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Brad DeLong: "It was intended as a proof-of-concept: to demonstrate that introducing very small market-imperfection frictions into a DSGE framework generated very Keynesian-monetarist conclusions."

That looks like a sensible answer. NK is neither a barter model nor a Keynesian-monetarist model.

if the interest rate is 100% in a barter economy does that mean that you could deposit 100 bananas with the bank and get 200 back next year ?

If so, won't you and I both trade less apples and bananas as the interest rate goes up even under barter as we would rather trade present fruit for future fruit ? If the CB in the barter economy is targeting a certain level of present fruit trading it seems like interest rates would still give it some control.

My attempt to get to grips with this question: Link Here NR

Kevin: OK, but what are those market imperfections? Are they just monopolistic competition + sticky prices? Or do they include frictions that prevent barter exchange, so that people can only buy and sell goods using their accounts at the central bank?

MF: "if the interest rate is 100% in a barter economy does that mean that you could deposit 100 bananas with the bank and get 200 back next year ?"

Suppose that were true (and it were true for apples, and carrots etc as well). Then if the central bank set a stupidly high nominal (and real) interest rate, that would cause a boom. Everyone would work very hard and produce a very large amount today, and sell it to the central bank. Intertemporal substitution of leisure.

On the other hand, suppose it were false, and that the only way the central bank can set an interest rate in a barter economy is by passing a law that says it is illegal to borrow or lend except at the official interest rate. Then (with identical agents) there would be zero effect, because there is no borrowing or lending in equilibrium anyway. Everyone would want to lend apples and bananas, but could find no willing borrowers.

It is not at all obvious how a central bank can set a rate of interest in a barter economy. What even *is* a "central bank" in a barter economy?

Nick E: from a very quick skim, I think you and I are on the same page.

Nick,

"It is not at all obvious how a central bank can set a rate of interest in a barter economy. What even *is* a central bank in a barter economy?"

I offer 1.05 million apples to Joe for an airplane. Joe says it will take one year for him to construct the airplane. I change my offer to 1 million apples for an airplane 1 year from now. If Joe doesn't deliver the airplane, I expect to receive 1.05 million apples 1 year from now instead to fulfill the debt. I am expecting 5% real apple interest either in the form of the airplane or 5% more apples than what I gave to Joe.

A central bank could set a nominal interest rate on a debt contract between an apple producer and an airplane producer.

I offer 1 million apples to Joe for an airplane to be delivered one year from now. After that year has passed I receive one of the following:

1. An airplane
2. 1.05 million apples if the relative price of apples per airplane has not changed (5% real interest)
3. 1.00 million apples if the relative price of apples per airplane has fallen by 5% (5% inflation interest)

The central bank would exist primarily to track relative price changes over time so that all debts are settled in nominal (rather than real) terms. With a multitude of barter goods all trading against each other a central bank could then create a unit of account to track the relative prices.

In essence a central bank in a barter economy would be a book keeping agency (tracking relative prices over time) and an enforcement authority making sure that debts were always settled in nominal terms.

"Otherwise underemployed producers would barter their way back..."

I think you've got a different interpretation of "barter." In the model, "exchange" is all against your budget constraint. The households (really a representative agent, but we'll say households) optimize, exchange labor for goods, and their budget constraints are satisfied. The firms are different. If a firm can change its price during the period, it optimizes, and pays for the labor it uses in production with the proceeds of its sales of goods - the firm has a resource constraint that must be satisfied. With monopolistic competition there are some profits that are rebated to the households. If a firm can't change its price, then it's not optimizing - it just satisfies whatever demand comes in the door. But the sticky-price firm still has a resource constraint that needs to be satisfied. You're right that, if the sticky price firm could negotiate prices with the households, it would do it. But it can't - those are the rules as Woodford set them down. All of this has nothing to do with the mechanism of exchange - what gets traded for what, and how. In that sense, this is no different from standard competitive equilibrium models we're used to thinking about. Budget constraints are satisfied, firms satisfy resource constraints, but the model has nothing to say about how the exchange actually happens - because that doesn't matter. This is just standard non-frictions economics.

Steve: suppose that a New Monetarist like you built a hybrid New Monetarist/New Keyensian model. You keep monopolistic competition and Calvo pricing, but added things like imperfect trust so that money became essential for trade. And "money" consists of every agent (or household and firm) having a chequing account at the central bank, which can have either a positive or negative balance, and the central bank chooses the rate of interest to pay (or charge) on positive (or negative) balances.

I think that that hybrid NM/NK model like that would be very different from an otherwise similar model in which monetary exchange was not essential.

The only way I can make sense of the NK model is that it is like a hybrid NM/NK model, except that the model builders left the NM part implicit, rather than spelling it out explicitly.

For example: when you say "... and pays for the labor it uses in production with the proceeds of its sales of goods..." and "...there are some profits that are rebated to the households..." I ask myself what exactly those "proceeds" are, and in what form are the profits rebated to households? Is it money? If not money, what exactly does the firm use to pay its workers and shareholders? And I can't make sense of the NK model unless workers and shareholders are (implicitly) paid in money, and use that same money to buy goods from other firms.

The Walrasian auctioneer calls out a price--a nominal interest rate.

Everyone turns in the amount of consumer goods they want to consumer and the amount they want to produce and sell.

If there is a surplus, the Auctioneer calls out lower prices, but the lower prices just apply to some fraction of the sellers.

Everyone turns in their orders again.

There is still a surplus. The firms who could sell at the lower price sell the amount they want. The buyers all buy what they want. Some of the sellers who can only sell at the initial price want to sell more than buyers buy.

Sell and buy for what? What? Have we really gotten much further than everyone figuring out what they are going to do?

Anyway, let's say the sellers actually produce the stuff. And then the Walrasian auctioneer can just tell each seller to make a delivery to some buyers.

Come on... it is really just about the math.


Question for Nick and Steve, intended to sidestep Nick's medium-of-exchange and not medium-of-account fetish just for the moment:

Is it possible to have a pure barter economy with monopolistically competitive firms but still have Calvo-type NK price stickiness? Here is what I mean by "pure barter" in this case: There is *no* MOA, and thus there is no price level. You can define the price level in terms of any good at any particular moment in time, but there is no universal price level, trades are not quoted in any common denomination. It is always X apples for Y bananas. Everyone always exchanges their stuff directly for some other stuff in a negotiated ratio.

Under these conditions, is there still a NK story where some firms can be stuck with their old "prices" (perhaps all of their most recently established exchange ratios and the implied price level that would connect them all)?

Bill: I'm afraid you lost me there.

dlr: I think I would answer "no" to your question.

I can imagine a Cournot-Nash equilibrium (where each firm sets quantity) without a Medium of Account. But Bertrand-Nash equilibrium (where each firm sets a price) seems to me to be undefined unless we specify whether prices are set in dollars, gold, silver, apples, bananas, or something. And if there are n firms, there are only n-1 relative prices, so they can't all set a price.

I think I would answer "no" to your question.

This is what I thought, too, but I'm not sure. If this is correct, it seems central to the conversation.

Steve is arguing that firms can "barter" in the NK model but still experience price rigidity. But that doesn't bridge the gap, because it doesn't explain what we mean by "barter." Here's the thing... In my view, the NK model is really only explicit on one aspect of exchange: There is no necessity for a medium of exchange. Households, for example, can make whatever exchanges they please, subject to their budget constraint. Apples for bananas is OK. This is why Woodford can talk about a cashless economy but still have a price level. And this is why Buiter then calls the unit of account in this version of the model "phlogiston." Because the NK model seems to implicitly model an economy with an MOA but not (necessarily) an MOE, and the MOA seems to float in the ether as the eleventh commandment (or, I think Woodford would say, an equilibrium selection result determined by a reaction function and constrained by fiscal solvency).

A price level and medium account alone can violate one definition of "barter." Exchanges are still mediated by a common unit, unlike a potential definition of barter that allows direct ratio exchange. This common unit can create friction that would be impossible in a pure barter economy. I think if the fractional firm rigidity is dependent on a price level, and thus a MOA, then the entire Calvo rigidity in the NK model would be eliminated by barter as defined. Even if the MOA requirement is only implied by fact that the particular rigidity exists in the first place.

Nick,

For n goods there are n*(n-1) / 2 relative prices (not n-1 relative prices).

For instance there are four goods A, B, C, D there are 6 possible combinations
AB
AC
AD
BC
BD
CD

Nick,

Does the Bertrand-Nash equilibrium assume price consistency across multiple barters? What I mean is that the producer of good A could set one relative price A/B, producer of good B could set another B/C, producer of good C could set another C/D, and producer of good D could set his to D/A. And so with price consistency, producer of good A could sell A to get B to get C to get D to get back to the same quantity of good A that he started with. Without price consistency the same seller of good A would get more / less of good A going through multiple barters back to A.

The question would seem to be, who is the beneficiary of price inconsistency? Perhaps the person who has to go through the longest barter chain to get what he / she wants? If I produce good A and I state the price of good A in terms of B, I endure "barter friction" as I progress further through the chain.

"It is not at all obvious how a central bank can set a rate of interest in a barter economy"

After reading Nick E. post (linked to above) I'm thinking about it like this...

- Assume a fruit economy where all fruit has to be consumed in the current period.
- Present fruit can be bartered at interest for future fruit.
- After people have agreed lending/borrowing of fruit then fruit production take place based on subsequent demand.
- If the interest rate is too high and some loans don't get made that otherwise would happen then there will be insufficient borrowing, and total fruit production will be too low.
- If the CB (for whatever reason) is better at setting the interest rate than the market would be, then the role of the CB is to set the rate at the level that optimizes fruit production
- Nothing changes if you choose a unit of account to measure economic activity

Market Fiscalist,

What you are talking about is a real interest rate - fruit now for fruit later. The problem is unless the central bank is producing fruit, it can't maintain that real interest rate.

If instead you have two goods (fruit and vegetables) the central bank can maintain that the nominal interest payments are made without producing either by allowing the relative price of fruit and vegetables to change.

Think about a really simple competitive equilibrium economy. There's a representative firm and a representative consumer. There are two goods, labor and a consumption good. To make it interesting, suppose there's also a fixed stock of capital, and consumption goods are produced, under constant returns to scale, from capital and labor. Everything's nicely behaved, and so the competitive equilibrium will be efficient. There are many ways to structure exchange in the model, however, that will lead to the same equilibrium allocation. For example, we could suppose that the firm possesses the capital, but the consumer owns shares in the firm, and the firm acts in the interest of its shareholder. At competitive equilibrium prices, everything happens simultaneously. The consumer goes to work for the firm, goods get produced, and the goods are returned to the consumer as wages and dividends. Alternatively, we could suppose that the consumer owns the capital and rents it to the firm. There is then a competitive equilibrium wage rate and a rental rate on capital. Again, we could think of everything happening simultaneously. The consumer works for the firm, rents capital to the firm, goods get produced, and the goods go back to the consumer as wage payments and rental payments. Alternatively, take the last arrangement, but suppose that things don't happen simultaneously. Instead the consumer receives IOUs from the firm in exchange for labor and the use of the consumer's capital. Then, when the firm produces goods, it discharges the IOUs with the output it produced. All of these arrangements give you the same equilibrium quantities. The actual mechanics of exchange are irrelevant in frictionless economies. That's the kind of world Woodford constructs, except that he wants to include a friction - sticky prices. He thinks (rightly or wrongly) that price stickiness is where the action is, and he wants to eliminate all other frictions so he can focus on that. When we do deep monetary economics, we get into all the other frictions we might think are important in generating a role for assets in exchange, and for thinking about why credit arrangements look like they do. Then, the mechanics of exchange do matter - that's what we're interested in. Why are assets traded and how? Why do we have banks? How do asset exchanges by central banks matter? Why is collateral used in credit transactions?

The actual mechanics of exchange are irrelevant in frictionless economies. That's the kind of world Woodford constructs, except that he wants to include a friction - sticky prices. He thinks (rightly or wrongly) that price stickiness is where the action is, and he wants to eliminate all other frictions so he can focus on that.

Yes, but the mechanics stop being irrelevant in one key respect the moment you add the sticky price friction. Specifically, sticky prices (seem to) require more than just monopolistic competition; they (probably) require a price level. Prior to the sticky price friction, it is possible for a NK or RBC model to truly be exchange agnostic: jump right past whether there is a price level or how trades are conducted and right to budget constraints and equilibrium quantities. But the argument here is that by introducing a Calvo friction you must (probably) also be quietly introducing a price level and an MOA. And that this *is* part of the mechanics of any exchange because it excludes pure barter, defined as a system which allows negotiated quantities without need to reference a tertiary denominator in transactions, i.e. an MOA.

Steve: "The actual mechanics of exchange are irrelevant in frictionless economies."

Agreed. But if we include one friction - sticky prices - then the mechanics of exchange matter a lot.

For example, let us replace your fixed stock of capital with a fixed stock of land, and assume land is homogenous. And assume that land is the unit of account. And assume that the prices of output and labour are sticky in terms of land.

Start in competitive equilibrium, then suppose there is a preference shock, so that people become more patient (lower rate of time preference). If prices of output and labour were perfectly flexible, both P and W would fall, leaving W/P unchanged, and Y and L unchanged, and reducing the rate of return on holding land (land's rent/price ratio) to satisfy the consumption-Euler equation. But suppose that P and W are temporarily fixed.

Compare the effect of that same shock in two economies with different mechanics of exchange:

1. Firms pay labour and land rents in output. Households buy and sell land for output. (Output is the medium of exchange.)

2. Households buy output with land. Firms pay labour and land rents with land. (Land is the medium of exchange.)

In economy 1, Y and L stay at competitive equilibrium. There is an excess demand for land (the consumption-Euler equation is not satisfied) but nothing else is affected, since no land is traded in equilibrium anyway (because all agents are identical).

In economy 2, Y and L fall below competitive equilibrium. The Marginal Product of labour is above W/P, and W/P is above the Marginal Rate of Substitution between consumption and leisure. But the consumption-Euler equation is satisfied. At the margin, households are indifferent between extra consumption and extra land. They would like to trade labour for consumption directly (so would firms) but the mechanics of exchange don't permit them to do this (by assumption).

"That's the kind of world Woodford constructs, except that he wants to include a friction - sticky prices."

Yes and no. The only *explicit* friction is sticky prices. But by asserting that the consumption-Euler equation continues to hold despite sticky prices, he is *implicitly* assuming a mechanics of exchange that is more similar to my second model than to my first model above. (The analogy isn't exact, because he assumes flexible W.) And that (implicit) assumption about the mechanics of exchange must rest on some (implicit) assumption about trading frictions.

You Steve are one of the very few econobloggers who takes the "mechanics of exchange" seriously. That is what I like about New Monetarist Economics. What I am trying to persuade you to do is look at the *interaction* between two sets of frictions: those that give rise to monetary exchange; those that give rise to sticky prices. If prices are sticky, the mechanics of exchange matter a lot more than when prices are perfectly flexible.

Start with an RBC model with monopolistic competition.

Now suppose that firms must announce prices in advance, for example, to avoid them ripping off customers who have traveled a long way to buy the firm's goods.

Now suppose all the things you normally suppose to explain why money is essential for trade.

Now you've got an interesting NM/NK model.

I am on the same page as dlr, who beat me to it.

Frank: "For n goods there are n*(n-1) / 2 relative prices (not n-1 relative prices)."

You are correct. If prices are perfectly flexible, arbitrage ensures that n(n-1)/2 collapses to (n-1). If prices are sticky, it only collapses to (n-1) if we assume that one of the n goods is the unit of account (each firm only chooses to price its good in terms of one other good).

But that is a detour from our discussion here.

I thought it was a model of a barter economy where intertemporal contracts are only possible with the central bank as one party. It is impossible for a general glut to develop in a given period, for the reason you say. And in fact there is no unemployment in the Keynesian sense in Interest and Prices. But it is possible for there to be excessive demand for the basket of goods in one period relative to the basket of goods in some other period. In the absence of an appropriate nominal interest rate chosen by the central bank, this will result in variations in the price level, which are considered undesirable. If sticky prices prevent the price level from adjusting, there will be an inefficient distribution of leisure and consumption across periods.

On the other hand, suppose it were false, and that the only way the central bank can set an interest rate in a barter economy is by passing a law that says it is illegal to borrow or lend except at the official interest rate.

I am pretty sure that Interest and Prices explicitly assumes that the central bank has a monopoly on intertemporal transactions, so Woodford seems to be contemplating something like this.

"What I am trying to persuade you to do is look at the *interaction* between two sets of frictions: those that give rise to monetary exchange; those that give rise to sticky prices."

You don't have to persuade me of that. I agree. In an NK model, of course, there are no frictions "giving rise" to sticky prices, unless you take the literal costs of changing prices seriously. In practice, what we use as a unit of account, and why we write contracts in terms of that unit of account is of course intimately related to what we use as a medium of exchange. But none of that is in an NK model. You shouldn't torture yourself trying to figure out how one could tell a story about monetary exchange inside an NK model.

Isn't it just a model of an economy where everyone uses debit cards? Like when talking about the money multiplier, first you cover the deposit only (cashless) economy, then you talk about the cash and deposit economy and the currency-deposit ratio. So, b).

"Now suppose that firms must announce prices in advance, for example, to avoid them ripping off customers who have traveled a long way to buy the firm's goods.

Now suppose all the things you normally suppose to explain why money is essential for trade.

Now you've got an interesting NM/NK model."

That just gets you the Lucas model, where only unanticipated monetary policy changes have an effect - which isn't really NM/NK. You need random staggered prices (i.e. Calvo) to get NK.

dlr above seems to be asking "What happened to the Clower constraint?". The way I understand it is that the unit of account in Woodford is a claim on a quantity of a liability of central bank. The liability is also dominated in (future) claims on the CB's liability. Because the CB gets to decide what the unit of account is it can choose both the "interest rate" (you give me X claims today in exchange for X(1+r) claims tomorrow) and whatever quantity of these liabilities it wants to. This more or less means that the quantity doesn't matter, which is what lets him (Woodford) go forth and consider the whole thing without reference to quantity of money (which can be said to exist, but it always adjusts to whatever it needs to be). Also, whether or not the non-CB institutions can issue interest bearing assets is irrelevant - they're perfect substitutes.

The price level then is the quantity of claims on CB's liabilities.

notsneaky: "That just gets you the Lucas model, where only unanticipated monetary policy changes have an effect - which isn't really NM/NK. You need random staggered prices (i.e. Calvo) to get NK."

If the firms announce prices at the beginning of the period, then the shock is revealed, then the central bank announces the monetary policy instrument, you have a New Keynesian model. The central bank can and (generally) should respond to the shock, but firms can't. True, it's not the same as the Calvo version, but it's not the same as Lucas/Sargent/Wallace either. It would be different if I changed the order of moves.

I'm not so sure. If all firms choose prices together then it should be like Lucas, even if they have to choose prices ahead of time. Same is true if (the same) fraction chooses ahead of time and the remainder has flexible prices. In both cases only unanticipated monetary shocks have effect on output, and for one period only. For anticipated monetary policy (say, the kind that results from following a monetary rule) to have effects on output you need the price changes to be staggered, like in Calvo.

I'm also thinking that dlr might be right above about how with sticky prices the price level is sneaked in, but I'd have to think more about that one.

Remember that in those models the nominal wage is flexible.

Notsneaky: remember the original intent of NK models: to demonstrate that a feedback/contingent rule for monetary policy could outperform a k% rule. For example, if the AD function is p+y=m+v, and there are shocks to v, if p is set in advance of the shock, then the contingent rule set m=-v leads to less variance in y than the simple rule set m=0.

Well, that may be true but that's not the "New Keynesian" model of Woodford. In fact, Woodford explicitly refers to the kind of model you describe as the "New Classical Model".

Another way to put it:

m+v=p+y, but p is set on the basis of expected m+v, so m+v=p(E(m+v))+y, so y is the optimal level of output up to an unpredictable shock. If m is always adjusted to keep m+v constant then y is always y-optimal. But if you choose m to try to get y permanently higher, to the extent that's predictable, you can't. That's the Lucas result, not a "New Keynesian" result. This is sort of a question of proper (and somewhat arbitrary) taxonomy but what makes this "New Classical" is that there's no inflation/output trade-off, monetary policy only works to the extent it's unpredictable (even if that only means that it's offsetting an unpredictable shock), and its effect last only for one period.

To get something New Keynesian you need prices to be staggered. In other words, m+v=p(E(m+v),E(m(t-1)+v(t-1))+y. Of course if it's possible to always keep m+y constant, say at c, then we have m+v=c=p(c,c)+y --> y(c). Absent other problems, you can always be optimal here. Two things can go wrong. First, the choice of m occurs with error, so that m(t-1)+v(t-1) is not c which introduces gradual adjustment. Or, and this is the part that Woodford stresses, what is optimal output actually varies over time. So having y=y(c), a constant "trend" output, is not actually optimal. That's where the CB has to try and forecast what the optimal level of output will be and to the extent they can't predict that perfectly, you get persistence in the effects of monetary policy, and an actual inflation-output trade-off.

And to get staggered prices you need Calvo, not just plain ol' sticky prices. That's why everyone does Calvo and not "prices are set before a shock occurs". If all you needed was "prices are set before shock occurs" these models would be much simpler. But they wouldn't be "New Keynesian", they'd be (perhaps a milder version of) "New Classical".

notsneaky: "That's the Lucas result, not a "New Keynesian" result."

I disagree. NK's late 1970's early 1980's disagreement with the Lucas Sargent Wallace proposition was not about making Y *permanently* higher, it was about "activist" monetary policy being able to reduce the *variance* of Y (relative to Y*). LSW said that "activist" monetary policy would be no better than a k% rule, unless the central bank had an informational advantage, and even if it did have an informational advantage, it could get the same results by simply announcing that information. But if the CB can change M *before* firms can change P, NK's argued, the CB has an *effective* informational advantage, because it can act on its information, while firms cannot.

(This was confused at the time with 2-period price setting, because they assumed full contemperanous information within-period. But if firms set price at the "beginning" of the period, then the shock is revealed, then the CB sets M, then Y is determined, then a new period begins,...the CB has an effective informational advantage.)

You young uns...

The price level then is the quantity of claims on CB's liabilities.

Yes, but that doesn't capture (what I see as) the issue here. The issue is that it is impossible to claim that you have an exchange agnostic model but also have a price stickiness friction that matters. That is, it seems impossible to disentangle how exchange works from whether a price level exists. The NK is not exchange agnostic as SW claims. It simply appears to be Walrasian before any price rigidity enters the picture, because the equations focus only on budget constraints. But the "model," to the extent it exists outside of the canonical equations, always and everywhere claims to include a medium of account -- at least in Woodford's writings. And this means it includes only exchanges that reference a common denominator, irrespective of whether they use an MOE. I see this MOA as very important to the NK model and I believe that SW ignores its importance. Ironically, I think this is because he, like Nick, is way too focused on the importance of the MOE in the actual world, which is in fact written out of the NK model. To a new monetarist, the NK model does look like an RBC model.

Nick would argue that the MOE is not written out of the NK cashless model; instead, CB liabilities become the MOE. I don't think this is quite right. It seems easy to imagine a world that is 100% compliant with Woodford's cashless economy, where people use multiple MOEs, none of which are CB liabilities. You go to the store and swipe you card and the store keeper gets shares in an index fund or ounces of gold or gallons of heating oil -- all commonly used. The price of your exchange, however, is denominated in CB liabilities (dollars) and the swipe creates a second price (the price of the MOE in MOA terms) that is referenced to determined how much of the MOE you must give. The various MOE prices are all fully flexible (centralized auction markets) while the MOA price is sticky and defines the price level. The point is that this world is compliant with Woodford, retains Calvo effects, and does mean that the supply and demand for the MOE is macroeconomically irrelevant as their prices are flexible in terms of the MOA. Yet the price level, exchange and the MOA all matter. Now, whether this world is actually likely or whether the CB could retain control over the MOA without any demand for it as a means of payment is an open question as McCallum said:

Then, with respect to that (unrealistic) case, there is one component of Woodford’s argument that seems
unsatisfactory in principle, namely, his statement that “the unit of account in a purely fiat
system is defined in terms of the liabilities of the central bank” (2000, p. 257). Certainly
the liabilities of the central bank would be a leading contender for the role of the medium
of account (MOA) in an economy with no medium of exchange (MOE), but there is no
necessity that it be the one that prevails. Prices will, in a market economy, be quoted in
terms of whatever medium market participants find most convenient. Just as central bank
currency can be supplanted by some other MOE if its supply is managed too badly (e.g.,
under hyperinflation conditions), the central bank’s contender for the MOA can
conceivably lose out to a private challenger. And it is the unit of account actually
prevailing in market transactions that is of macroeconomic importance; it is stickiness in
terms of prices used in actual transactions that is relevant for the definition of real rates of
interest that influence aggregate demand.15 Thus it is not clear that the central bank can
control the interest rate(s) of macroeconomic importance—Rt in equation (1)—in a world
in which there is no monetary aggregate that facilitates transactions and hence serves as
the dominant medium of exchange and, as a consequence, also becomes the medium of
account.16

Like I said, it's a question of taxonomy which is always going to be somewhat arbitrary. But the other thing that happened in the early 80's was the Volcker recession/disinflation.

The "narrative" I was taught (and it seems John Cochrane has a different one) was that at the time rational expectations and New Classical Economics (not to mention RBC) led many economists to believe that reducing the high inflation of the late 70's would be relatively costless as long as the CB credibly committed to a low inflation level. The resulting recession however was quite severe and unemployment went up a lot (higher than today). This caught those who believed in the power of rational expectations by surprise and made it plain that what was needed were models with more than just sticky prices. One where there was an actual trade off between unemployment and inflation and one where a discussion of a "Cold Turkey" vs "Gradualist" disinflation policy was relevant. And that meant inflation persistence. This spurred the "New Keynesian" work of the 80's (true, it did start earlier but it didn't really take off till mid 80's); before Calvo there were Fisher, Taylor, Mankiw, Akerloff etc., just not in a fully dynamic framework.

(as a side note I actually tend to agree with Steve that the present, Woodfordian, "New Keynesian" model has more in common with the RBC/New Classical one than with that particular strand of work)

In the model you describe above. Suppose that initially p is very high, maybe because m has been high in the past. Then, before firms set prices, the CB announces (credibly) that from now on p will be low and that they will be picking a new low m (plus offset whatever shock to v might occur in that period). Firms believe it, they pre-set p low, and this is achieved with no reduction in output.

This is a "New Classical" not a "New Keynesian" result.

So in the sense that "only unanticipated monetary policy matters" this is NC. In the sense that "this beats a k% rule" I guess you can call it NK.

notsneaky: "So in the sense that "only unanticipated monetary policy matters" this is NC. In the sense that "this beats a k% rule" I guess you can call it NK."

Agreed. But when we try to give empirical content to "unanticipated", we have to answer "how long is the period?". In strictly NC models, like Lucas 72, "unanticipated" means "not part of the information set right now", or "unperceived". What killed NC theory in 1982 was trying to make sense of a world where monetary policy causes a recession because people do not know that monetary policy is currently causing a recession right now. It was all over the news.

Building a macro model where the Lucas Sargent Wallace Policy Ineffectiveness proposition was false (we can do better than k%) was very much the game in the mid to late 70's, and those building such models saw them as NK models. I wish I had my graduate macro lecture notes here (they are in my office) but IIRC Laidler and/or Parkin were already making this NC/NK distinction in 77/78.

"Then, before firms set prices, the CB announces (credibly) that from now on p will be low and that they will be picking a new low m (plus offset whatever shock to v might occur in that period)."

This is related to the "how long is the period?" question, but with Calvo pricing there never is a time before *all* firms set prices.

"And that meant inflation persistence."

As an aside, Calvo pricing does not generate inflation persistence/inertia, it only generates price level persistence/inertia. But macroeconomists went for Calvo pricing because it made the math easier.

Ay, you're definitely right about the inflation persistence part.

But thinking about it a bit more, I'm wondering what you mean by "But macroeconomists went for Calvo pricing because it made the math easier". Easier relative to what? The "fix prices one period in advance" (or "before the shock occurs and CB moves") model you have above is definitely mathematically simpler than ye ol' Woodford model with Calvo pricing, at least in terms of the algebra. Something like the state-dependent pricing model (Caplin-Spulber or such) would be mathematically harder - in fact, I'm not aware of any fully dynamic versions of it though there probably are some - but I don't think that's what you're referring to.

notsneaky: For example. That tiny change in the Calvo model generates inflation inertia, but makes the math a lot harder.

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