# Is MV=PY useful?

No.

First, we have to understand what the equation of exchange is: without additional assumptions, it’s a tautology. Velocity, “V”, is defined as the number such that MV = PY will hold. Unless V happens to be relatively stable, or obey some kind of predictable pattern in response to other variables (e.g. the nominal interest rate), the equation tells us nothing.

As James Hamilton observes (and as economists since the 1980s have understood), “V” isn’t stable: instead, it moves around almost exactly opposite to “M”, as nominal GDP (“PY”) does its own thing. Of course, this isn’t entirely fair. Financial innovation has made “V” meaningless today, but decades ago, the old-school monetarists had reason to think that it was stable.

But even then, I contend that the equation of exchange was near-useless as a practical way of thinking about monetary policy. Why? Well, we have to think about why it could conceivably be a valid approximation in the first place. This involves constructing some model where money is closely related to consumption, perhaps through a cash-in-advance constraint or through complementarity in the utility function. And in such a model, the assumption that “V” is stable translates into an assumption that there is some kind of tight constraint connecting economic activity to real money balances.

But in such a model, the nominal interest rate is a sufficient statistic for the extent to which this constraint binds—after all, it’s the cost of holding money. If a lack of money is hurting output in the direct way implied by MV=PY, the nominal interest rate has to be high enough that holding money is costly, and agents in the economy cut back on activities complementary to money. Maybe an 8% nominal interest rate is just enough to make certain activities uneconomical: operating a cash-intensive business, or spending regularly at a market. Regardless of the specific effect, a truly meaningful shortage in quantities should be reflected by a spike in prices. And that price is the nominal interest rate.

Scott Sumner is fond of citing the following remark from Milton Friedman:

“Low interest rates are generally a sign that money has been tight, as in Japan; high interest rates, that money has been easy.”

This is very true, and very wise. But this is precisely the kind of observation that MV=PY cannot rationalize: given the economic model implicit in the equation of exchange, nominal interest rates are sufficient to summarize the stance of monetary policy. And that’s why the basic monetarist model is such a poor tool for analyzing the effect of money.

Don’t take it from me. Take it from Milton Friedman.

(Disclaimer: Since I don’t want to perpetuate any popular misconceptions, I should mention that no credible monetary economist is a “monetarist” anymore, at least in the old sense of the term. The profession moved on long, long ago. But since I still see MV=PY popping up quite frequently on the internet, I think it’s important to emphasize what a poor model it really is.)

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### 73 responses to “Is MV=PY useful?”

1. Scott Sumner

I agree with much of what you say, but:

1. If MV=PY were a model, it might be a poor model. But it’s not a model. I think you are claiming that the QTM is a poor model, which I don’t agree with.

2. M2 velocity tends to be fairly stable in the long run. In the long run, increases in M2 produce roughly proportionate increases in NGDP.

• I think we might be in agreement, though exactly what the “quantity theory of money” means is a little difficult to pin down. On its own, MV=PY is a tautology rather than a model—it has to be coupled with some kind of claim about the stability of V to mean anything. Even, then it’s not clear what the theory implicit in the equation is describing: is it saying that the causality can ever run from M to Y? (Many people interpret it this way, and it seems necessary if the quantity equation is ever going to hold in a world with relatively stable V and sticky prices.) Is the quantity equation, or some more richly specified quantity theory, a good description of that feedback, good enough to draw at least basic inferences about the effect of monetary policy on the real economy?

I don’t think it really can be. As I said in the post, MV=PY can only describe the effects of monetary policy on the economy in a world where the direct constraint between money and economic activity constitutes the linkage—and in that world, the nominal interest rate is a sufficient statistic for the stance of monetary policy (regardless of inflation, expectations of the interest rate, etc. etc.).

If we’re looking at MV=PY as a way to model the medium to long term effects of monetary policy on the price level, then I think it’s probably fine: there is always a money demand equation lurking in the background, and except in the short term (where sticky prices interfere) the money demand equation provides a linkage between policy and the price level. But I don’t think that economists are at any lack for effective ways to think about long-term price stability; everyone’s pretty convinced that a Taylor rule will work. For our purposes, the short-term properties of a model are the really important ones—and that’s where the QTM (at least in its purest form, unaugmented by some kind of New Keynesian sticky prices/monopolistic competition mechanism) really falls down.

On point (2), I’m not surprised that M2 velocity tends to be relatively stable in the long run, but I think we could just as easily interpret causality as running in the other direction. M2 is mainly a reflection of highly liquid wealth held by households, and it’s not surprising that this quantity would have a relatively constant ratio with nominal GDP.

• couldn’t agree more, both with the post and your response to Sumner.

2. David Beckworth

Matt:

Very few people use MV=PY as a theoretical model. It is just an accounting identity. However, as an accounting identity it can be useful to help one think more carefully about monetary policy. In particular, it helps one understand why nominal spending growth has been sluggish. For example, see my posthere.

This statement is wrong:
“As James Hamilton observes (and as economists since the 1980s have understood), “V” isn’t stable: instead, it moves around almost exactly opposite to “M”, as nominal GDP (“PY”) does its own thing. ”

First, V has not always moved opposite M. It only has done so when the Fed was doing a good job stabilizing nominal income as it did during the Great Moderation. Before then, when the Fed was mess they were anything but moving in opposite directions. See the figures and discussion in here .

Second, given that V has not always moved opposite M it is inaccurate to say PY does its own thing. The Fed effectively stabilized nominal income during the 1983-2007 period by adjusting the stance of monetary policy to offset shocks to money demand. This is what cause PY to stabilize and appear to do its own thing–the Fed was sort of adjusting M to respond to changes in V (though this is not completely accurate since the Fed only controls the base, not the money supply). See
Nick Rowe for the thermostat analogy.

• “Second, given that V has not always moved opposite M it is inaccurate to say PY does its own thing”

No, it is exactlybecause V has often, but not always, moved opposite M that it is in fact accurate to say that PY does its own thing.

If V *always* moved exactly opposite M then PY would be doing nothing at all.

• David Beckworth

PY doing nothing at all does not mean it is doing its own thing. PY doing nothing at all is the result of monetary authorities perfectly responding to changes in V.

• I agree that monetary policy is a big part of the reason for the relative stability of nominal GDP in the last several decades. It is possible to imagine a world where your interpretation of events is correct—there have been a bunch of (technological? preference-based?) shocks to velocity, and the monetary authority has offset them in order to ensure that nominal GDP remains stable. As you say, since the Fed only controls base money rather than monetary aggregates, this isn’t exactly the right story, but it could be true to an extent.

But this doesn’t really seem to match the data. The rise in the monetary base, the asset whose quantity the Fed actually controls, has been extraordinarily consistent from the 80s up until the implementatation of QE: http://research.stlouisfed.org/fred2/series/BASE. It’s hard to see how, quantitatively, the Fed is changing base money by enough to offset these shocks to velocity. Instead, it seems as if there are regular shocks to the liquid bank deposits tallied in monetary aggregates that do not have much effect on nominal GDP, but mechanically lower velocity calculated via V = PY/M.

And regardless, I don’t think that MV=PY is an effective way of representing these relationships. What happens if there is an increase in money demand (for which “1/V” is some kind of weird, reduced-form statistic) that the Fed doesn’t accommodate by increasing M? V falls, but then nominal interest rates will rise (by a lot) and this will bring V back up, possibly to the point where it’s the same as before. What is the actual transmission mechanism such that PY is affected? It’s buried so deeply under the surface that I can’t understand it at all.

To make this more concrete, keep in mind that in a MIU model where consumption and money are separable in the utility function, you still get an equation like MV=PY (where V is a function of the nominal interest rate R), but you get the complete neoclassical dichotomy as long as prices are not sticky. So MV=PY is definitely not enough to give us real effects from monetary policy.

• David Beckworth

Matt:

I don’t want to oversell the equation of exchange here, but the Fed’s influence on nominal spending is more than just through its influence on the monetary base. The Fed also influences activity through the anchoring of nominal expectations, so to some extent it probably anchored V as well. Also, the level of the monetary base is not the right place to look. It is better to look at growth rate. The year-on-year growth rate prior to QE2 does show shows there was considerably variability. http://research.stlouisfed.org/fred2/graph/?g=n4

On thinking about relationships with the equation of exchange, again I refer to my post where I look at it in terms of BmV=PY. Here, M is decomposed into monetary base (B) and the money multiplier (m). Changes in velocity can be thought as changes in demand to broad money, while changes in the money multiplier can be viewed as changes in the demand for the monetary base. This sheds more insight, but yes it still limited in uncovering the underlying structural relationships. If one understands its limitations, it can still be useful as summary statistic–when broken down into its BmV=PY form–on what is happening to nominal spending.

3. David: “PY doing nothing at all does not mean it is doing its own thing”

Yes, I agree but that’s the point. If V always moved opposite M, so that PY did nothing, then you would have been correct, PY would not be doing it’s own thing.

But in the data PY does move, V moves too, sometimes opposite to M and sometimes not, thus the data is not inconsistent with the statement that PY is doing its own thing.

Furethermore, and more to the point, the statement of yours that I originally quoted seems to be incorrect and Matt’s statement is, at the very least, not refutable in the data.

4. David Beckworth

I am not arguing that PY has never changed. I am only arguing that the offsetting of M and V from about 1983 forward–when there is an offset— that Matt seems to be pointing to is the result of conscious policy choices that effectively aimed to stabilize the growth rate of PY. Thus, the stable growth rate of PY is not some random accident, but the result of the Fed effectively aiming to offset changes in V. In other words, PY is not doing its own thing even though it may appear to be so. PY is being driven by policy choices that cause M to offset V. (Actually, by setting expectations properly the Fed may have been managing V too.)

The same is true for before early 1980s. Here, however, the Fed was not doing a good job to offset shocks to V and even exacerbated them. Thus, M and V did not offset each other and the growth of PY was more volatile. Here too the PY was ultimately driven by policy choices–or the lack of good policy choices–in terms of offsetting changes in M to V.

See my post link above for the figures on the PY growth rate before and after the early 1980s.

• David,

I’m not acutally disputing the interpretation you give, I made the same point here (http://canucksanonymous.blogspot.com/2010/12/what-does-world-look-like-if-fed-is.html)

Nonetheless, as a point of logic your giving just an interpretation and your not establishing that Matt’s interpretation is inaccurate.

You said ” given that V has not always moved opposite M it is inaccurate to say PY does its own thing”.

If V always moved opposite M then it would be inaccurate to say PY does its own thing since PY would do nothing.

If V didn’t move then it would be inaccurate to say PY does its own thing since it would move in concert with M.

The fact that V moves but in a way that is not systematically related to M is the one case in which you can say that PY is doing its own thing.

Your argument presumes that PY doesn’t do its own thing and then offers an interpretation of the data that is consistent with that assumption, as such it is not a counter argument to Matt’s original statement.

• I should clairfy, the important point here is that because V moves in a way that is not systematically related to M then so does PY.

Thus, PY moves in a way not systematically related to M. That goes directly against the QTM. That, I believe, was the point Matt was making.

• Thanks. This is a good summary of the point I was originally trying to make (though I was incapable of being so succinct!).

I think David’s point is that the QTM would be a good description of the world, except that the Fed behaves in a way such that velocity shocks are precisely offset, and all we actually see in the data are residuals unaccounted for by the QTM. But in operational terms it doesn’t look like this is what the Fed is actually doing (there aren’t big injections of base money whenever V goes down).

5. David Beckworth

Okay, I see the QTM point. If that was Matt’s original point then I am agree with him.

6. Brian M

Coming back to the original question: is MV = PY useful? The interesting debate this blog post has generated would suggest that the answer is definitely yes.

7. My “first cut” theory of money demand would be that people tend to demand a quantity of money that is proportional to the rate at which they intend to spend it. I’m not sure how exactly one derives this from “deep” monetary theory, but it seems like common sense: if your intended nominal spending doubles, then, ceteris paribus, you will choose to hold twice as much money. Assuming that “money” is the medium of exchange for all transactions, then “the rate at which they…spend it” is PY, so, to the extent to which their intentions are realized, M is, under this theory, proportional to PY, and V is simply the reciprocal of the behavioral parameter that represents the constant of proportionality.

Now obviously a more realistic theory would allow money demand to depend on the nominal interest rate, though introspection tells me that the elasticity is pretty small. But in any case, I would find it puzzling if the Hicksian money demand function L(i,Y) were not (at least approximately) linear in Y. And if it is linear in Y, then the money demand equation can be rearranged in the form MV(i)=PY. So while MV=PY is, in itself, only the definition of V (a tautology, if you like, but only because definitions are by their nature tautologies), it turns out to have a straightforward behavioral interpretation.

You say:

…given the economic model implicit in the equation of exchange, nominal interest rates are sufficient to summarize the stance of monetary policy

I don’t see this. The measure of the stance of monetary policy is whatever you define it to be. In the context of the equation of exchange, the interest rate is isomorphic to any measure of the stance of monetary policy holding nominal GDP constant, though the isomorphism need not have any specific (e.g. linear) form. However, (1) there is no reason to hold nominal GDP constant when measuring the stance of monetary policy (indeed there is every reason not to do so), and (2) the mere existence of an isomorphism doesn’t imply that each side of the isomorphism is equally useful. In other words, nominal interest rates are not sufficient, in the context of the equation of exchange, to summarize unconditionally the stance of monetary policy; even subject to the necessary condition, they are not necessarily the best way to do so; and that necessary condition is in any case one that defeats the purpose of measuring the stance of monetary policy.

Milton Friedman himself would have suggested using M to measure the stance of monetary policy. If we assume that V is constant and then explicitly measure monetary policy ceteris paribus for changes in PY, then all the information in M is also contained in the nominal interest rate. But Friedman’s whole point was that it is a mistake to measure monetary policy ceteris paribus for changes in PY. P and Y are our objectives: if we hold them constant by construction, there is little point in doing monetary policy at all.

• Andy,

I submit that you’ve missed the point.

You write: “if your intended nominal spending doubles, then, ceteris paribus, you will choose to hold twice as much money”.

I think that’s entirely false, personally for me it is false. There are months where I spend twice what I usually would but in no cases do I double my real money holdings. I finance all virtually all my purchases by credit card and each month when my paycheck arrives I pay off my bills and imediately invest anything left over leaving a cash balance near zero.

I suspect that this sort of behaviour, or the potential for this behaviour, is what Matt had in mind when he quite correctly observed that “Financial innovation has made “V” meaningless today…”

• Perhaps your personal money holdings are only a residual, not a choice, so they don’t reflect a behavioral parameter. However, the bank that issued your credit card still has to settle your transactions, and its demand for reserves is going to depend on how much it thinks you are spending.

• I don’t think so, I think that as long as HSBC has capital they can settle their trades without having to double their reserves if the volume credit card purchases doubles.

They simply borrow the reserves in for a day. If the system finds itself short of reserves then this shows up in interbank lending rates.

So, as Matt claims, the short term nominal rate is a sufficient statistic and you can get nothing more by looking at the world via MV=PY>

• The reason why your assertion is false is right there in your description: “They simply borrow the reserves in for a day.” i.e. their demand for money has increased and they expressed that by trying to borrow the money. Your decision has to spend more not led to an increase in your demand for base money (since you’re basically using bank money) but it has led to an increase *someone’s* demand for base money.

8. Andy, thanks for the comment. I agree that it’s possible to construct a money demand function where money is approximately proportional to PY. In practice I don’t think that this is quite accurate, but it’s a completely reasonable theoretical construction, and it is consistent with virtually any account of the real effects of monetary policy—including, say, the canonical New Keynesian model. Even in an MIU model where prices are flexible and consumption and money are separable in the utility function (so that we recover the neoclassical dichotomy), you get something like M = PY/V(R). If we’re thinking about MV=PY in this broad sense, it is definitely wrong to say that the nominal interest rate is a sufficient statistic for the impact of monetary policy.

The premise of my post, though, is evaluating MV=PY not just as a plausible specification for a money demand curve but as a predictive account of the real effects of monetary policy. And this is where I think it’s really unsatisfactory. As I understand it, the basic “quantity equation leads to real effects” story is this: in the short term, prices are sticky and V also changes very little. Hence a decline in M will be reflected by a decline in Y.

But how does this actually happen? Presumably people need money to conduct transactions, and they are short of money (or more accurately, their bank is short of reserves). But as Adam P points out, if a bank is short of reserves, it will borrow those reserves at the fed funds rate; if there is some kind of aggregate shortage severe enough to make a real difference in consumption, it must be reflected in the rate.

This is why I think that MV=PY is near-useless for reasoning about the short-term real effects of monetary policy.

In the medium and long-term, maybe someone already has a real channel in mind (i.e. constant NGDP growth is a good way to prevent too many people from hitting credit constraints), and MV=PY is simply being used as a way to think about the fact that nominal GDP and M are roughly proportional over longer horizons. If so, I’m fine with it. But I still don’t think it can deliver that real channel itself.

9. Benjamin Cole

I think it is time to start thinking about, and promoting, the reduction in interest paid on reserves. The economy may do a Japan.

10. merijnknibbe

1. What’s M? I think our definition of money is somewhat obsolete. In the USA, 44 million people receive food stamps (food debit cards): means of exchange, store of value and even, to an extent, unit of account. It’s in fact: high powered M1, as it is time stamped money. Increasingly, such kinds of money are driving out real money (copy debit cards, Groupons, those kinds of things – often time stamped). Trivial? 44 million people – that’s not trivial anymore.

2. GDP is not a good measure of: PT, as GDP measures value added, not sales. Second hand trade is, by definition, not included in GDP (though selling fees are). Trivial? Existing houses, the second hand car market (larger than the new car market!), lots of art and antiquities – again: not trivial. Ooops, forgetting stocks, which are second hand items too. Land: another one. Total Expenditure is presumably a much better indicator for PT than GDP. Targeting nominal total expenditures would do better than targeting NGDP (nominal expenditires are, because of lower house prices and lower sales of houses, presumably quite a bit more below trend than nominal GDP)

3. Utility functions do not exist (try to measure one). Skip them. Its the Phlogiston of economics. Utterly unscientific nonsense. What’s the dimension of utility? A thermometer is used to measure temperature, which devise is used to measure utility? (“revealed preference” does not work, as hal Varian implicitely admits in his “Samuelsonian economics in the twenty first century”article). Just forget it.

• Doc Merlin

1. Agreed
2. No, GDP measures sales to end users, not value added. “Second hand trade is, by definition, not included in GDP”
Yes, it is, its part of Household final consumption expenditure.

3. Utility functions do exist, and we can measure them, they are just an ordinal measure (its a list of what we prefer). We can treat them as cardinal for very specific purposes and when we go outside those purposes and try to use them as purely as cardinal for other purposes is when they break down.
Example of a utility function: I prefer A to B to C to 2A to D to, blah blah.

11. Lee Kelly

Popper popularised the idea that tautologies are scientific no-nos, but few people understand the context of that prohibition.

MV = PY is a tautology, but statements about MV = PY may not be. Since it is the latter with which we are primarily concerned, it doesn’t matter whether MV = PY is a tautology.

The relevant questions are: do the variables and relations in MV = PY correspond to observable phenomena? Can we measure these variables, perform calculations, and derive true statements about other phenomena? Can these derivations be tested against experience? Answers these questions cannot be answered a priori, because they concern statements about MV = PY that are not tautological.

It is beta like the use-mention distinction found in most introductory logic textbooks.

In any case, I find MV = PY very useful.

12. I used to dislike MV=PY. Then 2 years ago I changed my mind. I saw that MV=PY forced us to recognise that money is special. We don’t just hold a stock of money, like we do other assets. Writing down a stock demand for money function, like the stock demand function for houses, bonds, jewelry, etc., misses the point completely. Money circulates. We buy and sell everything else with money. It wouldn’t make sense to write MV=PY if M were houses, bonds, or jewelry. An excess demand for money disrupts every other market in the economy, because money is used in every market. An excess demand for houses, bonds, or jewelry does not cause a general glut. An excess demand for money does.

You bet MV=PY is useful. (MV=PT would be better, though.)

• Doc Merlin

Question, Nick:
Excess demand for money means that we are valuing future consumption over current consumption. Why is this a problem? Doesn’t this just mean that interest rates should adjust to account for this? I can understand this being a problem when interest rates are held fixed by a central bank, but with free floating rates, why would this be a problem?

• Matt Waters

To be honest, I’ve had a hard time following a lot of the comment here. It’s hard for me to get my head around higher interest rates meaning looser policy and vice versa.

That said, I believe the issue with free floating rates is the zero-rate limit. An increased demand for holding money is equivalent to sacrificing current consumption for future consumption. When all the banks were failing in 2008, we indeed cut back spending considerably since we weren’t sure whether any money would be left in the years to come.

As preferences change for future consumption instead of present consumption, interest rates respond by heading downward. Supply of credit, though, hits a certain point where the nominal interest rates go below zero and people just hold money instead. The equilibrium point, where the number of creditors equals the number of debtors, is below zero. The interest rates would have to be below zero to get find enough people willing to sacrifice future consumption for present consumption.

That is where “MV=PY” helps shed light on the issue with deflation. If the equilibrium rate was above zero, MV, theoretically, wouldn’t change. At >0 rates, it does not make sense for anyone to hold onto money. They either spend it or invest it, at the risk-free rate or risk-free plus risk premium. At the zero rate, much of the money stays in vaults instead of being spent or invested. Finally, since the P in PY is sticky particularly for wages, the Y component has to fall through unemployment. When Y falls, the equilibrium interest rate become even more negative as demand for money goes up even more, leading to a vicious cycle of more and more unemployment.

• I still don’t understand why this won’t show up in interest rates. In your “in praise of MV=PY” post, you talked about how an excess demand for money causes us to spend less, since that’s the only way that we can guarantee (at the individual level, not the aggregate) that we will accumulate more money. I have a simpler way: going to the ATM.

I know this sounds facetious, but it’s really not. First let’s clarify exactly what we’re discussing here: when I talk about “money”, I mean either (1) base money or (2) liquid deposits included in monetary aggregates like M2. In case (1), as long as you have any liquid wealth, it’s trivial to get more base money: you can either immediately go to the ATM and make a withdrawal or transfer your wealth into an account that allows you to make a withdrawal.

Since this case is a little silly, I assume that you’re talking about case (2): consumers need liquidity in a broader sense, and the only way they can amass more of it is by spending less. I agree that this can be a problem. Unless nominal interest rates are high, however, it cannot be a monetary problem: the only way that low “M” can be a meaningful constraint on the accumulation of bank deposits is if the nominal interest rate is high. (Otherwise it’s cheap for banks to borrow the necessary reserves through the fed funds market.) A shortage in quantities should always show up in the corresponding price.

Maybe we’re not really talking about “money,” but instead about wealth. One can imagine a world where consumers suddenly realize that they’ve borrowed too much and need to save. But in this case, it is possible for consumers to increase their savings in the aggregate, unless we’re at the zero lower bound and the real interest rate can no longer move to equilibriate the market. (There is no “paradox of thrift” without the zero lower bound.) And if the zero lower bound is the relevant constraint, and real interest rates are the transmission mechanism, MV=PY is not even close to being insightful.

13. Doc Merlin

@Lee Kelly:

Popper was full of crap. The most important things in science are tautologies.

• Lee Kelly

He wasn’t “full of crap.” My point was that people misunderstand the context of his prohibition of tautologies. Popper never claimed that tautologies were useless, unimportant, or uninteresting. He stressed the fact that tautologies lack empirical content, i.e. predict no empirical phenomenon, and he was right: an empirically testable proposition cannot be tautological. And this is important methodologically. Unfortunately, many people argue as though tautologies are to be avoided for all purposes, and that anyone claiming to be a scientist should discard tautologies in all cases. This was not what Popper argued. If he was “full of crap,” then it was not for this reason.

While a tautology is, in and of itself, bereft of empirical content, it does not follow that propositions about the tautology must also be tautological. Since it is primarily with this latter class of statements with which we are concerned (when not doing pure mathematics or modeling), whether the equation of exchange is, in and of itself, a tautology is irrelevant to the actual propositions being argued. It remains to be demonstrated that a particular proposition about the equation of exchange is tautological. The situation is not different for other famous equations like F = ma or e = mc2.

14. I think Nick gives the best short hand answer. How else can you explain the sudden and “deep dive” of PY (nominal spending) that ocurred during the second half of 2008 and first half of 2009, if it were not for the fact that the Fed was terribly contractionary at exactly the same time that people “craved” for money just like the deprived smoker (me) craves for nicotine?
Also, on the velocity (in)stability, by redefining money – such as MZM – instead of M2 velocity stability is recouped.

• If they are “craving” money, why isn’t the nominal interest rate higher? Again, the nominal interest rate is the price of holding base money. If the problem was a massive increase in money demand, that should have pushed up the nominal interest rate—otherwise no one would really be “craving” money, which would be very cheap to hold and could be acquired by anyone willing to pay a small premium.

I agree that there is a fundamental monetary problem at work in this recession: namely, the zero lower bound on interest rates, which has prevented the real interest rate from adjusting to its equilibrium value. I suppose you can think about this as a “craving” for money: money has a very valuable property, the fact that it will always pay at least a zero nominal return. This prevents any other assets from paying less than zero—after all, investors would rather see 0% than -1%.

But this story has nothing to do with the transactional properties of money; in fact, in a world without paper currency, it’s entirely conceivable that the return on base money would be set below zero. The problem of the zero lower bound is thus conceptually independent of the properties of money embodied in the equation of exchange, and MV=PY can’t possibly be a good model if you believe the zero bound is the main problem. (which I do, and I assume you don’t)

• Lee Kelly

Why would an increase in money demand increase interest rates? An increase in money demand could increase interest rates, but it could also reduce interest rates, or perhaps it could just be neutral. Surely, the influence of larger cash balances on interest rates depends on how the additional cash balances are financed. For example, perhaps people delayed the purchase of a new car, or maybe they decided to sell short term bonds. The former case increases the supply of savings, while the latter case probably reduces the supply of savings by a small amount. Holding all else constant, these two cases would appear to decrease and increase interest rates respectively.

In any case, I think one must distinguish between the case of an increased demand for money and an excess demand for money. The argument is not just that money demand increased in 2008 (both narrowly and broadly defined), but that the Fed passively tightened its policy by not increasing the money supply in proportion. An excess demand for money has different consequences for interest rates than an increase in money demand satisfied by an increase in supply. In particular, when there is an excess demand for money, real interest rates may rise even while nominal rates are falling.

But perhaps I just do no understand the point you are trying to make. I have no formal training on these matters, and I am sometimes thrown by unfamiliar terms and equations.

• If they are “craving” money, why isn’t the nominal interest rate higher?

Because they are also craving bonds.

The nominal interest rate is not, in some absolute sense, the price of holding base money; it’s a relative price, money vs. bonds. Relative to goods, the shadow price of money is still very high, and (because goods prices are sticky) there is a shortage.

It happens people are craving both money and bonds, but the craving for money is what matters, because people get paid in money, so they can always (as long as they have a job) expect to receive money, which they will then have, as long as they don’t spend it. So they spend less.

(Actually, even relative to bonds, the nominal interest rate is not the price of holding base money; it’s the price of holding your base money in the form of cash. Other than cash, base money pays interest — and at a higher rate than T-bills.)

15. After telling my students that money spent (MV)=money received (Py) , I tell them that rain falling from the sky=rain hitting the earth. That gives them the idea of what ‘tautology’ means. Then I apply the equation to shares of GM stock, where M=number of shares, V=number of times per year a share is spent, P=number of shares to buy a unit of y, and finally that y=units of goods bought with GM shares (y is not total output of goods). It seems to get the idea across.

16. apj

I may have missed it in the comments above, but why has nobody focussed on Y? If people want to contend that the money supply (which even monetarists could never decide the proper definition for) influences only prices, then not only has the V got to be stable (er, no), but so does Y (ie. full employment……also, no).

17. Nathan Tankus

welcome to the general theory. it’s nice to know the modern economist is just getting around to what’s contained in there. I’m not saying keynes has all the answers, indeed no one can. But his writings are a good jumping off point and for all the times people say that they’ve moved on from “keynesianism” they still make the same elementary mistakes keynes pointed out. what’s most ironic is those who go against keynes understanding almost the most call themselves “new keynesians”. angry bear had a run of a few blog posts going back to what keynes actually wrote. the profession should keep on doing that.

18. Doc: “Question, Nick:
Excess demand for money means that we are valuing future consumption over current consumption.”

No it doesn’t. That’s an excess demand for *all* assets, like bonds, shares, land, used furniture, etc. “Excess demand for money” means we are valuing the medium of exchange over every other goods.

Matt: a disclaimer. Half of my brain thinks like you; the other half thinks like…ummm…me. It all depends which side of the bed I get out of.

A full response would take a dozen blog posts just to get you to see the possibility of the other way of looking at things. So let me just throw a couple of thought-experiments at you:

1. Take your favourite New Keynesian macro model. Woodford, presumably. Start in full equilibrium. Now suppose the central bank has a temporary brain fart and raises the interest rate for no reason at all. The result is a recession, right? Everyone wants to consume less today, to satisfy the consumption-Euler equation (they know the central bank will recover its sanity next period, so future consumption goes back to full equilibrium natural rate). So the brain fart causes a drop in output and employment for one period.

Suppose the output good in your model is backscratching services. Why don’t the underemployed backscratchers simply scratch each others’ backs? Sure, they would all prefer to sell their backscratching services for future consumption, but they can’t, because there are no buyers. Exchanging your labour for a backscratch today is a second best, but it’s a lot better than sitting idle and getting nothing except leisure. Why, in other words, don’t they resort to barter, and to hell with the consumption-Euler equation?

The agents in your model are leaving unexploited gains to trade lying on the table in plain sight.

2. Suppose the central bank stopped buying and selling bonds, and switched to buying and selling gold. Instead of the interest rate as the instrument, it uses the price of gold. Would that mean that Pg now becomes a sufficient statistic for monetary policy, in the way you claim i is currently a sufficient statistic? If people want more money, they can always sell gold. Suppose the central bank does both bond market operations and gold market operations. Does that mean that both i and Pg are each sufficient statistics, or that the combination {i,Pg} is a sufficient statistic? Why does the central bank even need to buy and sell bonds (gold) for i (Pg) to be a sufficient statistic for monetary policy? Individual agents can always buy or sell either, so their prices should reflect the scarcity of money. In fact, isn’t the price of *any* good (assuming it’s a perfectly flexible price) a sufficient statistic for monetary policy? What’s so special about the price of bonds?

(Glad you’re blogging. It’s going to be good arguing with you.)

• Thanks for the reply. Glad that you look forward to arguing with me! : )

Exchanging your labour for a backscratch today is a second best, but it’s a lot better than sitting idle and getting nothing except leisure. Why, in other words, don’t they resort to barter, and to hell with the consumption-Euler equation?

This is a little hard to map onto the canonical New Keynesian model, where profit-maximizing firms are distinct from consumers. If you make a variant of the model where each consumer owns a firm, I agree that a puzzle like this may show up: in theory, it would be optimal for a consumer/firm to tell other firms “look, let’s produce stuff at marginal cost and share it with each other, not bother with all these silly markups”. But in reality, this seems not to happen to any appreciable extent, and I assume that there must be some kind of practical barrier making it infeasible (and I don’t think that practical barrier is a shortage of money).

In fact, isn’t the price of *any* good (assuming it’s a perfectly flexible price) a sufficient statistic for monetary policy? What’s so special about the price of bonds?

Consumers generally have a certain amount of wealth that they want to hold from period to period, and they face a portfolio decision about how much of this wealth to keep in the form of money vs. bonds. The nominal interest rate is the foregone interest from holding money (one safe short-duration asset) rather than T-bills (another safe short-duration asset). In equilibrium, it must be equal to the liquidity services that the money provides over T-bills—so if there is some serious shortage of money and, at the margin, money would provide a lot of liquidity value, it should show up in the rate.

I agree that other intertemporal prices (say, the price of a loan denominated in gold) can carry information about the stance of monetary policy with respect to money as a medium of exchange. But since base money and T-Bills are equivalent in virtually every way (short term, backed by the government, viewed as riskless) except for certain liquidity benefits, the nominal interest rate has easily the highest signal-to-noise ratio of any price. It conveys directly what the shadow value of base money in providing liquidity services is.

19. One more:

3. Suppose that bling is the medium of account, but not the medium of exchange. The central bank has a monopoly on leasing bling, and can produce and lease as much bling as it wants. People get utility out of wearing bling, but it’s the real stock of bling, M/P, that gives utility (they like to show off their wealth). The demand function for bling is M/P = L(Y,i) where i is the rental rate on leases of bling.

The central bank, like a good New Keynesian, controls inflation by following some sort of Taylor Rule for setting the interest rate on leases of bling. So the stock of bling, M, is demand-determined. Add a Calvo Phillips Curve, and a Consumption-Euler equation IS curve, and you have a complete NK model.

Is anything missing from that model?

• Nope. As long as bling shares the properties of currency as a unit of account (including the zero lower bound), this is a perfectly good model. In fact, I think it’s a good metaphor for thinking about the issue.

20. Matias Vernengo

The problem is that you accept that V is unstable, but still have a natural rate of unemployment, then you can use the rate of interest to keep demand under control. Withe the NAIRU it’s still true that all inflation is excess demand, and that can result from loose monetary policy. You’re still a monetarist. That’s why Keynes argued that there was no natural rate of interest in the General Theory.

21. Scott Sumner

Matt, You said;

“For our purposes, the short-term properties of a model are the really important ones—and that’s where the QTM (at least in its purest form, unaugmented by some kind of New Keynesian sticky prices/monopolistic competition mechanism) really falls down.”

Fine, but every monetarist from Hume to Fisher to Friedman has assumed sticky prices and real effects in the short run. So by your definition of new Keynesian, every important quantity theorist is a new Keynesian. I’m not sure anyone takes the “pure” QT seriously.

You said;

“Unless nominal interest rates are high, however, it cannot be a monetary problem: the only way that low “M” can be a meaningful constraint on the accumulation of bank deposits is if the nominal interest rate is high.”

In my view this confuses the price of money and the price of credit. 1/P is the price of money. When money is tight 1/P rises and i tends to fall. Compare nominal rates in the 1930s, when money was ultra-tight, and the German hyperinflation, when money was ultra-easy. Low interest rates generally mean tight money and falling prices, and high interest rates generally mean easy money and rising prices.

In another thread you said that things like rising real estate prices and a rising Tobin q were basically lower real interest rates on capital. OK, so what happens if all sorts of asset prices crash, indicating tight money by your definition of real interest rates (as in late 2008), but the nominal rate on T-bills is low. In 2008 I saw all the other asset markets are giving the “right answer,” and the T-bill markets is merely showing a demand for liquidity, unrelated to whether money was too easy or too tight.

Nick, You prefer MV=PT to MV=PY. Suppose 99% of “T” by value is transactions in forex markets and derivatives, and that the size of these transactions is unrelated to PY. Would you still feel the same way?

• Fine, but every monetarist from Hume to Fisher to Friedman has assumed sticky prices and real effects in the short run. So by your definition of new Keynesian, every important quantity theorist is a new Keynesian. I’m not sure anyone takes the “pure” QT seriously.

Well, my contention is that the sticky-price/monopolistic-competition view of the real effects of monetary policy can’t be embodied in MV=PY, which is a description of money that focuses on its role in exchange (while the sticky-price/monopolistic-competition story is all about money as a unit of account). It would be really weird if an equation designed to describe the exchange process happened to also provide a good model for another channel of monetary policy. And while one might argue that the macroeconomic role of money as a medium of exchanage is still significant, that’s precisely the case in which the nominal interest rate is a sufficient statistic (if you need to hold money to conduct transactions, it costs you the nominal interest rate).

In my view this confuses the price of money and the price of credit. 1/P is the price of money. When money is tight 1/P rises and i tends to fall. Compare nominal rates in the 1930s, when money was ultra-tight, and the German hyperinflation, when money was ultra-easy. Low interest rates generally mean tight money and falling prices, and high interest rates generally mean easy money and rising prices.

“Price of money” wasn’t a good choice of phrase on my part; “price of holding money” would be more accurate. I absolutely agree that “low interest rates generally mean tight money and falling prices”, but that’s because I have a different model in mind for the real effects of monetary policy: I think it’s all about money’s role as a unit of account, while a view that finds MV=PY useful must necessarily believe that exchange is important as well.

OK, so what happens if all sorts of asset prices crash, indicating tight money by your definition of real interest rates (as in late 2008), but the nominal rate on T-bills is low. In 2008 I saw all the other asset markets are giving the “right answer,” and the T-bill markets is merely showing a demand for liquidity, unrelated to whether money was too easy or too tight.

Again, I think that a low nominal rate on T-bills says very little about the effective stance of monetary policy; in fact, I agree with you (and Milton Friedman) that, if anything, it says that policy has been too tight. I’m merely arguing that if you think that money’s role as a medium of exchange is a key part of the monetary transmission mechanism (which I don’t), you have to acknowledge that the relevant shadow price is the nominal interest rate. If the nominal interest rate is low, it isn’t tough to acquire base money for the purposes of exchange.

The real interest rate is much more important, and while it’s not easy for the Fed to glean whether the current short-term real interest rate is “correct”, I think that looking at inflation expectations and (yes) asset prices is a good place to start.

22. Scott: Dunno. I wouldn’t go to the stake for either MV=PY or MV=PT. Both are crude but useful heuristics, nothing more. But we use money for (nearly) all transactions, not just purchases of newly-produced final goods and services (Y). If there’s an excess demand for money, not just markets in Y get affected. The markets for used cars and used houses and everything else gets affected too. I expect that includes markets in forex and derivatives too. The trouble is, V is some sort of weird weighted average of all transactions velocities. Which is why you can’t push MV=PT too far.

• Lee Kelly

I always thought the use of Y instead of T was mostly because people were concerned with employment in the production of goods and services. The used car salesman did not produce the car sells: his income is derived from the service he provides bringing car and customer together. Income and production are the same thing for the economy as a whole; it seems to me that using T rather than Y can obscure this point. But the best equation surely just depends on the particular problem and purpose at hand: neither is categorically better.

Maybe I have utterly misunderstood these matters. Again, I don’t have formal training.

23. BTW: let’s re-formulate Friedman’s old question for New Keynesians. Instead of asking whether V or the multiplier is more stable, let’s ask whether V or the natural rate of interest is more unstable. I don’t know what the answer is.

24. Compare Scott Sumner’s comment above to my reply in the Nunes thread earlier. Matt insists that the interest rate is the price of money. Scott insists that 1/P is the price of money. They’re both right, and they’re both wrong. There is no such thing as an absolute price. The price of money in terms of bonds is the interest rate. The price of money in terms of goods is 1/P.

When bonds become perfect substitutes for money, we get into these arguments about whether it’s really a shortage of money or a shortage of bonds that is the problem. I think Nick makes a plausible case for the former: money is special because people expect to receive it in the normal course of economic life, so when there’s a shortage of money, people curtail their spending to satisfy their demand. If there were a shortage of bonds that were not also a shortage of money, this wouldn’t be an issue.

25. I think Nick makes a plausible case for the former: money is special because people expect to receive it in the normal course of economic life, so when there’s a shortage of money, people curtail their spending to satisfy their demand.

It seems hard to interpret this as describing a shortage of base money specifically. I agree that if I find myself short of wealth, or even liquid assets, then I might curtail my spending in an attempt to recover my position. In fact, I believe this is very important in understanding the current recession: faced with a sudden decline in wealth and a greater precautionary need for liquid assets, everyone suddenly cut back on spending relative to income. The zero lower bound meant that the real interest rate couldn’t fall enough to bring the market back into equilibrium, and thus we had a “general glut”.

But I cannot fathom how this would be due to a shortage of base money. It is difficult to increase your overall wealth, or even your holdings of liquid assets, in a short time—that’s why a sudden rush to save will force the real interest rate to move downward by so much. It is exceedingly easy to hold more in the form of base money. If I’m a consumer who wants more base money, as long as I have any savings in any reasonably liquid account I can withdraw cash from an ATM.

Of course, no consumers really care about their cash position that much, but that’s my point. They care about their wealth and their liquid assets. And the monetary policy can’t pose any barrier to the accumulation of liquid assets unless it creates a shortage of reserves, which is exactly the opposite of what is currently happening. As you point out above, the interest rate on reserves is actually slightly higher than the rate on T-bills, so that there is no cost from holding reserves at all.

In fact, I think this is the key question: how can there be a shortage of base money when holding wealth in the form of base money rather than bonds is literally costless?

I agree that there may be a shortage of liquid assets, investments serving as stores of value, etc. etc. I just don’t see any connection to base money (except via the zero lower bound).

• And the monetary policy can’t pose any barrier to the accumulation of liquid assets unless it creates a shortage of reserves, which is exactly the opposite of what is currently happening.

How is it the opposite of what is currently happening? Banks have a voracious appetite for reserves, which the Fed is refusing to satisfy. Banks certainly aren’t experiencing a surplus of reserves, or they would be trying to get rid of them. Collectively, of course, they can’t get rid of their reserves, but individual banks can attempt to do so by making loans or purchasing other assets. But they’re not doing so. Loans are not particularly easy to get, and prices of banks’ assets are not rising rapidly. Banks like the reserves and want more of them.

If the Fed were to satisfy fully the banks’ appetite for reserves (by increasing the supply of reserves without at the same time increasing the demand), it would indeed make more liquid assets available to the public. Banks would make more loans and thereby increase the supply of bank money without reducing the supply of other liquid assets.

• Sure, banks are willing to accept whatever reserves the Fed feeds them. But this isn’t because banks (or the consumers that use them) need reserves for transactional purposes: instead, it’s because interest rates are such that reserves and T-Bills are essentially equivalent (up to minor differentials in interest rate), and banks are happy to hold their liquid risk-free assets in either form. Since MV=PY is explicitly an equation that describes exchange, the only way it has much hope of describing the real effects of monetary policy is if these effects are occurring via money’s effect on transactions—and when banks can costlessly substitute reserves for other liquid assets, base money cannot possibly be having any effect.

You could claim that the economy is suffering not from a shortage of base money specifically, but of liquid assets in general. Since the Fed increases the supply of short-term liquid assets when it uses reserves to buy long-dated Treasuries and other assets, unconventional monetary policy conceivably has the power to relax this constraint. I think that this can be a valuable channel for monetary policy: let the Fed embrace its role as a financial intermediary and buy up more assets financed by demand deposits (reserves). It’s not clear to me, however, that this is really the fundamental problem facing the economy—and regardless, since “liquid assets” aren’t used in exchange in quite the way envisioned by MV=PY, it’s unclear that the equation of exchange offers much of a descriptive account here.

If the Fed were to satisfy fully the banks’ appetite for reserves (by increasing the supply of reserves without at the same time increasing the demand), it would indeed make more liquid assets available to the public. Banks would make more loans and thereby increase the supply of bank money without reducing the supply of other liquid assets.

Banks demand reserves because, at the current expected rate of inflation, even a 0.25% nominal interest rate is not low enough for the savings/investment market to clear. There’s a surplus of savings, and this shows up as excess demand for assets like reserves.

It’s not immediately clear why pumping more reserves into the system will address this fundamental problem: even if it hits zero, the nominal interest rate wouldn’t be enough to equilibriate the market. As I mentioned above, if the Fed has an advantage over private banks as a financial intermediary (and it probably does), then by borrowing short and lending long it might be able to narrow risk and yield spreads and lessen the problem posed by the zero lower bound.

But none of this has anything to do with the value of base money for transactions purposes, which at the current margin is zero. As such, I fail to see why the equation of exchange is at all relevant.

• Andy,

Matt is entirely correct here.

Where do you get the idea that the lack of credit growth is due to banks preffering reserves to making loans to quality credits?

The problem here is that, in the first place their isn’t enough desire to borrow, private agents are attempting to transition to a lower debt to income ratio. This is exactly what you’d expect from a set of agents with an overhang of exhisting debt whose assets have fallen in value and who face significant costs to bankruptcy.

Secondly, and complementary, those lower asset prices mean that the costs of intermediation are higher so banks would ration new credit no matter how much they had in reserves. This was the point of the original Bernanke-Gertler stuff.

26. Matt: (How do you do those neat quotes, BTW?)
“This is a little hard to map onto the canonical New Keynesian model, where profit-maximizing firms are distinct from consumers. If you make a variant of the model where each consumer owns a firm, I agree that a puzzle like this may show up: in theory, it would be optimal for a consumer/firm to tell other firms “look, let’s produce stuff at marginal cost and share it with each other, not bother with all these silly markups”. But in reality, this seems not to happen to any appreciable extent, and I assume that there must be some kind of practical barrier making it infeasible (and I don’t think that practical barrier is a shortage of money).”

Assuming each consumer owns a firm simplifies this question, but isn’t essential. (I could re-formulate the question, but I would have to bring the workers in on the barter deal too.) But let’s stick with that simplification.

Think about what additional assumptions we would need to resolve that puzzle — what practical barriers we would need to build into the model to prevent people doing that sort of barter swap. For example, we could assume that goods have to be consumed at the point of production, in non-synchronised times and places, and that consumers are anonymous so they can’t use trade credit to be redeemed at their own firms later. Or, that there is no double-coincidence of wants, and it’s impossible to get 3 (or more) people together in the same place at the same time. Something like that.

Then notice that those assumptions about practical barriers needed to resolve the puzzle are exactly the same as the assumptions economists make to explain why people use a medium of exchange. Those same assumptions make money “essential” (in Hahn’s sense) for trade.

So, there’s a sort of internal contradiction in the canonical New Keynesian model. On the one hand, as you acknowledge in response to my “bling” thought-experiment, it’s a model where money is only a medium of account, not a medium of exchange. And yet, at the same time, to explain why people leave unexploited gains from trade on the table (those unexploited gains from trade exist even in normal times, due to monopolistic competition, but get bigger still in recessions) we need to add extra assumptions that make a medium of exchange essential for trade.

Is the canonical New Keynesian model a model of monetary exchange? Or is it a barter model with prices fixed in some numeraire that is not used as a medium of exchange? It can’t be both.

(Steve Williamson, BTW, interprets the canonical NK model as a barter economy. But then he’s consistent, because he says that the only way monetary policy matters in the NK model is that firms’ relative prices get distorted given non-zero inflation plus staggered Calvo pricing.)

Where do you get the idea that the lack of credit growth is due to banks preffering reserves to making loans to quality credits?

Credit quality is a continuum. There are no “quality credits” in any absolute sense. But, on the margin, banks prefer reserves to making loans to the credits actually wishing to borrow, as evidenced by the fact that they are not lending. And if banks were more eager to lend, they would offer credit on better terms, and borrowers would be more willing to borrow. And banks would reduce the threshold of acceptable credits. Instead, they prefer holding reserves.

Of course, if the Fed buys T-bills, it will increase the demand for reserves by as much as it increases the supply, since the former holders of T-bills (if they are not themselves banks) will be content lend the proceeds to banks at a rate lower than the IOR rate. However, if the Fed buys something else, the sellers will not be content to hold the entire proceeds as bank deposits and will need some inducement to do so; thus the demand curve for reserves will not shift sufficiently to offset the increase in supply, and there is at least a hope that, via such operations, the Fed will eventually be able to satisfy the demand for reserves.

• Andy,

You’re assuming your conclusion. You can’t know for sure if the lack of loans reflects restricted supply or lack of demand.

If I recall correctly, the credit rationing models such as by Stiglitz and someone (Weiss?) essentially have both features. Banks ration credit and you get a lemons problem where the best credits don’t want to borrow at prevailing rates.

• All I’m assuming is that the supply curve for credit slopes upward and the demand curve slopes downward.

• Andy,

I think the second paragraph here is absolutely right. But it sounds like you’re just describing conventional portfolio balance effects: when the Fed creates bank reserves and spends them on long-term assets, it decreases the supply of long-term assets for private investors and causes them to rebalance, raising the price of those assets and lowering the yield.

But there are cogent models where these portfolio balance effects are not operational: for instance, the Eggertsson and Woodford 2003 BPEA paper. I don’t think that the assumptions necessary for their result hold completely in the real world (and neither do they); however, the usefulness of the portfolio balance channel depends on the exact extent to which these assumptions fail to hold. That is deeply uncertain, and I don’t think that an equation like MV=PY that models the process of exchange (rather than the intricacies of portfolio theory) even begins to get at the problem.

28. Scott Sumner

Matt, Now I’m lining up with you against Nick. I also see the unit of account role of money as being key, not the medium of exchange role. As a result I prefer the Cambridge equation (M=kPY) to the Fisherian version (MV=PY).

Another advantage of the Cambridge equation is that our common sense explanation (to students) of k happens to be true, whereas our common sense explanation of V (number of times a year the average dollar is spent) happens to be false. So I have no problem with you criticizing MV=PY on those grounds.

Andy, Good point about prices. In micro the relative price of a good (relative to all other goods) is the most common interpretation of the “price” in supply and demand models. So my definition follows that tradition. But you could also define the value of money relative to assets. If we do so, then money was incredibly tight in late 2008, as the price of TIPS, corporate bonds, stocks, real estate, and foreign exchange all plummeted. So even then the price of Treasuries is not a good definition of the price of money, because it’s an outlier, all other asset prices moved in the opposite direction to nominal T-bonds. Whether we use goods or asset prices, we get the same story–money was tight. Only nominal Treasuries were an outlier, and thus are perhaps the single worst possible definition of the price of money.

29. Jeff Hallman

Where do you get the idea that the lack of credit growth is due to banks preferring reserves to making loans to quality credits?

There are perfectly safe loans (T-bills, for example) that the banks could be making that pay more than zero percent interest. They’re not doing so because the Fed’s interest rate on excess reserves pays them more than the T-bill rate. If the Fed keeps this up, we will eventually end up with something like the 100 percent reserves regime that Milton Friedman used to talk about. Depository institutions will have reserves as their only assets, the Fed will hold enough Treasury debt to match base money outstanding, and private financial intermediation will all happen outside the banking system. Not a bad system, but getting there will be a long and painful process.

30. Scott: heresy! Splittism! Me and Bill will exile you from the quasi-monetarist club!

Take your own model. Assume all workers are self employed, so W=P. Start in equilibrium. Assume sticky wages (prices). Halve the money supply. Does this cause unemployment? If you answer “yes”, then why don’t the unemployed just barter with each other and make each other better off? (Their relative wages (prices) haven’t changed.)

31. Scott Sumner

Nick, You probably understand my model better than I do, so I’ll just throw out a few thoughts. I used to think my model was that tight money increased W/P. Now I’m more inclined to say tight money increases W/NGDP. If sticky W is the problem, then doesn’t barter implicitly overcome that by preventing W/NGDP from rising during periods of tight money? I.e., by making wages no longer sticky in terms of NGDP, even if they still are sticky in terms of P?

I’m willing to entertain the possibility that there are thought experiments showing that changing the value of the medium of account (without changing the medium of exchange–if they differ) can cause unemployment if wages are denominated in terms of the medium of account, not the medium of exchange. AND, that there are barter scenarios that make demand shortfalls seems impossible. I.e. perhaps both the medium of account and medium of exchange roles of money are necessary conditions for monetary disequilibrium.

But here’s the thought experiment that makes me skeptical of the transactions approach. Assume gold is the medium of account and all wages and prices are denominated in terms of gold. Dollars are the medium of exchange, and the rate of exchange between dollars is floating, as the supply of dollars rises by 50% per year. At the cash register you are told how many dollars you need to pay up to cover the gold sticker price at today’s exchange rate. The 50% annual growth rate of dollars is obviously plenty of “money,” hence there are no recessions due to shortfalls of transactions money. But the price level follows the path of a gold standard economy, zero trend inflation with alternating bouts of inflation and deflation. Recessions occur during the deflation years even though the supply of transactions balances keeps rising by 50% per year.

Now if you insist on pricing the transactions quantity of money in gold terms, then our two models collapse into one.

32. Itfitzme

I hear this commnet alot from people trying to understand the basics of economics. And it gets repeated, not with an understanding of the deeper contexf of trying to find a useful approach to mometary policy, but rather like a ten year old repeating “that’s gay” on the playyard. This is unfortunate as this single equation sets the foundation for a world of understanding of the boundary conditions of the economy. Expanded out, in all the sources of money and markets, it yields basic insight into how the economy is connected. It serves as a framework from which to hang numerous concepts. It serves as a launching pad to a variety of processes. MV=PQ is no more a tautology than every equation in physics, beginningn with F=ma, the basic equation of force.

Will MV=PQ solve questions of monetary policy and inflation? It hasn’t been so far. Maybe never. Is this our only interest in economics? Certainly not. But to call it a tautology because it doesn’t lead to one particular interest is foolish. We miss what ww dismiss. And to set a course for the future of economists that outright dismisses a fundamental relationship as useless is to deprive of us of potential discovery.

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