in the face of rapidly accelerating technological growth worries me, since it does seem to me that this very well could occur. And even setting aside the techno-utopianism, the historical examples described above, such as Japan in the 1980s, demonstrate that we have seen very large shifts in the structural growth rate in actual real-world economies.

I want to support NGDPLT: it is probably superior to price level or inflation targeting anyway, because of the incomplete markets issue. But unless there is a solution to this critique that I am missing, I am not sure that NGDP targeting is a sustainable policy for the long term, let alone the end of monetary history.