The problem with velocity

Nick Rowe argues that the “natural rate of interest” in modern New Keynesian economics is no better than the “velocity” in monetarist models, and quite possibly worse:

The Old Keynesians have been replaced by New Keynesians. And the Old Monetarists have been replaced by….umm…mostly New Keynesians too. (Us “quasi monetarists” are too few and too lacking in influence to really count). So the old debate is now moot. But velocity isn’t totally dead as a concept…

So now I’m going to respond with “Y tu mama tambien!”.

Very very crudely, and over-simplifying massively, New Keynesians replace PY=MV with delta(PY)=(natural rate of interest – actual rate of interest). If the central bank sets the actual rate of interest below (above) the natural rate of interest, then nominal income will rise (fall)…

So. Neither is constant. Which is more stable? Velocity, or the natural rate of interest?

At least velocity never goes negative, which is more than you would say yourselves about your natural rate of interest. And your mother wears army boots!

“Stability” isn’t the right criterion. Consider this: over the past 50 years, the ratio of GDP to government spending has been remarkably consistent, always confined between 4 and 6, and staying within even narrower intervals over the medium term. That’s more stable than velocity! If I were a fanatical Old Keynesian, I might use this as evidence that we should really be looking at the government expenditure multiplier as the key to policy.

Of course, this would be silly. Government expenditure doesn’t create all other activity in the economy through some “multiplier” process. Instead, it’s relatively consistent with respect to GDP because voters and politicians want it that way: their preferences over taxes and government services are such that they’ve sought a government that accounts for somewhere between one-sixth and one-fourth of the economy. In other words, the causation runs from GDP to government spending, not the other way around.

Is velocity any different? I doubt it. To the extent that velocity is “stable”, what’s actually happening is that consumers want to hold money balances as a relatively consistent fraction of nominal income. Sure, the ratio is stable, but the denominator causes the numerator, not the reverse.

This is tough to verify, of course—if the relationship actually is stable, then without auxiliary assumptions we can’t say where the causation lies. But some historical episodes offer hope. Consider, for instance, the savage recession of the early 80s, which is near-universally acknowledged as the result of Volcker’s fight against inflation. Can we identify a change in the monetary base that matches the magnitude of the recession, or even comes close? Not at all; it’s barely a blip. What about a higher-level monetary aggregate like M2? Again, nothing. Compare that to the obvious slump in nominal GDP. When it mattered, velocity wasn’t so stable after all.

Why? It’s easy to interpret with the right theory. Consumers desire money balances roughly in proportion to their nominal income, with some adjustments made for the nominal interest rate. Consumers are also sluggish in reoptimizing their portfolios. When the Fed contracts the supply of base money even slightly, slow reoptimization means that a dramatic increase in the nominal interest rate is necessary to clear the market. Since interest rates are now well above the “natural rate”, we see recession and disinflation.

Does velocity-centric monetarism offer any similarly coherent account of the Volcker recession? I don’t see it. What made velocity collapse between mid-1981 and 1983?

Ultimately, velocity is just a residual, one without much practical role in monetary policy.

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34 Comments

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34 responses to “The problem with velocity

  1. Matt: “Does velocity-centric monetarism offer any similarly coherent account of the Volcker recession? I don’t see it. What made velocity collapse between mid-1981 and 1983?”

    How about this:

    Desired velocity depends on the expected rate of inflation. (Witness what happens to velocity in hyperinflations for empirical confirmation). When Volcker started talking about getting inflation down, and showed he was serious by contracting the supply of base money even slightly, expected inflation fell, and so desired velocity fell too. That fall in desired velocity caused the fall in nominal income. Given sticky prices and/or wages, that fall in nominal income meant a fall in real income. ?

    (By the way, I am pretending to be much more velocity-centric than I really am. I am taking up a fake extreme position just to show that some New Keynesian arguments against velocity and the money supply multiplier can equally well be used against New Keynesian macroeconomics.)

    Thanks for responding to my post by the way. And it should really be read together with my second post http://worthwhile.typepad.com/worthwhile_canadian_initi/2011/06/y-tu-actual-rate-of-interest-tambien.html . (I should have made them both into one post.)

    • Nick: “Desired velocity depends on the expected rate of inflation. (Witness what happens to velocity in hyperinflations for empirical confirmation). ”

      So, basically ALL the work is in explaining velocity and we’ve reduced the quantity theory to just a terminology.

      On one hand, we can directly explain the downturn via the changes in real interest rates without mentioning velocity.

      On the other we can explain it with an appeal to velocity but then need to appeal to what is essentially the interest rate story to explain what happened to velocity.

      So what did bringing velocity into this actually ad?

      • Adam: so, by mentioning expected inflation, I am implicitly talking about interest rates? OK. But here’s Matt: “Consumers desire money balances roughly in proportion to their nominal income, …”. When Matt says that, isn’t he implicitly talking about velocity?

        That was just another “Y tu mama tambien” response. Here’s a real one, if you like:

        Suppose “money” was not in fact the medium of exchange — suppose it did not circulate and have a velocity, in other words. Suppose it was just bling, and used as a medium of account, and had a demand function M/P=L(Y,i) but people used barter exchange in a backscratching economy. If the central bank reduces the supply of bling, that will cause interest rates to rise (people try to sell bonds to buy bling, so the price of bonds falls). But, in a barter economy, that rise in interest rates cannot cause a recession. Involuntarily unemployed backscratchers would just scratch each other’s backs, and get back to full employment that way.

        All New Keynesian models implicitly assume monetary exchange, rather than barter, and so implicitly invoke velocity. A medium of exchange circulates.

        Just finished writing a draft post on this. I expect i had better post it.

    • But velocity really depends on nominal interest rates, right, since they’re the wedge between holding wealth as money and holding it in some kind of savings vehicle? (This was especially true back in the early 1980s when all checking accounts paid zero interest.) In the long run it depends on inflation thanks to the Fisher equation—inflation ultimately determines equilibrium nominal interest rates—but this definitely doesn’t happen in the short run. And through the Volcker recession, nominal interest rates were at extremely high levels—until the very end, they were higher than ever before.

      Maybe consumers were extremely forward-looking and anticipated lower nominal interest rates (due to lower inflation), and decided to start holding more cash ahead of time (due to some kind of costly adjustment). But it’s hard to imagine that they were ahead of the bond market on this score, and 3-year Treasuries still had high nominal yields for most of the recession: http://research.stlouisfed.org/fred2/series/GS3?cid=115

      I know that this is partly an extreme position you’re staking out for the sake of argument, so I don’t want to belabor the point too much. But I just don’t see how velocity is useful device for understanding the 80s recession—to the extent that it says anything valid, one needs to fall back on an interpretation that includes the New Keynesian intuition about the actual vs. natural interest rates. As Adam asks, what does velocity actually add?

    • But, in a barter economy, that rise in interest rates cannot cause a recession. Involuntarily unemployed backscratchers would just scratch each other’s backs, and get back to full employment that way.

      All New Keynesian models implicitly assume monetary exchange, rather than barter, and so implicitly invoke velocity. A medium of exchange circulates.

      It’s true that you need some kind of money for this to be possible—one of the key ingredients in New Keynesian models is monopolistic competition, which is hard to interpret when everything is done by barter. (If the only the owners, not the workers, are able to barter, then I suppose you could get the same result—but if they’re able to barter in such a complicated environment, you have to ask why they don’t all get together and agree on a Pareto-improving decrease in markups during a recession.)

      But I don’t think this has much to do with the properties of the medium of exchange. In fact, imagine the following: everyone keeps most of their wealth in an electronic reserve account at the Fed, and all payments are made frictionlessly at the beginning of each period by changing accounting entries for those reserve accounts. No one needs all the wealth they’re keeping in the reserve account for liquidity purposes—instead, they hold it there because it’s a decent investment, as the Fed pays interest on reserve accounts. The IOR rate is the sole instrument of monetary policy.

      In this environment, all the New Keynesian machinery still works. (In fact, it’s basically the “cashless economy” that Woodford discusses in his book.) But at least at the margin, there are no monetary frictions to speak of, and it’s hard to say that “velocity” really means anything.

      Yet I don’t see why monetary policy in this environment is fundamentally different from monetary policy in a world with cash. All the same ingredients are in play; the Fed can adjust the nominal interest rate just as easily as it currently does, and monetary policy has the same effect on intertemporal decisions. But if “velocity” is obviously a meaningless concept in this world (where we see the same monetary phenomena), how is it supposed to mean anything in a world with cash?

  2. Matt again: “Is velocity any different [to the Old Keynesian G/Y ratio]? I doubt it. To the extent that velocity is “stable”, what’s actually happening is that consumers want to hold money balances as a relatively consistent fraction of nominal income. Sure, the ratio is stable, but the denominator causes the numerator, not the reverse.”

    Suppose that the G/Y ratio is less than desired by an individual. What can he do about it, as an individual? Nothing (except vote for a party that promises higher G).

    Suppose that the M/PY ratio is less than is desired by an individual. What can he do about it? He can increase his sales of other goods, and/or reduce his purchases of other goods, and that way increase his particular stock of money M to get to his desired individual M/PY ratio. But if everyone does this, there is excess supply of all other goods, so PY falls, and so aggregate M/PY increases to the desired ratio that way.

    • I agree—it’s not meant to be a perfect analogy. I’m just trying to emphasize the fact that there are many “stable” relationships in the data where causality can go either way, and assuming some kind of multiplier isn’t valid.

      Note that in your story about M/PY, nominal interest rates are lurking in the background. Consumers are making an intertemporal choice (whether to increase sales/reduce purchases today in order to hoard more money for tomorrow), and their decisions will therefore be governed by intertemporal prices. In particular, if “everyone” tries to increase their money holdings, the nominal interest rate will rise to clear the money market.

      The problem actually comes when that nominal interest rate (combined with the expected trajectory of inflation) is higher than the natural rate, and there is not enough demand to sustain full capacity today.

  3. David Beckworth

    Matt:
    Why do you continue to think of money in terms of the monetary base only? Assets used as money today include checking accounts, saving accounts, money market accounts, and repos. These all are medium of exchange. I don’t understand your focus solely on the monetary base.

    And again, velocity may be just a residual but it is an informative one. If measured with a broad monetary aggregate it provides a nice and quick way to get a sense of the demand for money (see here for more). MZM velocity, for example remains depressed and is one reason why nominal spending remains sluggish.

    • Why do you continue to think of money in terms of the monetary base only? Assets used as money today include checking accounts, saving accounts, money market accounts, and repos. These all are medium of exchange. I don’t understand your focus solely on the monetary base.

      In the post I looked at M2 velocity as well, and pointed out that it crashed in exactly the same way as base velocity.

      In general, I look at the base for two reasons: (1) it’s what the Fed actually controls, and (2) it is not particularly substitutable for other kinds of money. Most of the base is paper currency, which has uses that are very different from the uses of bank deposits. I can’t buy a house or make purchases at Amazon or trade equities with paper currency, and I can’t evade taxes or eat at the food trucks outside my building with my checking account. Monetary aggregates treat the two as substitutable when they really aren’t—not even close. They’re both “media of exchange” in some sense, but the kinds of transactions for which they’re useful are entirely different, and in my view it’s silly to lump them together.

      And again, velocity may be just a residual but it is an informative one. If measured with a broad monetary aggregate it provides a nice and quick way to get a sense of the demand for money.

      The demand for money depends on many variables, and I’m not sure exactly what aspects of it “velocity” is capturing. But let’s take a step back: why does “demand for money” matter to the economy? Presumably because “excess demand for money” (whatever that is) results in a recession. How does that happen? As I mentioned in my response to Nick above, there will inevitably be an effect on the nominal interest rate: it will rise to clear the money market, and if this means it rises above the natural rate, we’ll see a recession. There’s no way around this: when people decide to not to spend today, they’re making an intertemporal choice, one that will be governed by intertemporal prices.

  4. David Beckworth

    Matt:
    Does velocity-centric monetarism offer any similarly coherent account of the Volcker recession? I don’t see it. What made velocity collapse between mid-1981 and 1983?

    I hesitate to call what Nick and other quasi-monetarists embrace a "velocity-centric monetarism." Rather, it is a belief that an excess demand of money (rather than excess demand for safe assets–except when the safe assets are money) causes recessions. This understanding is equivalent to saying the actual interest rate went above the natural interest rate. These two understandings are not mutually exclusive. See Bill Woolsey for a good, but accessible discussion on this point.

    Note that excess money demand perspective only requires that desired money demand exceeds available money stock. This could occur because money demand is changing or the money supply is changing. All that matters is there is a relative change. Thus, one cannot point to what appears to be a relatively stable monetary base as you do above and conclude anything about excess money demand (aide: you seem to focus on the level of the monetary base instead of the growth rate. Take a look, for example, at the monetary base percent change from a year ago for the Volker recession. You don’t get quite the clean picture you claim above. )

  5. I hesitate to call what Nick and other quasi-monetarists embrace a “velocity-centric monetarism.” Rather, it is a belief that an excess demand of money (rather than excess demand for safe assets–except when the safe assets are money) causes recessions. This understanding is equivalent to saying the actual interest rate went above the natural interest rate.

    We mainly agree, then. But I think that “excess demand for money” is a needlessly imprecise phase; after all, there will always be equilibrium in the money market, as the nominal interest rate adjusts to whatever level is necessary to clear it. There is no “excess” on either side of this market. The problem comes when the nominal interest rate determined by equilibrium in the money market is above the natural rate, and the economy is forced below full capacity.

    I say that demand for safe assets matters because it widens the yield spread between safe assets and all other assets. Since “all other assets” are the ones that matter for the economy, holding the interest rate on safe assets constant, a widening of the spread is effectively contractionary. It’s possible, then, that even if the Fed brings the interest rate on safe assets down to zero, the spread will be too large to avoid recession.

    The fundamental problem here is that the interest rate on safe assets can’t fall below 0%; I suppose you can view this as a problem of “excess demand for money”, but I think it’s more precise to just talk about the nominal interest rates.

    Thus, one cannot point to what appears to be a relatively stable monetary base as you do above and conclude anything about excess money demand

    Sure—it’s possible that there is a demand shock. But it’s hard to imagine that a conscious decision to increase money demand would be enough to cause an enormous runup in nominal interest rates—after all, those high rates make holding money very expensive. To me, it’s more sensible to interpret this as a supply shock, one that leads to a sudden increase in nominal interest rates due to the short-term inelasticity of money demand (which itself is the result of slow portfolio reoptimization).

    (aide: you seem to focus on the level of the monetary base instead of the growth rate. Take a look, for example, at the monetary base percent change from a year ago for the Volker recession. You don’t get quite the clean picture you claim above. )

    Fair enough. As I pointed out, though, velocity wasn’t very stable, and the changes in base money and monetary aggregates were not commensurate with the massive slowdown in nominal GDP.

    • …I think that “excess demand for money” is a needlessly imprecise phase; after all, there will always be equilibrium in the money market…

      Nick is going to argue — and rightly so — that the phrase “money market” is needlessly imprecise, because all markets involve money. I think what you’re actually talking about is what should properly be called, in generic terms, the “bond market,” and in more specific terms, the “short-term bond market” or the “market for short-term loans” (possibly just overnight loans if you want to be that specific).

      But let me try to make the phrase “excess demand for money” precise. At any particular time, there are people who have money and would prefer to have an equal value of something else given current prices, and there are also people who have something else (perhaps an abstract thing like leisure) and would prefer to have an equal value of money given current prices. If the quantity of unsatisfied demand for money by those in the latter category exceeds the quantity of unsatisfied supply of money by those in the former category, then we can say that there is, in aggregate, an excess demand for money.

      Now it’s clear that, for some specific categories of “something else,” such as high quality bonds or listed stocks, there is unlikely to be much if any excess demand or supply of money. But for the broad category of “something else,” an excess demand for money is likely to be quite common. Shoppers who haven’t completed their purchases are “people who have money and would prefer to have an equal value of something else;” unemployed workers are “people who have something else [specifically leisure in this case] and would prefer to have an equal value of money.” In today’s economy, we can be fairly certain that the unsatisfied demand for money by unemployed workers (and others) exceeds the unsatisfied supply of money by shoppers (and others).

      Of course, in an economy where monopoly power is more common than monopsony power (and where perfect price discrimination is impossible), it is likely that an excess demand for money, in my sense, is the normal state of affairs, because monopolists “who have something else” will deliberately set prices at a level where they “would prefer to have an equal value of money.” Nonetheless, in the actual economy, the excess demand for money clearly varies over time, and we should be concerned about periods when it is unusually high.

      • To anticipate your objection, money may not be what unemployed workers really want. Rather, they want wealth, generically, or they want consumption. But my definition is precise. If you could offer someone a job and somehow require them not to spend or invest their paychecks but to hold them in the form of money, would they still accept? In some cases, no; in some cases, yes. To the extent that there are enough “yes” answers, there is an excess demand for money. Moreover, for some unemployed workers, wanting wealth is exactly equivalent to wanting money, because they will choose to hold their marginal wealth in the form of money, given its relatively attractive yield of zero, which is only slightly less than what other, less convenient, safe assets yield right now.

      • I suppose that whenever there are multiple margins of adjustment, there’s more than one theoretically valid way to describe “supply” and “demand”. Let me make the case for my choice.

        When we’re talking about the supply and demand for money, I think we should specifically look at the margin between money and short-term bonds. Why not some other margin? Because this margin isolates the liquidity premium for money, and separates it from the intertemporal decisions of the consumer. When we talk about trading money for goods and services, we’re combining (1) a decision to spend today rather than tomorrow and (2) a decision to lower the fraction of your portfolio held in the form of money. That’s too messy. I think it is more precise to talk about (2) separately: conditional on a particular intertemporal consumption plan, how will you construct your portfolio?*

        There is never disequilibrium along the margin between money and short-term bonds: the nominal interest rate adjusts to whatever level is necessary to make the marginal agent indifferent between the two.

        If there is any “disequilibrium”, it’s along the intertemporal margin. At the current interest rate, everyone wants to consume more tomorrow than today. But production capacity is no higher tomorrow than today (or, at least, not enough higher). If the economy is at full capacity tomorrow, it has to be below capacity today.

        This isn’t exactly “disequilibrium”; under most definitions, it would still be called an equilibrium, since the device of monopolistic competition allows us to view below-capacity production as an equilibrium phenomenon. Nevertheless, if there is anything close to “disequilibrium” in this model, it’s happening along the intertemporal margin, not the margin between money and bonds. The nominal interest rate always adjusts to clear the latter margin; the problem is that the former margin only clears after consumption and production today have fallen sufficiently far.

        ——

        * I recognize that these can’t quite be separated, since holding a portfolio that’s relatively heavy on money means a lower rate of return on your wealth, which tightens your budget constraint. But that’s a second-order issue.

      • To anticipate your objection, money may not be what unemployed workers really want. Rather, they want wealth, generically, or they want consumption. But my definition is precise. If you could offer someone a job and somehow require them not to spend or invest their paychecks but to hold them in the form of money, would they still accept? In some cases, no; in some cases, yes. To the extent that there are enough “yes” answers, there is an excess demand for money. Moreover, for some unemployed workers, wanting wealth is exactly equivalent to wanting money, because they will choose to hold their marginal wealth in the form of money, given its relatively attractive yield of zero, which is only slightly less than what other, less convenient, safe assets yield right now.

        You do anticipate my objection. I think this needlessly conflates the money/bonds margin, the intertemporal margin, and the labor/leisure margin. It don’t know whether to call your example above “excess demand for money”, “excess demand for savings”, or “excess supply of labor”.

        In general, you seem to be saying that if people have excess demand for wealth, and they would hold that wealth (if they managed to obtain it) in the form of money, there is also “excess demand for money”. This has some appeal, but I don’t think it’s the right way of looking at the situation. At the current level of wealth, there is neither excess demand nor supply of money relative to bonds; we see equilibrium along this margin. The real “disequilibrium”, insofar as one exists, is in intertemporal asset markets. That’s where the excess demand is.

        Suppose that there is a shortage of apartments due to rent control. There are two kinds of apartments, high-rise and low-rise, which have identical costs. Different consumers have different preferences over the two, and there is excess demand for both due to the ceiling on rents. Any two people renting different kinds of apartments can trade if they like, possibly with under-the-table side payments. (But someone currently renting can’t trade with someone else who is not.)

        Now imagine that the group of consumers currently shut out of the apartment market due to rent control disproportionately prefers low-rise to high-rise, and that most of the adjustment taking place if rent control was lifted would actually be in low-rise apartments. Do we talk about “excess demand for low-rise apartments”, since that’s where most of the unrealized demand is? I think it’s more accurate to talk about “excess demand for apartments”, clearly separating the disequilibrium (which is in the market for all apartments) from the more specific preferences of whatever consumers currently happen to be shut out of the market.

        In fact, in my example there is no “excess demand” for low-rise among the consumers currently in the market; I’ve stipulated that they can trade apartments with each other in exchange for (flexible) side payments, so that there currently is equilibrium along the high-rise/low-rise margin. In this context, talking about “excess demand” for low rise would be misleading.

        I feel the same way in your example. Sure, maybe the individuals you’re discussing would hold most of their wealth in money. But the real “excess demand” is for wealth, not money. Given the portfolios people currently have, the marginal investor is indifferent between money and bonds.

  6. I think your analogy is flawed, and so is your epistemology. Government spending is chosen by policymakers; money holdings are chosen by individuals, on whose behavior policymakers might be able to depend.

    …consumers want to hold money balances as a relatively consistent fraction of nominal income. Sure, the ratio is stable, but the denominator causes the numerator, not the reverse.

    I think this limited notion of causation breaks down completely when you consider a thought experiment in which the relationship is perfect. Suppose everyone demands money balances equal to an exactly constant fraction of their income. And suppose the central bank has complete control over the quantity of money. In that case, the CB can, using the quantity of money as its instrument, ensure that aggregate nominal income is equal precisely to whatever level it prefers (provided that there exists some effective transmission mechanism for monetary policy at the relevant horizon, but not depending on the specifics of the mechanism, of which the CB need have no knowledge whatsoever). And suppose the CB has a certain preference for nominal income and does assure, using the quantity of money as its instrument, that its preference is realized. Do you want to claim that, in this example, there is no causation running from the quantity of money to the level of nominal income? Do you want to claim that the velocity of money is not a useful concept in an economy that has this characteristic?

    Of course the relationship between money balances and income is far from perfect in the real world, but the difference is, in principle, only a matter of degree. I mean, if the interest rate elasticity of money demand were very small and the demand function reasonably stable, then the example would still be approximately true, and you would be hard pressed to argue that causal propositions that are true in the perfect economy are suddenly completely false in the not-quite-perfect one. Ultimately, you have either to assert a dubiously narrow concept of causation or to make a new argument based on some relevant way in which that the real world is qualitatively different from one that approximates the behavior of the ideal one in my example.

    • I actually thought about whether to mention this in the post, and in an attempt to make my posts a more reasonable length I decided not to.

      I agree that under a certain monetary policy regime, where the central bank perfectly targets the quantity of money, causation can go the other way. If the quantity of money supplied is higher than the quantity demanded at the current level of NGDP, then interest rates will plummet to 0% and NGDP will rise until it is brought into line with the supply of money. Similarly, if the quantity of money supplied is lower than the quantity demanded at current NGDP, then interest rates will skyrocket and cause a contraction until NGDP matches the supply of money. So if there is a consistent demand relationship, it is possible that we’ll see causality in both directions, and my statement about causality was an oversimplification.

      But I downplay this example because it involves a strangely counterfactual monetary policy: nowhere in the world does the central bank actually target a certain level of money and sit still while there’s blood on the streets as NGDP adjusts to its new level. (Volcker supposedly did this, but it was really a ploy to get the public to accept the tight monetary policy necessary for lower inflation; his Fed was well aware of the trajectory of the federal funds rate, and even had some discretion in manipulating it because it had freedom to choose between various monetary aggregates as “targets”.) In the real world, the Fed has always adjusted interest rates in light of their short and medium-term effects on output and inflation—and in this light, if we’re going to attribute any causation, it’s better to say that NGDP causes money. (Then again, maybe it’s wrongheaded to even talk about causation between two jointly determined endogenous variables like these.) My main point is that the implicit monetarist model where “M” has some causal effect on “PY” through “V” is not right.

  7. Matt: I’m going to go slightly off-topic here, and then return to reply to your reply about barter.

    Why do New Keynesians assume monopolistic competition instead of perfect competition?

    1. Because, at the micro level, monopolistic comp looks more plausible. Set that aside.

    2. Because, sticky prices are more plausible and easier to model under monopolistic competition, because the firm’s objective function is a smooth function of its price (small menu costs etc.). Set that aside.

    3. Because, starting in equilibrium, we get symmetric responses to increases and decreases in AD under monopolistic competition. Increases in AD cause Y to increase, and decreases in AD cause Y to decrease. That’s not true under perfect competition, where it’s asymmetric. A decrease in AD causes Y to fall, but an increase in AD causes no change in Y. That’s because firms&workers are already selling as much as they want to, and so min{Qs, Qd}=Qs in this case, so they ration sales if Qd increases. Let’s set that aside by only considering *decreases* in AD. (Or, simply ignore the short side rule, and assume that Q=Qd).

    If we set aside those (very good reasons) for assuming monopolistic competition, there is no problem in taking the limit of a New Keynesian model as the taste for variety approaches zero (as the elasticity of demand facing an individual firm approaches infinity. It then becomes a model of a perfectly competitive economy in the limit. And the model’s predictions remain (qualitatively) the same.

    In other words, I am not arguing that barter destroys the New Keynesian model because it makes the assumption of monopolistic competition untenable. That’s a separate (and interesting) issue, but one I don’t want to push here.

    So avoid that issue by taking the perfectly competitive limit of a NK model. It still says a decrease in AD will cause a recession. And I’m saying it won’t, if we allow barter.

    Start in the (efficient) competitive equilibrium natural rate. Hold prices fixed. Now reduce AD. The NK model says Y falls. I say, that if Woodford’s “cashless” really means “barter”, then it can’t. Firms and workers will barter their way back to full employment..

    • That’s a good point—in fact, if the production technology is linear, the basic log-linearized equations governing the New Keynesian model don’t depend on the elasticity of substitution at all, so one could say that even the (local) quantitative predictions hold as we approach the perfectly competitive limit. (Though not, of course, at the limit itself.)

      In response to your point, let’s think about three universes:

      (1) All exchange is done by barter, and there is no need for money.

      (2) Barter is impossible, but monetary frictions do not matter in determining the demand for money at the margin; the direct liquidity benefits from money have reached a satiation point, and nominal interest rates are set by a policy of interest on reserves.

      (3) Barter is impossible, and there are nonzero liquidity benefits from money at the margin. The resulting liquidity premium determines the nominal interest rate and affects consumption decisions.

      I think you’re implicitly ruling out the possibility of (2). As far as monetary policy is concerned, (2) is effectively “cashless” because the demand for the liquidity services provided by cash is irrelevant in determining interest rates, consumption, and so on. Quantity-theoretic monetarism can’t possibly be useful in this situation. But barter is still impossible: you can only trade goods and services for money. Money is irrelevant because everyone has a big enough cushion that at the margin they’re only using it as a store of value, not a medium of exchange; nevertheless, money has inframarginal relevance.

      Basically, introspection tells me that barter cannot possibly work for anything more than a very small set of goods and services. I’m not sure how much you disagree—you don’t seem to be claiming that barter is a realistic mechanism, just that Woodfordian economics is inconsistent because it doesn’t have a good way of ruling barter out. But I think the model is completely consistent: in particular, (2) is a cashless model without barter.

      • Matt,

        One of the problems underlying this discussion you’re having with Nick is that he believes very strongly that there can be no recession without monetrary disequilibrium of some sort. He very strongly believes that if barter is costless then you never have a recession.

        However, anyone who’s ever seen the RBC paradigm knows that as a purely theoretical matter this wrong. Nick is very fond of stating how NK models only make sense in a monetary exchange economy but anyone who’s ever seen the canonical version know that this is also wrong.

        The canonical version I have in mind has a clearing labour market as in the RBC type models, the basic shocks are to productivity as in RBC (you can also have monetar policy/interest rate shocks if you want).

        This is basically an RBC model with monopolistic competition, price stickiness (not wage stickiness) and Taylor rule interest rate setting to generate the Phillips curve and scope for a central bank to do something useful.

        If the interest rate is wrong you get a recession, output and employment fall, even if barter is costless. This recesson is not very familiar feeling to those in the real world because the fall in employment is entirely due to people withdrawing labour supply but that is how the model works (as do RBC models).

        Nick denies all of this.

      • Nick and I are definitely operating within different frameworks. To me, the problem with talking about “barter” is that it seems to be a direct way of circumventing sticky prices, which are a necessary ingredient in a New Keynesian recession.

        Without sticky wages or some other kind of labor market rigidity, I believe that countercyclical markups are essential for monetary policy to cause a recession (or expansion). Here’s the “proof”: if there are not countercyclical markups, then the real wage does not decline, and workers will not voluntarily supply fewer hours. (This comes from the intratemporal Euler equation–if consumption weakly decreases, then the marginal utility of consumption weakly increases, and if the real wage stays constant this means that the marginal utility from working more and spending that money weakly increases as well… so labor supply has to weakly increase.)

        Countercyclical markups, meanwhile, are caused by sticky prices.

        Barter can stop a New Keynesian recession insofar as it allows agents to circumvent monopolistic competition and sticky prices. But that’s almost tautological: without sticky prices and the resulting countercyclical markups, recessions arising from monetary policy failing to hit the natural rate of interest are impossible unless we have some other device like sticky wages. (Even a very small degree of price stickiness, however, changes the properties of the model dramatically.)

      • Matt,

        agreed with everything your saying. Nick is clearly using it to circumvent the sticky prices and monopolistic competition.

        I think you can go further though, seems to me that monpolistic competition is something that would still exist in a pure barter economy. The monopolistic competition is really a property of the production technology, the industrial organization, and the fact we organize production into firms at all, is presumably due to some efficiency gains. It’s a form of organization capital. We’d still want to do this if goods trade was frictionless and thus we didn’t use money.

        The sticky prices on the other hand aren’t explained in the canonical form of the model, they’re just imposed exogenously as a constraint of nature. Again, in a trivial sense, this has nothing to do with monetary exchange.

        But now we don’t need money to get the conclusions of the model at all.

        I suspect Nick would say that without money you can’t have nominal anything, so you somehow can’t talk about price sticky prices. I don’t see that that’s true though.

  8. Matt: “Basically, introspection tells me that barter cannot possibly work for anything more than a very small set of goods and services. I’m not sure how much you disagree—….”
    I agree. (At least as a modelling strategy, but sometimes I have my doubts and wonder whether we macroeconomists aren’t missing that whole sector of the household and informal sectors that don’t use money and are about as large as the monetary economy we are all fixated on. But set that aside.)

    I simply cannot tell whether Woodford is modelling a monetary exchange economy without cash (whatever that means), or a barter economy. Without explicit frictions, or at least an ad hoc “let’s assume a CIA constraint or “it’s illegal to swap apples for bananas and the only markets that exist have money exchanged for the other good””, it’s impossible to tell. But implicitly it must be some sort of monetary exchange economy, where barter is impossibly costly, because his conclusions would not make sense otherwise.

    If Woodford’s model is a model of a monetary exchange economy, in which money pays *the* market rate of interest, so people are satiated in money, then….it’s a model of a permanent liquidity trap. To my way of thinking, there is a whole spectrum of rates of return on different assets, with less liquid assets having to pay higher yields in equilibrium (leaving aside risk and term structure spreads). “Money” is special because it is the *most* liquid of all assets, and this difference in degree becomes a difference in kind, because being the most liquid it is the only asset that is traded in all markets. As Andy said above, the term “money market” is a misnomer. Every market is a money market.

    Gotta go fix a car.

    • If Woodford’s model is a model of a monetary exchange economy, in which money pays *the* market rate of interest, so people are satiated in money, then….it’s a model of a permanent liquidity trap.

      Not really, at least in the way that matters. The problem with a liquidity trap is that as long as you have paper currency, the nominal interest rate can never go below zero. In the hypothetical model we’re discussing here, the steady-state nominal interest rate presumably would be set (via interest on reserves) at a level much higher than zero, so that this would not “permanently” be an issue.

      (And maybe there wouldn’t even be any paper currency.)

      To my way of thinking, there is a whole spectrum of rates of return on different assets, with less liquid assets having to pay higher yields in equilibrium (leaving aside risk and term structure spreads). “Money” is special because it is the *most* liquid of all assets, and this difference in degree becomes a difference in kind, because being the most liquid it is the only asset that is traded in all markets.

      But if there’s enough money, its liquidity premium relative to “cashlike” assets will actually go away; that’s what happened in Japan, and that’s what has nearly happened in the US. (if not for the IOR floor keeping rates an inch above zero) It is entirely possible to imagine a world where the liquidity premium on money is either consistently zero or consistently tiny, and the Fed’s policy instrument (through which it affects the “whole spectrum of rates” you discuss) is the IOR rate.

      The fact that we’re in a monetary exchange economy, and that barter is impossible, doesn’t mean that money has much value at the margin relative to other, moneylike securities. Maybe there’s a lot of inframarginal value in the first few billion and virtually nothing beyond that. Maybe banks are clever and design a system for transferring assets that barely uses base money at all. The fact that barter is impossible doesn’t mean that monetary frictions have to be large or economically relevant at the margin.

  9. Bill Woolsey

    Matt:

    Suppose all money pays interest, and the interest rate on money changes with all other interest rates in the economy. The difference between the interest rate on money and other assets stays contant.

    The economy begins in equilibrium. The price level is such that the real quantity of money equals the real demand to hold money.

    I think the reason for the focus on interest rates is because of an assumption that the interest rate paid on money is sticky, and so changes in market interest rates impact the opportuntity cost of money and so cause the real demand to hold money to adjust to the real quantity. This is institution specific–sticky interest rates paid on money. Give that up, and the focus on interest rate breaks down.

    P.S. Central banks like to stablize interest rates. Does that preference tell us something about monetary economics? Does it make it a good idea? How much of monetary economics is being driven by this preference of central bankers? Should it be?

    The quantity of money is increased, creating an excess supply of money. It is possilble, and likely that some of those with excess money will purchase bonds. Bond yields fall, and so does the interest rate paid on money. The opportuntity cost of holding money is not changed. It doesn’t decrease. There is no increase in the real demand to hold money.

    How is there a return to equilibrium? Real income may raise, increasing the real demand for money. Or, the price level may rise, reducing the real quantity of money

    • I think the focus on interest rates is more fundamental — it isn’t just the result of the central banks’ tendency to smooth nominal interest rates. Monetary policy needs to affect real consumption decisions through some mechanism, and in a world with sticky prices I think that mechanism is the real interest rate.

      I’m not sure exactly how to interpret your example, because I’m a little confused by how the “interest rate paid on money” falls—are we assuming that all money is inside money created by banks?

      Regardless, I think that a fall in nominal interest rates (assuming that short-term expected inflation doesn’t fall commensurately — and there’s no reason that it would) will raise consumption and output almost axiomatically. If expectations about the medium-term future are more-or-less pinned down, a decline in the real interest rate will increase consumption and investment today, through intertemporal substitution and a decline in the cost of capital. Why wouldn’t this happen?

  10. Jeff Hallman

    Is velocity any different? I doubt it. To the extent that velocity is “stable”, what’s actually happening is that consumers want to hold money balances as a relatively consistent fraction of nominal income. Sure, the ratio is stable, but the denominator causes the numerator, not the reverse.

    Sorry to rain on the parade, but if this was right, empirical studies would show output Granger-causing money and not the reverse. In fact, they usually find the opposite. This has always been one of the monetarists strongest arguments.

    • Well, I’m saying that the “stable” relationship between money and output is best interpreted as a case of output causing money, not the other way around. (Though there is some ambiguity about what causality really means here—see Andy Harless’s comment and my response.) I’m not saying that money can never cause output. In fact, in the 1980s recession, it surely did: a (relatively small) contraction in the money supply was enough to send the economy into a deep recession.

      Econometrically, I expect that it’s easier to pick out the obvious money-causing-output episodes, rather than the general, slow, long-term tendency for money to match nominal income. (Though apparently, in the modern, post-Volcker era, there’s some doubt about whether money does even Granger-cause output: http://www.wiwiss.fu-berlin.de/institute/wirtschaftspolitik-geschichte/berger/publikationen/working_papers/m_y_US_080215_final.pdf). The former operates at very short lags, while the latter depends on (slow) consumer portfolio reoptimization, as I mentioned in the post.

      Basically, my contention is that in practice, the Fed sets interest rate policy to achieve certain output and inflation goals. This policy results in a certain long-term trajectory for nominal GDP, and along that trajectory the Fed is basically changing the money supply to match (relatively short-term inelastic) consumer demand. To keep the economy on that trajectory, the Fed may tighten or loosen when circumstances warrant—but it is precisely in these episodes that the “stable” velocity relationship breaks down. Sure, money is causing output, but it’s not causing output in a way that follows any kind of monetarist framework. Instead, it’s best interpreted along neo-Wicksellian lines: the difference between the actual rate and the natural rate causes an expansion or contraction.

      To sum up: yes, money causes output. But at least under a typical policy regime, the stable relationship comes from output causing money.

  11. Scott Sumner

    I wish I had gotten here earlier. I’d like to challenge the empirical evidence you rely on in making your argument. I think it’s easy to develop a velocity-centric model of the 1982 recession. Interest rates on three year T-notes fell from 16.22% in Sept 1 1981 to less than 10% in late 1982. That’s a huge drop, and by itself could have caused velocity to drop sharply.

    It’s also easy to find deep slumps associated with changes in the base. The biggest drop in the base in the 20th century was 1920-21, and that was also the most severe deflation of the 20th century. Coincidence? The base declined about 8% between October 1929 and October 1930 (when the bank panics kicked in.) And of course 1930 was a severe recession. These earlier examples are better than recent cases, as when monetary policy is endogenous you would not expect much correlation between the base and the goal variable.

    The Keynesian alternative (interest rates) performs very poorly in many recessions. Sometimes tight money causes high rates, but other times tight money causes low rates (i.e. 1930 and 2008.) So rates are not a reliable gauge of the stance of monetary policy. (The base became meaningless once IOR kicked in during October 2008.)

    Of course all intermediate targets are inefficient, so I don’t wish to defend monetarism. We shouldn’t target i or M, we should target NGDP futures.

    You said:

    “Monetary policy needs to affect real consumption decisions through some mechanism, and in a world with sticky prices I think that mechanism is the real interest rate.”

    I’d say monetary policy needs to affect nominal output and expenditure decisions through some mechanism, and in a world of sticky prices AND ALSO in a world of flexible prices, that mechanism is the hot potato effect. No need to bring in interest rates. Then we can explain why NGDP shocks affect RGDP by assuming sticky wages and prices, no need to bring in interest rates at all. They are an epiphenomenon.

  12. John Blanchard

    Let me preface this by noting that I’m not an economist, just a physicist who’s been reading Matt’s blog since before it was cool. Being a physicist, it seems as if the core issue in much of this debate over exchange and differences between schools of thought is related to determining what symmetries exist in the system, and as such, what quantities can be said to be conserved. To me, the presence of a “velocity” term (especially multiplied by an amount of money “M”) suggests a desire to talk about some kind of monetary momentum, which has a good intuitive feel to it. I imagine that symmetry and conservation already provide some of the foundation of all of these theories, as economics is certainly, at heart, applied mathematics (I know Matt at least is a better mathematician than I am), but to the uninitiated, it’s unclear where this comes in. Might it be worth discussing some of these ideas from that perspective?

  13. flow5

    No, PT=MVt. Problem solved.

  14. flow5

    “Ultimately, velocity is just a residual, one without much practical role in monetary policy”

    You just committed suicide.

  15. Pingback: What does it mean to explain? (And why it matters.) | Ignis Rates Views

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