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On the neutrality of money, Keynes wrote,

In my opinion the main reason why the problem of crises is unsolved, or at any rate why this theory is so unsatisfactory, is to be found in the lack of what might be termed a monetary theory of production.

The distinction which is normally made between a barter economy and a monetary economy depends upon the employment of money as a convenient means of effecting exchanges - as an instrument of great convenience, but transitory and neutral in its effect. It is regarded as a mere link between cloth and wheat, or between the day's labour spent on building the canoe and the day's labour spent on harvesting the crop. It is not supposed to affect the essential nature of the transaction from being, in the minds of those making it, one between real things, or to modify the motives and decisions of the parties to it. Money, that is to say, is employed, but is treated as being in some sense neutral.

That, however, is not the distinction which I have in mind when I say that we lack a monetary theory of production. An economy, which uses money but uses it merely as a neutral link between transactions in real things and real assets and does not allow it to enter into motives and decisions, might be called - for want of a better name - a real-exchange economy. The theory which I desiderate would deal, in contradistinction to this, with an economy in which money plays a part of its own and affects motives and decisions and is, in short, one of the operative factors in the situation, so that the course of events cannot be predicted, either in the long period or in the short, without a knowledge of the behaviour of money between the first state and the last. And it is this which we ought to mean when we speak of a monetary economy.

vimothy: nice quote. But even here, assuming Keynes is absolutely right, is it the dollar amount of money that people care about,"..and affects motives and decisions..." or is it the real amount? Because if it's the real amount, we still get neutrality.

My understanding of Keynes is that he considered the possibility that the dollar amount of money might be what people cared about, not the real amount.

If people may make an investing decision between bonds and dollars, then they demand money as a store of value, not a medium of exchange. In this case their demand for money is nominal, not real.

JP: You might be right about Keynes. i don't know.

But i strongly disagree with your second point. When people demand money as a store of value, they only care about the real value of their store, not the nominal value. They are thinking "will these dollars buy me enough food to stay alive over the winter?". You can't eat dollars.

If we used cattle as money, it would be different.

Out of curiosity, what about if we used stocks (i.e. equities) as money?

I'm not sure if the demand for stocks is considered by economists to be a real demand or a nominal demand. After all, we can't eat stocks. Dunno.

But would an economy with stocks as money be similar to one with cowrie shells, cattle, or gold as money? (i.e. one in which "we can't separate the physical from the monetary dimensions of money")

What's the empirical evidence for money illusion? A quick google search seems to suggest it's quite prevalent.

Patrick: maybe. But I can never tell if that's the "Man bites dog" bias in reporting results. (We only look for and report the rare ones.)

Generally though, the existence of money illusion would be an argument that any positive or negative inflation is a bad thing. Because it confuses people. Best to target 0%. Or, at least, decide on a target and stick to it, so that people can eventually adjust.

One anecdote: I have been impressed recently with just how much difficulty accountants have with the idea of adjusting balance sheets for inflation. They really don't like adjusting historical book values for the CPI. It just opens up a whole can of worms they don't want to think about. That's a form of money illusion.

Keynes goes on to write (in "A Monetary Theory of Production"),

One of the chief causes of confusion lies in the fact that the assumptions of the real-exchange economy have been tacit, and you will search treatises on real-exchange economics in vain for any express statement of the simplifications introduced or for the relationship of its hypothetical conclusions to the facts of the real world. We are not told what conditions have to be fulfilled if money is to be neutral. Nor is it easy to supply the gap. Now the conditions required for the 'neutrality' of money, in the sense in which this is assumed in... [for example] Marshall's Principles of Economics, are, I suspect, precisely the same as those which will insure that crises do not occur. If this is true, the real-exchange economics, on which most of us have been brought up and with the conclusions of which our minds are deeply impregnated, though a valuable abstraction in itself and perfectly valid as an intellectual conception, is a singularly blunt weapon for dealing with the problems of booms and depressions. For it has assumed away the very matter under investigation.

Even if the above is in some respects an overstatement, it contains, I believe, the clue to our difficulties. This is not the same thing as to say that the problem of booms and depressions is a purely monetary problem. For this statement is generally meant to imply that a complete solution is to be found in banking policy. I am saying that booms and depressions are phenomena peculiar to an economy in which... money is not neutral.

Moreover, per Davidson, I'd argue that the onus is on those with the additional restrictive axioms to justify their use, not on Keynes who has the more general theory.

Oliver Blanchard justified the neutrality of money axiom (in "Why does money affect output? A survey") as "very much a matter of faith, based on theoretical considerations rather than on empirical evidence."

The key thing for the non neutrality of money is to understand that in the presence of pure (Knightian) uncertainty you are induced to hold liquidity, as a refuge, in a monetary account. This is a nominal value not a real one since a non physical unit of account has no real cost of production and storage just a number printed physically or recorded electronically!

Nick Rowe,

I do not see why you are so fixated with the long run Phillips curve! By the way how do you define long run? Something that is running over real time? an analytical construct(abstract)? a trend? a term period that matures?

vimothy: I strongly agree with Keynes' statement here:

" If this is true, the real-exchange economics, on which most of us have been brought up and with the conclusions of which our minds are deeply impregnated, though a valuable abstraction in itself and perfectly valid as an intellectual conception, is a singularly blunt weapon for dealing with the problems of booms and depressions. For it has assumed away the very matter under investigation."

And it is not an overstatement.

In my view, the fact that we live in a monetary exchange economy (as opposed to a "frictionless" barter economy, or an economy with a centralised Walrasian auctioneer) is crucial to understanding the business cycles. The very idea of a "shortage of AD", for example, only makes sense in a monetary exchange economy. It's meaningless otherwise.

But living in a monetary exchange economy is a *necessary* condition for non-neutrality. It's not a sufficient condition. And understanding what those other necessary conditions are, and how they operate, is also essential.

And that brings me to Panyotis' second comment.

What is the best way to understand what those other necessary conditions are, and which ones are important, and how they operate? My strategy is *first* to assume them all away. Then bring them back in slowly, one by one, and see what effects they have, and how big those effects are likely to be, and whether they seem to match the data. And also, how long they are likely to last. You see, there is no single definition of the "Long-Run" independently of a particular theory of what causes those short-run non-neutralities. When you get a good theory of those non-neutralities (for example, when you get a good theory of sticky prices, which we don't have yet), that theory will also tell you how best to define the distinction between the "Long Run" and "Short-Run".

Panyotis: first comment. I think people will want to hold money even if there were no Knightian uncertainty. Because barter is such a pita!

The fact that (modern) money has no (or negligible) costs of production, and is not (usually) a physical thing does *not* mean that people care about the nominal rather than the real value (in terms of other goods and services) of the money they hold. It's the exact reverse, as I thought I made clear in my cowrie shell example.

Panayotis: sorry. I misspelled your name. Blame it on my bad eyeglasses or cheap computer screen.

JP: Sorry, I just noticed your other comment:

"Out of curiosity, what about if we used stocks (i.e. equities) as money?"

Good question. A 2-1 stock split would be the case under which the quantity of stocks would have no real effects, where we only care about the real value of the stocks. Indeed, some "backing" theorists, and Fiscal theorists, use just that analogy between the stock split and the quantity theory. In fact, the helicopter money thought experiment only works exactly (for neutrality of money) when the new money is distributed across the population in proportion to each individual's existing holdings. Which is exactly like the stock split case. Otherwise, if the helicopter flies over at random, it will change the distribution of real money balances across the population, even if prices rise in the same proportion.

Nick: When you see you agree with Keynes, what do you mean? Given the conditionality in the sentence you quote, it is not easy to parse your statement.

Are you agreeing that "the conditions required for the 'neutrality' of money... are... precisely the same as those which will insure that crises do not occur"?

Or are you agreeing that "If this [supra] is true, the real-exchange economics... is a singularly blunt weapon for dealing with the problems of booms and depressions"?

BTW, Keynes did not argue that unemployment was caused by price and wage rigidities.

vimothy: I agree with the first of those sentences. So I would begin the second sentence by saying "Since this is true.." and then agree with it too. I would replace "singularly blunt" with "impotent".

The only thing wrong with what Keynes said there is that when he says "...you will search treatises on real-exchange economics in vain for any express statement of the simplifications introduced or for the relationship of its hypothetical conclusions to the facts of the real world. We are not told what conditions have to be fulfilled if money is to be neutral." it was a bit of an exaggeration when he wrote it, and is even less true today.

One way to read my post (though it wasn't what I intended when I wrote it) is to say that it describes (or at least, is a way to start thinking about) "...what conditions have to be fulfilled if money is to be neutral."

"BTW, Keynes did not argue that unemployment was caused by price and wage rigidities." Yes and no. My interpretation of Keynes is that greater wage and price flexibility *might* (or might not) help reduce unemployment in a recession, but that good monetary policy could do the same job better. What confuses the interpretation is that Keynes in the GT thought of monetary policy as changing M/W, hence the "monetary policy by the Trades Unions" language.

Thanks. Just to make sure I get the real/nominal distinction and the general gist of your post... So in a cattle-as-money economy, at any given point some people have real demand for cattle (as the medium of exchange) and a nominal demand for cattle (as something to eat). Right?

Would it be fair to say that in a stocks-as-money economy, the same effect is present? Some people have a real demand for stocks (as the medium of exchange) while others have a nominal demand for them as investments?

And finally, is it only in a modern economy such as ours that the demand for money has become a purely real demand? And it is only in the latter scenario that the trick you talk about in your post becomes possible, and in an economy using stocks or cattle as money the trick doesn't work?

JP: "So in a cattle-as-money economy, at any given point some people have real demand for cattle (as the medium of exchange) and a nominal demand for cattle (as something to eat). Right?"

Right. Let M be the number of cattle you own. Let P be the price of other goods in terms of cattle. Then both M/P and M affect your utility. With paper, instead of cattle, only M/P affects your utility.

"Would it be fair to say that in a stocks-as-money economy, the same effect is present? Some people have a real demand for stocks (as the medium of exchange) while others have a nominal demand for them as investments?"

No. Stocks are still only bits of paper. So if you double the number of stocks through a stock split, and halve their value, nobody cares. So a 2 for 1 stock split would halve the value of each stock. But if you double the number of stocks by issuing new stocks to buy real assets, which will affect the total dividend stream in future, and the real value of each stock may go up or down.

(By the way, it is a puzzle why companies should do stock splits if they are neutral. One theory is that a stock split is a pure symbol -- a way the company can signal that it expects future earnings to increase. A second theory is that "denominations matter". If we only had $100 bills it would be impossible to make change. If we only had pennies, buying anything big with cash would mean a lot of counting. Discussions of monetary neutrality normally ignore the distribution of denominations of notes and coins. I can understand why investors don't like shares in very big denominations (you want to buy half a share). For some reason, stock markets don't like shares is small denominations, like below $1. Dunno why. Hassles of counting them? Some sort of symbolic signal?

"And finally, is it only in a modern economy such as ours that the demand for money has become a purely real demand? And it is only in the latter scenario that the trick you talk about in your post becomes possible, and in an economy using stocks or cattle as money the trick doesn't work?"

Yes. The historical transition of money from physical commodity to pure abstract symbol. Which is all the more credit to people like Hume, who could think of it as a pure symbol when it still wasn't, in his day. Scottish banking ahead of the times??

Nick Rowe,

I never said that we do not hold any type of money for other motives such as for transaction purposes in arbitrage in time/space, hedging and speculation. I said that holding nominal fiat money for uncertainty purposes makes money non neutral. Think about it! It is not a reflection of purchasing power but a refuge in liquidity, a "flight to safety of last resort". It is a protection of your hesitation to finance and spend that makes it non neutral and you have no cost to produce it and store it. A commodity money with other uses and cost cannot do so efficiently. The facility of purchasing power is in real terms but the facility of liquidity is in nominal terms.

As far as my second question, about your definition of long run, your answer is not clear to me. You see depending on your answer there are different analyses of the relationship you are examining.

When you say that something in the long run is independent of the short run, you are assuming some form stable attractor, like throwing a marble into a bowl. In that case, it would behoove you to present the bowl.

But there is another way to check this. When you say that something in the long run is independent of the short run, then over a long period of time -- and we do have over 100 years of economic data -- you should find that the short run relationships cancel out. That means, sometimes the slopes are positive, and sometimes they are negative, so that they end up canceling out to be vertical.

But if the slopes are always negative or always positive, then it is impossible for, over the long run, the slopes to be vertical. If you are always moving to the right, then you cannot say, "In the long run, you are not moving to the right".

In the case of a relationship between unemployment and the price level, you would need equal periods of when there is high unemployment during deflationary periods and high unemployment during inflationary periods, so that, in aggregate, there is no relationship. Or you would need high unemployment during inflationary periods to match the low unemployment during inflationary periods, etc.

In the specific case of money illusion, it might be helpful to look at this from the lense of debt driven money.

Suppose that there is an economy in which promises to deliver 1 unit of X were widely traded and acted as money. Say that 1 unit of M was a promise to deliver one unit of X *within* one year, where X was a real good. What would such a promise be worth? Well, it would be worth X or less -- since you could always deliver X right away, but if you thought X might get cheaper, then you would wait a bit. At most, 1 unit of M would cost as much as 1 unit of X, but generally it would cost less.

Now I ask, is "M" a real good or a "nominal" good? The only difference between M and a real good is the time shift and option value. Such an economy *should* suffer from nominal effects.

Now suppose you changed money to not be a promise to deliver 1 unit of X, but a promise to deliver 1 M contract within a year. I.e. a promise to deliver a promise.

In that case, the economy should also suffer from nominal effects. But now, you can get rid of X entirely, since by buying and selling the promises to deliver X, you do not actually need to ever deliver X. And since the cost of M is always less than or equal to the cost of X, you can just assume that no one ever delivers X at all.

Now, the quantity of X is irrelevant, only the quantity of promises to deliver X become important, since these are what you need to buy to cover your short position. Inflation is a period of many people incurring promises, and deflation is a period of people refusing to incur the promises. This contains important economic information.

So whether or not you believe the economy should suffer from nominal illusion depends on what you think the numeraire is. If it was truly arbitrary, then it wouldn't matter. But if the numeraire was a debt obligation, then it would matter, even if the underlying was a fictional good, or a real good that no one ever took delivery of.

The above applies to *changes* in the price level -- the actual price level is still arbitrary. But the importance of changes in the price level is sufficient to argue that nominal effects should exist, as most analysis is done on the margins, not the absolute value.

"Inflation/deflation is a period of many people.."? Period? Many People? percent rate of change? Please, explain.

P :)

You can imagine a fiat economy in which the money supply grows faster than output (and this could be because the economy is suffering a supply shock, it doesn't matter) or you can imagine a barter economy in which the number of promises to deliver a good increase relative to the supply of output.

Both are isomorphic. In both cases, the price of the of the money (or promise) will fall in terms of goods.

There is no distinction between the "nominal" effect, and the "real" effect. As soon as you allow contingent contracts to enter into your economy and be traded as goods -- e.g. as soon as your economy consists of forward looking agents -- then money becomes just as much of a "real" good as an apple. It is just a contingent contract -- in this case, I showed how you could view it as a contract to deliver another contract to deliver a real good. If you admit that these contingent contracts are "real" and should affect the economy, then you must admit that money is real and should affect the economy.

Only in the case where your agents cannot enter into contingent contracts can you argue that prices are not real -- money illusion is a valid concept only in a timeless static economy in which no one bothers about being forward looking.

Panayotis: "I said that holding nominal fiat money for uncertainty purposes makes money non neutral. Think about it! It is not a reflection of purchasing power but a refuge in liquidity, a "flight to safety of last resort"."

I disagree. The usefulness of holding a certain amount of money as a refuge in liquidity depends on how much you might be able to buy with it if ever you needed to exercise that liquidity, not on how many bits of paper you are clutching. If they were worthless bits of paper, to take an extreme case, they would provide zero liquidity.

"As far as my second question, about your definition of long run, your answer is not clear to me. You see depending on your answer there are different analyses of the relationship you are examining."

Agreed. Which means it is clear to you. The very distinction between long and short run will depend on the theory of why money is not neutral. It might be a length of time, or it might have nothing to do with time. The long run might be the mean of a probability distribution, and each short run point an observation within that distribution. Or, as RSJ suggests, the long run might be some sort of stable attractor to the short run points.

It would all depend on the particular structure of the equations, and why at least one of those equations does not exhibit the neutrality property.

RSJ: "But if the slopes are always negative or always positive, then it is impossible for, over the long run, the slopes to be vertical."

It can be possible. For example. If monetary policy can be described as a stochastic process Mt = Mmean + et, where Mmean is the mean and et is white noise, and the equations of the economy are Pt=Mmean and Yt=Mt-Pt, then you will observe an upward sloping relationship between Mt and Yt whether you look at 100 or 1,000 years of data. But the relation between Mmean and the mean of Yt will be vertical, as will the relation between the mean of Pt and the mean of Yt, and you could usefully call those a "Long Run" relationship. A central bank's choice of Mmean will have no real effects on the probability distribution of Yt.

Ahh, I see what you mean.

By long run, you mean the relationship between the expected value of two variables, as opposed to the expected correlation of two variables. I was talking about the latter. But there is no such thing as a correlation of means...

Now I'm confused. When you draw your vertical line -- what constitutes the "points"?

Two points.

First, regarding your stochastic function, a policy of Pt=Mmean that excludes the Brownian motion step and random jump effects that can be calibrated as asymptotic hyperbolic functions (i.e, power law specification) will have real effects.

Second, again your identity (definition, measure) of long run is critical on your function. "The might be.." is too fuzzy to justify our claim of the "long run Phillips curve". Are you identifying it as an analytical abstraction based on some probability density function, devoid of real time? Is real time involved, equilibrium trend? Assumptions are important and we have to pay attention to them.

Third, "worthless pieces of paper" is a trust call. Money must be trusted to be held for any motive including transactions. Otherwise, it is not money and the point is circular. If money is trusted and can be held the refuge function in the presence of pure uncertainty makes its effect nonneutral.

RSJ,

I understood your argument about the presence of contingent claims and is a good one. However, I did not understand your identity (definition, measure) of inflation, about the period, people. Please, crarify.

RSJ: "By long run, you mean the relationship between the expected value of two variables, as opposed to the expected correlation of two variables. I was talking about the latter. But there is no such thing as a correlation of means...

Now I'm confused. When you draw your vertical line -- what constitutes the "points"?"

Here's a story. Every 10 years a new central banker is appointed. Each central banker is drawn from a probability distribution of central bankers, and each has a different Mmean, which he announces when he begins his term, and firms set Pt accordingly. Each point on the LR curve is one central banker (actual or hypothetical). The probability distribution of Yt is independent of the central banker, so the LR curve is vertical. But an econometrician observing the data in {M,Y} space, who did not know the model, would conclude that it would be better to appoint a central banker with a high Mmean. (Lucas Critique, 1975).

If I assumed that central bankers did not announce Mmean, so firms had to learn it by statistical analysis, the results would be different.

This model is actually a really crude stylised oversimplification of the current New-Keynesian orthodoxy.

But, of course, it's just one story and one model, and one interpretation of what the LR curve means.

(BTW, Mt Pt and Y should strictly be interpreted as the *logs* of the variables, since otherwise this model would fail my unit test. I wanted it linear for simplicity, rather than multiplicative).

Panayotis:

"First, regarding your stochastic function, a policy of Pt=Mmean that excludes the Brownian motion step and random jump effects that can be calibrated as asymptotic hyperbolic functions (i.e, power law specification) will have real effects."

You lost me. Are you talking about price level (or inflation) inertia? If so, then yes. The transition from one monetary policy regime to another can be nasty. (Canada 1982).

"Second, again your identity (definition, measure) of long run is critical on your function. "The might be.." is too fuzzy to justify our claim of the "long run Phillips curve". Are you identifying it as an analytical abstraction based on some probability density function, devoid of real time? Is real time involved, equilibrium trend? Assumptions are important and we have to pay attention to them."

Agreed. This post is not a model. It's a post about models. My own preferred interpretation is to think of LR curves as mapping the set of all possible counterfactual monetary policy regimes, where each regime includes its own past, present, and future.

"Third, "worthless pieces of paper" is a trust call. Money must be trusted to be held for any motive including transactions. Otherwise, it is not money and the point is circular. If money is trusted and can be held the refuge function in the presence of pure uncertainty makes its effect nonneutral."

Yes. Yes. And No.

Try this thought-experiment. You were planning to hold $500 for the refuge function. Then a currency reform replaces 100 old dollars with one new dollar. I say you will now hold $5 for the refuge function.

Nick Rowe,

You do not see that when you hesitate to finance and spend, resources are not used and as an alternative you hold instead liquidity in the form of money that you trust. There goes Say' Law and money is not neutral as long as it is not a produced real good that employs resources to produce. This is not for transaction purposes demand for money that facilitates purchasing power.

Nick Rowe,

Regarding the stochastic specification, the point I am trying to make again and again about assumptions is that reality of an occurence is the reaction based on a forecast which is mispecified as is your function. More generally, the occurence and its reaction are non monotonic to each other and this brings a surprise which is the catalyst of a shock that brings a feedback. A surprise can be discovered but with a lag and the process is gradual. Your mispecified and simplified function is one of many examples of that surprise that brings real effects. It is time that economics realizes the permanent significance of surprise that destabilizes and shocks any system. I am not picking on your specification, I am only using it as an example to make a point I have been trying to make in other comments.

Panayotis: "There goes Say' Law and money is not neutral..."

The neutrality of money does not rest on Say's Law. If anything, it's the contrary, as Patinkin for example showed. Start in equilibrium, then double the money supply. At the existing price vector, there is now double the real stock of money, an excess supply of money and an excess demand for goods (violating Say's Law, which says there cannot be a generalised excess demand or supply of goods). It is precisely that excess demand for goods that causes prices to rise, and double, returning all real variables to the original level, including the real stock of money. You *need* to violate Say's Law to explain why money is neutral.

Nick Rowe,

You misunderstood me, maybe my English, of course you violate Say's Law which is EXACTLY MY POINT!Of course Patinkin would have been one of my references on what I argue altough it is more than that! I wished my English was better. Thank you for your patience.

Nick Rowe,

In case there is a misunderstanding on my part. I am not refering to the real balance effect which I associate with the transactions facility whether for arbitrage of non simultaneous time/space, hedging and speculation purposes but hesitating to spend, finance and employ resources in the presence of pure uncertainty or ignorance on what to do. The supply of resources in this case does not bring its own demand because monet is held instead.

OK, I see what you mean by "long run". You are exploring the whole state space, and you say

"In the long run", corr(X,Y) = corr(E(X(s)), E(Y(s))) where s runs over all the policy options.

I was thinking of "long run" as referring to time, in the sense that I am imagining a system with feedbacks, giving it a push, and then evolving it according to some flow.

For example, when I say "assets are liquid in the long run", I understand that during each particular auction, someone desperate to sell the asset might have to accept a low price, but then later on, others would notice this low price, and bid it back up to the expected return. That might take 1 week or 1 year, depending on the type of security and the ability of borrowers and lenders to restructure their debts. Or, assuming that a firm starts out with a lot of market power, over time, that firm grows, competitors come in, and the market power is exhausted.

And then you generalize to the steady state by assuming a flow of pushes:

For example, if the strength of the reaction function for adjusting the price of a security was inversely proportional to the maturity of the security, then short dated bills might "always" be illiquid in the steady state, whereas long dated bonds would be extremely liquid. Or, with a steady flow of new firms, you might reach a steady state where the "typical" firm continues to have market power, even though each individual firm's market power is diminishing.

In my case the economic equilibrium may be different from the long run case, due to a constant flow of short run effects. Whereas I *think* your model doesn't allow for an economic equilibrium to differ from the long run case -- correct me if I am wrong. Perhaps I am totally wrong.

So let me ask, do you believe that, at any point in time, if you were to take a census of firms, that their average costs would equal their marginal costs? Do you think, that in 100 years, or 10 years, the results of this census would change, moving towards some long run value?

And one more thing re: nominal versus real costs.

Say you have a vector of commodities: (gold, silver, corn, tin). Gold is also used as money. Is the price vector (1, silver/gold, corn/gold, tin/gold) a "real" or nominal thing? If the price of the three commodities in terms of gold were to double, would that be a "real" or nominal effect?

Then you can extrapolate to promises to pay gold, etc.

So I think there is some confusion in that people talk about doubling *units of measurement*, say from one pound to one gram -- and argue that this should have no effect, and extrapolate from that observation the belief that changing the price vector should have no effect. But as soon as you change the price vector without currency reform, then there is an effect, since all of a sudden gold is less scarce relative to tin or corn. Or equivalently, promises to pay gold are less scarce relative to the actual stocks of gold, tin, or corn, etc.

RSJ,
Yor definition of the "long run" is not analytical but in real time. However, tha adgustments you give them time to occur could be frustrated and interfered by other shocks that occur in real time which are not constant or regular. So your results as of anybody else that uses different time identity are variant by the identity empolyed.

P,

"So your results as of anybody else that uses different time identity are variant by the identity employed"

Yes, if you change the units of measurement, the result will be a different set of numbers.

For example,

Suppose you have many micro-firms, {f_i} each characterized by the unique ability to assemble as unique form of capital, {K_i}, as well as a (financial) return function, R_i(K_i). Say that R is a partial concave function that is rapidly diminishing (e.g. hits zero), to reflect the fact that companies will lose money if they over-invest. Let I and M be the left and right inverse functions, so that R(I(0))) is the minimal level of the capital stock needed to get any return at all, with I(0) > 0, and R(M(0)) is the maximal level of capital stock beyond which the firm will lose money.

The budget constraint is:

Y_i = R_i(K_i) + wL_i + ...

Where the partial derivatives of L_i and all the other factors of production with respect to K_i is zero -- since the firm is a price taker -- only the cost of capital for the firm changes as the firm grows. R(K) can be thought as the internal required rate of return on invested capital, which is different from what an investor receives. The investor will receive the consol rate, x.

The time period is important, so use the force of interest rate with a base period of 1 year if you like. I.e. e^x is the annualized consol rate.

As long as R(K) > x, then it makes sense for the firm to re-invest all profits. As soon as R(K) = x, then the firm should stop re-investing as it has reached it's optimal size, which will be M(x), and at that point it pays a cash-flow equal to xM(x). So the time path of the capital stock is:

dK/dt = R(K)K

with some initial condition K(0) = K_0, equal to the initial capital endowment.

Investors expend funds to invent the capital variety and endow the firm with an initial stock, and then they can sell it to the equity markets. The firm will start growing and then stop exactly when K = M(x). So the equity value of the firm is M(x)e^(-xt), where t is the time needed to reach K = M(x) from where you are now, via re-investment. K_0 is completely determined, because if the investors endow it with too much stock, they get earn less, and if they endow it with too little they also earn less. The "magic" level of initial endowment is I(x) -- this maximizes the inventor's return, independent of the cost of inventing the firm.

So now we can look at an invention model as a random variable that takes values in the space of Return functions. It represents the (stationary) probability of inventing a type of capital with return function R in one year.

The (annualized) return on invention will be the expectation ER(x) = . ER(x) is a strictly decreasing convex function when it is > 0, and is identically 0 thereafter. And so either invention is not feasible -- ER(x) < 1 for every x. Or, there is a unique consol rate so that the return from inventing capital is exactly the same as the consol rate, allowing no financial arbitrage. Call the arbitrage-free consol rate x*, so that ER(x*) = e^x*

Now the equilibrium distribution of capital will be that given by the invention model, the rate of return for the economy as a whole will be a constant, x, and given some initial distribution of capital, you can model the rate of investment demand, dK/dt, etc.

The result is that you can have a macro-equilibrium in which the goods market is always in disequilibrium -- most firms are not at their optimal size, but enough new firms are being created just as the old ones max out.

The "steady state" will have an aggregate expected return on capital that is greater than the consol rate, yet investors only receive the consol rate.

I.e. as an emergent phenomena, the marginal product of capital is always greater than the rate of interest, and each individual firm has their own (unique) MPK, yet nevertheless no investor makes more or less money by purchasing equity in a firm with a high MPK than a low MPK, because the cost of equity adjusts to even that out.

And in the same way, you can calculate opportunity cost for each firm as the loss in equity value from diverting 1 dollar away from re-investment and into dividends. You will see that the opportunity cost is falling with time, meaning that the cost of capital is increasing with time, and yet in aggregate, the opportunity cost is also constant.

And you will also notice that the return function M/Ie^(-xt) has a fibre in which you can "pull forward" returns now in exchange for paying future returns later. Basically you can push the concave function to the left or to the right.

If you assume that the equity owners will not allow firms to buy or sell debt in anyway that lowers the return function, but that lenders will not be willing to sell-debt that increases the return function, then you can generate an "expected" yield curve as the shift that occurs when you push the return curve to the left.

Finally, as R(K) is nothing more than an expectation of the future returns available to the firm as a result of investment, you can play around with changes in sentiment that send R(K) --> aR(K), or R(K) --> R(K/a) and see how this causes aggregate investment to fall, shifts in the yield curve, as well as causes the consol rate to fall, etc. If you model a(t) as brownian motion, or some other motion, you will get volatility in investment and returns, etc.

That is just a little toy model, but the point is not to get all hung up that you need to use units. So what -- there are many interesting things to say nonetheless.

Of course, in the real world, the arbitrage free rates are not maintained -- the bankers get lower funding costs, drive up the price of real estate, and the economy collapses.

Damn the html! The inventor's expected return is, ER(x) = E[M(x)/I(x) e^(-xt)]. I made the error of using brackets.

By the way, from this (extremely simple) model, you can explain a situation in which:

Each typical firm has (primarily) diminishing average returns, but returns in aggregate do not diminish. If you define the aggregate capital stock as the sum of K = running total of costs of assembling the capital -- then you can have stable P/E ratios even though the P/E ratio of the "typical" firm is falling with time. You can also get large surges in investment as a result of an expectations shift, say R goes to 1.2R can result in a 50% increase in investment. Or you can assume that the random variable changes, which will also cause large capital investment shifts, etc.

RSJ,

Thank you for agreeing with me that your results as of anybody else that uses a different time identity are VARIANT by the identity employed. I have been saying that all along and in a few words regarding the use of the term of "Long Run". The arguments can get quite circular if we do not identify our terms carefully. This not a criticism of your efforts or Nick Rowe's but maybe I can save you the trouble. Personally I have moved to an alternative framework of occurrence and surprise I have developed which I admit after many comments that is difficult and complex. I am still working at it and maybe I should reduce the math level I am using. The fight is going on!

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