Are AD shocks hard to identify?

Tyler Cowen directed me to a Greg Mankiw essay on inflation:

And as a textbook author, I sometimes get the suggestion that the whole discussion of the Phillips curve be removed from my books on the grounds that the idea is hopelessly out-of-date. By contrast, my own thinking is closer to that of George Akerlof (2002), who in his Nobel prize lecture called the Phillips curve “probably the single most important macroeconomic relationship.”

I have a hypothesis about the source of this disconnect. In the original paper by Phillips (1958) and the famous follow-up by Samuelson and Solow (1960), the Phillips curve was presented as an unconditional relationship—a negative correlation between inflation and unemployment. Some periods, most notably the 1960s, do exhibit a simple downward-sloping scatterplot of points. But that unconditional relationship is long gone. Using data for the past several decades, the scatterplot of inflation and unemployment is now a cloud of points.

My perspective, however, is that the Phillips curve is best considered a conditional relationship. If you think (as most economists do) that monetary shocks—or aggregate-demand shocks more generally—push inflation and unemployment in opposite directions in the short run, then there is a short-run Phillips curve. But this downward-sloping curve is conditional on what shock is hitting the economy.

Mankiw understands the problems with the traditional Phillips Curve, but would like to keep the basic concept, always keeping in mind the distinction between supply and demand shocks. My preference would be to mostly remove inflation from macroeconomics, and instead directly focus on the relationship between nominal GDP shocks and unemployment.

Mankiw identifies one problem with the traditional Keynesian approach:

Whenever inflation moves away from the Fed target, as it dramatically did in 2022, observers are tempted to attribute the change to a shock to aggregate supply or aggregate demand. That might provide some clue as to how transitory the change is likely to be and how much corrective action the central bank needs to take. The problem is that because we don’t know the natural rate of unemployment with much precision, it is hard to disentangle supply and demand. That is true even with the benefit of hindsight, but the task is even more formidable in real time when data are preliminary and incomplete. And it is in real time that policymakers need to respond. . . .

The 2022 inflation surge is a case in point. Even now, I don’t think we can say for sure what happened. The surge could have resulted from pandemic-related interruptions in supply chains. It could have resulted from excess demand, as the 3.6 percent rate unemployment rate was plausibly below the NAIRU, which may well have been altered by the pandemic experience as workers rethought their relationship with the labor market.

From an NGDP perspective, we know exactly what happened. Although there were supply problems in 2022, those have resolved over time. The cumulative excess 11% NGDP growth over the past 4 1/4 years fully explains the excess 9% in PCE inflation. It was essentially all demand side for the period as a whole, despite a portion of the 2021-22 inflation being supply side.

In contrast, if you look at unemployment as a way of ascertaining whether the economy is experiencing excess inflation, you run into exactly the problem identified by Mankiw, we don’t know what the natural rate of unemployment is at any given moment in time—even retrospectively.

To be clear, I am not saying the Phillips Curve model is wrong, at least in the sophisticated version preferred by Mankiw. Rather it is not useful to policymakers.

Mankiw is correct that inflation caused by demand shocks is associated with movements in unemployment that correspond to the basic logic of the Phillips Curve. It is quite plausible that there was a period of time during 2022-23 when unemployment was below the natural rate. The real problem is that it is not a useful tool for policymakers—they are better off trying to stabilize NGDP growth at 4% and avoid trying to guesstimate the natural rate of unemployment.

For similar reasons, I’d prefer the Fed try to stabilize NGDP futures contract prices along a 4% growth path, and not try to guesstimate the natural rate of interest, which is just as unobservable as the natural rate of unemployment.

PS. A few weeks back, Michael Sandifer developed a Chatbot trained on my money illusion blog posts from 2009-24. Eventually, I plan to do something with this, but I have not gotten around to it yet. If you scroll way down in the right column of this blog, you’ll find the link. If I’m hit by a truck, this Chatbot will take over my commentary on current events and do future movie reviews. (Let’s hope it doesn’t endorse Trump!) I guess that means I’m roughly 5% or 10% immortal.


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35 Responses to “Are AD shocks hard to identify?”

  1. Gravatar of Lizard Man Lizard Man
    12. July 2024 at 05:53

    I am still not convinced that a NGDP level target is always the best approach, or even the approach that the Fed should have taken during the pandemic. The results that the Fed got during the pandemic are so vastly, vastly superior to what they got from the Great Recession and the long, too slow recovery in employment that it seems difficult to me to argue that the costs of the excess inflation were not dwarfed by the benefits of the very swift return to full employment. I honestly believe that when you have a once in a century supply shock for which there really aren’t historical precedents, getting back to full employment as quickly as possible is a good rule of thumb. For more normal situations in which the monetary authority isn’t operating in the dark, sure, do NGDPLT. But for the situation in which the monetary authority has no idea what full employment is, drive down unemployment as rapidly as possible and only afterwards pivot or return to NGDPLT. Because ideally NGDPLT should be set at a level that typically produces a moderate amount of inflation (as opposed to much inflation or deflation). My understanding is that due to people’s cognitive biases, you want to have some inflation to provide more flexibility to the economy, but not so much that ordinary people start taking inflation into consideration when making decisions. But a shock like COVID causes a situation in which no one really knows what level of NGDP growth produces a level of inflation like that. So the Fed has to somehow get that information, and the only way they can get that information is to run the economy hot and then see what they have to do to get inflation down again.

  2. Gravatar of Sara Sara
    12. July 2024 at 06:39

    Nobody will use your chatbot.

    First of all, other AI models can read your posts.
    Secondly, monetary economics is a pseudoscience. You’ll be obsolete in 30 years.

    Decentralized finance is the future. No longer will your ilk be permitted to reduce real income by devaluing currency.

    Your thugs, of course, will want to implement CBDC’s on a closed ledger, but nobody will use it.

    It’s game over. You lost. Deal with it.

  3. Gravatar of Travis Allison Travis Allison
    12. July 2024 at 07:53

    Scott, do you or Michael Sandifer have an easily downloadable file of all of your posts with links? Also, your Econlog posts? I have learned so much from you over the years. I frequently go back to old posts and if something happens to you, I’d like to continue to do that.

  4. Gravatar of spencer spencer
    12. July 2024 at 08:06

    re: “a situation in which no one really knows what level of NGDP growth produces a level of inflation like that.”

    Money flows hit an all-time high in November 2020.

    Targeting N-gDp is simply a concession:

    The figures used for determining economic flows are non-conforming, as determined by the limitations on all analyses based upon broad statistical aggregates, namely, data is not currently being compiled accurately, or in a manner which conforms to rigid theoretical concepts.

  5. Gravatar of spencer spencer
    12. July 2024 at 08:11

    re: “monetary economics is a pseudoscience”

    we knew this already:

    In 1931 a commission was established on Member Bank Reserve Requirements. The commission completed their recommendations after a 7 year inquiry on Feb. 5, 1938. The study was entitled “Member Bank Reserve Requirements — Analysis of Committee Proposal”

    its 2nd proposal: “Requirements against debits to deposits”

    Member Bank Reserve Requirements: Analysis of Committee Proposal, Box 107 (stlouisfed.org)

    After a 45 year hiatus, this research paper was “declassified” on March 23, 1983. By the time this paper was “declassified”, Nobel Laureate Dr. Milton Friedman had declared RRs to be a “tax” [sic].

    Monetarism has never been tried. Monetarism involves controlling total reserves, not non-borrowed reserves as Paul Volcker found out. Volcker targeted non-borrowed reserves (@$18.174b 4/1/1980) when total reserves were (@$44.88b).

    Monetary policy should delimit all required reserves to balances in their District Reserve bank (IBDDs, like the ECB), and have uniform reserve ratios, for all deposits, in all banks, irrespective of size (something Nobel Laureate Dr. Milton Friedman advocated, December 16, 1959).

  6. Gravatar of spencer spencer
    12. July 2024 at 08:30

    It took years for Volcker’s inflation to subside. Targeting N-gDp will accomplish the task much faster.

  7. Gravatar of ssumner ssumner
    12. July 2024 at 08:31

    Lizard, It was wise to get back to the trend line quickly, but you can also do that with NGDPLT. There was absolutely no benefit to overshooting and creating a labor shortage in 2022. None at all.

    In addition, high inflation creates an increased risk of recession, as we saw in 1970, 1974 and 1981-82.

    Sara, I’m flattered that you have devoted such a large share of your life to reading my inconsequential blog, and then spent even more time writing long and inane comments. (Or does a Russian chatbot write the comments.)

    Travis, All of the old posts are still publicly available here and at Econlog.

  8. Gravatar of ssumner ssumner
    12. July 2024 at 08:57

    Travis, I should add that I hope to maintain this access even after I am gone. I’ll let you know when I have something more definitive.

  9. Gravatar of Tacticus Tacticus
    12. July 2024 at 09:25

    “In the original paper by Phillips (1958) and the famous follow-up by Samuelson and Solow (1960), the Phillips curve was presented as an unconditional relationship—a negative correlation between inflation and unemployment.”

    I assume that Mankiw has actually read Philips (1958), but the original paper says nothing like this! How can someone as distinguished – and the author of so well-known a textbook – as Mankiw write such a ridiculously inaccurate statement? This type of writing by economists truly drives me mad.

    Samuelson and Solow (1960) is also not a great paper, having just re-read it for the first time in a few years, but it has also been massively distorted by people since.

    I’d throw out the Philips Curve, personally, except for a ‘history of economics’ or ‘history of economic thought’ book/chapter.

  10. Gravatar of ssumner ssumner
    12. July 2024 at 13:46

    Tacticus, What struck me was that the 1958 paper was about wage inflation, not price inflation. Is that what you are referring to, or was the Phillips paper about conditional correlations?

  11. Gravatar of Travis Allison Travis Allison
    12. July 2024 at 14:51

    Scott, yeah, I could find some software and scrape your site and Econlog. It just would be nice to not have to go through the hassle if you already have all your articles in a folder. You could zip them up and make them available via a password protected web page. Then you could give out the password to real people to make sure that robots don’t download the files and you get hit with large data charges.

    Of course, it’s totally up to you. I’m very grateful for your Internet presence. You’ve added a lot to my intellectual growth over the years.

  12. Gravatar of ssumner ssumner
    12. July 2024 at 15:05

    Travis, Understood. I’ll look into options.

  13. Gravatar of Ericsson Ericsson
    12. July 2024 at 17:42

    In general I like the NGDP approach. But you are still not getting away from guesstimating unobservables like potential growth, right? I guess you assume 2% real and 2% inflation. Or how else do you arrive at 4% NGDP target? If we don’t know the natural rate of interests, we certainly know nothing about potential growth.

    Or do you have some other way of gauging unobservable potential that guides your target?

  14. Gravatar of Michael Sandifer Michael Sandifer
    12. July 2024 at 18:26

    Travis Allison,

    The custom GPT will produce the entire blog post of interest if you request it.

  15. Gravatar of Michael Sandifer Michael Sandifer
    12. July 2024 at 18:31

    I think this generally represents the future of publishing. No longer will single, polished academic papers or books be produced, but instead the rough ideas and data will be uploaded into AI bots that will produce papers, articles, books, audio, videos, and other media, customized for the user. Current LLM technology can facilitate this currently, very imperfectly, with important limits.

  16. Gravatar of Michael Sandifer Michael Sandifer
    12. July 2024 at 18:33

    Scott,

    You might be happy to know that the premium version of Google’s LLM, Gemini Advanced, cited a blog post of yours tonight when I initiated a discussion about the global savings glut.

  17. Gravatar of ssumner ssumner
    12. July 2024 at 19:03

    Ericsson, A few comments:

    1. Strictly speaking, it’s not necessary to estimate the trend rate of RGDP growth. You can just target NGDP at 4% and let inflation end up where it will.

    2. Politically, it may be better to estimate trend RGDP growth before setting the NGDP target, as you say, so that the Fed can say that they still have a 2% inflation goal.

    3. It’s vastly easier to estimate long run trend RGDP growth than the natural rate of interest, because the natural rate of interest is much more volatile. Perhaps an order of magnitude more volatile. Trend RGDP is probably around 1.8% to 2.2%, whereas I have no idea what the natural rate of interest is—it can be anywhere from 4% or 5% to a negative number depending on what’s going on with the business cycle.

    Thanks Michael.

  18. Gravatar of Ericsson Ericsson
    13. July 2024 at 04:31

    So the 4% target is not a composition of potential and inflation, but just assessment of NGDP growth rates that are conducive of stable macro conditions (based on more recent experience?).

    I still fear that people / politicians want to know that the CB is targeting .5% inflation or 3.5%. Then you will have to estimate potential growth that, even though you say this is “simple” because it does not move around like natural rates, we still have no idea if it is 1.5/2.5%, especially in real time. Perhaps 1% inflation is not a big issue given measurement errors, but with level targets errors would push you further away from ideal trends (say 3% inflation over 10 years than 2%).

    Again, perhaps this does not matter for providing an anchor for nominal contracts or the stability of the regime.

  19. Gravatar of ssumner ssumner
    13. July 2024 at 07:13

    Ericsson, Again, inflation simply does not matter at all, except in a political sense. What matters for economic stability is NGDP growth. Contracts are signed based on estimates of NGDP growth, not estimates of inflation.

    Back around 2000, Chinese inflation was zero and NGDP growth was around 10%. Do you think Chinese workers were thinking to themselves “I see inflation is zero, hence I’ll be happy with a 2% raise”? No, they were looking at NGDP growth rates, and demanding big raises.

    There is no “ideal trend” for inflation, there are ideal trends for NGDP growth. Inflation cannot even be adequately defined, how can it possibly matter for the economy?

  20. Gravatar of Don Geddis Don Geddis
    13. July 2024 at 09:02

    @Sara said: “No longer will your ilk be permitted to reduce real income by devaluing currency.”

    But (low, stable) inflation (“devaluing currency”) has no long-term effect on real incomes. Your claim is just factually wrong.

    You don’t seem to be able to get the basics of monetary economics right. No wonder your conclusions sound so silly.

  21. Gravatar of Ericsson Ericsson
    13. July 2024 at 11:13

    But in the case of low growth and high inflation, you have the same spiral! Inflation is high, thus NGDP is “too high” and the regime generates too high wages relative to productivity. I agree that NGDP is what matters, but I also think the real and nominal components by themselves matter, at least for politics and policy.

    Without an adequate explanation for why RGDP + inflation would evolve nicely around stable trends with 4% NGDP Trend growth, it’s hard to see how policy would be able to change. Think about wage negotiations, and especially in countries/regions where wages are collectively bargained through workers/employee organisations. There the fight is typically around what part is real and what part is nominal. In your proposal, incomes should always grow at the aggregate at 4%, in spite of real components either higher or lower. For you this is the key benefit to offset shocks, but what happens when wages are constantly above what is motivated by real growth / productivity (say your 4% target is 3 inflation and 1 real)? Or is this a non problem? Just very curious.

  22. Gravatar of Philippe Bélanger Philippe Bélanger
    13. July 2024 at 14:35

    I am really puzzled by the approach of Mankiw and others who claim that we can’t know whether the inflation we recently experienced is caused by demand or supply. Real GDP is back to its pre-pandemic trend and the cummulative inflation since January 2020 is around 20%. That is as clear a demand shift as you will ever see in the US. Even if you think that monthly inflation was sometimes caused by supply, we know that supply changes can’t account for the cumulative inflation because the economy is back to potential. If there had been a permanent shift in supply, real GDP would be below trend; but it clearly isn’t. Sometimes I feel like I am going insane reading economists on Twitter talking about temporary issues with supply chains as if these could explain the entire inflationary episode.

  23. Gravatar of Edward Edward
    13. July 2024 at 16:43

    Do you remember what I told you?

    I told you that your over the top rhetoric would lead to violence.

    And once again, I am correct.

    You called him Hitler, and now he was shot. Lying has consequences. There are people out there stupid enough to believe your lies, and they’ll act on what you say. You may not want to harm him, and you may be doing it for political purposes because you have no moral values. But your lies lead to violence. People out there begin to think that he might actually be Hitler, because of your idiotic rhetoric.

    You, and the left in general, are unhinged.

  24. Gravatar of ssumner ssumner
    13. July 2024 at 17:54

    Ericsson, I’m not sure exactly what problem you are worried about. Say you get 1% growth and 3% inflation. Why would that suggest a problem with monetary policy?

    Philippe, You said:

    “Sometimes I feel like I am going insane reading economists on Twitter talking about temporary issues with supply chains as if these could explain the entire inflationary episode.”

    I feel your pain.

    Edward, Just when I think Trumpistas cannot go any further down into the gutter, they surprise me. Have you no shame?

  25. Gravatar of Don Geddis Don Geddis
    13. July 2024 at 19:12

    @Ericsson: “Think about wage negotiations, and especially in countries/regions where wages are collectively bargained through workers/employee organisations. There the fight is typically around what part is real and what part is nominal.”

    I’ve done collective bargaining negotiations, many times. Not once have I ever heard anyone discuss “what part is real and what part is nominal”. That is a framework that macroeconomists use. Normal, ordinary people have no idea what you are talking about. It never comes up.

    People want their (nominal) dollar wages to increase. Most people view inflation as a topic entirely unrelated to their own wage increases. They “deserve” their nominal wage increases, while — separately — inflation “steals” their purchasing power. But there is no (intuitive layman) connection between the two.

  26. Gravatar of Don Geddis Don Geddis
    13. July 2024 at 19:17

    @Ericsson: also, “Inflation is high, thus NGDP is “too high””

    No, not at all. If NGDP is on target, in a monetary scheme that is targeting NGDP, then it isn’t “too high” — even if inflation is high. The whole point is not to care about inflation. Care about NGDP instead. If it is on target, then that’s all you need to know. How it divides between real GDP growth and inflation is something out of the control of the central bank, and not something to worry about.

    (Of course, more real growth and less inflation is always better; but you don’t get to choose the amount of real growth. Why does it matter to you, if inflation happens to be higher or lower?)

  27. Gravatar of Ericsson Ericsson
    14. July 2024 at 10:17

    @DonGeddis, I can’t speak to your experience in wage negotiations (perhaps from the states where unions/employer associations are a small fraction of wage setting? Or where central agreements play a small/no role for overall wage setting?)

    In European countries where this is the norm for wage formation, the space for wage increases crucially depends on the assessment of productivity. It’s all over the news and from insiders, a crucial point of discussion.

    This does not mean that this could not change with a NGDP target. Perhaps parties accept just setting central agreements at 4%, irrespective of real/nominal divide. I have no clue how these dynamics would work.

    @ssummer, not sure it’s a problem for monetary policy per se. I am mainly worried that this might make it difficult to implement. But perhaps macro performance would be so superior that people/unions/ employers don’t care about the macro split between nominal and real.

  28. Gravatar of ssumner ssumner
    14. July 2024 at 10:39

    Ericsson, You said:

    “But perhaps macro performance would be so superior that people/unions/ employers don’t care about the macro split between nominal and real.”

    People clearly prefer more real and less inflation. But it’s just as clear that monetary policy cannot do anything about that split.

    As for productivity, real wages depend on real productivity and nominal wages depend on nominal productivity. That’s why NGDP targeting is best—workers mostly negotiate nominal contracts, not real contracts.

  29. Gravatar of Don Geddis Don Geddis
    14. July 2024 at 13:14

    @Ericsson: you say, “the space for wage increases crucially depends on the assessment of productivity”

    This is the key step where you go wrong. That’s just not true.

    Sumner correctly explains your mistake: “nominal wages depend on nominal productivity … workers mostly negotiate nominal contracts”

    Ericsson, you are confusing real with nominal. The “space for wage increases” crucially depends on NOMINAL productivity, not on real productivity. What matters is how much revenue the business receives, per worker labor hour. If the business receives more nominal revenue, the workers demand their “fair share” of that incoming nominal revenue.

    Actual real productivity plays almost no role in collective bargaining negotiations. (After all, a business can’t actually pay workers if they simply don’t have the nominal revenue to cover those labor costs.)

  30. Gravatar of Ericsson Ericsson
    14. July 2024 at 15:55

    @DonGeddis, I am not confusing real with nominal. Either you are not reading my posts or I am expressing myself poorly. I was not discussing wage setting in the US but in Europe (see above), where wages (in many countries) are centrally negotiated. Currently, discussions take off at 2% inflation, and anything above is attributed to real productivity. There is (most of the time) no discussion about the inflation component as there is, most of the time, trust in the 2% targets.

    Of course the final salary adjustment is in nominal terms, but I am referring to the negotiations (in times of normal inflation or small deviations from the target). There is no uncertainty in the nominal part of wage negotiations when the inflation target is somewhat credible, only the real part. Hence negotiations are on “real productivity”. I think if you study economies with centrally negotiated wages and (credible) targets, you would find these aspects all over the place

    @ssumner, I think I am unclear. Let me rephrase: I have a hard time understanding the numerical target. Why not 3%, or 5%? Should the target be revised? And if so, how often?

    Sure, recent history gives some guidance, but not fully. To me it seems totally arbitrary. Ok 2% targets were largely arbitrary too.
    But if you have the ability to change, is not better to have some robust process to choose the target than just say that a fairly arbitrary number does well? If policymakers are to be convinced to move away from IT, there needs to be more meat on the bones.

  31. Gravatar of Scott Sumner Scott Sumner
    14. July 2024 at 20:01

    Ericsson, You said:

    “If policymakers are to be convinced to move away from IT, there needs to be more meat on the bones.”

    I presume you are new here, but I can assure you that I’ve answered all your question in great detail many, many times, here and elsewhere. Don’t take this the wrong way, but you must understand that I cannot write a 10,000 word essay every time someone asks me a complex question in a comment section. Right now, I’m working on a new paper which will be published by Mercatus, making the case for NGDP targeting.

    As for the optimal NGDP growth rate, it depends on many factors, including population growth and the nature of the tax system. If you don’t index capital income taxes, that leads to a lower optimal NGDP growth rate. The optimal NGDP growth rate will be higher if population growth is higher. I believe 4% is a reasonable compromise for the US, but 3% or 5% would also be OK with me. You are correct that both the 2% inflation target and the 4% NGDP target are estimates of what is optimal, not something where there is a rigorous proof of optimality.

  32. Gravatar of Don Geddis Don Geddis
    14. July 2024 at 20:03

    @Ericsson: You keep making claims, without evidence, that are not plausible. “in Europe … There is … no discussion about the inflation component as there is, most of the time, trust in the 2% targets. … when the inflation target is somewhat credible”.

    That’s just not true. Here is Eurozone inflation for the last two decades: https://static01.nyt.com/images/2022/09/30/business/30eurozone-inflation-promo/30eurozone-inflation-promo-superJumbo.jpg

    Perhaps there was a brief time, 2001-2007, when Eurozone inflation was reliably very close to 2%. But CERTAINLY NOT in the last 15 years. Eurozone annual inflation is NOT “credibly” at 2% every year. It just isn’t. It goes up and down, from negative 1/2% to 4% (or 10%!).

    And it strains credulity to imagine that “central negotiations” are so stupid as to not be aware of this, and to just pretend — against all evidence — that the target is reliable. That there is “no discussion”, “no uncertainty”, about annual inflation, as you claim.

    You’re claiming that you know “how things work” in European “centrally negotiated” collective bargaining. I don’t believe you.

  33. Gravatar of Junio Junio
    14. July 2024 at 21:06

    Dear Scott:

    You said to Travis: “I should add that I hope to maintain this access even after I am gone. I’ll let you know when I have something more definitive.”

    I don’t know how other readers would feel (nor you), but I, for one, wouldn’t mind a book containing what you consider your best blog posts over the years. I would understand though why you might not be comfortable with that.

    PS: There are many great posts hidden away from the reader which is unfortunate. The most memorable one to me, for whatever reason, continues to be “The Autistic Macroeconomist”.

  34. Gravatar of ssumner ssumner
    15. July 2024 at 09:38

    Thanks Junio, I hope that at some point in the not too distant future an AI will be able to create just such a book from my blog.

    Ironically, I had intended to use the autistic macroeconomic theme in my book entitled “The Money Illusion”, but the publisher said it was offensive. If you read the post, I don’t think it was offensive. Glad you liked it.

  35. Gravatar of Tacticus Tacticus
    15. July 2024 at 12:18

    ‘Tacticus, What struck me was that the 1958 paper was about wage inflation, not price inflation. Is that what you are referring to, or was the Phillips paper about conditional correlations?’

    Yes, the main cause of my anger is that the paper is about wages, not about general inflation.

    But, yes, it also nowhere posits some sort of universal or eternal ‘Philips Curve.’ It specifically, albeit not in detail, looks at why the correlation between unemployment and wage growth has changed over time, eg changes in the power of trade unions.

    It’s not a great paper, but it’s fine. Samuelson and Solow (1960) is a bad paper.

    ‘I had intended to use the autistic macroeconomic theme in my book entitled “The Money Illusion”, but the publisher said it was offensive. If you read the post, I don’t think it was offensive. Glad you liked it.’

    I can see why the publisher would advise against including it. It’s not offensive, but I think you can make the same economic points without involving autism.

    Medieval economic historians, of course, will tell you that a paucity of coins after the decline of the Roman Empire was a major cause of economic stagnation in Europe for several centuries!

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