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It is only savings in the form of the medium of exchange that can lead to the so-called paradox of thrift.

I don't think this is true. Consider the Hall-Krugman "WORLD'S SMALLEST MACROECONOMIC MODEL" and let M stand, not for money, but for antiques, or land or old paintings. Do the conclusions change in any important way? I don't think so. Nor did Keynes if I understand Chapter 17 of the GT correctly. It's quite possible that I don't of course, or that Keynes was simply wrong. But if his reasoning and my reading are right, it's the store-of-value function of money that's the problem: "...men cannot be employed when the object of desire (i.e. money) is something which cannot be produced and the demand for which cannot readily be choked off." What makes money the problem is not the stuff itself but the nature of the demand for it: low elasticity of substitution etc.

That Hall-Krugman model (I think it's really just a variant of the Barro-Grossman 1971 model) is a model of a monetary exchange economy. "M" has to stand for money. The only way M could stand for antiques is if we changed it to make it a barter model (or antiques were used as money - as a medium of exchange).

If it's a barter model, with antiques as the only store of value, then you cannot get unemployment. The unemployed would like to swap their labour for antiques, but if for some reason they cannot, they simply directly swap their labour for consumption goods directly. Their first-best choice would be to swap labour for antiques (the store of value), but their second-best choice would be to swap labour for perishable consumption goods. Staying unemployed, and wasting their labour, is definitely third-best.

I think you are interpreting Keynes correctly, and that Keynes was wrong.

Let me see if I can find the place where I was arguing the same point in a previous post.

Kevin: have a read of this earlier post: http://worthwhile.typepad.com/worthwhile_canadian_initi/2009/05/imagine-theres-no-money.html

and the comments here (my exchange with himaginary): http://worthwhile.typepad.com/worthwhile_canadian_initi/2009/05/imagine-theres-no-money.html?cid=6a00d83451688169e2011570a08faa970b#comment-6a00d83451688169e2011570a08faa970b

I have no problem with the equation of exchange as long as we define v suitably. My problem is when we move from an identity to a theory. For me, the quantity theorists should be able to explain why velocity has made the short term movements that's it taken. Otherwise, it appears that velocity just moves to make the equation of exchange hold. I was chatting with a group of economists who marveled at velocity's recent declines -- money supply growth and nominal gdp declines. It didn't bother them that they couldn't explain velocity's path. Should short term velocity become another measure of our ignorance?

Forgive my ignorance: What is the Hall/Krugman model?

malcolm: "The world's smallest macro model": http://web.mit.edu/krugman/www/MINIMAC.html

Note the crucial implicit assumption: workers cannot consume their own output. And even if we ruled that out by assumption, there is no market in which one worker can directly swap his output for another worker's output.

In other words, it assumes that all exchange must be of money for goods. That's fine. But where exactly does that assumption appear? The answer is not obvious.

On your earlier comment, what do you think would be a suitable definition of V? (And "quantity theorist" can mean many things to different people.)

But on your basic point: yep, V moves around. So does every other behavioural relation between PY and anything else.


Malcolm at 10:52 has it exactly right. MV=PY and the quantity theory is utterly useless. What determines economic outcomes are equilibrium conditions, Euler equations and the like. It's real risk-adjusted expected rates of return that determine the demand for money, consumption and real investement and hence aggregate demand. All of these things can be expressed without ever mentioning velocity.

Now, you might respond that these things all go into determining velocity but the question is, what is added by reexpressing things as MV=PY? My approach explains V from more primitive things and doesn't actually need to refer to V at all to explain observation and make predictions. The quantity theory on the other hand says nothing without the equilibrium conditions to explain V.

A perfect example is given by case when the natural real interest rate is negative and inflation expectations are too low so the real return to holding money is higher than the natural real rate. The Euler equation correctly predicts that V will fall one for one with increases in M leaving PY unchanged. Now the quantity theory allows us to observe V falling one for one with increases in M but doesn't allow us to explain it and the quantity theory can't tell us that the solution is to promise future inflation.

MV=PY is nothing more than an identity that is useful for heuristic understanding of how PY can exceed M but offers no economic content without the equilibrium equations that can all be expressed without evver mentioning V.


An aside first: I normally interpret the "Quantity Theory" to mean "if you double the supply of money the price level will double". The Equation of Exchange MV=PY is just one of many ways (and not the best way, in my opinion) of arguing for the quantity theory. This is just a semantic point. But I think my use of words is clearer, because you can believe/disbelieve that a doubling of M will cause a doubling of P quite independently of believing/disbelieving MV=PY.

Substance: MV=PY IS an equilibrium condition (or can be interpreted as such), just like I=S. The question is, whether MV=PY is a more or less useful way of formulating an equilibrium condition than M=kPY.

To say the same thing another way:
1. The actual stock of money equals the desired stock,
2. Actual velocity equals desired velocity
are two different ways of formulating what is essentially the same equilibrium condition. Which one is more useful? I was arguing that the second formulation is more useful, in that it reminds us that money is different from other assets, that it is a medium of exchange, and that the ways individuals can adjust their holdings of the medium of exchange are qualitatively very different from other assets.

Yes, Euler equations are also very useful; I would certainly not deny that. But are they always sufficient by themselves?

Let me give you just one example to show they might not be:

Take the World's Smallest Macro Model mentioned above. That model's equilibrium conditions are, essentially, Euler equations. No problem. But where precisely in that model is barter exchange (or even workers' consuming their own output) formally, mathematically, assumed to be impossible? In other words, what equation (explicitly or implicitly) makes "M" in that model really mean "money" (medium of exchange)?

(I think I can answer the question I just posed, but it is not easy, and I am not certain I can answer it properly). There is more to a model than just the Euler equations. And sometimes, by looking just at the Euler equations, and thinking that's all there is to it, you miss what's hidden. And the assumption of monetary exchange in that model is there, but it is well and truly hidden.

Or, to pose my question a different way, how would you rewrite that model so that it allowed consumption of own goods, and barter exchange, as well as monetary exchange, so that the conclusions of the original model came out as a special, limiting case, under certain parameter values?

Here's my (crappy) answer:

I would add an equation that says C = (1-a)Ch + (1-b)Cb + Cm

where C is total consumption, Ch is consumption of home-produced good, Cb is consumption of barter goods, and Cm is consumption of goods bought for money, and a is some sort of dislike of eating your own stuff (preference parameter), b a transactions cost of barter. Then I would explicitly model the barter market, as well as the market where C is exchanged for M, and formally include quantity constraints on Cm from disequilibrium in that market, when solving for the agent's choice problem.

My version would approach the original version when a and b approached 1.


I grant you that the WSMM assumes that workers cannot consume their own output, nor can they work around that restriction by swapping output. That’s par for the course in macro; involuntary unemployment is inconceivable if we can all provide satisfactory employment for ourselves by mowing our own lawns or cooking meals for each other.

Krugman doesn’t spell out what happens when P is fixed above its optimal (full employment) level. That’s fair enough since he is trying to get the reader thinking, rather than providing pat answers. As I visualise it, agents make their decisions in simple textbook GE fashion. A Walrasian auctioneer announces the price vector (1,P,P) for (i) antiques (the numeraire, call it money if you must but to me it’s just a numeraire), (ii) labour and (iii) newly produced goods. The agents make their consumption decisions on that basis, setting: C = ((1-s)/s)(M/P). Output will be set equal to planned consumption.

To get out of the demand-constrained regime M must rise and/or P must fall. Obviously if M is the supply of genuine, 18th century hallmarked antique silver it cannot rise, so the only hope is for the general price level to fall in terms of silverware. But that's ruled out by assumption.

I will readily admit that my approach is simplistic. There may be good arguments for exploring Clower-type concerns about the role of money in macro. All I’m saying is that even a very simple model which ignores those issues can generate the paradox of thrift. Nominal rigidity does the trick.

Kevin: I'm not 100% sure if I am misunderstanding you, or if you are misunderstanding me. Let me try this anyway.

If worker A cannot directly exchange goods with worker B, but must first exchange his goods for antiques, then exchange antiques for B's goods, the antiques are functioning as a medium of exchange. Antiques are money.

You only get a paradox of thrift in that model when the good M (whether it's antiques, gold, or little bits of green paper) serves as a medium of exchange, in an economy where it's either difficult or impossible (by assumption or by building a model to make it so) to do direct barter exchange without going through a medium of exchange.

M in that model is the numeraire, but it's also (implicitly assumed to be) a medium of exchange. You could make labour the numeraire, and it wouldn't affect the results. You could take a purely imaginary good ("venus dust") and use it as numeraire, and it wouldn't affect the results.

I have no quarrel with simplistic models. I have no quarrel with just assuming monetary exchange (as long as some economists try to go behind that assumption). But we should be clear when we are making that assumption, and what it means.

You can look upon V as a kind of global aggregate reserve ratio - I'm not talking about the reserve ratio used by banks, but a more general kind, such as when you decide how much cash you need to keep on hand to pay your bills & the analogous behavior by corporations.

MV=PY is an identity, but to say V and Y are constant (or whatever) is a theory.

Generally V is constant, except for times such as now when people (and banks) are nervous and what to hold a lower reserve ratio of expenditure to money.

Does this make sense?

Alex: yes, but I would say that V is more like a sales/inventory ratio, where money is the reserve inventory in question.

If V is actual V, MV=PY is an identity. If V is desired V, MV=PY is an equilibrium condition.

If you are going to use MV=PY for forecasting, or policy analysis, you need some sort of theory of what determines V, or what might cause it to change. I'm not sure whether I would want to use MV=PY for forecasting or policy analysis. The only point of this post was to point out that MV=PY reminds us of important things that M=kPY does not. And people (economists) need to be reminded of those things. It's more a conceptual issue, than forecasting or policy analysis.

I have always treated MV=PY as an identity. I'm not even sure I understand what you mean by desired velocity. My desired velocity is infinite but I like to have a liquidity reserve with 0 velocity. So higher average velocity, means that unexpected expenses have arisen. Can the unexpected be part of an equilibrium condition (I suppose yes - if they follow an expected distribution).
In fact thinking about this, isn't this making a stock/flow mistake. I have a desired stock of money not a desired velocity of circulation. Changes in the velocity come from changes/imbalances between desired and actual money balances.

I am sure that velocity has some uses.

Desired velocity seems a bit odd to me. What multiple of my money holdings do I want to spend of final goods and services..... hmmm..

This is as opposed to, "how much money do I want to keep in my wallet and checking account."

I think that expenditure primarily depends on income. The income expenditure process does involve money passing through cash balances (as you say.) But, then excess supplies or demands for money disrupt that flow. So, supply and demand for money, with money demand being positively related to nominal income (not necessarily proportional) gets at the heart of the problem.

I must grant, however, that the increasing the demand for money by spending less being always something that can be done, as opposed to selling more, is important. In reality, however, isn't the problem that it is easier to cut spending than to sell more? Perhaps it has something to do with workers being price takers? Suppose someone is a handyman working from time to time when a purchase is needed. And, the pay for each job is negotiated. I want to buy a bottle of wine. So, I will get a job and work one hour at $4. I want to have some money in my pocket. $10 will be enough. I will work 2 hours at $5.

This would be as opposed to having a salary from a regular employer and an irregular pattern of expenditures. Naturally, you adjust spending to ajust money holdings to desired holdings.

If I own bonds, I can sell them if I need money. There usually doesn't seem to be a problem of being unable to find a buyer. Now, if someone is selling wheat, and desires to hold more money, and chooses to sell more wheat to get the money by lowering the price of wheat, then this action, (the lowered price) raises the real supply of money. Choosing to sell more (with the lower price) fixes the problem directly. But does sellng bonds do that? To me, the lower bond prices and higher bond yields would not fix the problem at all--it is a path by which the increased demand for money leads to lower demand for final goods and services. (The Keynesian path that gets emphasized so much.) And so, the things that people really do sell to accumulate money cause the problem too.

My understanding of the paradox of thrift vs. monetary disequilibrium comes from Yeager. He credits Keynes with the fundamental proposition of monetary theory. The individiual can ajust the quantity of money held to the amount demanded by changing spending or selling things. The economy has a whole must adjust the demand for money to the quantity by changing nominal income. Well, that is Keynes version. Yes, we can see how this is a bit like changes in income (real?) cause saving to adjust to invesment. I generally think of the fundamental propostion (as does Yeager, I think) as the market demand for money must adjust to the quanttiy, and I aways think that these adjustments can come through changes in interest rates (away from the natural interest rate,) real income (away from potential income,) or the price level, with the last being the long run equilibrium effect and the first two being distruptive.

Yeager also has pointed out that since money demand is positively related to nominal income, falling nominal income reduces the demand for money. (I guess that follows from above.) And so, the clower business that is discussed in terms of income contrained consumption (following Keynes) is wrong. If less consumption leads to less income, the lower income leads to a lower demand to hold money, and the resuling excess supply of money will result in more expenditure. As explained above, the problem is an excess demand for money at full employment levels of income. When income falls enough to clear up the excess demand for money, then there is no "room" for income contrained consumption to cause further decreases in income. If income falls any further, there is an excess supply of money.

None of that is meant to deny that people might choose to hold more money realtive to their incomes because of various sorts of worries that develop in a depressed economy. But, of course, it is the increased demand for money that causes the problem.

Yeager always said that the clower business might happen in a barter economy! As you have argued that these sorts of models require money, this always comes back to me. Yeager's point was that in a money economy, if the quantity of money doesn't fall, and real income does fall, then the positive relationshion between real income and the demand to hold money should generate an excess supply of money if income falls "too much." Where does that leave the "multliplier" and clower's income contrained consumption?

to make the story more explicit, I think what you mean by an desired velocity is given by desired stock of money / desired consumption (over whatever accounting period we a using = 1 year?). If for some reason imbalances arise then I will change consumption to build up or down the stock of money and velocity will rise or shrink. Part of this may be due to changes in the desired velocity or part may be due to transitory effects as the stock of money is adjusted. Now does this get us anywhere useful?

reason: you can think about desired velocity as just desired money stock divided by PY. But you can also think about desired money stock as just PY divided by desired velocity. The two are formally equivalent. And changes in money stock come from differences between desired and actual velocity.

Bill: excellent comment, as always.

Yes, thinking about velocity seems odd to me, as well. (I have always been a good British M=kPY man). And it's odd because we don't think of other assets this way. But sometimes we need to force ourselves to think in odd ways, especially one that forces us to recognise that money is not just like other assets.

If all markets are clearing, then the two ways of getting more money are equally easy in principle. I can always find a trading partner. It all depends on my elasticity of supply of the things I sell vs my elasticity of demand for the things I buy. But if markets are not clearing, I can't always rely on finding a trading partner. I need to find a trading partner to sell more; I don't need to find a trading partner to buy less. And at the macro level, in a general glut, you know that many people certainly won't find a trading partner to let them sell more.

(And the same problem occurs, only in reverse, when there is an excess supply of money and excess demand for goods, like the repressed inflation in Cuba. You need to find a willing seller to help you get rid of money, but you can't, so you work less instead, so less goods get produced and supplied, so you work even less, and you get the Barro-Grossman supply-side multiplier.)

Yeager is right that Clower quantity constraints can happen in a barter economy too. If the price of butter is too low, I cannot buy as much butter as I want, and so buy more margarine than I otherwise would. That is true regardless of whether I buy them with money or through bartering my labour.

But Yeagar is wrong if he says that this is equally important in barter and monetary economies. A barter economy with n goods has n(n-1)/2 markets, a whole web of them. A monetary exchange economy has only n-1 markets, with money serving as the hub. If the price of money is wrong, it disrupts all markets, because everyone has to travel via the hub and spoke system. If we could switch to barter, we just bypass the hub.

I will return later to the rest of your comment.

Metaphorically speaking, when you compare economy to automobile, M can be deemed as gasoline you pour into engine, V as rpm of engine, P as heat engine emits, and Y as the speed of the car. If there is gasoline leak in engine, then no matter how much you pour in the gasoline, rpm wouldn't go up, and the speed wouldn't go up either. In today's economy, this leak is called liquidity preference or flight-to-liquidity.

If the leak is fixed, then rpm would go up as you open throttle wider, and the car would gather speed. But at some point, the speed would go up no more, and only heat would go up thereafter. The economy/engine in this situation is called overheated. I think Nick is referring that threshold rpm as desired velocity.

Yes, this metaphor is too simplistic and common, but that's as far as I can think of about what desired velocity means in MV=PY equation. I hope this intrigues someone to come up with much better metaphor for understanding.

BTW, Speaking of velocity, the following parable is also interesting:

Bill: continued, bonds and wheat.

If the prices of some goods (like bonds, or wheat) are flexible, then the price of bonds or wheat falls to eliminate the excess demand for money in the market for bonds or wheat. But there is still an excess demand for money in all the other markets. This appears as a relative price distortion (the interest rate is too high, the relative price of wheat is too low), but I see that as more of a symptom, or side effect, than the underlying problem. It may alleviate the fall in output, by reducing the nominal demand for money, but does not cure the problem.

(Of course, someone could also correctly argue, as Adam P does for example, that the excess demand for money is a side effect of the original underlying problem of an excess supply of savings, rather than vice versa. But I would argue that an excess supply of savings, like an excess demand for bonds or antique furniture, can only cause a general glut insofar as it spills over into an excess demand for money.)

I really like your next 2 paragraphs on Yeager, Clower, Keynes, and the paradox of thrift. That seems in line with my thinking. But my mind is not yet clear on the Yeager vs. Clower bit, on the multiplier. I need to read more Yeager.

Nick, you say "But I would argue that an excess supply of savings, ..., can only cause a general glut insofar as it spills over into an excess demand for money.)

Yes, on this we all agree. Thus the fundamental question is WHY the excess demand for money? The answer is that the real risk-return profile of money is more attractive to some investors than is the real risk-return profile of the available real investment. Since nobody, not the treasury or central bank, can magically improve the real return distribution of the available real investments the only solution is to make the real return distribution of money look worse.

I emphasize, again, that this has nothing at all to do with the quantity of money today, people have enough cash to fund desired purchases so giving more money today, in a way that leaves the real return to holding money unchanged, will not change anyone's behaviour.

Adam: we are closer than I sometimes think we are. (Though I am not sure that _everyone_ would agree with my saying "But I would argue that an excess supply of savings, ..., can only cause a general glut insofar as it spills over into an excess demand for money.")

But let me ignore where you and I agree, and focus on where we might disagree.

"Since nobody, not the treasury or central bank, can magically improve the real return distribution of the available real investments..."

I'm not sure about that. In models where we assume that next period (the "future") we are back at full employment, so the relevant AS curve is vertical, that would be right. All the central bank can do (or try to credibly commit to doing) is to raise the future price level, thus lowering the real return on money. But maybe there's also a "near future" in which the AS curve is not yet vertical. To say the same thing a different way, if people thought that near future monetary policy would be very tight, and cause real GDP to be lower, this would reduce today's real return on investment.

"I emphasize, again, that this has nothing at all to do with the quantity of money today, people have enough cash to fund desired purchases so giving more money today, in a way that leaves the real return to holding money unchanged, will not change anyone's behaviour."

Again, I'm not sure. I can see the logic behind the absolute liquidity trap position, in which money and bonds are perfect substitutes at the margin, and desired velocity is indeterminate, so a temporary OMO is irrelevant. But I wonder if it's empirically correct. Not everybody holds Tbills. Some people (and firms) may be (are) liquidity or medium of exchange constrained. Many interest rates are a long way from zero. And it's not obvious to me that those liquidity and risk premia are exogenous with respect to current money supply. Because I don't understand those liquidity premia well enough (and nor does anyone, I think).

Stepping back, I'm really following a more oblique strategy in this post (and others). Rather than tackling the current recession (with 0% Tbills) head on, I am trying first to understand better how money works even in normal times. By backing up and taking a run at it, I might be able to take the limiting case of my better understanding of normal times, as nominal interest rates on Tbills go to 0%. Not sure if it will succeed, but it seems worth a try.

Nick, Very interesting discussion. I'm afraid I went the other way, from MV=PY to M=kPY. I suppose that reflects my medium of account view. I think Kevin is right that any good that is the numeraire is susceptible to the paradox of thrift. Where I would disagree with Kevin is that I would call the numeraire "money," even if it wasn't the medium of exchange. Monetary models are models of the value of the numeraire---that's what they do.

Thus you get a paradox of thrift in the 1930s when people hoarded gold in America, even though gold was no longer the medium of exchange. Why? Because it was still the medium of account. The hoarding of gold in late 1937 raised the purchasing power of gold. Since there was a fixed exchange rate between Federal Reserve Notes and gold, this also raised the purchasing power of cash. This reduced prices, and since wages were sticky, both nominal and real GDP also fell. So the attempt to save gold was just as contractionary as the hoarding of cash would have been.

Regarding V vs k:

k really is the share of gross income that people choose to hold as money.

V is not the average number of times a unit of money turns over in purchases. There are many kinds of money, and there are many kinds of purchases that don't involve final goods. So velocity doesn't mean what the common sense definition suggests it should mean, whereas k does.


The gold standard story doesn't work because redeemability tied gold to the medium of exchange.

If there is a shortage of gold at the current price level, this is going to create a shortage of money because of redeemability. And the shortage of money creates the monetary disequilibrium that forces the price level to drop, crearing up the shortage of gold.

If, on the other hand, we have a decentralized barter economy, where gold is the numeraire, then a shortage of gold doesn't lead to a surplus of everything else. All the counts for everthing else is their relative prices and pair by pair exchanges. With a Walrasian auctioneer, the price of gold gets cleared, along with everthing else, by changing the price level. But, if there is no auctioneer, it is only in the gold market that inability to change the numeraire causes problems.

Suppose we have a gold standard, their is a shortage of gold, and redeemability is suspended, so that gold trades at a premium in terms of the medium of exchange. How is there a paradox of thift? Why does income and output need to fall to bring saving equal to investment?

By the way, I don't agree that gold was no longer used as the medium of exchange in the thirties. It was used as settlement media.

In the Selgin free banking stories using a gold standard, the only monetary use of gold is for interbank settlements. The money used by the nonbanking public is all deposits and banknotes. I don't thing that means that gold is no longer used as money. Settlements among banks, I think, is a use of money--generally.

Scott wrote:
"Thus you get a paradox of thrift in the 1930s when people hoarded gold in America, even though gold was no longer the medium of exchange. Why? Because it was still the medium of account."

However, Keynes wrote:
"We have shown above that for a commodity to be the standard of value is not a sufficient condition for that commodity’s rate of interest to be the significant rate of interest."

Then what is sufficient condition? To be the medium of exchange? The answer is yes, I think. The characteristics which cause liquidity trap as Keynes described in this chapter fit very well into the characteristics of the medium of exchange.

Then, is to be the medium of exchange the only sufficient condition? In other words, is to be the medium of exchange necessary condition to cause liquidity trap? According to Keynes, the answer is no. Let's see what he said in section 5 of the chapter 17.

"Consider, for example, an economy in which there is no asset for which the liquidity-premium is always in excess of the carrying-costs; which is the best definition I can give of a so-called “non-monetary” economy.
since land resembles money in that its elasticities of production and substitution may be very low, it is conceivable that there have been occasions in history in which the desire to hold land has played the same role in keeping up the rate of interest at too high a level which money has played in recent times."

On another point Scott raised:
"V is not the average number of times a unit of money turns over in purchases. There are many kinds of money, and there are many kinds of purchases that don't involve final goods. So velocity doesn't mean what the common sense definition suggests it should mean, whereas k does."

Keynes addressed that question, too. Now, from Chapter 15.

"In a static society or in a society in which for any other reason no one feels any uncertainty about the future rates of interest, the Liquidity Function L2 or the propensity to hoard (as we might term it), will always be zero in equilibrium. Hence in equilibrium M2 = 0 and M = M1; so that any change in M will cause the rate of interest to fluctuate until income reaches a level at which the change in M1 is equal to the supposed change in M. Now M1V = Y, where V is the income-velocity of money as defined above and Y is the aggregate income. Thus if it is practicable to measure the quantity, O, and the price, P, of current output, we have Y = OP, and, therefore, MY = OP; which is much the same as the Quantity Theory of Money in its traditional form."

Here M1 is the money that does turn over in purchases which involve final goods. And M2 corresponds to what I called "leak" in my comment@09:37,June 17.

himaginary, I don't see how your velocity comment addresses my point. I understand that MV=PY is true if you make it a tautology. But it certainly is not true if you define PY as nominal GDP, M as M1, and V as the average number of times a unit of M1 is spent each year. Most transactions are not counted toward nominal GDP, and lots of transactions don't involve M1. Keynes uses the term "theory," so I presume he doesn't mean tautology.

Bill, The term "barter economy" with gold as a numeraire is ambiguous to me. If you have a numeraire, I consider that a monetary economy. Suppose people hoard gold in this barter economy and the real value of gold rises. Assume wages are sticky in gold terms. Now you get mass unemployment. I'd call that the paradox of thrift. If you say that wages aren't sticky, then I'll agree, but that's always true. Even in a monetary economy you need wage/price stickiness to get a paradox of thrift.

Scott: You are right that I ignored the distinction between MV=PY and MV=PT. And it's a valid criticism. And it's the MV=PT formulation that does what I want it to do in this post. Consider two individuals, both have the same income, but A makes his income from buying inputs, working on them, and selling them again, while B uses no purchased inputs. I would expect A to have a higher desired stock of money than B.

But I really don't want to push MV=PY (or MV=PT) too far. I'm not saying it's the only way to look at money, aggregate demand, or is the source of all wisdom. But it does force us to think about money in a way that recognises the way in which money, as the medium of exchange, is different from other assets.

I fully agree with Bill on the medium of exchange vs medium of account issue. A too low price for the medium of account would still allow workers and firms to trade labour directly for goods at an unchanged, equilibrium real wage, unless we also have too low a price for the medium of exchange, and rule out barter. This was the point I was making in my money-as bling post.

Assume J is the stock of jewelry, and we have a demand for jewelry J=kPY, where P is the price of output in terms of jewelry. Start with all prices in equilibrium, and then double all prices in terms of jewelry (or halve the price of jewelry in terms of all other goods). Would we get a halving of real output and employment? Certainly not. Line ups at jewelry stores yes; but not a great depression. Suppose a misguided government passed a law halving the price of jewelry, and imposing price controls on jewelry. Would you and I be blogging about the disasterous macroeconomic consequences of this policy? No. But formally, this is no different from halving the monetary base with sticky prices. Except for the fact that money is also the medium of exchange, and jewelry isn't. (My guess is that the total vale of jewelry is about the same as the total value of base money, so it can't just be a matter of degree.)

I have made a rare sabbatical trip into my office, and the Carleton library, and have been reading or re-reading some old Leland Yeager papers. I am very much following his line here, it turns out. The one thing I don't see in Yeager is his recognition that you need to find a willing partner to buy more money, but you don't need a willing partner to sell less money. But I see a lot of other interesting stuff besides.

Yes, jewelry has a price of its own, and money doesn't, and that is important, because it makes the price of money harder to adjust than the price of jewelry. But even if we make them the same in that dimension, by assuming the government fixes the price of jewelry, there are three other important differences between M=kPY and J=kPY.

1. Jewelry has a market of its own and money doesn't.
2. Money appears on one side of every market, and jewelry appears only on one side of one market.
3. We regularly receive money in the course of our other business, and we accept money not because we necessarily plan to hold it, but because we plan to exchange it for something else. We do not regularly receive jewelry in the course of our other business.

1,2, and 3 are just saying that money is the medium of exchange, and jewelry isn't.

Thinking about MV=PY vs MV=PT some more, I would say that changes in MV cause changes in PT, and changes in T cause changes in Y. (Or, changes in Y are part of the changes in T).

Actually, haven't we seen a reduction in all transactions, not just transactions in newly-produced goods? Like reduced sales and turnover in housing markets, and other asset markets?

I just wanted to point out that V vs k matter was discussed in Chapter 15 of GT. Maybe I should have rather cited the beginning paragraph of the chapter:
"WE must now develop in more detail the analysis of the motives to liquidity-preference which were introduced in a preliminary way in Chapter 13. The subject is substantially the same as that which has been sometimes discussed under the heading of the Demand for Money. It is also closely connected with what is called the income-velocity of money; -- for the income-velocity of money merely measures what proportion of their incomes the public chooses to hold in cash, so that an increased income-velocity of money may be a symptom of a decreased liquidity-preference. It is not the same thing, however, since it is in respect of his stock of accumulated savings, rather than of his income, that the individual can exercise his choice between liquidity and illiquidity. And, anyhow, the term “income-velocity of money” carries with it the misleading suggestion of a presumption in favour of the demand for money as a whole being proportional, or having some determinate relation, to income, whereas this presumption should apply, as we shall see, only to a portion of the public’s cash holdings; with the result that it overlooks the part played by the rate of interest."

As for tautology, he also wrote the following footnote at the end of the paragraph I cited in my previous comment:
"If we had defined V, not as equal to Y/M1, but as equal to Y/M, then, of course, the Quantity Theory is a truism which holds in all circumstances, though without significance."

And I don't think Keynes expected aforementioned "a portion of the public’s cash holdings", or M1, could be measured exactly. So of course it's a theory thing. Therefore, the distinction between MV=PY and MV=PT, and/or what nominal GDP actually counts, is not very important here. The important thing is, I think, how he related this equation to his theory of liquidity preference.

We sometimes change the price of money. It's called redenomination, and it doesn't entail disastrous macroeconomic consequences, if conducted properly.

As for paradox of thrift, I side with Kevin and Scott in that goods other than the medium of exchange can cause the problem. As I noted in himaginary@11:19AM June 18, Keynes asserted in effect that excess demand toward medium of exchange is not necessary condition for liquidity trap. And, it's worth emphasizing that what is important is not what happens in goods-money market per se, but what happens in labor market as a result. If there is massive excess demand toward the high-liquidity goods which can be supplied without employing much labor force, then there would be disequilibrium in labor market. In this process, it doesn't matter whether the demanded goods is the medium of exchange or not, or excess demand appears in only one goods market or in n-1 goods markets.

Of course not every goods can cause the problem, but gold certainly can, as Keynes pointed out as follows:

"Unemployment develops, that is to say, because people want the moon; - men cannot be employed when the object of desire (i.e. money) is something which cannot be produced and the demand for which cannot be readily choked off. There is no remedy but to persuade the public that green cheese is practically the same thing and to have a green cheese factory (i.e. a central bank) under public control.

It is interesting to notice that the characteristic which has been traditionally supposed to render gold especially suitable for use as the standard of value, namely, its inelasticity of supply, turns out to be precisely the characteristic which is at the bottom of the trouble."

himaginary. With all due respect to Keynes, the quotations you provide are horribly confused. His statement that if you define V as not equal to Y/M1, but rather equal to Y/M, then it is a truism, is just a nonsensical statement. If you "define" V either way it is a truism. I've never sensed that Keynes understood the MV=PY equation, nor does he seem to have any idea what the "Quantity Theory" is. The Quantity theory is a hypothesized causal relationship. MV=PY is not the "Quantity Theory," It's not a theory at all.

His theory of liquidity preference is worthless, as it doesn't account for inflationary expectations. Maybe "worthless" is too strong, but say valueless for it's major application--the liquidity trap.

Nick, The problem with MV=PT is that it tells us very little about aggregate demand. Only a tiny percent of "T" is sales of final goods. The vast majority is financial transactions. I am interested in NGDP, which is why I like PY on the right side.

Bill said that if there is a shortage of gold, then there is automatically a shortage of money. Why is this so? Suppose an increase in the demand for gold causes the value of gold to double and all prices fall in half. Now the transactions demand for cash falls in half. Assume the supply of cash has not yet changed. Where is the shortage of cash? Isn't there a surplus?

I do agree with you that if workers can barter goods for labor directly, then wages are flexible and there is no involuntary unemployment. But this thought experiment doesn't carry much weight with me because I think the business cycle (or disequilibrium if you prefer) occurs precisely because wages are not sticky.

I would also be interested in Bill's view on your assertion that excess demand in the gold market doesn't imply excess supply of all other goods. I don't know enough about Walrasian economics to comment, but I wonder if this is the generally accepted view. If so, why? And if not, why is the general view wrong?

I also am a bit confused about the jewelry example. I have trouble following examples that are not what I think of as the key macro problem. So in my view depressions are caused if the demand for jewelry rises and jewelry is the medium of account. In that case if the equilibrium price level falls in half, but wages and prices don't change then you have problems. AD starts falling. Or if prices fall but wages don't they real wages rise. The example you provide is the opposite, you assume all prices double. So I guess the point is that prices are too high. And then what? Are they free to then fall back to equilibrium? I'm not clear as to what drives P and Y in your model. Are prices held at twice their equilibrium level forever? Or are they expected to fall? Expected deflation can certainly cause a depression. I confess I am not used to thinking about models where prices are rigid and out of equilibrium forever.

I like to go back to my old wildcat banking example. To me the bottom line is: What causes deflation? And my answer is that it is caused by a rise in the real value of the medium of account. And deflation is what causes depressions. And it is sometimes true that when the medium of account is rising in value, so is the medium of exchange. But not always. Under wildcat banking, currency notes traded at a discount. Thus you might have had a period in American history where the medium of account (gold) gained value, say because of more industrial use of gold. But there might not have been any shortage of currency. Suppose during this period the banks kept churning out increasing numbers of banknotes, each of which traded at greater and greater discounts to the par value. The medium of account says tight money and the medium of exchange says easy money. In this "horse race" the medium of account beats the medium of exchange, doesn't it? You'd have deflation and depression, despite plenty of cash.

Bill asked:

"Suppose we have a gold standard, there is a shortage of gold, and redeemability is suspended, so that gold trades at a premium in terms of the medium of exchange. How is there a paradox of thrift? Why does income and output need to fall to bring saving equal to investment?"

The answer is because if the public desires to hold twice as much gold as a fraction of nominal income, and the supply of gold is fixed in the short run, then nominal incomes must fall in half to accommodate their desire. If gold were not the numeraire then the nominal price of gold could rise, but we have ruled out that option.


"I do agree with you that if workers can barter goods for labor directly, then wages are flexible and there is no involuntary unemployment. But this thought experiment doesn't carry much weight with me because I think the business cycle (or disequilibrium if you prefer) occurs precisely because wages are not sticky."

Presumably that's a typo in the last line, and you meant to write "...wages are not flexible"?

Barter doesn't necessarily mean wages are flexible. We can at least imagine that both wages and prices are sticky, and W/P is sticky. Suppose jewelry is the medium of account, we start in equilibrium, and hold all prices and wages fixed, then an accident destroys half the stock of jewelry. There is an excess demand for jewelry, clearly. But if jewelry is not required to buy and sell labour or goods, this should not cause unemployment. The real wage W/P stays at the equilibrium level, labour demand and supply curves don't shift, so employment stays the same.

Will AD fall? There might be a tiny temporary fall in AD, as people buy less newly-produced goods in order to buy more jewelry, but as soon as they realise there is no more jewelry to buy, they go back to buying what they did before.

I'm not sure about the wildcat banking example. How acceptable were those wildcat notes as media of exchange? My guess is that they were not universally acceptable, and did not have a uniform value (some people would be willing to accept them at par, others not at all). So there might indeed have been a shortage of media of exchange as we know it now, because those notes were not very liquid? They had high transactions costs?

Actually, that is an interesting case. Because if those notes had high transactions costs (it was costly to find out if they were genuine, and how convertible they were), then what you have is an economy that is halfway to barter.


There isn't a lot of value in going on and on about barter economies that use "numeraire."

Still, I think you are mistaken. And I will make one more effort.

Suppose that that equilibrium exchange ratio between bread in labor is 20 minutes of labor for a loaf of bread. In the labor/bread market, people who want to supply labor and demand bread do so, and are matched by people who what to supply bread and demand labor. There are, of course, problems with a double coincidence of wants.

Now, further, let us suppose that oranges are the medium of account, with an orange defining "the orange." Suppose in the initial equilibrium, wage is 9 oranges and the price of bread is 3 oranges. (20 minutes per loaf of bread.)

Now, we are going to assume that the orange price of labor is sticky. And, if people try to sell more labor for bread, the bakers raise the orange price of bread. If the bakers can't get the labor they want for their bread, they lower their orange price. But, that is not happening now. The equilibrium exchange ratio is 20 minutes of labor for a loaf of bread. And the prices of 9 oranges an hour and 3 oranges a loaf reflect that relative price.

Over in the orange market, the price of oranges is always one orange. So unlike the bread market, if people want to exchange labor for oranges, the price of oranges cannot rise. And, we are assuming the orange price of labor won't fall.

The orange prices of just about everything need to fall in order to raise the relative price of oranges and clear the orange market. This is true, and you are assuming, then, that there is an impefect market process that will make this happen. And because wages don't fall, unemployment is generated.

Where is this market process?

Nick is pointing out that over in the bread/labor market, the relative price of bread and labor has not changed. It should clear.

He is arguing that even no oranges are the medium of account and the only way to clear that market is for their to be lower prices (and wages) in terms of oranges, the actual impact of a shortage of oranges will be like a shortage of any other good faced with a price ceiling.

Sure, if their is a price ceiling on gasoline, the frustrated gasoline buyers do something else with their income. It doesn't result in a generalized inability to sell on other markets.

While there is no price ceiling, the orange definition of the orange is acting as one. (And, by the way, the obvious solution is for the orange price of an orange to change--making the unit of account abstract rather than defined in terms of the orange. OK, it is complicated enough.)

If, everyone is selling their bread, labor, and what have you for oranges, and there is a shortage of oranges, then there is going to be a difficulty of selling everything. Well, that means that oranges are the medium of exchange, not simply the medium of account.

If you want to discuss what wildcat banking really was about, I can explain to you why I think that that shortages of gold generated shortages of banknotes without causing lower discounts on banknotes so that there was a shortage of gold and equilibrium in the banknote market.

But I have no problem with imagining such a situation. Now... how exactly does a shorage of gold generate surpluses of other goods and services so that their prices fall? Yes, lower prices of other goods will raise the relative price of gold and clear the market. Market clearing require that other prices fall. Market clearing requires surpluses of other goods. But how?

For a related puzzle, what exactly determines the discount on all the banknotes? In reality, banknotes traded at par in the city of their bank of issue, and the discounts were mostly about transportation costs. When a bank was actually in default, the discount had to do with transportation to the capital (where the collateral was) and the value of the collateral (because bank default often occurred because the "official" collateral, say, state government bonds, were in default.)

But we can imagine a system where the "wildcat banks" are effectively issuing fiat currency and some kind of scarcity value determines their price in terms of the unit of account. What is this market about? Is it perhaps the market where these banknotes trade for gold? Then, if their is a shortage of gold, either the nominal price of gold rises above is "official price" or else, we assume this is impossible, and so when there is a shortage of gold and a surplus of a particular banknotes, we determine the market price of the banknotes. Being denominated in gold, that would be a discount (or premimum.) But, of course, a shortage of gold results in a lower price of the banknotes being exchanged for gold. And this creates a shortage of the banknotes.

If we imagine, as you seem to be, that the banks are issuing lots of banknotes and creating inflationary pressure, then yes, this raises the demand for gold (and everything else.) The shortage of gold results in a lower price of banknotes. And so, the effort of the banks to expand the quantity of money just results in a lower price of banknotes.

But, suppose the problem is with gold. A greater demand for jewelry. People try to buy gold with banknotes (like always.) But, rather than the price of gold rising, the price of banknotes fall. This creates a shortage of banknotes. And it is that shortage of banknotes that causes people to reduce expenditures on everything. This lowers prices of goods and services in terms of gold (that is how prices are quoted) and so the relative price of gold rises.

A surplus of banknotes created by banks doesn't magically result in lower prices for them. It causes inflationary pressure, but the market for gold is assumed to determine the discount on banknotes, and so reverses the problem. I do think that this would work no better than a scheme based on redeemability or even a central bank contracting in response to inflationary pressure.

But, changes in the gold market only impact the price level through their impact on money. In the case of redeemability, this is obvious. If there is a shortage of gold, people redeem money for the gold they need to make jewelry. The monetary contraction lowers prices, raises the relative price of gold, and clears the market. This works even if the monetary system uses no gold, or that the amount of gold it uses is independent of the quantity of money and the price level. (With indirect redeemability, the medium of account isn't used by the monetary system)

But, the special case where the money all trades at discounts and premiums doesn't avoid this problem. Sure, banknotes can trade against one another and cause changes in the premiums against one aother. But what determines the exchange rate with gold? What happens?

With no Walrasian auctioneer, monetary disequilibrium is what makes the price level ajust to clear the market for the medium of account.

I have never worried much about barter economies with mediums of account. But I think Nick's logic is sound.

"His theory of liquidity preference is worthless, as it doesn't account for inflationary expectations."

I think that's because it aimed to account for deflation. And, with due respect, I think he succeeded in it, as Krugman once praised in his blog:

himaginary: but deflationary expectations are just negative inflationary expectations, so Scott's point is correct. On the other hand, it is easy to modify the theory of liquidity preference (at least when it is added to the theory of loanable funds in the ISLM model), by adding a "wedge" for expected inflation between the IS and LM curves. See this earlier post of mine: http://worthwhile.typepad.com/worthwhile_canadian_initi/2009/02/is-lm-and-two-wedges-understanding-the-second-wedge.html

Nick: But inflation occurs when economy is in full-employment condition, and deflation occurs when it is not. So there is asymmetry in generating mechanism. And liquidity preference causes problem only in the latter case. I think, as Krugman praised, Keynes's contribution on clarifying this matter shouldn't be underestimated (I thought you agreed with Krugman when you posted this comment).

BTW, reading Scott's blog posts such as this and this, now I understand that he thinks that the zero bound of nominal interest rate doesn't really pose a problem, therefore liquidity trap is not really a trap. It was gold standard that caused problem in 30s, and we Japanese just happened to have a very bad central bank in 90s. And Keynes accomplished virtually nothing in GT. These ideas may be proved to be correct in the future, but as for now, they don't seem very persuasive (although I do agree that BOJ made bad mistakes in past 20 years).

Nick, Yes, that was a typo. Regarding sticky wages and prices, my view is that monetary shocks cause unemployment because they raise real wages. That is, I think wages are much stickier than prices, especially asset prices. In a model where the real wage and nominal wages are fixed, I don't know what would happen. My hunch is that output would fall, but how fast that would happen is something I don't know. You might be right that the jewelry market would be so small that it wouldn't matter much.

Bill, You said:

"With no Walrasian auctioneer, monetary disequilibrium is what makes the price level adjust to clear the market for the medium of account."

This is the monetarist transmission mechanism. But I now think the Ratex mechanism is actually the key. More demand for gold raises the real value of gold, this depresses prices in one of several possible ways. In an open economy prices fall immediately through PPP, the quantity of money plays no role. It will adjust later. That's basically what happened in 1933 (except the price of gold changed, not the demand, and prices rose.) In a closed economy an increased demand for gold will reduce the future expected price level, which will immediately reduce current prices through speculation. Real wages rise and output falls. Now it is true that one can also tell the story with money, especially if money is a dual medium of account. But I think the gold market is more revealing, because that's where the action was. The Fed would continually adjust the quantity of money to reflect changes in the world supply and demand for gold. So the inflation and deflation story can also be told through the medium of exchange in that case. But my point is that gold is the causal factor, the quantity of money is then endogenous. Gold is the dog, money is the tail. It doesn't have to be that way, but I believe it usually was. (BTW, I keep talking about the gold standard because with fiat money the media of account and exchange are the same, so there aren't any important implications for our debate (that I can see).)

Himaginary and Nick, Yes, you can add a wedge, but it doesn't solve the problem if you continue to assume that monetary policy only shifts the LM curve. But that's not even close to being true. Monetary policy shifts the IS curve, even in a real interest rate diagram, and that's something that even modern Keynesians often overlook. Some people think the Wicksellian equilibrium interest rate is now negative. How did that happen? Because tight money in 2008 drove NGDP sharply lower. That's not something Keynes understood at all.

BTW, I was going to make the same point as Nick, Keynes overlooked the Fisher effect in both directions.


I don't just speculate that the gold standard caused the so-called "liquidity trap" of 1932. The WPI had fallen 50% in four years. In the first four months after we left the gold standard it rose 14%. The Keynesian model, even the new Keynesian model has no explanation for that sharp price level increase. None. Those models say prices rise when you are at full employment. Well we were farther from full employment than ever in 1933, and yet we had very fast inflation.

I'm not the only one who saw Japan's monetary policy as being deflationary. How else can you explain why they raised rates several times when Japan was in deflation? If you have a monetary policy so tight as to cause deflation, then obviously rates will fall close to zero, but that's no liquidity "trap" in the sense of something they are trapped in. Even Krugman argued they could escape with a policy of inflation targeting. So I don't really differ with him there. I just think his praise of Keynes is silly, because his model says Keynes's theory of the liquidity trap was wrong.

himaginary: (Japan? Wow!): Yes, Keynes made significant contributions to Macro. In many ways I am a Keynesian (but not just a Keynesian). And liquidity preference was one of those contributions. But it wasn't enough. We need to integrate liquidity preference, loanable finds, and the wedge of expected inflation/deflation between real and nominal interest rate. Regardless of what causes inflation/deflation, and expected inflation/deflation, we need to allow expected inflation/deflation to affect aggregate demand.

Scott: I am comfortable with the idea that monetary policy can affect: LM; IS; and the wedge of expected inflation/deflation between them.

Ratex can certainly add a short-cut on any transmission mechanism. But I think there must be some underlying non-ratex transmission mechanism that would (eventually) work anyway, without Ratex. In other words, if something is going to happen, with or without ratex, ratex will just help the economy jump quickly to the final destination.

"The WPI had fallen 50% in four years. In the first four months after we left the gold standard it rose 14%. The Keynesian model, even the new Keynesian model has no explanation for that sharp price level increase. None. Those models say prices rise when you are at full employment. Well we were farther from full employment than ever in 1933, and yet we had very fast inflation."

That is interesting. What happened to nominal wages, when prices rose 14%. Did they stay the same? If so, I can make sense of it. (Wages were stickier than prices). If nominal wages rose by (roughly) 14% too, that is a real puzzle.

"BTW, I was going to make the same point as Nick, Keynes overlooked the Fisher effect in both directions."

I think Keynes did address Fisher effect, or distinction between real and nominal interest rate, in his own unique way in chapter 17 of GT. I referred to that idea in previous comments like this. Although methodology may be rather crude, the implication of his analysis there is same as that of Krugman model: What happens is that the economy deflates now in order to provide inflation later.

FYI: Japanese economist Yoshiyasu Ono elaborated that Keynes's idea in chapter 17 in the following paper:

"Even Krugman argued they could escape with a policy of inflation targeting."

Krugman was the most vociferous voice to put pressure on BOJ for recent ten years. And there were also a bunch of Japanese economists and bloggers called "Rifure-ha", or "reflation school", who asserted BOJ should act more aggressively. The debate between reflation school and their critics went on and on. But nowadays the reflation school seems to have lost momentum a bit. Not least of the reasons for that setback is that Krugman himself seems to have backed off (e.g. his unsatisfactory response to your open letter). He now seems to be saying that though BOJ's policy was not perfect, it did what must be done after all. At one point, he wrote a sentence like this:
"Why did almost everyone believe in the omnipotence of the Federal Reserve when its counterpart, the Bank of Japan, spent a decade trying and failing to jump-start a stalled economy?"

"The WPI had fallen 50% in four years. In the first four months after we left the gold standard it rose 14%. The Keynesian model, even the new Keynesian model has no explanation for that sharp price level increase. None. Those models say prices rise when you are at full employment. Well we were farther from full employment than ever in 1933, and yet we had very fast inflation."

I think that is analogical to what happened in Argentina during and after currency board. Krugman warned deflationary pressure of currency board as early as in 2001:

I think that's something like a spring bounces back. But was all the deflationary pressure during the Great Depression due to gold standard? I think it's still an open question.

FYI, let's briefly explain what happened in contemporary Japan. Before the Great Depression, Japan was already in crisis since 1920, as an aftermath of the bust of boom during WW I. GDP deflator went negative since 1925 (1925-29 average=-2.3%). And foolishly, it returned to international gold standard in Jan 1930 with pre-war parity level. Naturally, deflation aggravated (1930=-10.7%, 1931=-9.8%), and there was a change of government. New government departed from gold standard in Dec 1931, and took a reflationary policy including fiscal stimulus. Then the economy recovered. The minister of finance of the new government, Korekiyo Takahashi, is said to have conducted Keynesian policy before Keynes, and is still revered in Japan.
Source (sorry, in Japanese): http://d.hatena.ne.jp/econ2009/20081219/1229666440

Nick, Sorry for the slow reply, I have had problems with my blog. Nominal wages were stable during that 4 month period. That's one reason why I like the sticky wage model. And I agree with you that there must be some none Ratex mechanism in the long run. For me, it is that prices are flexible in the long run, and the excess cash balance mechanism makes the QT hold in the long run.

himaginary, Good questions. I am relying on p. 142 in the GT, where Keynes doesn't seem to understand the Fisher effect. Is there a specific page in chapter 17 I could look at?

I will never understand Krugman's wildly inconsistent statements on Japan. Didn't the Japanese monetary base fall in 2000 and in 2006? Indeed wasn't the fall in 2006 quite sharp? Didn't the BOJ raise rates in 2000 and in 2006? How can someone seriously claim the BOJ has been trying to create inflation for 10 years? I don't understand what Krugman is saying there. The BOJ is very conservative. And I can also find recent quotes where he supports inflation targeting and QE. So who knows what he really thinks.

I don't think 1933 was at all like a spring bounceback, nor was Argentina. They were both caused by currency depreciation. In fact the statistical evidence overwhelmingly supports that argument. Both daily commodity indices and the weekly WPI in the US in 1933 strongly correlate with the dollar price of gold---which was FDR's policy instrument.

You obviously know more about Japan than I do, but I think currency depreciation is much more powerful than fiscal stimulus. Obviously doing both makes a recovery even more certain. The US recovery correlates more with monetary policy (including exchange rates) than fiscal policy. But I don't know much about Japanese history. When I used to study the gold standard I do recall the unfortunate timing of their gold resumption. (BTW, I am interested in Japanese culture and hope to visit someday.)

"I am relying on p. 142 in the GT, where Keynes doesn't seem to understand the Fisher effect."

P.142 seems prelude to chapter 17. The uniqueness of Keynes's idea, as I understand it, is in that he redefined the Fisher effect as arbitrage between goods and money. From his perspective, real rate of interest is interest on real goods, and money rate of interest is interest on money (of course). If the former is smaller than the latter, money becomes more valuable than real goods, hence the price of goods goes down. It goes down to the point where it bounces back, the point where expected change of the price of goods becomes positive. Then, money rate of interest equals real rate of interest plus expected rate of inflation, i.e. the Fisher equation holds. And this mechanism is exactly identical to what Krugman described as "What happens is that the economy deflates now in order to provide inflation later" when he explained his model .

I agree that currency depreciation caused the needed inflation in US and Argentina (maybe it's needed in Latvia now). What I meant by a spring bounceback is that too strong exchange rate posed by gold standard or currency peg suppressed domestic price level too low, so when the burden was removed, it went up like a spring snaps back. I think this explanation is in line with conventional monetary and forex ideas.

Let me add a few episodes about Japanese pre-WW II history. It may help to understand current seemingly strange Japanese policy.

Korekiyo Takahashi's reflational policy I mentioned in my previous comment caused currency depreciation, too. But it also caused frictions with other countries. Then, those other countries such as US and UK, organized bloc economy and tried to shut out Japanese import. So Japan tried to shape its own bloc, and invaded China and east Asia. You know what happened after that. Maybe the memory of those dark ages, along with images of US labors smashing Japanese goods with hammer in 80's, is one of the reasons why Japanese policymakers are so reluctant to depreciate its currency.

And, Takahashi's reflational policy also included direct BOJ underwriting of government bonds. When Takahashi tried to balance budget and slash military expenditures after economy recovered, he was assassinated by army. Thereafter, BOJ became almost a wallet of army, which prepared the ground for hyperinflation after WW II. Many people say that trauma is the main reason BOJ takes too conservative policy nowadays.

Himaginary. On the Krugman point it would help me if you could tell me exactly where in the paper he makes his argument. But let me add on to what I said before. Japan has averaged -1% deflation. We have averaged 2% inflation (3 points higher.) The question is what is best? If -1% is best, then there is no Japanese "problem" to be solved. If 2% is best, then why call it "irresponsible" as Krugman does. I just think his use of terms, while interesting and provocative, can also cloud the real issues. I think the BOJ should target 2% inflation or 4% NGDP growth.

I see your point about exchange rates and springs, but would add this. The US wanted some inflation in 1933, and got some with currency depreciation. Argentina got a huge amount of inflation, because the devalued way too much. So I think you can't just look at the fact of depreciation, but also the amount. I sometimes refer to these examples to prove a point, but in practice I would not like to see such a sharp depreciation in Japan, I think a much smaller one could achieve their goals.

I do know a bit about the history, although not as much as you. And by the way, I oppose US attempts to tell Japan what to do. But I don't think this fully explains things in Japan:

1. If Japan were simply to keep the yen from appreciating, this would over time lead to similar inflation rates as the US (not identical of course.) In fact, the yen has risen strongly in the last couple years. The BOJ could have at least prevented that from happening.

2. If this is really the explanation, then the liquidity trap is not really a problem for Japanese fiscal and monetary policy to solve, but rather an inevitable result of a currency policy forced on Japan by the US and others. It is very similar to what I argued about the 1932 liquidity trap in the US---that the real problem was the gold standard. That is a political issue. My view is that the US no longer worries about Japan as much as in the 1980s, and that the Japanese could have a more expansionary policy without too much pushback.

3. If this is the US policy, it is foolish, as what our firms gain from a stronger yen, they lose from the deflation lowering the costs of manufacturing in Japan. This is the famous example that central banks can't set real exchange rates in the long run.

The sentence of Krugman I quoted in my previous comment, "What happens is that the economy deflates now in order to provide inflation later", can be found in the page I linked:
It's at the end of section 2. This paper (or essay) can be read as a summary version of the famous "It's baaack" paper, so I recommend to read the whole thing.
As for the use of terms, may be the term "inflation target" was not so widespread as nowadays when he wrote this. I think that's why Krugman chose more eye-catching phrase.

I think BOJ did not aim -1% deflation rate on purpose. Rather, they were always too early to judge the economy recovery point. I think each time they raised interest rate, they sincerely believed that economy would recover and achieve needed inflation rate in spite of their action. So in my opinion, they were more fool than malign.

In 2003, MOF got tired of relying on BOJ monetary policy, and took action by itself. It intervened in forex market in unprecedented scale. How big was it? Normally, we have capital account deficit, but that year we had capital account surplus. Please see first graph in my blog post where I tried some analysis on this intervention:

But it didn't achieve currency depreciation. Rather, what it did was preventing yen from appreciating. Anyway, Japan is said to have recovered thereafter, and the MOF official who conducted this intervention, Zenbe Mizoguchi, is regarded as hero by the so-called "reflation school" (which I explained above) in Japan.

Why didn't the intervention continue? Well, according to John Taylor's "Global Financial Warriors," he and Alan Greenspan wanted to stop it there. They thought it was enough, although Japan did not fully escape from deflation at that point.

Himaginary, The Krugman model you refer to is a flexible price model, where deflation does not cause any unemployment. But more importantly it is very similar to gold standard models, as it assumes the future price level is fixed. I have argued in several published papers that gold standards will produce "liquidity trap-like" results, but without a true liquidity trap. In that situation, prices could rise, and then be expected to fall. But it is a very artificial assumption.

As you correctly point out with your 2003 example, Japan was not "trapped" in deflation, it was a question of whether they were willing to engage in currency depreciation. When they did so, things got a bit better, but they didn't push it far enough to get actual inflation. To me, this is the key issue. The almost steady fall in the Japanese GDP deflator since 1994 is no accident. Either the Bank of Japan doesn't understand monetary economics, or they are intentionally targeting a roughly 1% deflation. Remember that if you are truly targeting a stable price level, and if prices fall 1% a year for three years, you should now be targeting 3% inflation to catch up to your target path. It is pretty clear to me that the BOJ does not want any inflation, despite 15 years of mostly falling GDP deflator. So I no longer buy the excuse that the BOJ is simply making mistakes. But even if they are, that's not being "stuck" in a liquidity trap (as Krugman sometimes asserts) it is a problem of continuing to make mistakes--a very different type of problem.

"it assumes the future price level is fixed."

I would rather say that it assumes the future price level, P*, is in equilibrium where full-employment is accomplished. Krugman tried to analyze how economy arrives at equilibrium, not at some artificial price level.

It's true that if P falls enough, it won't cause unemployment. That's what Krugman said in the last paragraph:
"Of course, it is not necessary that Japan do anything. In the quasi-static IS-LM version of the liquidity trap, it appears as if the slump could go on forever. A dynamic analysis makes it clear that it is a temporary phenomenon - in the model it only lasts one period, although the length of a "period" is unclear (it could be three years, or it could be 20). Even without any policy action, price adjustment or spontaneous structural change will eventually solve the problem. In the long run Japan will work its way out of the trap, whatever the policy response. But on the other hand, in the long run ..."

Himaginary, I must strongly disagree with this assertion:

"I would rather say that it assumes the future price level, P*, is in equilibrium where full-employment is accomplished. Krugman tried to analyze how economy arrives at equilibrium, not at some artificial price level."

Full employment equilibrium does not determine the price level. Even in the Keynesian model, at best it determines the minimum price level. Once the SRAS curve becomes vertical, prices can go up to infinity. Indeed that is the whole problem with the liquidity trap view, they ignore the fact that policymakers can raise the future expected price level as high as they wish. But it is even worse, because the (old) Keynesian model is wrong about the SRAS. Prices can rise even without being at full employment. As the US saw in the Depression a currency depreciation will cause rapid inflation even in a depressed economy. So I don't think the full employment level has anything useful to teach us about inflation.

I admit that my statement about P* was sloppy. Thank you for pointing it out. And I think it's time to leave here (it's fortnight-old post now), so I'd like to concentrate on comment at your blog about this theme hereafter.

Thank you for letting us occupy here for so long.

himaginary: No problem! It is good to see a good discussion going in the comments.

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