## Considerations of the Relationship Between Price Elasticities and Expectations in Price Formation

As I have already written in my introduction just after I had sent off the final draft of my paper I noticed a rather glaring error. This error can be best understood by comparing equation 1.10 and equation 2.10 from my paper both of which I shall reproduce here. (Note that a guide to the algebraic terms used can be found at the very beginning of my paper).

Note that equation 1.10 represents how the price of what I call in the paper a ‘pure’ financial asset — say, a company bond — is set, while equation 2.10 represents how the price of what I call in the paper an ‘impure asset’ — that is, one that has a financial and a real component (say, oil or gold) — is set. The difference is rather obvious. In equation 1.10 all that matters is (a) the price expectations variable in its complete form, that is the series of variables in the middle of the right-hand side of the equation and (b) the supply variable in its complete form, that is the series of variables at the very end of the equation. The intuitive meaning of this is that the price of a pure financial is set only based on expectations and increases or decreases of a supply of this asset.

Equation 2.10 tells a different story. First of all, we have two expectation terms. The first is the same as the one found in equation 1.10. This denotes the amount by which investors think that the price will rise purely due to financial considerations. So, let’s say that there a large group of speculators who think that gold is going to rise in price as people become more anxious about central bank actions. This will be reflected in this term. The second term, however, refers to the extent to which investors think that the price will rise due to real market considerations. So, let’s say that there a group of speculators that think that the real demand for gold is going to increase because a new technology has emerged in some line of production that requires gold to work or, alternatively, say that gold is becoming more fashionable in the jewelery market.

In reality, these two terms have a great deal of overlap. Imagine, for example, that the demand for gold increases suddenly in India because of fears of inflation. Generally we would tend to attribute this increase in demand to the financial component of our equation. In India, however, while gold is used as a store of value the manner in which this is done is cultural — brides, for example, are endowed with gold jewelery as part of their dowry. But the distinction between whether the jewelery is thought of as an asset and whether it is thought of as a decorative product is murky to say the least. As The Jewelery Company website notes,

Gold jewellery is simultaneously a status symbol and instrument of adornment as well as an investment.

I think, however, that despite these complications it is didactically useful to separate notionally financial demand from real demand. It allows us to conceive of the fact that markets for ‘impure assets’ are part determined by what investors think is taking place on the financial side of the market and part determined by what is taking place on the real side.

The real problem that I discovered, however, is in the price elasticity terms that are used in these equations as represented by the lower-case delta (the Greek letter that looks like a small ‘d’). What do these terms mean? Well, think about it this way: if 100 new assets are introduced in a market in which the price is \$100 per asset what effect does this have on the price? This will depend on a number of different factors such as the stock of assets outstanding in the market at any given point in time and the effect this introduction of new assets has on expectations.

So, we include a price elasticity term. Let’s say that the introduction of 100 new assets onto the market — which will be represented in the equation as setting the qZ term to 100 — has the effect of decreasing the price by \$10. We can then set the price elasticity term at 0.1 and we will get precisely this outcome.

The problem here is twofold and interrelated. First of all, the price elasticity term does not work in the same way for the price expectations variables — that is, the variables denoted by Pes — as it does for quantity variables like qZ. This is because price expectations variables are self-fulfilling. If the market thinks that the price is going to rise by 20%, given a few qualifications regarding market confidence and profit expectations, the market will basically rise by 20% as investors pile in. Whereas in the case of quantity a certain amount of an asset is created or destroyed and the price effect responds to this creation or destruction. We might say, then, that the price expectations variables are active while the quantity variables are  passive.

Secondly, the price elasticity term is actually intimately tied up with the confidence term, which is represented in the equation by the small-case Greek letter gamma which looks like a small-case y. As I just said the amount by which a market price will respond to an increase/decrease in the quantity of an asset will depend on how this increase/decrease affects expectations. This means that there is a relationship between the confidence term and the price elasticity term.

This does not, however, mean that they are identical. The price elasticity term is an outcome of the confidence term, but the confidence term is not fully determined by the price elasticity term. Intuitively this is because there are things that can affect confidence that have nothing to do with increases and decreases in the quantity of an asset. A company, for example, might increase their amount of shares outstanding substantially but because investors expect that this company is going to use the funds for what appears to be an investment drive with great potential expectations may be positively reinforced by this increase in share issuance, thus not only offsetting the quantity increase but even causing the price to rise.

My mistake was to include the price elasticity term in the components of the equation that deal with price elasticities. In actual fact, the price elasticity term should only be included where expectations are not playing a role; that is, it should only be included in the last two components of equation 2.10 — those which deal with quantity supplied and real quantity demanded respectively.

This, however, leads to a further problem. Namely that these two variables cannot really affect the market price in the case of pure and impure assets until the following period unless they outweigh the speculative effects caused by the price expectations term. Put simply: in any given period it does not matter how much real supply and demand increase or decrease, rather all that matters is expectations unless the real supply and demand outstrip the speculative activity brought about by the expectations. Expectations, in a sense, ‘override’ real considerations unless these real considerations outweigh the expectations; so, even if the market is suddenly flooded with an asset its price will still rise if investors think that it will rise. It is only in the next period that these increases or decreases have any real effect on the price and this is only insofar as they affect expectations.

In a sense my equations were not radical enough. I was still working on the assumption that real supply and demand actually had a first order effect on price. But it is now clear to me that they usually only have a second order effect — i.e. they can only effect price by way of the effect they have on expectations. In order to deal with this we have to set a lag on these variables and then tie them to the price expectation variables in the period that follows them. But I think that this post is long enough, so I will save that for another day. The more I think about it, the more complicated it becomes to represent these dynamics in a neat manner.

Philip Pilkington is a London-based economist and member of the Political Economy Research Group (PERG) at Kingston University. You can follow him on Twitter at @pilkingtonphil.
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### 40 Responses to Considerations of the Relationship Between Price Elasticities and Expectations in Price Formation

1. Ramanan says:

Your claim: “…consistent with the national accounting framework and inspired by the recent move toward Stock-Flow Consistent modelling in Post-Keynesian economics.”

Well, as soon as you start writing equations in your paper, alarm bells start to ring. Equation 1.1 on page 29 (paper typo: why two equations labeled 1.1?) to 1.3 itself proves you are unsure of what you are talking of. What’s “total private financial investment” and what’s “government financial investment”? General vaguely defined terms.

I can haz example to prove 1.3 plz?

The funny part is you start saying “basic identities of an income and expenditure approach” but what you then have is not the income-expenditure identity at all.

It is good to get accounting right. Words such as income has specific meaning in national accounts and business accounts but your terminologies are self-made.

The phrase expenditure is sometimes used freely although national accounts reserve its use for specific flows. But income on the other hand has a more specific meaning to it not like your discussion on page 29.

Then comes equation 1.4 where you seem to not understand the meaning of the concept “elasticity”. Price elasticity of demand for something measures the sensitivity of the change in demand for that thing when the price changes. You have it the other way round.

At any rate. 1.4 is meaningless. I suppose you want to capture the fact that prices change when there is a change in demand for a financial asset but equation 1.4 is no way of saying this thing. It is not even close.

The statement after that has no meaning – how can delta be both less than 0 and greater than 1? I assume it is a typo as is the sentence following that: “higher price elasticity of demand is represented by a lower value and a lower price elasticity of demand is represented by a higher value.”

???

Then you randomly mix transactions involving purchases of financial assets and goods and services.

Overall in your paper, prices seem to move on expectations – which is okay but nowhere do you have anything like a “price clearing” mechanism in selected markets. That is, you simply have equations for prices at time t+1 which depend on prices at time t and the expectations.

But apart from that and some vague “Capacity to Increase Production/Offload Inventory” you don’t have anything.

Making models of stocks and flows requires one to understand national accounting terminology, concepts and the framework. Instead you end up with the most vague terminologies.

The reason you go astray is that you have no mechanism to find the price itself. The way you should proceed is to conjecture a mechanism and then how expectations of price changes themselves affect this mechanism which then use it to find prices at t+1.

Perhaps you have it in the meaningless 1.4 and its partner for “real”. But that is a purely demand dependent thing. In other words, you talk of Kalecki and all but where are the “costs”?

But the biggest genius of the paper is when you add two prices – that of financial ones to that you call “real” to make one price. That’s as silly as adding the S&P 500 index and CPI to come up with some new price index!

• I suppose I should take this point by point. I’m going to ignore points about typos.

What’s “total private financial investment” and what’s “government financial investment”?

The paper is clear on this. Private financial investment is all the purchases made by the private sector of financial assets — so, households, firms, banks, hedge funds and so on. Government financial investment is all the purchases made by the government sector of financial assets — so, state and local government purchases, central bank purchases (yes, I’m aggregating) and so on. There is thus no “proof” of equation 1.3, it is an identity. In a closed economy ALL investment in assets must be either from the government or private sector. And all investment will generate saving — if I buy a stock from you, you get money that is counted as saving.

The funny part is you start saying “basic identities of an income and expenditure approach” but what you then have is not the income-expenditure identity at all… It is good to get accounting right. Words such as income has specific meaning in national accounts and business accounts but your terminologies are self-made.

Yes. My terminologies are self-made because the framework for understanding this does not exist. I see no reason why these relations cannot be thought of in terms of income-expenditure. Do you have a theoretical objection to this?

Then comes equation 1.4 where you seem to not understand the meaning of the concept “elasticity”. Price elasticity of demand for something measures the sensitivity of the change in demand for that thing when the price changes. You have it the other way round.

Yes, I have reversed the meaning of elasticity. If there is an established term for this in economics please inform me of it and I shall replace the term ‘elasticity’ with that. Otherwise, I don’t think its too much of a stretch to use the term ‘elasticity’. Kaldor did something similar in his 1939 paper with his ‘elasticity of expectations’.

At any rate. 1.4 is meaningless. I suppose you want to capture the fact that prices change when there is a change in demand for a financial asset but equation 1.4 is no way of saying this thing.

Yes, that is what I want to say. Please be specific about WHY the equation does not say this.

The statement after that has no meaning – how can delta be both less than 0 and greater than 1?

Yes, typo. Should be the other way around. Thank you.

Overall in your paper, prices seem to move on expectations – which is okay but nowhere do you have anything like a “price clearing” mechanism in selected markets. That is, you simply have equations for prices at time t+1 which depend on prices at time t and the expectations.

Why do we need this price-clearing mechanism?

The reason you go astray is that you have no mechanism to find the price itself.

What do you mean?

That’s as silly as adding the S&P 500 index and CPI to come up with some new price index!

Why is that silly?

• Ramanan says:

“if I buy a stock from you, you get money that is counted as saving.”

which is wrong and that’s the reason for stressing the importance of knowing these things.

If you buy a stock from me, it just changes the form of my saving not the saving itself.

Example:

I earn \$100 in salary, pay \$20 as taxes and consume \$80.

I sell you stocks worth \$50 from my assets.

My saving? \$100 – \$20 – \$80 = 0.

While you are right nobody is bound to use the language of national accounts, it is important that you do not mix your own with them – else there’ll be inconsistencies.

On your point on adding S&P 500 and CPI … these two are different things. It’s like adding apples and oranges – even worse. Relevant to this is the fact that these two prices are determined by different ways. And if you add them, you end up having something like today’s price of iPods being determined by what happened in the stock market the day before, yesterday and today.

You can say what happens in the stock market affects everything else in a way but that is a more complicated thing.

Kaldor’s definition may be right but doesn’t prove your definition is right. At any rate, he is talking of elasticity of expectations and the one I picked is the price elasticity of demand.

“In a closed economy ALL investment in assets must be either from the government or private sector.”

It is meaningless. What is investment in assets? Is it purchases of assets? If that’s so, even household purchase assets. Is it issuance of liabilities. Well even households have liabilities to the banking sector.

The fact that anyone issues liabilities doesn’t by itself mean the price will change. The government keeps issuing bonds but your equation implies a one-directional movement of prices which is not the case. Prices move up or down. Take your equation on an excel sheet and see how far prices move in say 30 periods.

• NeilW says:

“My saving? \$100 – \$20 – \$80 = 0.”

Nope. You nicked \$50 of Phil’s saving by swapping it for your pre-existing assets.

Big fail there – by not looking at the entire system.

• 1)

If you buy a stock from me, it just changes the form of my saving not the saving itself.

Yeah, that’s fine. How does that violate the identity?

If + Gf = Sf + Tf

2)

On your point on adding S&P 500 and CPI … these two are different things. It’s like adding apples and oranges – even worse. Relevant to this is the fact that these two prices are determined by different ways. And if you add them, you end up having something like today’s price of iPods being determined by what happened in the stock market the day before, yesterday and today.

No, you’ve completely misunderstood what I’m doing. If you add up all the real prices (CPI) and all the financial prices you just get a different index. Nowhere in my paper does it imply that real prices are determined by stock prices. I think you have to read it more closely.

3)

It is meaningless. What is investment in assets? Is it purchases of assets? If that’s so, even household purchase assets.

Sure, and households are part of the private sector, no?

4)

The fact that anyone issues liabilities doesn’t by itself mean the price will change. The government keeps issuing bonds but your equation implies a one-directional movement of prices which is not the case.

Which equation implies that an increase in quantity will lead to a price change?

• Ramanan says:

“Nope. You nicked \$50 of Phil’s saving by swapping it for your pre-existing assets.

Big fail there – by not looking at the entire system.”

Lol.

When I buy Phil’s stock, it neither changes my saving nor his. His saving is his disposable income minus consumption.

The transaction is just an exchange of assets – unlike what Phil makes it out to be.

• Ramanan says:

“Yeah, that’s fine. How does that violate the identity?

If + Gf = Sf + Tf”

Because there is no identity such as that.

Purchase of financial assets doesn’t by itself create saving.

Does QE create saving? No. It exchanges in asset for another. I thought this point is repeated often in blogs.

“Nowhere in my paper does it imply that real prices are determined by stock prices. I think you have to read it more closely.”

First nobody in the world adds indices such as that. Also, because when you combine the two price indices into one … one of your equations has prices of goods and services depending on other things.

If you want to display the two equations together you may want to display it in some matrix form or something rather than just adding them up.

“Sure, and households are part of the private sector, no?”

Ok my bad. But let’s go back to it.

But what is “financial investment expenditure” ?

Which thing in SNA is “financial investment expenditure”?

“Which equation implies that an increase in quantity will lead to a price change?”

Equation 1.4.

Look at it as a sequence relation. Every year the government issues bonds. Then put it on excel and see how prices keep changing for no good reason.

• 1) QE increases the amount of financial assets in the economy. Think it through, Ramanan. The central bank — in my framework, Gf — creates money and buys bonds. Those holding bonds get cash balances and there is no net change for their financial saving. Meanwhile, the central bank gets the asset and thus their financial saving increases. There is a net increase in financial saving in the system as a whole — Sf rises.

2) Yes, nobody adds them. But conceptually we can if we please.

Also, because when you combine the two price indices into one … one of your equations has prices of goods and services depending on other things.

This is a very vague statement and I don’t understand the point. Perhaps you can be clearer?

3)

Which thing in SNA is “financial investment expenditure”?

As you said, in the current SNA it is counted as saving. That’s fine with me. I call the process financial investment because it can create saving. See: the QE example above. We might also think of stock issuance which creates saving — a company issues stock, a household buys it, the company’s saving increases (cash balance) and the household’s remains the same (stock replaces cash). We have a net increase in saving.

4) I think you’ve missed the other variables. If the government issues more bonds but investors think that the price will remain the same then the price will remain the same. This will show up in the demand-side of the equation.

2. ivansml says:

I’ve read your paper. To stay constructive, I’ll just comment on two specific things:

1) Your main argument against market equilibrium is that it cannot accommodate expectations in consistent fashion, and this is supposed to be shown by figures 1.2 – 1.4. This makes no sense. Your “argument” is just confusion stemming from the attempt to represent multidimensional system in a single two-dimensional picture (which, suprisingly, doesn’t work). An equilibrium model where expectation of future price enters current demand has 3 endogenous variables, and in fact can be represented as both figure 1.2 and figure 1.4, depending on which of the three equations we substitute into the other two. Both description are equivalent, both represent the market equilibrium model and both are consistent.

2) As for your proposed model of asset prices, I’ll confess I’m lost – where does equation 1.4 come from? I believe we argued about similar point before, but since this equation links price dynamics to realized expenditures, which seems rather crucial for the theory, I would expect more explanation in the paper. And if we just take it as given, the equation implies that expenditure will be negative if price decreases, which clearly cannot happen.

• 1) Yes, I would imagine that you can integrate it in a three-dimensional model but I think that this would raise problems of its own. Perhaps you can give me a source on this and I can criticise it properly?

2a) Equation 1.4 is something of an identity. All expenditure on financial assets — just like on real assets — is also income and thus, ultimately, savings. All expenditure on such assets will also change the price of an asset. This will not be one for one. And that is why the elasticities term is there. You might be right that I should explain this better as Ramanan seems completely befuddled by it as well.

2b) I’m not sure if negative expenditure is a problem. When you turn the expenditure function into a price expectations function as I do in equation 1.5 then price expectations can accommodate a fall in the price due to a fall in the expected price. I suppose if you want to retroactively interpret equation 1.4 in this light, a negative expenditure might mean sales.

• 2b – continued) Think in this regard of a Keynesian consumption function. Can it account for a fall in income? I think we would have to assume negative consumption for this to be the case, no?

• ivansml says:

1) I don’t think a simple mathematical fact needs reference. And of course more generally, economic literature on temporal/sequential/intertemporal general equilibrium is huge, going back at least to Hicks. For a specific example, De Long et al. paper you cite has the same structure – individual agent’s demand is a function of current price and expected future price, supply is fixed and price is set so that demands sum to supply. They assume rational expectations (plus some funky noise traders), but one could just as easily use adaptive expectations.

2) Modelling price formation is definitely not an identity, it’s a key element of any asset pricing model! You are effectively assuming that expenditures = sum of asset purchases is determined by demand (given by expected price change), all these purchases find their seller counterparts somewhere in the background, and price adjustment is a function of traded volume. This makes no sense, since large volume could in reality be associated with either increase or decrease in price.

And if you interpret negative expenditures as sales, you clearly need to define your variables better – I assumed sales are counted in income. Example: there is a market for a single company stock. In period t, Alice sells 200€ worth of stock, Bob buys 300€, Cindy buys 150€ and David sells 250€ (everyone else does nothing). What’s Y_ft and E_ft in this economy? I’d say Y_ft = E_ft = 450€, and clearly one cannot have this value negative – it can be zero if there is no trading, or positive if there is.

• (1) I criticised Delong’s paper in the paper. It is a slightly different criticism to the basic supply and demand models. I won’t repeat it here but it runs something like this: “The EMH assumes an information equilibrium that looks very like a basic inverted S&D model. Delong assumes this as a base case and then introduces ‘noise traders’ as a sort of exogenous component… I want to move away from anything resembling a market or information equilibrium.”

(2a)

No its not. It is a function of the amount of money pumped into the market by investors subject, in turn, to the elasticities variable (there are problems with this though, as I highlight above). This has nothing to do with volume. A very large amount of money could be used to, say, bid up the price on one stock but there might only be one trade — i.e. the trade where the flush investor says “I will give you \$x for that stock…”.

(2b) I think that this is a more substantial criticism. But nevertheless I have to go back to the Keynesian consumption function: can a consumption function show a decline in income? If so, does it require negative expenditure? If not, does it mean that the approach is inherently flawed?

• ivansml says:

Right, it’s volume times price (money flow) – but since the price is just one number within a period, that’s almost the same thing.

Consumption function surely allows for decrease in income.
Y = (a + bY) + I + G => output/income goes down if exogenous variables (I or G) go down.

• 1) I don’t get the criticism here… is it a criticism?

2) Do I and G then have to be negative?

• ivansml says:

It’s the same criticism as before – you’re assuming that price change is positively related to the amount of money that changed hands in the market, and I don’t see why that should be the case (Ramanan above is saying the same thing).

No, I and G don’t have to be negative, because in Keynesian cross model it’s the level of consumption that is modeled. If we instead specified that *change* in consumption is a function of income (as you do with prices), we’d run into the same difficulty.

• 1) Why should price not be the same as the amount of money that changes hands? Take one market with one asset, one investor and one seller. The investors says “I’ll give you \$500 for that asset”. What is the price of the asset? It’s \$500. It’s really that simple. The question I’m raising is: what causes this money to change hands. That’s where things get interesting.

2) Ah… now we’re getting somewhere. Yes, you are absolutely right. I’ve confused changes with levels. I am going to write a post clearing this up. Thank you.

Update: All done. See here. Thanks.

• ivansml says:

1) This breaks down immediately when you have many identical shares of the asset. Clearly there’s a big difference between “I give you \$500 for 10 shares” and “I give you \$500 for 20 shares”.

• I’m not sure I follow. The price is set by the marginal asset bought. The final bid in a given time period sets the price, as it were. And that retroactively sets the price on all other assets bought. Do you get what I mean?

Also \$500 for 10 shares is \$50 a share, for 20 it’s \$25 a share. You’re talking about two entirely different prices. In the first the bid is \$50 in the second it is \$50.

3. Ramanan says:

It will take me ages to walk you through the flow of funds analysis but consider this.

“We might also think of stock issuance which creates saving — a company issues stock, a household buys it, the company’s saving increases (cash balance) and so does the household (stock). We have a net increase in saving.”

First I am a bit suspicious of your use of “net”, It is usually used as a kind of opposite of gross. But anyway …

When a company issues stock to you in an IPO, your saving doesn’t change. The household has less cash and more stock. The company’s saving also doesn’t change. Cash is not saving – it is one form of saving. A company’s saving is its retained earning. Does issuance of stocks BY ITSELF lead to retained earning? No.

A company may find itself with more cash than it began with because it retained some earning (not in your example). But this does not mean ANY cash increase (as in your example) is saving.

Saving is disposable income minus consumption. You cannot just look at cash balances and calculate the saving.

Let me give another example. You earn \$100 pay taxes of \$20 and consume \$50 and pay a monthly bank installment on previous loans of \$30. You are left with the same cash balance you started with. But this does not mean you saved \$0.

Even though you are same cash balances than you started with, your saving is \$100 minus \$20 minus \$50 which is plus \$30.

The underlying point is increase in cash balances is by itself not saving.

• 1)

When a company issues stock to you in an IPO, your saving doesn’t change. The household has less cash and more stock.

I wasn’t going to get into it but this isn’t actually necessarily true. If we look at my framework we’ll see that if the price of the share rises after the household buys it, the saving of the household increases. This is actually a very important point and one that I am trying to get across: saving, in a sense, depends on expectations!

2) Are you telling me that if I have a company with \$0 net income and I issue shares worth \$1000 and I put this \$1000 in a bank earning interest that I have \$0 in saving?

• Ramanan says:

Can’t submit this comment for some reason … hopefully doesn’t appear many times …

\$30 in principal payment in above to be clear.

4. Ramanan says:

“I wasn’t going to get into it but this isn’t actually necessarily true. If we look at my framework we’ll see that if the price of the share rises after the household buys it, the saving of the household increases. This is actually a very important point and one that I am trying to get across: saving, in a sense, depends on expectations!”

Well in national accounts that is capital gains and is something different, not counted in saving.

” Are you telling me that if I have a company with \$0 net income and I issue shares worth \$1000 and I put this \$1000 in a bank earning interest that I have \$0 in saving?”

Well you earn the interest but that’s different. That is why I used the phrase “by itself” above. You made it as if the amount of stock itself is saving.

“company’s saving increases (cash balance) and so does the household (stock). “

• Well in national accounts that is capital gains and is something different, not counted in saving.

Sure, call it that if you want. So, now we’ve established that what I mean by If = Sf counts income received, capital gains and so forth.

Well you earn the interest but that’s different. That is why I used the phrase “by itself” above. You made it as if the amount of stock itself is saving.

Let’s say that the interest rate is 0%. But the company takes the \$1000 and puts it in a savings account. What are that company’s savings?

• Ramanan says:

“now we’ve established that what I mean by If = Sf counts income received, capital gains and so forth.”

No you haven’t.

Only if you give yourself the task of going through these things in detail will you see what’s happening.

• NeilW says:

You’re wasting your time here Phil. It’s the usual problem of assumed definitions.

The Lawyers get around that problem by putting a capital letter on any word which is defined in the document.

Any entity that creates a financial asset and a financial liability by balance sheet expansion increases the total quantity of financial things that can be saved.

Company shares come into being by fiat. They initially have a nominal value on the asset side and a corresponding ‘Shares Issued’ entry on the liability side.

The company then just swaps that new asset for somebody else’s cash asset.

Financial Saving is could be said to be the sum of every financial asset not in the hands of the original creator.

• Ramanan, you’re not really refuting what I’m saying. You’re just trying to translate it into the language of the national accounts. That’s fine. I have no problem with you doing that — indeed, I appreciate it to some extent — but please don’t paint it as a criticism when its not.

Neil, yes, that is the underlying intuition. As I state in the paper the first equation assumes a fixed supply of financial assets. In this world every asset sold is one bought and increases in financial savings only come from the fact that the asset’s price might increase. But when I introduce the supply side it becomes clear that financial savings can increase by issuance of new financial assets provided that they don’t negatively impact the price by the same amount.

5. Nick Edmonds says:

Phil,

This is intended as constructive criticism, but I also struggled with the definitions here. I’ve no problem with terms being used with unconventional meanings, if appropriate, but it then becomes really important to spell out how you are using them (we can be forgiven for being lax on this in blog posts perhaps, but maybe not in working papers). The use of the term “saving” is a good example. You are clearly using it very differently from its conventional use, which is fine, but there was not enough there for me to work out exactly what you meant. Personally, I would have found a more detailed explanation of terms an enormous help in following your argument. Just a suggestion.

• Yes, I’m getting the impression that I have to be fairly precise in my definition of financial savings. So, let’s work it out.

My original intuition is that financial savings (which is equal to financial investment) is a sum of all assets times their price.

So, take an economy with 1,000 bonds and 1,000 shares. The bonds are worth \$200 and the shares are worth \$400. Total financial saving is then \$600,000.

Likewise total financial investment must be \$600,000 because someone would have to have bought these bonds and shares at this price in order for them to have this price.

Do you follow? Is this clear?

Honestly, I didn’t think that I was departing from conventional S = I usage in this sense. Yes, I’ve included a price component, but I clearly laid out an equation where I stated that S = I = Price.

• Nick Edmonds says:

Your reply there puzzles me slightly because that sounds like you are using “saving” as a stock and I had until now assumed you were using it as a flow, particularly from the way you relate it to income and expenditure, which are conventionally flows. (Under normal definitions, “saving” is a flow, but the term “savings” is usually used to refer to a stock).

So, if you are using “saving” that way, then I think I understand even less about how you’re using “income” and “expenditure”. But my point wasn’t really about the meaning of specific “terms”. It was just the more general point that I felt readers like myself would find it easier to follow with more detailed definitions.

• Saving can be either a stock or flow as you say, right?

So, a flow of expenditure builds a stock of saving, right?

I don’t see how this is any different to the typical I = S equation. Are we talking about stocks or flows? I personally never thought it mattered much.

The stock of saving = the stock of investment undertaken

And…

The flow of saving at any given point in time = the flow of investment at any given point in time

Am I missing something here?

• Nick Edmonds says:

Actually what I said was “saving” is conventionally a flow and “savings” is often used to refer to a stock. In fact, whilst “saving” is fairly well defined (as income less final consumption expenditure), “savings” is a bit of vague term – I don’t think it’s clear exactly what would count as savings.

And my initial response to “a flow of expenditure builds up a stock of saving” would be that that is incorrect, because “expenditure” usually means use of resources on acquisition of goods and services and building up a stock of savings, to me, means use of resources to acquire financial assets. But it does, of course, depend on what you mean by these terms.

And I don’t really want to get into an argument over this. I’m not trying to prove a point – I was just saying I found it difficult to understand some of the terms. If other people understand it OK, then that’s fine – just ignore me.

It’s an interesting point as to whether one should look at stocks or flows when thinking about asset prices. Most approaches, I think, would focus on stocks and would look at the relationship between price and the amount agents wish to hold. However, in fact, prices are determined at the margin by the flows between buyer and seller. The assumption is that the flows are an accurate reflection of decisions taken over stocks, but with imperfect markets, that’s not necessarily the case.

• And my initial response to “a flow of expenditure builds up a stock of saving” would be that that is incorrect, because “expenditure” usually means use of resources on acquisition of goods and services and building up a stock of savings, to me, means use of resources to acquire financial assets.

I don’t really get this part. In any standard textbook at the beginning of chapters on Keynesian economics it is usually laid out as such,

1.1. Y = E

And then, a few lines later we get,

1.2. Y = C + S + T

And,

1.3. Y = C + I + G

If Y = E — i.e. if income = expenditure — then equation 1.2 can be restated,

1.4. E = C + S + T

So, expenditure equals consumption plus investment plus government spending. Surely what we are talking about here is a flow of expenditure being broken down into three sub-flows. Right?

Now, if we turn to equation 1.3 we can derive the familiar identity,

1.5. I + G = E = S + T

Note that we can put Expenditure in the middle there. I would think this to now mean something like: the expenditure flow (I + G) feeds into the flow (S + T).

That’s great. Now, the stock relation here is surely that a “stock” of savings and taxes, in the form of accrued income, builds up? Am I missing something here? Perhaps I’m not thinking clearly.

• Nick Edmonds says:

Your (1.4) and (1.5) seem to imply that C = 0. Can I just check that is what you meant.

• Sorry, you’re quite right. Usually we can cancel the C’s but with the E in the middle the equation should read,

1.5. C + I + G = E = C + S + T

Sorry, I’m packing right now… Anyway, that shouldn’t make a difference to the argument.

• Actually Nick, the more I think about this the more I think that what you’re saying is important. I’m going to have to write something up on this. Stay tuned.

6. Ramanan says:

“Ramanan, you’re not really refuting what I’m saying. You’re just trying to translate it into the language of the national accounts. That’s fine. I have no problem with you doing that — indeed, I appreciate it to some extent — but please don’t paint it as a criticism when its not.”

But you said that although it is your own definition, it is consistent with national accounts. You also use the phrase “national accounts” in your paper.

I understand your point – if the definitional system are yours, I shouldn’t be using national accounts to criticize. For that what I have to say is that the system of national accounts is a tightly self-consistent system. Some may have criticisms here and there but nonetheless it is quite a fantastic formalism. There is just too much effort to make concepts look intuitive and closer to what it actually is.

Any other system – although very much possible – requires a substantial effort to be thoroughly self-consistent.

7. Ramanan says:

In G&L models, prices are cleared by supply and demand in some cases for example – equities.

So asset demands depend on other things price expectations. Price themselves however are cleared. But in the next time-step, asset demands – and supplies are cleared by prices but since asset demand in the previous step depends on expectations, hence the new price depends on what economic units expected it to be and on various other things.

Of course you can take issue with this – add dealers etc and you have something not clearing really and your model will have their inventories and then you model what the specialists will do with their inventories and react.

Something of the sort may interest you and I guess that’s something you are aiming for. Kaldor also stressed the role of dealers in financial markets.

• Ramanan says: