The real problem with the money multiplier

David Glasner argues the money multiplier is a useless concept.  I’m sympathetic to that claim, and yet I think he goes to far in his criticism of Friedman and other monetarists.  Although the concept is useless, it’s not wrong, and it’s hard to see how it does much damage.  Here’s David:

So in Nick’s world, the money multiplier is just the reciprocal of the market share. In other words, the money multiplier simply reflects the relative quantities demanded of different monies. That’s not the money multiplier that I was taught in econ 2, and that’s not the money multiplier propounded by Monetarists for the past century. The point of the money multiplier is to take the equation of exchange, MV=PQ, underlying the quantity theory of money in which M stands for some measure of the aggregate quantity of money that supposedly determines what P is. The Monetarists then say that the monetary authority controls P because it controls M. True, since the rise of modern banking, most of the money actually used is not produced by the monetary authority, but by private banks, but the money multiplier allows all the privately produced money to be attributed to the monetary authority, the broad money supply being mechanically related to the monetary base so that M = kB, where M is the M in the equation of exchange and B is the monetary base. Since the monetary authority unquestionably controls B, it therefore controls M and therefore controls P.

If I understand David correctly he’s a bit confused about the money multiplier.  It is simply a ratio, regardless of what David was taught in school. In his example the multiplier equals k, which is the ratio M/B.  But unless I misread him, he seems to believe multiplier proponents viewed it as a constant, which is clearly not true. Rather they argued the multiplier depends on the behavior of banks and the public, and varies with changes in nominal interest rates, banking instability, etc.  This is how it’s taught in the number one money textbook, and this is the version Friedman and Schwartz used in the Monetary History, which focuses heavily on explaining changes in the multiplier.

And yet I agree with David that the multiplier is useless, mostly for “Occam’s razor” reasons.  Think about the Equation of Exchange:

M*V = P*Y

If you want to model nominal GDP, and M represents M1, then you have to model both M1 and M1 velocity.  In that case:

M = k*B

So now the equation of exchange is:

B*k*V = P*Y

But in that case why not skip the middleman, and go right for:

B*(base velocity) = P*Y

After all, both k and V are positively related to the nominal interest rate.  You have one thing to model (base velocity), not two (the multiplier and M1 velocity).

In any case, it’s silly to focus on either B or M; focus on the goal/indicator of policy, NGDP.  The multiplier doesn’t help you do that, and hence is useless.  But if people want to use it, they aren’t making any sort of logical error as long as they understand how it changes in response to changes in interest rates and other variables, and the monetarists were able to do that.  The Monetary History is a masterpiece of multiplier analysis.

When people say “there is no such thing as a money multiplier,” they are literally saying there is either no such thing as B, or no such thing as M. Obviously they don’t mean that.  Rather they are trying to say “the multiplier is not fixed, as the monetarists and textbooks believe.” Except the monetarists and textbooks didn’t claim it was fixed.

Here’s Stephen Williamson:

The money multiplier is probably the most misleading story that persists in undergraduate money and banking and macroeconomics texts. Take someone schooled in the money multiplier mechanism, and confront them with a monetary system – such as what exists in Canada, the UK, or New Zealand – where there are no reserve requirements, and they won’t be able to figure out what is going on. Confront them with a system with a large quantity of excess reserves (the U.S. currently), and they will really be stumped.

Interesting.  I wonder if Friedman was “schooled in the multiplier mechanism”?  David Glasner says he was. And yet Friedman obviously would not be perplexed by either a lack of reserve requirements or massive quantities of excess reserves.  In fairness to Williamson, most undergrads would be perplexed, but then they are perplexed by lots of things.  I don’t think my students would be perplexed.


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78 Responses to “The real problem with the money multiplier”

  1. Gravatar of dannyb2b dannyb2b
    28. March 2014 at 17:38

    sorry, off topic

    If NGDP targeting was adopted starting from today by the fed how would you go about it? More QE, negative interest rates maybe?

  2. Gravatar of Jason Jason
    28. March 2014 at 17:58

    I put together an argument for the equation:

    P = a f(NGDP,MB) MB^(f(NGDP,MB) – 1)

    where f is a function of NGDP and the (currency component of the) base. It’s only the currency component because that works the best empirically (it works remarkably well) …

    http://informationtransfereconomics.blogspot.com/2014/03/how-money-transfers-information.html

    This however turns out to be effectively a model of “base velocity” you describe …

    http://informationtransfereconomics.blogspot.com/2013/07/the-information-transfer-model-and.html

  3. Gravatar of ssumner ssumner
    28. March 2014 at 18:49

    Danny, Neither, they would reduce the base.

    Thanks Jason.

  4. Gravatar of Frances Coppola Frances Coppola
    28. March 2014 at 19:05

    Scott, there are an awful lot of people out there who ARE perplexed by the money multiplier. Or rather, they are perplexed when they discover that it doesn’t work in the way that they were taught. It would be immensely helpful if it was taught properly in the first place.

  5. Gravatar of dannyb2b dannyb2b
    28. March 2014 at 19:11

    “Danny, Neither, they would reduce the base.”

    QE or lower rates reduce the base? How? I thought the opposite.

    Why would expectations just move because the fed is targeting something like ngdp? Does it not matter how effectively they can reach their target? Like I can target a top speed of 200mph in my car by nobody expects me to achieve it in a stock ford mondeo.

    If the fed is doing ngdp futures targeting with the same counterparties as now wont the result be the same in terms of excess reserves?

  6. Gravatar of Noah Noah
    28. March 2014 at 19:52

    Great post.

  7. Gravatar of wufwugy wufwugy
    28. March 2014 at 22:12

    I am also interested in the answer to dannyb2b’s question. When I promote NGDPLT elsewhere, I get a lot of “through which mechanisms can the Fed successfully target NGDP?” responses, and I don’t know the answer. The main answers I’ve seen thrown around here are “forward guidance” and “unconventional stimulus”, but those aren’t explanations so much as they’re part of the question

  8. Gravatar of A Cross A Cross
    28. March 2014 at 23:34

    Oh, Frances, I read your posts and read your comments, but do you read? Do you have any comprehension? Scott specifically said most undergrads would be perplexed. That would mean, obviously, given that undergrads are more schooled than most of the seven billion people in the world, that most “people” would be perplexed. What about that merited a comment repeating what he said but in the form of a, I guess, rebuttal? How do you know it’s ‘taught’ wrong instead of just being beyond the abilities of most people? Where would you get that info? Do you have evidence for the assertion? Of course you don’t.

    You seem so confused about nearly everything. I know you really want to contribute, but seriously it’s just not happening.

  9. Gravatar of Ben J Ben J
    28. March 2014 at 23:38

    Dannyb2b,

    Scott is saying that expectations of higher NGDP growth lowers demand for the base, not that QE and lower rates causes the base to be lower.

    You should read this post to get a feel for why he thinks expectations will achieve this:

    http://worthwhile.typepad.com/worthwhile_canadian_initi/2011/10/engdp-level-path-targeting-for-the-people-of-the-concrete-steppes-.html

  10. Gravatar of Benjamin Cole Benjamin Cole
    29. March 2014 at 00:45

    OT but not way off:

    John Cochrane’s latest post is again that the Fed is now causing lower inflation. The “sign” is wrong, he posits.

    If what Cochrane says is true, the current Fed regime of IOER, QR and low interest rates is anti-inflationary.

    If so, could this current Fed regime be maintained for another 10 years, say with QE at a steady state of $25 billion a month?

    That would eliminate another $3.6 trillion in federal debt from taxpayer liabilities. And I guess Cochrane would keeping the regime in place would help keep the lid on inflation.

    Seems like a wonderful opportunity to deleverage America.

  11. Gravatar of Saturos Saturos
    29. March 2014 at 02:07

    I think the complaint would be that if monetarists want to say that monetary policy is all about the supply and demand for money, and if they don’t say as you do that the base is all that matters, then they have to show their critics that base demand as a fraction of aggregate money doesn’t simply move one-for-one with base injections so long as the “real determinant of monetary policy” (interest rates or whatever) doesn’t change. So even if it’s true that monetary aggregate supply and demand drives NGDP, base injections can’t boost NGDP by themselves as they’ll simply be offset by more base money demanded as a fraction of M1 – that component of the demand for base money is endogenous to changes in the base, and it’s only demand for a higher aggregate that is exogenous to the base.

    So in a permanent helicopter drop thought experiment, those who don’t see the base as primary would have to say that it must be M1 that is dropped to cause a change in NGDP – although broad money demand doesn’t move one-for-one with exogenous base injections, base demand as a function of the broad money stock may do. I think that is the implication of saying that the injected base “isn’t guaranteed to get out into circulating money, as the monetarists insist”.

  12. Gravatar of Saturos Saturos
    29. March 2014 at 02:13

    You’ll be pleased to know though that Noah Smith on Twitter thought this post was great!

  13. Gravatar of dannyb2b dannyb2b
    29. March 2014 at 02:41

    Ben J

    That article doesn’t really explain much. It seems to imply that the only reason that the fed isn’t reaching its current inflation target is because the fed does quite have enough credibility because its not doing enough in terms of asset purchases. Why does asset purchasing affect credibility? Asset purchases seem like concrete steppes to me.

  14. Gravatar of ssumner ssumner
    29. March 2014 at 04:46

    Frances, Good point. My only point is that some people suggest that the economists who use the multiplier concept are deluded. That’s very different from saying some undergrads get the wrong message. Many undergrads also think the fiscal multiplier is a constant.

    Danny, Try working backwards. First figure out the expected NGDP growth rate, and then work backward and ask what is the real demand for base money if NGDP is expected to grow that fast. Then use open market operations to set the base at that level.

    wufwugy, They can use their policy tools to impact either the supply or demand for base money, in order to assure the market for base money is in equilibrium when expected NGDP growth is on target.

    Saturos, My response to that would be the same as to any other faulty “liquidity trap” argument. The liquidity trap is not the right way to think about things. Rather the real concern is that a central bank might set such a low NGDP target that the real demand for base money exceeds the quantity of eligible assets that the central bank is allowed to buy. In that case they have three choices:

    1. A higher NGDP target
    2. Expand the categories of eligible asset
    3. Negative IOR

  15. Gravatar of Dustin Dustin
    29. March 2014 at 04:50

    Ben

    Is the US gov’t not paying off debts held by the Fed?

  16. Gravatar of Major_Freedom Major_Freedom
    29. March 2014 at 05:27

    If an idea is useless but you then point out that it’s true as a premise of another argument, then you are presenting that idea as useful.

    This post provides us with a good reminder for why pragmatism cannot be the basis for truth. Even its supposed practitioners choose to make use of “useless” ideas that are true.

  17. Gravatar of Major_Freedom Major_Freedom
    29. March 2014 at 05:42

    The equation

    B*(Base money velocity) = P*Y

    Is only correct if B is the only money that existed, and it was turned over “velocity” number of times over a given period, which equals to P*Y.

    But B isn’t the only money that exists. Velocity is a fudge factor yes, but that doesn’t mean it can be just any factor, such as Base velocity = k*V, or V=Base velocity/k.

    Velocity means “number of times the previous factor is turned over”.

    But P*Y is not “number of times Base is turned over.” It is the number of times all monies in total are turned over, of which the Base is but one component.

    So you can’t write B*(Base velocity) on the left hand side.

  18. Gravatar of Major_Freedom Major_Freedom
    29. March 2014 at 05:42

    Hey A Cross, hiw does your foot taste?

  19. Gravatar of Major_Freedom Major_Freedom
    29. March 2014 at 06:12

    Interesting use of the word useless:

    “In any case, it’s silly to focus on either B or M; focus on the goal/indicator of policy, NGDP. The multiplier doesn’t help you do that, and hence is useless.”

    Ok…

    In any case, it’s silly to focus on either NGDP; focus on the goal/indicator of policy, free market in money. NGDP doesn’t help you do that, and hence is useless.

    It is silly to want socialist policies in this day and age.

  20. Gravatar of Tom Brown Tom Brown
    29. March 2014 at 06:46

    Dustin, they do pay them off, but the bulk of (~95% or so?) the interest payments are remitted back to the Treasury. That’s my understanding.

  21. Gravatar of Tom Brown Tom Brown
    29. March 2014 at 07:29

    Scott, what do you think of David’s story about Fischer Black vs Milton Friedman?

  22. Gravatar of Lorenzo from Oz Lorenzo from Oz
    29. March 2014 at 08:20

    Nicely clarifying, thanks.

  23. Gravatar of Patrick R. Sullivan Patrick R. Sullivan
    29. March 2014 at 08:29

    From Williamson;

    ‘Take someone schooled in the money multiplier mechanism, and confront them with a monetary system – such as what exists in Canada, the UK, or New Zealand – where there are no reserve requirements, and they won’t be able to figure out what is going on. Confront them with a system with a large quantity of excess reserves (the U.S. currently), and they will really be stumped.’

    Another opportunity to recommend Calomiris and Haber;

    http://www.amazon.com/Fragile-Design-Political-Princeton-Economic/dp/0691155240

    Where the reader will learn that Canada and New Zealand have very different financial/monetary systems than the UK, because the Game of Bank Bargains was conducted differently.

    Canada and New Zealand are two of only six countries in the world with both stable banking systems (no crises in the last 40 years) and adequate provision of credit (at least 83% of GDP). The UK, not so much, nor the USA.

    Btw, the other four ‘stable and adequate’ are Australia, Hong Kong, Singapore and Malta.

    Calomiris and Haber also have chapters on Brazil and Mexico where the money multiplier worked with a vengeance, until the people revolted and put an end to it.

  24. Gravatar of Steve Steve
    29. March 2014 at 09:44

    Do you suffer from ‘money illusion’?

    http://realestate.msn.com/blogs/post–do-you-suffer-from-money-illusion

    Silly article, but entertaining that it’s aimed at the general public.

  25. Gravatar of Frances Coppola Frances Coppola
    29. March 2014 at 12:17

    A Cross,

    I spend quite a lot of my life explaining to people who have studied economics and/or finance how the money multiplier really works. So my comment was not a rebuttal and I was not referring to just anyone. It was a heartfelt complaint. The money multiplier is not properly taught.

    I may disagree with people here, but I am certainly not confused and I do not lack comprehension.

  26. Gravatar of ssumner ssumner
    29. March 2014 at 12:50

    Tom, Black and Friedman had very different ways of looking at money. It’s often difficult for one person to see the perspective of the other.

    Even among us MMs there are differences—do you emphasize money as a MOA or MOE?

    Patrick, That list of countries includes a lot of former British colonies. But not Britain.

  27. Gravatar of Andy Harless Andy Harless
    29. March 2014 at 14:12

    It’s misleading (and a matter of definitional choice) to say that the money multiplier is just a ratio. It’s also misleading (though certainly true) to say that monetarists didn’t think the ratio was fixed. The theory was that a given change in the base would result in a potentially predictable change in the aggregate, that one could, at least in theory, hold constant all the factors that might affect the money multiplier and do meaningful thought experiments in which exogenous changes in the base have predictable effects on the aggregate. The implicit premise was that exogenous changes in the base could be isolated from changes in the multiplier. People who “deny the money multiplier” are denying that such an isolation is possible, essentially saying that any change in the base will necessarily affect the multiplier and that there will always be more parsimonious ways to model the effects of changes in the base. Strictly speaking, if you want to define the money multiplier as a ratio that can always be calculated, then obviously it must exist, but it’s clear to me what people mean when they say it doesn’t exist.

    I think the issue here is largely a (perhaps intentional on the part of the monetarists) confusion between average and marginal. Keynesians make a clear distinction between the average propensity to consume (which can be calculated) and the marginal propensity to consume (which can only be estimated and many people will argue is essentially nonsense). For the theory, the latter is what matters. One could make an analogous distinction between the average money multiplier and the marginal money multiplier (or more precisely, between the average and marginal propensities to hold reserves against deposits, from which the relevant multipliers would be calculated).

  28. Gravatar of Lorenzo from Oz Lorenzo from Oz
    29. March 2014 at 14:26

    Patrick, That list of countries includes a lot of former British colonies. But not Britain. Likely because “the City” has been a much bigger player in British politics. Not only were the colonies a case of “state first, banks second” but none of them were Great Powers whose success was significantly based on the ability to spend (i.e. borrow) opponents into the ground. This certainly created social interests with a powerful stake in the success of the British state, but it also created social interests the state had to be very concerned about. After all, the biggest single argument for Churchill’s biggest mistake (in his own estimate)–going back on the gold standard at the pre-war parity–was to maintain faith with bondholders.

    So, it was probably harder to create a stability-first bank bargain in the UK. By contrast, Australian public policy (for example) is so focused on (pragmatic) risk management that stability first is much easier to achieve. Especially given that, for Australia and the other colonies, access to “the City” was important, so local financial stability was a further boon to policy.

  29. Gravatar of benjamin cole benjamin cole
    29. March 2014 at 15:57

    Dan–
    Yes, the Treasury honors and pays off T-bonds held by Fed…but the Fed can simultaneously buy more T-bonds, thus maintaining its portfolio, for decades if need be…
    Cochrane has suggested the current monetary regime is anti-inflationary (as has S. WIlliamson).
    But Cochrane will never answer what then would it mean to simply maintain the regime…Fed St. Louis also has papers out that QE not inflationary…

  30. Gravatar of Benjamin Cole Benjamin Cole
    29. March 2014 at 17:15

    Dan-
    Add on-

    I regret to say I think modern USA “macroeconomics” is just politics in drag.

    No matter how intellectual, sophisticated, urbane, or calculus-strewn, the macroeconomic policies advocated by an economist comes back to their gut politics.

    Krugman will always supports government intervention and higher taxes on rich people and say the national debt is not that important.

    John Cochrane will always support cutting social programs, less government (except for anything to do with national security), and lower taxes on rich people, and says the national debt soon will be TEOTWAWKI.

    So, when it comes to Fed policy, you see the same thing. Krugman says it will do nothing, liquidity trap, you have to up federal outlays.

    Cochrane detests the idea of an “activist” Fed, or the idea of inflation or money-printing. This is in his gut, so QE is bad. He finds a reason for that gut reaction afterwards.

    Cochrane wants to say “QE equals hyperinflation.” But that hasn’t happened. And anyway, before hyperinflation you get inflation, and before you get inflation you have to have growth up to capacity. Meaning QE has to work initially, if it to cause inflation at all.

    So, the new line is “QE does nothing.”

    Market Monetarists are interesting, as our approach is actually a-political. In fact, in its pure form, it could nearly be program-trading on futures markets, and not very activist. You can have big defense outlays or little ones. Social spending as you please. Tax like you want.

    We just want to target a NGDP level. There is some politics in that, as some will want a lower (less activist) target and some will want a higher target (me!).

  31. Gravatar of ssumner ssumner
    29. March 2014 at 17:50

    Andy, I think we agree much more than you assume. I was basically trying to bring some clarity to the discussion. I don’t find statements like “the money multiplier doesn’t exist” to be particularly helpful, because it’s not clear what people mean. As I indicated in the post, one possible interpretation is that they mean the multiplier is not constant. You’ve said something a bit more precise, that they think the multiplier for marginal changes in the money supply is different from the average multiplier. That’s fine, and a statement like that would allow for a more intelligent discussion. I’m trying to improve the level of discourse so that people don’t simply talk past each other.

    I agree with you that the monetarists overstated the usefulness of the multiplier concept (just as I think the Keynesians overstate the usefulness of the fiscal multiplier.) I’m not a fan of using either multiplier. Indeed both have similar weaknesses, glossing over the difference between temporary and permanent changes in the key variables (the base or taxes.)

    But I do think it’s far to criticize those who claim the “textbooks” or the “monetarists” assume the multiplier is fixed. Both probably have flaws in their analysis, but they aren’t that detached from reality. It’s analogous to those who argue against the QTM on the grounds that velocity is not fixed.

    Lorenzo, Good point.

  32. Gravatar of David Glasner David Glasner
    29. March 2014 at 18:06

    Scott, Noah was right (about this post, I mean). Also Andy’s point about the difference between the average and marginal money multiplier was spot on. I was going to mention it myself, but I was getting tired. And I think that it is clear that the old Monetarists thought that the multiplier was a critical variable for the conduct of monetary policy. Otherwise how could Friedman have imagined that it would be possible, as he claimed, to replace the Fed with a computer programmed to implement his k-percent rule?

  33. Gravatar of Patrick R. Sullivan Patrick R. Sullivan
    30. March 2014 at 07:15

    ‘Likely because “the City” has been a much bigger player in British politics.’

    Not that simple. As readers of ‘Fragile By Design’ will find out. To whet appetites; Canada’s system developed due to the political requirements of keeping the French Canadians from ‘screwing the pooch’. I.e. the Quebecois are situated in a very strategic location, and had the ability to prevent western Canada from exporting through the St. Lawrence Seaway.

    As a result, the Queen of England still has the power to appoint the members of Canada’s upper house (Senate). That’s how earlier monarchs controlled the populist emotions in Canada, and they were spared the unit-banking system that developed in the USA. Essentially, Canada has the system Alexander Hamilton wanted for us.

    Yes, Scott, it’s no accident that all the stable and abundant-credit countries speak the language of Shakespeare. But, that’s not sufficient, as neither England nor USA qualify (South Africa almost does).

  34. Gravatar of Peter N Peter N
    30. March 2014 at 07:17

    ” In that case they have three choices:

    1. A higher NGDP target
    2. Expand the categories of eligible asset
    3. Negative IOR”

    The Fed took choice 2 during QE1, and it was working. Then they phased this choice out, and QE worked less well.

    Perhaps there’s a lesson here.

  35. Gravatar of TravisV TravisV
    30. March 2014 at 10:02

    Frances Coppola wrote a new analysis of events in the Eurozone last week:

    “Spain, The ECB And The Power Of Talk”

    http://www.forbes.com/sites/francescoppola/2014/03/30/spain-the-ecb-and-the-power-of-talk

  36. Gravatar of TravisV TravisV
    30. March 2014 at 10:12

    Dear Commenters,

    Frances Coppola wrote the following about the 4%+ increase in Spanish and German stocks since Monday:

    “These market movements do not seem to be driven by fundamentals. Rather, they appear to be driven by expectations that the ECB will undertake more aggressive monetary easing, perhaps by means of QE or negative interest rates on bank reserves. The ECB has signaled that it is considering both of these.

    But I fear these expectations are wrong. Signals don’t necessarily equate to action, and if markets respond to the signal by pricing in the action, then they may render the action itself unnecessary.”

    What are some good posts where Sumner explains why stock market reacts strongly to certain new QE surprises?

    This is the best I’ve been able to dig up so far:

    https://www.themoneyillusion.com/?p=16230

  37. Gravatar of Dustin Dustin
    30. March 2014 at 10:42

    Ben

    Rolling over US debt for decades sounds a lot like what many investors already do. It is also a lot like buying a 30 yr T’s. It is not something I would equate to absolving US gov’t debts.

  38. Gravatar of ssumner ssumner
    30. March 2014 at 10:44

    David, I basically agree with Andy’s point. My only point here was that the monetarists and the textbooks are both aware that the multiplier changes under certain circumstances. Also that the textbooks define the multiplier in an AVERAGE sense. But as far as the utility of the concept, I’m completely with you.

    Patrick, Thanks for the info.

    Peter, I have an open mind about the power of non-traditional asset purchases. My first choice would be a higher target, but I would not rule out the possibility that non-traditional purchases are more effective than traditional T-bond purchases

  39. Gravatar of TravisV TravisV
    30. March 2014 at 10:54

    Prof. Sumner read this post:

    http://seekingalpha.com/article/2115003-valuing-the-bull-market

    And his take was “Ah, it’s reverting to the gold standard correlation.”

    https://www.themoneyillusion.com/?p=26468#comment-326597

    I’m not quite getting it. He can’t be talking about this, can he (been going on since 1997):

    http://idiosyncraticwhisk.blogspot.com/2014/03/a-regime-shift-in-interest-rates-and.html

  40. Gravatar of TravisV TravisV
    30. March 2014 at 11:31

    Tyler Cowen reads a new paper and is intrigued by the Austrian theory of credit expansion:

    “Austrian business cycle theory refuses to die”

    http://marginalrevolution.com/marginalrevolution/2014/03/austrian-business-cycle-theory-refuses-to-die.html

    Have Shinzo Abe, QE3 and the Evans Rule made the global economy more stable? I still think so but hmmmm……

  41. Gravatar of TravisV TravisV
    30. March 2014 at 11:41

    Prof. Sumner answered my question:

    https://www.themoneyillusion.com/?p=26468#comment-326766

    All he meant was that under the gold standard, there was generally a positive correlation between stock prices and interest rates (and presumably inflation expectations).

  42. Gravatar of flow5 flow5
    30. March 2014 at 11:47

    The money multiplier is the CB’s expansion coefficient. It represents CB credit, or bank credit proxy, divided by legal (required reserves).

  43. Gravatar of flow5 flow5
    30. March 2014 at 11:51

    2012-11 ,,,,, 0.11 ,,,,, 0.55
    2012-12 ,,,,, 0.15 ,,,,, 0.51
    2013-01 ,,,,, 0.17 ,,,,, 0.59
    2013-02 ,,,,, 0.15 ,,,,, 0.60 oil top
    2013-03 ,,,,, 0.16 ,,,,, 0.49
    2013-04 ,,,,, 0.15 ,,,,, 0.50
    2013-05 ,,,,, 0.14 ,,,,, 0.54
    2013-06 ,,,,, 0.07 ,,,,, 0.48
    2013-07 ,,,,, 0.09 ,,,,, 0.40
    2013-08 ,,,,, 0.07 ,,,,, 0.28
    2013-09 ,,,,, 0.08 ,,,,, 0.28
    2013-10 ,,,,, 0.02 ,,,,, 0.26 real-output bottomed
    2013-11 ,,,,, 0.07 ,,,,, 0.29
    2013-12 ,,,,, 0.10 ,,,,, 0.25
    2014-01 ,,,,, 0.16 ,,,,, 0.34
    2014-02 ,,,,, 0.13 ,,,,, 0.38 Yield inflection point
    2014-03 ,,,,, 0.15 ,,,,, 0.33

    1st column = real-gDp
    2nd column = CPI

  44. Gravatar of Lorenzo from Oz Lorenzo from Oz
    30. March 2014 at 11:55

    Patrick: the Queen of England still has the power to appoint the members of Canada’s upper house (Senate) The Queen of England has no such power, nor does the Queen of the United Kingdom of Great Britain and Northern Ireland. I believe the Queen of Canada does, exercised locally by her Governor-General. Sharing monarchs is not the same as being subordinate to someone else’s monarch.

  45. Gravatar of Lorenzo from Oz Lorenzo from Oz
    30. March 2014 at 11:57

    Patrick: Canada’s system developed due to the political requirements of keeping the French Canadians from ‘screwing the pooch’. I.e. the Quebecois are situated in a very strategic location, and had the ability to prevent western Canada from exporting through the St. Lawrence Seaway.

    That sounds like the equivalent local Canadian risk-management issues that I identified for Australia.

  46. Gravatar of Lorenzo from Oz Lorenzo from Oz
    30. March 2014 at 12:02

    Patrick: I have downloaded “Fragile by Design” onto my iPad Kindle.

  47. Gravatar of flow5 flow5
    30. March 2014 at 12:05

    See:

    http://www.brookings.edu/~/media/projects/bpea/spring%202014/2014a_sheedy.pdf

    Debt and Incomplete Financial Markets:
    “A Case for Nominal GDP Targeting”

  48. Gravatar of Frances Coppola Frances Coppola
    30. March 2014 at 12:58

    Depressing post by Lars Christensen about deflationary bias at the ECB – asymmetric budget multiplier:

    http://marketmonetarist.com/2014/01/02/the-weidmann-rule-and-the-asymmetrical-budget-multiplier-is-the-euro-zone-50-keynesian/

    This (unfortunately) supports my argument that the ECB will not do much in the way of monetary easing (indeed it may not do any at all). Travis, I really would prefer to be wrong!

  49. Gravatar of Major_Freedom Major_Freedom
    30. March 2014 at 13:31

    Frances:

    You mean the ECB might cease engaging in OMOs?

  50. Gravatar of Frances Coppola Frances Coppola
    30. March 2014 at 13:43

    Major_Freedom,

    OMOs can be monetary tightening as much as easing.

  51. Gravatar of Major_Freedom Major_Freedom
    30. March 2014 at 18:00

    Frances:

    Yes, “tightening” and “easing” require a standard of measurement.

    I was just saying that even OMOs that one defines as “tightening”, isn’t “doing nothing.” It’s doing something. It is for example expanding the quantity of money from what it otherwise would have been.

  52. Gravatar of circuit circuit
    30. March 2014 at 18:01

    Scott:

    Robert Hetzel is on the record as saying that the textbook reserve-money multiplier model was irrelevant in the pre-2008 context given that the market for reserves under a regime of interest rate targeting renders the model untenable.

    However, in his recent book “The Great Recession”, he explains that the money multiplier model has gained relevance given that the Fed now has control over the monetary base and thus the nominal money stock is determined independently of the demand for real money.

    I wrote a post on this here (I discuss Hetzel in the second half):

    http://fictionalbarking.blogspot.ca/2013/11/on-irrelevance-of-money-multiplier.html

    Seeing as your views on policy are so close to Hetzel’s, I find it odd that you would disagree on this issue. I believe Mark S may concur with Hetzel about all this.

    Is Hetzel wrong about the model’s irrelevance in pre-2008 and relevance today?

  53. Gravatar of Philip George Philip George
    30. March 2014 at 20:07

    It is not that the money multiplier is irrelevant as that it is plain wrong. One of the fundamental principles of physics is the conservation law (of mass + energy, momentum, angular momentum, charge etc). In simple words it says that a closed system cannot create something out of nothing. The money multiplier violates this fundamental law and is the fundamental error of monetary economics.

    When this error is rectified the monetary aggregate you get is as seen in http://www.philipji.com/M1-and-Mc/.

    It will be noted that it accurately captures every movement of the economy since 1960. e.g. the recessions of 1973-75, 1980, 1981-82, 2000, 2007-08 besides various asset market booms and crashes.

  54. Gravatar of Major_Freedom Major_Freedom
    30. March 2014 at 22:16

    Philip George:

    The money multiplier concept isn’t one that is held to represent or describe or imply “something out of nothing”.

    It a purely mathematical relation. It is just the numerical factor that relates the quantity of commercial bank credit expansion, with the quantity of central bank money.

    For example, if the quantity of credit expansion is $10 trillion, and the quantity of base money is $1 trillion, then the “money multiplier” is 10.

    You should not attempt to corrupt economic science with physics and other hard sciences. Economics deals with acting man, with conscious beings. Physics deals with matter that has constancies in causal relations.

  55. Gravatar of Saturos Saturos
    31. March 2014 at 02:14

    Morgan Stanley economist knows how badly Draghi’s been doing, but still manages to put a positive spin on it: http://www.businessinsider.com.au/mario-draghis-favorite-joke-2014-3

  56. Gravatar of ssumner ssumner
    31. March 2014 at 05:51

    Travis, I should clarify that that is my impression, after looking at the interwar years. I have not studied the issue in depth.

    circuit, I’m not saying Hetzel’s wrong about the effect of QE on M2, it’s just that I believe there are more useful indicators than M2.

    Saturos, Sad.

  57. Gravatar of TravisV TravisV
    31. March 2014 at 06:25

    Janet Yellen Comments Give Stocks And Bonds A Boost

    http://www.businessinsider.com/janet-yellen-comments-boost-markets-2014-3

    Yellen highlighted “considerable slack” in the economy and the labor market, saying the Fed still had a long way to go to restore the economy to full health despite its decision to begin winding down its asset purchase program.

    “I think this extraordinary commitment is still needed and will be for some time, and I believe that view is widely shared by my fellow policymakers at the Fed,” she said in the speech.

    ……….

    “On the margin, it could be an attempt to offset the ‘six months’ comment from her press conference, but we’re reluctant to make too much out of the speech at this point.”

  58. Gravatar of flow5 flow5
    31. March 2014 at 07:54

    Only increases in currency held by the non-bank public reduce bank reserves. Whereas vault cash (applied & surplus), is a contingent liability that member banks hold in their vaults & ATM networks. In 1959 commercial banks were given the authority to use this vault cash (their liquidity reserves) to satisfy their legal (required), reserves (making the FRB-NY’s “trading desks” job of legal reserve management/monetarism harder).

    “Applied” vault cash (that quantity used to meet reserve requirements) & “surplus” vault cash (warehouse money), have both been excluded in the tabulations of the money stock. “Applied” vault cash is included in the tabulations of total & required reserve figures. Whereas the volume of “surplus” vault cash is obviously omitted from required reserve figures (but note that the BOG added “surplus” reserves to its total & excess reserve figures).

    Banks must maintain whatever volume of vault cash is necessary to convert their customer’s bank deposits into currency & simultaneously whatever volume is necessary to avoid excessive daylight overdrafts, or at the end of the day avoid overdrawing its account with their District Reserve Bank (e.g., whenever originating interbank credits, or debits).

    Any expansion of the non-bank public’s holdings of currency merely changes the composition (but not the total volume) of the money supply. There is a shift out of demand deposits, or OCD accounts, into currency. But a shift from transaction based accounts does reduce member bank legal reserves by an equal, or approximately equal, amount. Note: a bank’s legal reserves can be converted dollar-for-dollar into Federal Reserve Notes.

    Typically, an expansion of the public’s holdings of currency will cause a multiple contraction of bank credit & deposit accounts (relative to the increase in currency outflows from the banks) ceteris paribus. To avoid such a contraction the Fed offsets currency withdrawals using open market operations of the buying type (e.g., purchases of governments for the portfolios of the 12 Reserve Banks). But with the present volume of excess reserves, the “cash-drain factor “becomes another “exit” tool.

    The reverse is true if there is a return flow of currency to the banks. Since the trend of the non-bank public’s holdings of currency is up (ever since 1930), return flows are purely seasonal & cannot therefore provide a permanent basis for bank credit & money expansion.

  59. Gravatar of flow5 flow5
    31. March 2014 at 08:18

    Don’t be mislead by S&S’s “money multiplier” (i.e., “from 1981 to 2006 total credit market assets increase by 744%”. But Inter-bank demand deposits owned by the member banks held at their District Reserve bank fell by $6.5 billion).

    The BOG’s reserve figure fell by 61% from 1/1/1994-1/1/2001. The FRB-STL’s figure (& RAM), remained unchanged during the same period. And CBs ceased to be reserve “e-bound” c. 1995

    Legal (fractional) reserves ceased to be binding because:

    (1) increasing levels of vault cash/larger ATM networks (in 1959 a CB’s liquidity reserves began to count),
    (2) in 1990-1991 fewer applicable deposit classifications decimated requirements by 1/3,
    (3) retail deposit sweep programs (beginning 1994),
    (4) lower reserve ratios (since 1980 (including the “low-reserve tranche” & “exemption amounts”)), &
    (5) reserve simplification procedures

    have combined to remove most reserve, & reserve ratio, restrictions.
    —–

    The DAMB figure includes AMBLR plus the volume of currency held by the nonblank public (Milton Friedman’s “high powered money”).

    Any expansion or contraction of DAMB is neither proof that the Fed intends to follow an expansive, nor a contractive monetary policy. Furthermore any expansion of the non-bank public’s holdings of currency merely changes the composition (but not the total volume) of the money supply. There is a shift out of demand deposits, NOW or ATS accounts, into currency. But this shift does reduce member bank legal reserves by an equal, or approximately equal, amount.

    An expansion of the public’s holdings of currency will cause a multiple contraction of bank credit and checking accounts (relative to the increase in currency outflows from the banks) ceteris paribus. To avoid such a contraction the Fed offsets currency withdrawals by open market operations of the buying type (e.g., purchases of governments for the portfolios of the 12 Reserve Banks). The reverse is true if there is a return flow of currency to the banks. Since the trend of the non-bank public’s holdings of currency is up (ever since 1930), return flows are purely seasonal and cannot therefore provide a permanent basis for bank credit & money expansion.

    All currency gets into circulation, directly or indirectly, through the liquidation of time deposits, by the cashing of demand deposits. There is one exception in demand deposit creation; those historical instances when the U.S. Treasury borrowed from the Federal Reserve Banks. However, it cannot be said (as of time deposits), that increases in the public’s holdings of currency reflect prior commercial bank credit creation. It is more appropriate to say that expansions of currency are accompanied by concurrent expansions of Reserve Bank Credit.

    Likewise with the IOeR policy, the FED pays the banks not to lend (a.k.a. the 1966 S&L credit crisis).

  60. Gravatar of flow5 flow5
    31. March 2014 at 08:28

    In our managed currency system (not fiat money system), the aggregate volume of currency in circulation is determined by the effective demands for currency exerted by the public.

    But the public cannot acquire currency without diminishing, at the same time, and by an equal amount, its holdings of bank deposits (either directly or indirectly thru the currency route or via the CB’s undivided profits accounts). I.e., an expansion of the public’s holdings of currency automatically diminishes another type of money held by the public.

    The result is that the public’s aggregate holdings of money remains unchanged: only the components of the money stock have changed.

  61. Gravatar of TravisV TravisV
    31. March 2014 at 09:06

    The liberal media is falling head over heels for Atif Mian and Amir Sufi and their analysis of the top 0.1%:

    Paul Krugman:

    “Atif Mian and Amir Sufi, our leading experts on the macroeconomic effects of private debt, have a new blog””and it has instantly become must reading.”

    Unfortunately, Mian and Sufi think the Fed is powerless…..

    http://houseofdebt.org/2014/03/28/monetary-policy-and-secular-stagnation.html

    [Arnold Kling also just commented on Mian and Sufi on his personal blog]

  62. Gravatar of Doug M Doug M
    31. March 2014 at 09:28

    There are multiple defintions of M
    M0, M1, M2…Mn
    For all M
    MV=PY
    or….
    For any M there exists a V such that.
    MnVn = PY

    The money multiplier = Mn/M0

    Calculate the rates of change
    dM / M + dV/V = dP/P + dY/Y

    The only reason why one definition of Mn would be better than another is if dVn is nearly equal to 0.

  63. Gravatar of TravisV TravisV
    31. March 2014 at 10:31

    Frances Coppola pointed out to me that market expectations of Euro inflation are collapsing:

    https://twitter.com/darioperkins/status/448867834928435200/photo/1

    Meanwhile, here is the ECB’s inflation forecast:

    http://coppolacomment.blogspot.com/2014/03/why-ecb-wont-do-qe.html

  64. Gravatar of Morgan Warstler Morgan Warstler
    1. April 2014 at 06:15

    Frances, perhaps you can explain this:

    “But more importantly, taking working people out of tax does not increase the incentive to work if untaxed working incomes are higher than unemployment benefits – which in most cases, due to the minimum wage and earned income tax credits, they are.”

    1. Lowering income taxes on people increases their propensity to earn. It just does.

    Did you mean to say “if untaxed working incomes are LOWER than unemployment benefits”? If so, that makes more sense.

    2. I am looking forward to your critical analysis on the micro-economics of GI/CYB, because since I deliver full employment, and give all workers in the Economy greater incentives to work, so there’s lots in this article I am psyched to see you defend, particularly this:

    “Full employment (however defined) is no doubt desirable, but not at the price of the UK becoming a low-wage, low-productivity economy. ”

    http://www.pieria.co.uk/articles/the_chancellors_full_employment_ambition_is_not_quite_what_it_seems

    You understand Pareto power law, so you know the top 20% deliver 80% of the GDP, 20% are 80% of the sales etc.

    Which is why we can be so loving and kind and give the bottom 1/3 jobs that don’t require them to be very productive: singer, writer, musician, nanny, barber, BBQ pitmaster, craft brewer, yoga instructor, and on and on.

    When the less productive work for each other, they get to consume more.

    We are moving towards a service based economy, where the very productive jobs are not service based, or they manage service based digital (Internet) operations, but the hands on atomic end live human customer service jobs?

    They aren’t going to be making massive productivity gains and I don’t see why you’d want or expect it.

  65. Gravatar of Philippe Philippe
    2. April 2014 at 02:16

    Morgan,

    According to your logic, in a feudal system the monarch and aristocrats who do no work produce most of the GDP, whilst the serfs that do all the work produce next to nothing.

  66. Gravatar of Morgan Warstler Morgan Warstler
    2. April 2014 at 04:37

    I’m not really talking about Feudal systems, the glory of US is that we have so many petite bourgeoisie that they form the hegemony.

    Note: in the US, the “king” is literally in place by promising the serfs stuff paid for by the Oligarchs, tho in reality he plans on the petites paying for it.

    And when push comes to shove, his serf voters lose, his bureaucrats win, but the biggest winners are the oligarchs. The petites as the hegemony (playing against serfs, bureaucrats and oligarchs are able to play to a draw.

    I’m not saying we shouldn’t try to architect for reduce inequality… to stop Pareto consumption, no matter the production side.

    I’m saying the way to do that is for the serfs, to offer deals to support petites, while the petites GUT the oligarchs.

    We are going to have a service based economy for the bottom 80%, as such we want the top 20%, to have a more even distribution of the 80% of the wealth.

    We want ALL of the top 20% to consume yoga lessons and nannies etc. That creates more service demand.

  67. Gravatar of Philippe Philippe
    2. April 2014 at 05:02

    “while the petites GUT the oligarchs”

    How do you suggest they do that?

    “we want the top 20%, to have a more even distribution of the 80% of the wealth”

    Why you only want a more even distribution for the top 20%, and not for the population as a whole?

  68. Gravatar of TravisV TravisV
    2. April 2014 at 06:28

    Frances Coppola wrote:

    “Full employment (however defined) is no doubt desirable, but not at the price of the UK becoming a low-wage, low-productivity economy. “

    http://www.pieria.co.uk/articles/the_chancellors_full_employment_ambition_is_not_quite_what_it_seems

    Yes, but but but but but but. Madness.

    This reminds me of arguments from my left-wing friends that “Yes, I support full employment but only GOOD full employment. I support full employment if we do (a), (b), (c) and (d).”

    No. Everyone should support full employment. Unconditionally. No conditions.

    I don’t care if you’re left-wing or right-wing. Everyone should support full employment.

  69. Gravatar of Major_Freedom Major_Freedom
    2. April 2014 at 08:01

    TravisV:

    “No. Everyone should support full employment. Unconditionally. No conditions.”

    This is stark raving lunacy.

    You just claimed that I should support full employment, even if the cost is human misery and death. You’re saying I should support full employment brought about by murdering all the unemployed, or infringing on the liberties of others with guns.

    That is what “unconditonally” and “no exceptions” mean.

    Would you choose 100% employment and total impoverishment, or 98% employment in a wealthy society where vopuntary charity can support the 2% unemployed?

    TravisV, I hope you weren’t serious…

  70. Gravatar of Major_Freedom Major_Freedom
    2. April 2014 at 08:11

    TravisV:

    You see, what you said there is a consequence of what I will call “shallow” economic understanding.

    By saying unconditional and no exceptions, you are contradicting the reality of human action. Human action is goal seeking that utilizes scarce means. For most people, labor is not an end, but a means to achieving subsequent ends. Most people would not work for free or for below what is necessary for living for example.

    By putting absolute value on labor, which the old Marxists did by the way, you would open yourself up to having to support every and any action that would bring about full employment, including horrific actions that make people’s worse off. Let me repeat, you would have to support making people’s lives worse off, or annihilated, for the sake of work for work’s sake.

    That’s madness.

    Ah! If only you were more sophisticated in your economics, I wouldn’t have had to point this out to you.

  71. Gravatar of Philippe Philippe
    2. April 2014 at 08:22

    I don’t think TravisV was calling for mass murder, or arbitrarily forcing the voluntarily unemployed to work. I don’t know why you feel the need to make these hysterical comments.

  72. Gravatar of Philippe Philippe
    2. April 2014 at 08:48

    Morgan Warstler,

    I was hoping I might get a reply to this question: why you only want a more even distribution for the top 20%, and not for the population as a whole?

    If you think a more even distribution among the top 20% would be good, why don’t you think a more even distribution among the whole population would be good?

  73. Gravatar of Morgan Warstler Morgan Warstler
    3. April 2014 at 09:54

    Phillip,

    WATCH THIS GRAPHIC:

    http://chicago.cbslocal.com/2014/04/03/amazing-graphic-shows-chicagos-middle-class-disappear-before-your-eyes/

    That is what happens when you “try to worry about the whole”

    You can’t just shrug it off, Chicago is a prime example of the bottom 2/3 siding with elites rather than getting behind the top 20% and letting them gut the elites.

    THIS IS WHAT YOUR WAY GETS. That is your status quo.

    My approach is based on game theory, and being willing to admit that $ trumps votes.

    The top 1/3 (the private sector people ones who spend part of life in top 20%) have MONEY AND VOTES.

    The elites have only money.

    The bottom 2/3 have only votes.

    Now the A Player (the top 1/3) will charge in and gut the elites, the monetythe C player, the bottom 2/3 support the plans of the top 1/3.

    The top 1/3 will not take a deal with the C player, to take B’s $, and to give more free government stuff to C player.

    The top 1/3 intend to GUT the elites, keep the money for themselves, and BUT THEN:

    1. the A player is far richer. Base of GOP
    2. the B player is far poorer. Oligarchs
    3. The C player doesn’t lose any money, or get any new free govt. services, BUT the C player has FAR MORE CUSTOMERS to provide services too. Non-public employee Democrats.

    We get less yacht and Penthouse building, but more people wanting nanny’s and yoga lessons, and making weekly nail appointments etc.

  74. Gravatar of Morgan Warstler Morgan Warstler
    3. April 2014 at 09:59

    Phillip,

    I’m not a fan of country clubs.

    But the world I’m after has the top 1/3 all being able to join one.

    Because that system is the one that best ensures the bottom all 2/3 HAVE SERVICE JOBS.

    And it is clearly obvious that services jobs are the future of the masses in a growing digital economy, and that’s a fine thing – it’s far better than working in fields or factories.

  75. Gravatar of TravisV TravisV
    3. April 2014 at 10:14

    1/3rd 2/3rds, another CLASSIC post! By the way, folks, Morgan has a blog:

    http://www.morganwarstler.com

    And here are two Morgan comments from last year that I enjoyed:

    https://www.themoneyillusion.com/?p=22656#comment-264334

    https://www.themoneyillusion.com/?p=22642#comment-264145

  76. Gravatar of Frances Coppola Frances Coppola
    6. April 2014 at 05:49

    I haven’t been keeping up with comments here, sorry. But here goes.

    Morgan:

    1). “Did you mean to say “if untaxed working incomes are LOWER than unemployment benefits”? If so, that makes more sense.”

    No, I meant exactly what I said. But I should make it clear for people here exactly what I mean by untaxed income, since the post to which you refer was specifically about the UK, not the US.

    In addition to its minimum wage, the UK has EITC and various other in-work benefits for people on low incomes. People on very low incomes are taxed, but the vast majority of them receive more back in benefits than they pay in tax. Their income is therefore effectively untaxed, and for most people that untaxed income is higher than it would be if they were unemployed. Since their income is ALREADY untaxed, raising the tax threshold cannot increase their propensity to work. The main beneficiaries of the higher tax threshold are actually people on middle incomes.

    2)In the post, I said: “Full employment (however defined) is no doubt desirable, but not at the price of the UK becoming a low-wage, low-productivity economy.”

    Do please try not to assume that the US’s problems apply equally to other countries. The UK labor market is different from the US – it’s far more flexible, wages are less sticky and people are more mobile. Because of that, since the financial crisis the UK has had relatively strong employment, but very weak real wage growth (in 2011 there was even a fall in NOMINAL wages) and poor productivity relative to competitors.

    The UK’s poor productivity is in my view mainly due to collapse of investment in both the private and public sectors, which in turn is caused by a severely damaged financial sector, knock-on impact from the Eurozone crisis and cuts to public investment as part of the fiscal consolidation. If we don’t do something about the lack of investment, the UK will lose ground to more productive competitors.

    3) If you think the top 20% can generate enough demand to absorb all the productive capacity of the bottom 80% you are dreaming. You do know that marginal propensity to consume reduces as income rises, don’t you?

    Travis:

    “Everyone should support full employment. Unconditionally. No conditions.”

    It depends what you mean by full employment. I touched on this in the post. One of the things we learned from the “full employment at all costs” post-war drive and the inflation of the 1970s is that there needs to be some slack in the labour market to avoid inflationary pressures developing. Hence the NAIRU. There is considerable debate now about what the NAIRU now is (it differs from country to country) or even whether it still exists. Personally I wouldn’t like to assume that it didn’t, although we now know the Phillips curve relationship between inflation and unemployment is rather more complex (and possibly weaker) than we used to think. If you accept the existence of the NAIRU, then “full employment” is less than 100% of the workforce.

    I also refer you to my comment no 2) to Morgan above. The post is about the UK, not the US. The problems are different.

    Major_Freedom

    “Would you choose 100% employment and total impoverishment, or 98% employment in a wealthy society where voluntary charity can support the 2% unemployed?”

    Except that voluntary charity doesn’t support the unemployed and never has done.

  77. Gravatar of TravisV TravisV
    6. April 2014 at 09:03

    Frances Coppola,

    You’re right. I didn’t read the rest of your article and consider the context of your comment. Please accept my apology.

    I assumed you were arguing “I might support monetary policy A, but only if conditions B, C, and D are fulfilled.”

    But you were discussing the merit of certain tax cuts, which is a very different issue than monetary policy.

    I’m sorry that I made that hasty assumption.

  78. Gravatar of Ok, as Long as We're Talking about Scott Sumner, How About the Money Multiplier? | Last Men and OverMen Ok, as Long as We're Talking about Scott Sumner, How About the Money Multiplier? | Last Men and OverMen
    16. February 2017 at 06:38

    […]      https://www.themoneyillusion.com/?p=26479 […]

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