What does MV = PY actually mean?

It means V is PY/M.

And that’s all it means.  But the textbook description of MV=PY is sometimes a bit confusing, as it seems to say two conflicting things:

1.  V is the velocity of circulation, the average number of times a dollar is spent per year

2.  MV = PY is an identity.  But this suggests V is defined as PY/M

So which is it?  It turns out that when MV= PY was first created, V was probably something like #1, but today #2 is the accepted definition.

For example, some money is spent on things that are not a part of GDP, such as used goods, or intermediate goods.  So could we fix the definition by calling V the “average number of times a dollar is spent on final goods”?  Unfortunately no, as there are some final goods for which money is not spent.   Suppose that (on average) each dollar was spent 15 times per year on final goods transactions.  And suppose there were a trillion dollars in money in circulation.  Would NGDP be $15 trillion?  No, as NGDP also includes things like implicit rent on owner-occupied housing, for which no money changes hands.

Similarly, saving once had a common sense meaning that was different from investment.  Saving and investment (as defined in earlier eras) were not equal by definition.  But then economists found it useful to define saving as the funds spent on investment.  They became two sides of the same coin, like sales and purchases.

Now it’s not clear if these identities are useful.  I think they are, as (for instance) it’s simpler to model NGDP if it equals M*V, than if it equals M*V*ff, where ff is a fudge factor to account for the fact that there are issues like owner-occupied housing.

Oddly, there is another version of the equation of exchange where the common sense definition is exactly right:

M = k*P*Y

Where k is both:

1.  M/PY

2.  The average share of gross domestic income held as cash balances (globally).

It’s unfortunate that most textbooks rely on the version of the equation of exchange where the common sense definition is not equal to the official definition.

Suppose the government suddenly redefined cars as a capital good (they are currently considered consumer goods.)  Gross investment would immediately soar much higher (although net investment, which really matters, wouldn’t change all that much.)

So would saving still be equal to investment?  Yes, because at the same moment gross saving would also soar in value, as funds spent on cars would now get included into saving.

Many commenters on confused on that point.  They talk about Americans “spending” lots of money on housing during the housing boom, instead of “saving” the money. But according to the official definition, spending on new housing is saving.  Perhaps spending on cars should also be viewed as gross saving.

Even better, why not stop obsessing over the C+I+G+NX = GDP relationship, and just focus on NGDP.  The line between C and I is quite arbitrary, and not all that important for issues like the business cycle.  It’s NGDP that matters.

At one time Keynesians thought saving was really important for the business cycle, but in the New Keynesian era we all realized that it wasn’t, what mattered was monetary policy.  No more paradox of thrift.  Unfortunately some have forgotten that lesson, others have wrongly assumed that everything is different at the zero bound.  It isn’t.

PS.  This is inspired by a recent post by David Glasner.  This paragraph is worth commenting on:

OK, savings are the funds used for investment. Does that mean that savings and investment are identical? Savings are funds accruing (unconsumed income measured in dollars per unit time); investments are real physical assets produced per unit time, so they obviously are not identical physical entities. So it is not self-evident – at least not to me “” how the funds for investment can be said to be identical to investment itself.

The “S” and “I” that are used in national income accounting are both measured in dollar terms.  It’s not the number of houses built that matter, but the dollar value of expenditure on those houses.  So there is no “apple and oranges” comparison problem here.  Both saving and investment can be measured in either real or nominal terms. In either case they will always be exactly identical, because they are defined as being identical.  However, just as with MV=PY, I can imagine definitions of saving where S=I is not an identity.



43 Responses to “What does MV = PY actually mean?”

  1. Gravatar of Steve Roth Steve Roth
    20. February 2015 at 10:56

    On that “saving” conundrum, I’d very much like to hear your thoughts on this:


    V. weird, seems to me.

  2. Gravatar of Kevin Erdmann Kevin Erdmann
    20. February 2015 at 11:22

    I noticed a problem on this topic regarding housing. Since homes are real securities and mortgages are nominal, there is a disconnect in the accounting. The inflation premium portion of the interest expense is really an arranged saving plan, in real terms. When inflation is high or mortgage levels are high as a % of gdp, savings will be understated.

  3. Gravatar of flow5 flow5
    20. February 2015 at 11:30

    Per the last publication of the G.6 release, 93% of all demand drafts, bank debits, cleared thru demand deposit classifications (525 demand drafts/mo for Vt, as compared to 7.648/qtr for Vi on 10/1/1996), and 7% thru OCDs, NOW and ATS accounts. The Fed calculated the G.6 figures by dividing the aggregate volume of debits of these banks against their demand deposit accounts.

    Yet the 12/23/14 M2-Vi figure printed @ 1.538 x/qtr? – non sequitur! In other words, with this disparity, it is wanton apocrypha to presuppose, with if half of Americans are living paycheck-to-paycheck, that there is, e.g., no minimum monthly number of current bills, and undisposed income? – naught!

  4. Gravatar of Britonomist Britonomist
    20. February 2015 at 11:32

    flow5, you do realize nearly all of your posts are completely unintelligible, right?

  5. Gravatar of Richard A. Richard A.
    20. February 2015 at 11:34

    Both monetary equations have something to say. The classic equation of exchange, MV=PY, emphasizes money as a medium of exchange, while the Cambridge equation, M=kPY, emphasizes money as a store of value.

  6. Gravatar of flow5 flow5
    20. February 2015 at 11:34

    From a systems viewpoint, commercial banks (DFIs), as contrasted to financial intermediaries (non-banks): never loan out, & can’t loan out, existing deposits (saved or otherwise) including existing transaction deposits, or time/savings deposits, or the owner’s equity, or any liability item.

    When CBs grant loans to, or purchase securities from, the non-bank public, they acquire title to earning assets by initially, the creation of an equal volume of new money (demand deposits) – somewhere in the banking system. I.e., commercial bank deposits are the result of lending, not the other way around.

    The non-bank public includes every institution (including shadow-banks), the U.S. Treasury, the U.S. Government, State, & other Governmental Jurisdictions, & every person, etc., except the commercial & the Reserve banks.

    Thus not only does S never equal I, during the Great-Recession the proportion of savings impounded within the CB system dramatically increased – starving the economy.

  7. Gravatar of flow5 flow5
    20. February 2015 at 11:40

    It began with the General Theory, where John Maynard Keynes gives the impression that a commercial bank is an intermediary type of financial institution serving to join the saver with the borrower when he states that it is an “optical illusion” to assume that “a depositor & his bank can somehow contrive between them to perform an operation by which savings can disappear into the banking system so that they are lost to investment, or, contrariwise, that the banking system can make it possible for investment to occur, to which no savings corresponds.”

    In almost every instance in which Keynes wrote the term bank in the General Theory, it is necessary to substitute the term financial intermediary in order to make the statement correct. This is the source of the pervasive error that characterizes the Keynesian economics, the Gurley-Shaw thesis, the elimination of Reg Q ceilings, the DIDMCA of March 31st, 1980, the Garn-St. Germain Depository Institutions Act of 1982, the Financial Services Regulatory Relief Act of 2006, the Emergency Economic Stabilization Act of 2008, sec. 128. “acceleration of the effective date for payment of interest on reserves”, etc.

    The CBs can force a contraction in the size of the S&L system, & create liquidity problems in the process, by outbidding the S&Ls for the public’s savings. This process is called “disintermediation” (an economist’s word for going broke). The reverse of this operation cannot exist. Transferring saved TR or TD deposits through the non-banks cannot reduce the size of the commercial banking system. Deposits are simply transferred from the saver to the non-bank to the borrower, etc.

    The drive by the commercial bankers to expand their savings accounts has a totally irrational motivation, since it has meant, from a system standpoint, competing for the opportunity to pay higher & higher interest rates on deposits that already exist in the commercial banking system.

    The shift from demand to time deposits has converted spendable balances into stagnant money. This transfer added nothing to the Gross National Product, & nothing will be added so long as the funds are held in the form of time deposits. Shifts from transaction deposits, to time deposits, simply increases the aggregate costs to the banking system & adds nothing to the system’s income.

    But it does profit a particular bank, Citibank for example, to pioneer the introduction of a new financial instrument such as the negotiable CD until their competitors catch up; & then all are losers. The question is not whether net earnings on CD assets are greater than the cost of the CDs to the bank; the question is the effect on the total profitability of the banking system. This is not a zero sum game. One bank’s gain is less than the losses sustained by other banks.

  8. Gravatar of flow5 flow5
    20. February 2015 at 11:42

    20. February 2015 at 11:32

    flow5, you do realize nearly all of your posts are completely unintelligible, right?

    Sorry, my raw IQ scores were PERFECT.

  9. Gravatar of Britonomist Britonomist
    20. February 2015 at 11:47

    ^ Case in point.

  10. Gravatar of flow5 flow5
    20. February 2015 at 12:01


    Guess that’s why no one’s caught up yet – I discovered the Gospel 36 years ago. It shows that every recession since the Great-Depression is the Fed’s fault. It shows that Bankrupt U Bernanke was the sole cause of the Great-Recession (other factors were immaterial).

    It shows that monetary flows (our means-of-payment money times its transactions rate-of-turnover), i.e., the proxy for inflation, fell by 2/3 since Jan 2013 until Dec 2014, and that the proxy for real-output fell by 1/2 since July 2014 until Dec 2014.

    Declining rates, oil, the fall in gDp from 5 percent to 2.6 percent, and the rise in the dollar were no happenstance. Go fish.

  11. Gravatar of flow5 flow5
    20. February 2015 at 12:06

    There’s no benefit for me to explain any of this to you. What I know should be classified as “TOP SECRECT” by the U.S. gov’t. It is worth trillions of economic dollars.

  12. Gravatar of ssumner ssumner
    20. February 2015 at 12:22

    Steve, I’d need to know much more to comment. For instance, is that net or gross saving?

    Kevin, Good point, the budget deficit is also overstated when there is inflation.

    Richard, That’s right.

  13. Gravatar of Majromax Majromax
    20. February 2015 at 12:27

    @Steve Roth

    Wait, that graph icnludes firms’ net worth along with the non-stock portion of households? What about US-based firms who have equities owned by foreign investors, or household ownership of foreign firms?

    The difference between those lines looks to me a fair bit like the cumulative current account deficit.

  14. Gravatar of flow5 flow5
    20. February 2015 at 12:59

    Rates-of-change (roc’s), in monetary flows (our means-of-payment money supply times its transactions rate-of-turnover) = roc’s in all transactions in Irving Fisher’s “equation of exchange” MVt=PT.

    Roc’s in M*Vt = aggregate monetary purchasing power (not N-gDp, as in Keynesian economics).

    Roc’s in MVt = roc’s in N-gDp (which is simply a proxy for all transactions).

    Contrary to Friedman, the distributed lag effect of money flows are not “long and variable”. They have been mathematical constants for over 100 years.

    The mainstream Keynesian-economic metric variant, income velocity – Vi, a contrived figure, is calculated: by dividing N-gDp for a given period by the average volume of the money stock (M1, M2, & MZM), for the same period (viz., make believe).

    A decline in the income velocity of money (like during the Great-Recession), is supposed to suggest that the Fed initiate an expansive, or less contractive, monetary policy.

    This signal could be right – by sheer accident. I.e., the historical trend of Vt vs. Vi, at various intervals, moved in absolutely divergent paths – giving the income velocity economists false signposts (e.g., inflation in 1978).

    But we knew this already:

    After 7 years of compilation, see article: “Member Bank Reserve Requirements — Analysis of Committee Proposal”; published — Feb, 5, 1938.

    “In 1931 this committee recommended a radical change in the method of computing reserve requirements, the most important features of which were…”

    # (2) “Requirements against debits to deposits”
    # (5)”the committee proposed that reserve requirements be based upon the turnover of deposits”

    This research paper was DECLASSIFIED after a 45 year hiatus on March 23, 1983. See: http://bit.ly/M0JB7X

  15. Gravatar of Doug M Doug M
    20. February 2015 at 13:00

    MV = PY

    The monetarist view…V would probably be stable. If you want a stable growth in demand (PY) then you just needed to manage a stable growth in M.

    The market monetarist point of view seems to be that V is not necessarily stable, but if markets are efficient and we had a market for NGDP we could have highly accurate forecasts for PY based on current levels of growth of M. With these two pieces of information central bankers could dynamically tune M such that growth in demand is stable.

    The bond trader in me says that present value of all of these statics is intimately connected to the expectations of the future value of these numbers. But, since these expectations are always fluctuation, and sometimes radically, stable growth is BS, and so we shouldn’t bother trying to force a framework that will never fit.

    “stop obsessing over the C+I+G+NX = GDP” agree!

    “It’s NGDP that matters.” Disagree. NGDP growth matters more than the NGDP level… and employment, and productivity probably matter more than GDP. But…

    GDP = Employment * Producivity.
    GDP growth = Employment growth + Prodcuctivty growth.

    “They talk about Americans “spending” lots of money on housing during the housing boom, instead of “saving” the money. But according to the official definition, spending on new housing is saving. ”

    The home buyer is spending money. But, he is borrowing the money from savers to facilitate the transaction. So, money put into houses is both money spend and money saved.

    Savings = Investment is only true in a world without trade.
    As there is trade, if it is only true in a global sense, it isn’t a particularly useful concept.

  16. Gravatar of Jason Smith Jason Smith
    20. February 2015 at 13:07

    M V = P Y or M = k P Y can also be taken to be an information equilibrium condition; i.e. if you jiggle M around, it jiggles PY around in roughly the same pattern.


    The most general information equilibrium relationship, though is where:

    log PY = a log M + b

    The Cambridge equation just takes a = 1 and b = – a log k; it’s a specific case of information equilibrium.

    Even more interesting is that “a” can change slowly because it represents the ratio of the information content in a dollar of PY to a dollar of M. A dollar of M basically specifies exactly what it is — a dollar of money in a bank or your wallet; a dollar of NGDP could be a pack of gum, an mp3 download or a piece of an F-35. Knowing what a specific dollar of PY is going towards reveals more information than revealing e.g. which bank a specific dollar of cash resides in.

  17. Gravatar of Charlie Jamieson Charlie Jamieson
    20. February 2015 at 13:10

    The home buyer isn’t borrowing money from savers. He is borrowing from the bank. New deposits are created.
    Savings is income minus spending. Trying to differentiate between savings and investment is very tricky. If you spend your extra income on stocks, some might call that investment, others savings. A house might be considered spending, saving and investment. My college tuition is spending but also investment.
    When your savings fall in value, does that mean you are saving less? When you are spending all your income, but your stocks rise, does that mean you are saving more?
    These are interesting questions to ponder but show the difficulty or trying to separate savings and investment.

  18. Gravatar of Doug M Doug M
    20. February 2015 at 13:25

    “When your savings fall in value, does that mean you are saving less?
    When you are spending all your income, but your stocks rise, does that mean you are saving more?”

    Actually the opposite…according to the accounting of our Federal Government…

    If your net worth is rising faster than your earned income… that is, your securities portfolio, and asset value of your house are increasing, your calculated level of savings tends to decline… you are “saving less” even though you have more money in your “savings.”

    This is because savings is defined as earned income not spent. Appreciation is unearned income.

  19. Gravatar of Nick Rowe Nick Rowe
    20. February 2015 at 14:02

    Scott: I tend to agree. But on the other hand, money really does circulate, because most other goods and assets do get bought and sold for money. If we interpreted “M” as the stock of gold jewelry, then it would make much more sense to use k instead of V.

    Steve: Remember that “wealth” can double overnight, even if you save nothing, if all your assets double in price. With falling real interest rates over the last few years, it’s not surprising to see wealth growing faster than cumulated saving. “Income” and hence “saving” in national accounting terminology, does not include capital gans on assets.

  20. Gravatar of Kevin Erdmann Kevin Erdmann
    20. February 2015 at 14:10

    “The home buyer isn’t borrowing money from savers. He is borrowing from the bank. New deposits are created.”

    Charlie, isn’t the new deposit a form of savings?

    I’ve always wondered what’s up with flow5. He’s a bit boastful, but he seems to me to have some interesting views. But, his posts do tend to be opaque.

    He doesn’t seem at all like some of the resident trolls, even though he can be verbose. But, Scott seems to ignore him 95% of the time, and treat him with disdain the other 5%. Did he do something that I missed? Or, are his posts technically incorrect in some way that I’m too ill-informed to catch?

  21. Gravatar of bill woolsey bill woolsey
    20. February 2015 at 14:13

    I will grant that a redefinition of car purchases as investment rather than consumption would result in more saving. But the reason isn’t that car purchases would be saving. It is rather because car purchases are not consumption, so the reduction in consumption implies an increase in saving.

    However, most saving is not purchasing things that count as investment.

    An exception is that the part of business saving (earnings retained out of current profit) that is spent on newly produced capital goods is more or less the same example.

    Buying a home is saving? Well I suppose if Bill Gates uses part of his current income to buy a house, that would work. But for most of us, buying a home is investment, yes. And the saving is the monthly repayment of principle over the next thirty years. The purchase of the house is counted as investment, but if it is financed by a loan, the home buyer isn’t saving.

    When firms retain current profits and purchase corporate bonds, perhaps issued in a previous year, that is business saving but not investment.

    And the more traditional example is that when a household refrains from consumption and purchases stock, it is saving and not investment.

    The redefinition of some item of household expenditure from consumption to investment is a terrible example of the identity between saving and investment.

    When individuals save, they are not investing.

    But because the expenditure of one individual is the income of another, arithmetic shows that saving and investment must be equal (at least if saving is income less consumption and all expenditure is consumption or investment.)

  22. Gravatar of Charlie Jamieson Charlie Jamieson
    20. February 2015 at 14:40

    I view buying a home as ‘savings’ in the sense that instead of paying someone else (rent, income for him), you are keeping the money yourself in your home equity (deferred spending for you.)
    I know some people view home buying as consumption, as the house is usually a depreciating asset. But the real asset might be the real estate or the intangibles of the location.

    Most of what flow5 says is over my head. But I suspect there are some good ideas in there about the flow of money, which is critical. Money is like water — if it rains a lot in Seattle it doesn’t help Wyoming much.

  23. Gravatar of ssumner ssumner
    20. February 2015 at 14:47

    Doug, You said:

    “The bond trader in me says that present value of all of these statics is intimately connected to the expectations of the future value of these numbers. But, since these expectations are always fluctuation, and sometimes radically, stable growth is BS, and so we shouldn’t bother trying to force a framework that will never fit.”

    Either you favor switching from money to barter, or you haven’t done a very good job at explaining your views. If you don’t favor barter, then the paragraph I just quoted makes no sense.

    Jason, You said:

    “M V = P Y or M = k P Y can also be taken to be an information equilibrium condition;”

    Nope, it’s an identity. It holds true even if the economy is not in equilibrium.

    Nick, That’s right.

    Bill, All I am saying is that if you earn a million dollars, spend $800,000 on consumer goods and services, and spend $200,000 on a new house, then you’ve saved $200,000.

  24. Gravatar of bill woolsey bill woolsey
    20. February 2015 at 15:44

    Yes, Scott.

    And hardly anyone purchasing a $200,000 house earns $1,000,000.

    If you earn $50,000 a year, and use the $15,000 you saved up over the past 15 years plus a $135,000 loan to buy a house, and spending $50,000 on food, utlities, ect, there has been no saving. The $150,000 that had been accumulated in the past plus the $135,000 borrowed are not income. There is a $150,000 investment in a house and no saving at all.

    Of course, if this were a world with no trade or government, then there would have to be saving by someone in the economy to match this.

    By the way V = 1/k

    k = M/yP

    Velocity is the reciprocal of the amount of money people hold relative to their nominal income.

    If M = Ms, then this is an identity.

    If M = Md, then it is not an identity, or rather, MsV = Py is an equilibrium condition.

    But I will grant that isn’t the way the text books tell it.

  25. Gravatar of Charlie Jamieson Charlie Jamieson
    20. February 2015 at 16:18

    Bill, in that example, I maybe look at it like this:
    You allocated $15,000 of your existing savings into a financial asset — the title to the house.
    You borrow $135,000.
    Net position: Plus 15, minus 135.
    Assuming the house stays flat in value, every dollar you pay toward the loan (excepting interest) improves your net position, so that would be savings.
    So after one year you’d have your original 15 in the house, but now your loan might be minus 134. You’ve saved $1,000.

    Now, when you bought the house, the seller gets $150k. Assuming he owns it outright, his savings change from the title to deposits.

    Of course a house can also be consumption (houses fall apart and are consumed) and investments (the house could also appreciate in value.)
    I don’t know if you can separate investment from consumption. If I buy a truck, that’s consumption. If I put a snowplow on it, that’s investment. To the seller it’s all the same.

  26. Gravatar of Doug M Doug M
    20. February 2015 at 16:20

    Either you favor switching from money to barter, or you haven’t done a very good job at explaining your views.

    If that is what you took from what I had to say, then I must not have done a good job in explaining my views…

    The Freidman monetarists view and the market monetarists both suggest that a change to fed policy (money growth targeting or NGDPLT respectively) will lead to stable growth in aggregate demand and repeal the business cycle… or minimize the business cycle.

    The point that I was trying to make is that the economy is fundamentally unstable. It has built-in feedback loops. Systems with feedback are prone to chaos! Rather that pretend that the business cycle can be tamed, accept that it is wild. There will be crises, financial panics, banks failures, and recessions.

    This does not suggest in any way that we should abandon money and go to barter. Nor does this mean that markets are inefficient. In fact, the system is unstable because markets are efficient. They quickly incorporate new information.

    What does this mean from a regulatory point of view? We have it exactly backwards. We should not be trying to prevent failures. We should expect failure as the norm.

    I am not sure what the implications of this theory is from the point of view of monetary policy, except that we should not become arrogant, and a simpler policy is probably a better policy.

  27. Gravatar of Derivs Derivs
    20. February 2015 at 16:27

    “Bill, All I am saying is that if you earn a million dollars, spend $800,000 on consumer goods and services, and spend $200,000 on a new house, then you’ve saved $200,000.”

    Of course. This is a funny argument considering there are such specific accounting standards for this. Seems one should just be glad to be arguing over where something is categorized on the same side of the equation C+I+ = . Consistent to accounting, most consumption would be an asset transfer and not actually consumed at the time of purchase.

    If I buy dinner and tickets to the theater, that is clearly consumption. Net worth declines.
    If I buy a high end camera lens on e-bay (one I expect will actually increase in value, or at worst, sell tomorrow for the same price), even sell a few shares of stock to do it, I made an asset transfer, to me an investment, to me this remains savings (assets on my balance sheet), my net worth remains the same as before the purchase. Technically, on the net whole, I consumed nothing.

    Good thing to learn at a young age. Avoid buying depreciating assets.

  28. Gravatar of Charlie Jamieson Charlie Jamieson
    20. February 2015 at 16:57

    Derivs, another way to look it:
    In the example of the camera, you have swapped assets, and no new economic activity was created, although presumably each of you is happy with the swap.
    But if you buy dinner and tickets to the theater, you have helped create new economic activity.
    You could also look at it this way: dinner and tickets to the theater could be an investment, if it helps you win business, or even if it helps seal a personal relationship!

  29. Gravatar of Doug M Doug M
    20. February 2015 at 16:57

    Regarding housing…

    When you buy the house, you go to the bank and you borrow some money. You give that money to the seller, and the seller pays off whatever outstanding mortgage he had on the house. And rolls some of is profits into the down payment on his next house, and maybe saves some of his profits, or spends his profits and somebody else gets the cash… nonetheless,someone, somewhere, saved some money and that money is registered as an increased investment in housing.. The amount of new savings is only as much as the profit that the seller made.

    Now you live in your house and you make payments on your mortgage. The interest is an expense to you and income to someone else, and in the aggregate is a big zero on the savings scorecard.

    The principle payments are money saved. But the principal on a mortgage payment is trivial.

    Your house is providing housing services to you. It doesn’t matter if you are an owner occupant or a renter, you are paying rent. You are just paying (or not paying) rent to yourself. And that (non) rent is an expense!

    Now, suppose while you are living in this house your house doubles in value. Your mortgage is the same, but you owners equivalent rent increases. This means that you expenses are rising, cash flow is unchanged, your net worth is increasing, and your savings rate is falling!

  30. Gravatar of Jason Smith Jason Smith
    20. February 2015 at 17:44


    In response to my statement:

    “M V = P Y or M = k P Y can also be taken to be an information equilibrium condition;”

    You said:

    “Nope, it’s an identity. It holds true even if the economy is not in equilibrium.”

    Information equilibrium can hold for a system far from equilibrium defined by constraints (like an economic/ADM equilibrium or thermodynamic equilibrium).


    I’m not saying MV=PY is not an identity in economics, it just could have a much richer and more useful meaning if interpreted as information theory.

    You could say NGDP = A r where r is the interest rate defines a quantity A. But that’s an identity cannot be interpreted as an information equilibrium condition since log NGDP is not proportional to log r. The equation of exchange *can* be interpreted as an information equilibrium condition, which is interesting! It means MV = PV could be used to make hypotheses about empirical data that could be tested.

  31. Gravatar of Major.Freedom Major.Freedom
    20. February 2015 at 18:42

    The monetary equation of exchange and NGDP are only part of the story. Dollar denominated variable impky a corresponding real variable.

    When economists who only focus on money talk about “sticky prices”, they view spending changes as only money denominated changes.

    Sticky prices are not solely monetary. Spending is not solely monetary either. Sticky prices are equivalently money and real goods related. Sticky prices are real goods related no less than money related.

    If one is entitled to abstract from real goods so as to make claims of relationships between prices and money changing hands, then one is also entitled to abstract from money so as to make claims of relationships between prices and goods changing hands.

    Given sticky prices, a fall in money spending IS a fall in goods and services spending. Yet how many monetarists would claim that to solve output falls and idle labor, the way out of a fall in real goods and services selling is to encourage an increase in real goods production? After all, given sticky prices, a rise in real goods production will prevent recession.

    Now just because money is monopolized, it does not mean that we are forced or compelled to regard abstracted money variables as the key variables to manipulate so as to prevent a fall in output. Given sticky prices, a rise in spending IS a rise in goods being sold.

    Of course the reason AMMs don’t even look at increased production as a solution or preventative measure against recession, is because aggregate production cannot be directed by a single consciousness that the AMM can find affinity towards as an individual thinker himself. The AMM cannot politically or even intellectually take hold of how a single consciousness would control aggregate real goods selling. Real goods are after all heterogeneous. But money can be taken hold of as a single variable.

    Thus the unwarranted presumption is made that there might be some answer to recessions in money abstracted, or at least a solution to what is considered a problem of only money, which is abstracted money spending.

    But every AMM argument made about the solution being a rise in money spending given sticky prices, is at the very same time a solution being a rise in goods spending.

    Now it would not be correct to say that if we can’t increase one, I.e. rela goods, then we can solve the problem with only more of the other, as if more money given sticky prices causes more real goods selling, and as if more real goods selling given sticky prices does not cause more money spending. In fact neither cause the other. Yes, mathematically speaking more spending given sticky prices does “impky” more goods selling. But this is an identity, not a causal relationship. It is also false to view more goods selling given sticky prices as a cause for more spending. They are both equally false.

    But wait! Don’t businesses tend to produce more when their money demand goes up, given sticky prices? Isn’t it money after all that is a cause? No, it is not. For those who are able to spend more because of having a higher income, they must produce and sell goods and services! When you call for more NGDP given sticky prices, you are in fact also calling for people to sell more goods. That is what higher incomes given sticky prices means.

    Goods and money are two sides of the same coin, and both are the effect of prior causes. Those causes are where recessions are cured or not cured, as well as caused and not caused.

    If we lived in a world where all real goods except money were centralized, then it is almost certain that we would be reading RGDP targeting theorists claiming that recessions and unemployment are caused by states being too tight real goods-wise. We would be hearing claims that recessions are “mainly” and “for the most part” and “primarily” caused by tight real goods. Money would be sometimes identified as an issue, but it would be drowned out in a sea of RGDPLT pundits claiming that money spending fell so much 2008-2009 because the state tightened up real goods selling too much, and not because there is a monopoly in real goods that prevents individuals from knowing market prices.

    We would also be hearing plans on “Market Communist Productionism”, by Schmidt Sumler, who says the state should target his preferred rate of supply of goods and services being bought and sold, and then “leave it up to the market” to decide what real goods prices and interest rates are by way of having control over money. This would be ideal, allegedly, because when “the market” sells less money, then prices will rise, and if “the market” sells more money, then prices will fall. Given prices are sticky, a plan of RGDPLT will minimize the depths of recessions.

  32. Gravatar of Derivs Derivs
    21. February 2015 at 04:35

    My question. With so many M’s available, is their an agreed upon default M (1,2,3..) to be used for calculations of V?

  33. Gravatar of flow5 flow5
    21. February 2015 at 07:58

    This went over Milton Friedman’s head (1950’s correspondence). QE3 was contractual. The liftoff we got in 2013 was from “putting savings to work” (getting the CBs out of the savings business).

    Vt (not Vi), or the transactions velocity of money initially offset the Fed’s contractionary money policy. We got the boost in Vt from the FDIC’s expiration of unlimited transaction deposit insurance.

    Transactions between the RB and the CBs aren’t “asset swaps” when reserves are remunerated. They turn tradable liquid assets into circumscribed assets.

    Interbank demand deposits are assets defined by economists to be outside-of-the properties normally assigned to the money aggregates. IBDDs are not a medium of exchange. They do not circulate outside of the inter-bank market. They do not require Basel regulatory capital. They are not subject to reserve requirements. They do not represent “high powered money”.

  34. Gravatar of Saturos Saturos
    21. February 2015 at 08:05

    Unable to resist the me-bait here…

    So the NGDP(1) in this post is the kind that emphasizes the flow of M against the flow of new real (final) Y that is bought with transactions each year. NGDP(2) based on V(2) is an even more general tautology, with Y being everything that counts in the actual NGDP statistic that is reported, even if not something that is exchanged for money. So in the exchange view that Nick Rowe and I hold NGDP(1) fluctuations ought to be more correlated with recessions than (2) fluctuations are. Additionally, when (1) and (2) diverge, the exchange view would predict k to be a more stable function of NGDP(1) than NGDP(2), as a boost in society’s income solely through eg. imputed rents does not increase household spending power or give people more things to spend/exchange money balances for, and should not increase the demand to hold them. (Housing price increases would seem to increase spending – except that would be reasoning from a price change!) Treasury might choose to include all sorts of consumption in GDP and impute nominal values for them, but that isn’t necessarily going to raise cash wages or “put more money in pockets” that would change people’s spending or money-holding decisions. Thus such a biased increase in GDP (holding M constant) would not be accompanied by any deflationary pressure, as (2) predicts. (I think.)

    I think you need to see that for the numeraire to serve as the numeraire in our economy it also has to have (direct or indirect) exchange rates with everything it denominates, which means it is actually exchanged, which means there is (are) implicitly a market here that tries to clear. But I don’t want to rehash a long debate here, other than to reiterate that there actually ought to be some such clever ways to distinguish empirically MoA-centrism and MoE-centrism.

  35. Gravatar of Saturos Saturos
    21. February 2015 at 08:07

    “IBDDs are not a medium of exchange. They do not circulate outside of the inter-bank market.”

    flow5, I’m not quite sure the former is implied by the latter… it is our banks that handle most of our payments for us, you know.

  36. Gravatar of flow5 flow5
    21. February 2015 at 08:19


    “My question. With so many M’s available, is their an agreed upon default M (1,2,3..) to be used for calculations of V?”

    Agreed? No all the pundits are wrong. Money is the measure of liquidity (bank debits), the yardstick by which the liquidity of all other assets is measured.

    In 1996 Vt turned over 525/mo, as compared to 2.5/mo for Vi.

    Transaction deposits are driven by payments. Non-M1 components have extremely low turnover rates relative to M1. Barnett, Spindt, and Anderson (Divisia – aggregates”, “debit-weighted-money-index, MSI) never got it right.

    St. Louis Fed’s technical staff: “Although the evidence is mixed, the MSI (monetary services index), overall suggest that monetary policy WAS ACCOMMODATIVE [sic] before the financial crisis when judged in terms of liquidity.

    Scientific evidence “is proof, which serves to either support or counter a scientific theory or hypothesis. Such evidence is expected to be empirical evidence and in accordance with scientific method” – Wikipedia

    Scientific method is “a method or procedure…consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses” – Wikipedia

    The scientific evidence for the last 100 years is irrefutable. Every year, the seasonal factor’s map, or scientific proof, is demonstrated by the product of money flows.

    The FOMC’s monetary policy objectives should be formulated in terms of desired roc’s in monetary flows M*Vt relative to roc’s in real-gDp. Roc’s in N-gDp, can serve as a proxy figure for roc’s in all transactions P*T. Roc’s in real-gDp have to be used, of course, as a policy standard

  37. Gravatar of flow5 flow5
    21. February 2015 at 08:43


    The FBO’s IBDDs are telling. Recently: “Net Due to Related Foreign Offices” of these Foreign-related financial institutions have also dropped by a relatively large amount, by $202.2 billion” – John Mason.

    IBDDs may be converted into domestic currency or foreign currencies. The probability of speculative conversion is related to the liquidity and duration of their holdings.

  38. Gravatar of Scott Sumner Scott Sumner
    21. February 2015 at 09:43

    Bill, In the textbooks M is simply the quantity of money, you are right that it would not be a tautology for Md.

    Doug, First of all, Friedman never proposed using monetary policy to “tame the business cycle.” Second, if you say you oppose monetary policy I can only assume you favor barter. What other implication could I draw? Now if you said monetary policy X is better than monetary policy Y, that would be different, then I’d assume you don’t favor barter. Is that what you believe? If so, what is monetary policy X?

    Generally when people say they don’t favor using monetary policy, I assume they favor barter.

    Jason, Again, it holds whether you are in information equilibrium or not.

    Derivs, No, each M has its own V.

    Saturos, I’m not sure what you mean by NGDP 1 and 2. There is only one NGDP, isn’t there?

    I do agree that parts of GDP such as imputed rents are less important for the business cycle. In my view that’s because imputed rent doesn’t require labor to be produced.

  39. Gravatar of flow5 flow5
    22. February 2015 at 07:50

    “each M has its own V”

    Which makes each Vi, associated with each wider definition, increasingly wrong.

    Income velocity is a contrived figure, having no nexus with reality.

  40. Gravatar of flow5 flow5
    22. February 2015 at 07:58

    See: New Measures Used to Gauge Money supply WSJ 6/28/83



  41. Gravatar of flow5 flow5
    22. February 2015 at 16:30

    From MVt=PT we know 2 things about 2015 – that inflation will accelerate and that real-output will decelerate (Yellen’s manufacturing stagflation).

    We also know that one of the largest long-position squeezes in history is about to take place in the bond market.

  42. Gravatar of ThomasH ThomasH
    22. February 2015 at 17:35

    I must be a “Keynesian,” I still think changes in desired saving are important at the “ZLB.” This is not to say monetary policy policy is not important but experience has shown that near the ZLB central banks are reluctant to take measures to ensure that desired savings = desired investment. Of course it does not help that governments during recessions tend to act like credit constrained consumers and so cut back on investment when they should be increasing it. (Glad that The Economist recognizes that.)

  43. Gravatar of Robert Embree Robert Embree
    25. February 2015 at 23:52

    Hello Scott,

    Thinking more about the “marketing” ramifications of MV = PY, I was wondering if you could tell me why we use the term “nominal GDP targeting” rather than “MV targeting” or “aggregate demand targeting”. Obviously they are equivalent terms (if we accept your definition of aggregate demand as nominal GDP), but different groups might perceive the policy differently.

    I’ve written about this a little more here:

    – Robert

Leave a Reply