Intertemporal Say's Law

Say's Law says there cannot be a general glut: if some goods are in excess supply, other goods must be in excess demand. It's wrong, in a monetary exchange economy, as Say himself eventually realised.

Suppose you are short-sighted. You can observe the markets that are close to you in space, but you cannot see what is happening in markets farther away. Suppose you observe that the markets close to you in space are generally in excess supply. How would you diagnose the problem?

If you believed in Say's Law, your diagnosis would be easy: "The markets close to me in space are in excess supply, therefore the markets farther away must be in excess demand, and therefore the relative price of close goods to distant goods must be too high".

We are all short-sighted like that, in time rather than space. We can observe markets today, but we cannot see what is happening in markets in the future. Suppose we observe that the markets close to us in time are generally in excess supply. How would we diagnose the problem?

If we believed in Say's Law, our diagnosis would be easy: "The markets close to us in time are in excess supply, therefore the markets farther away must be in excess demand, and therefore the relative price of present goods to future goods (the real interest rate) must be too high".

Any economist who says that an excess supply of goods today means that the real interest rate must be too high is implicitly invoking Say's Law.

If there's an excess demand for money, some mutually advantageous trades won't get made, and Say's Law will fail, both across space and across time.

Comments

[Matt Young]

Ok, excess is defined as breaking say's law. Nothing wrong with that.

[Nick Rowe]

Matt: I've updated the post to define Say's Law.

[anon]

This idea of Say's law always holding across time is quite expressly found in JS Mill's essay on unsettled issues of political economy, and many other classical economists must have thought that way. Maybe the Austrians are like that, too.

It's actually quite compatible with a monetary exchange view of business cycles, as long as you keep in mind that all money is held in the view that eventually it will be spent. In this perspective, the business cycle might even be viewed as a feature, not a failure of the econony; a way of transfering purchasing power across time simply by matching economic booms to times of high, or brisk, demand for goods, and economic busts to times when demand for goods is lower, and agents care most about preserving their purchasing power for future times.

I do wonder what assumptions are needed to make this view "work", in some sense.

[BTW: I had to rescue this comment from spam. NR]

[Nick Rowe]

anon: "This idea of Say's law always holding across time is quite expressly found in JS Mill's essay on unsettled issues of political economy..."

Interesting. I didn't know that.

Suppose we had a one-period barter economy, then Say's Law would hold, because an offer to sell goods *is* an offer to buy (other) goods in exchange.

Suppose we had a two-period barter economy, but with all markets opening in the first period (so we can buy promises to deliver future goods and pay for them with present goods). Then again (intertemporal) Say's Law would hold. An excess supply of present goods would be the same thing as an excess demand for future goods.

Same if we had a centralised Walrasian market rather than multiple barter markets.

Start with a monetary exchange economy with full market-clearing in all periods. Now, for example, halve the stock of money in all periods, but keep all prices and interest rates fixed in all periods. In every period there will be an excess demand for money and an excess supply of all other goods. Say's Law fails. Every market has excess supply. (There is an excess demand for money in every market.)

[Min]

"If we believed in Say's Law, our diagnosis would be easy: "The markets close to us in time are in excess supply, therefore the markets farther away must be in excess demand, and therefore the relative price of present goods to future goods (the real interest rate) must be too high".

Or we might say, The markets close to us in time are in excess supply, therefore the markets farther away must be in excess demand, and therefore the relative price of **past goods to present goods** (the real interest rate) must be too **low**". ;)

Yes, we may have records of past markets, and looking back we can see markets that appeared to us at the time to follow Say's Law (which is one reason why we believe in it), but we were mistaken. We actually had an unfilled demand for the excess supply which we now have. ;) Or maybe they followed Say's Law at those times, and the excess demand is further back in time.

But we do not have to speculate, do we? If, in our present circumstances, there is excess supply, well, there was excess demand in the previous decade, wasn't there?

In a barter economy Say's Law is a tautology and holds for every market in every time and space locale. If I bring my chickens to market, they are **at the same time and in the same place** my supply of chickens and my demand for other goods and services. I do not need to know anything about other markets, distant in time or space. They are irrelevant.

[Min]

OC, when I say that the real interest rate is too low, I am assuming that it remains the same as it has been.

"Sie haben ihre Füße auf meinen Tischen
Und sagen: Es wird besser mit uns. Und ich
frage nicht: Wann?"

-- Bertolt Brecht, "Von Armen BB"

(They have their feet on my tables and say, Things will get better for us. And I do not ask, When?"

[Nick Rowe]

Min: "Or we might say, The markets close to us in time are in excess supply, therefore the markets farther away must be in excess demand, and therefore the relative price of **past goods to present goods** (the real interest rate) must be too **low**". ;)"

Shouldn't we say: "therefore the **past** real interest rate must have been too low"?

And if there were excess demand in the past, and excess supply now, that might be the correct diagnosis (Austrians will love that!) but there's nothing we can do now about that past too low real interest rate. If some capital goods unexpectedly fell to Earth like manna from heaven, would we destroy them? If God had created too much land, or if we suddenly discovered new land we didn't know existed, would that cause a recession?

"But we do not have to speculate, do we? If, in our present circumstances, there is excess supply, well, there was excess demand in the previous decade, wasn't there?"

If you are in a valley, and look back, it will always look like a hill. But it might be a valley cut into a flat plain.

"In a barter economy Say's Law is a tautology and holds for every market in every time and space locale."

Yep. And even in a monetary exchange economy, the amount of money offered for sale in that market is a demand for goods in that market, and the amount of goods offered for sale is a demand for money in that market. But money is bought and sold in every market.

[Min]

Nick Rowe: "If God had created too much land, or if we suddenly discovered new land we didn't know existed, would that cause a recession?"

Well, we have some history about that, don't we? :)

[Jacques René Giguère]

Nick Rowe: "If God had created too much land, or if we suddenly discovered new land we didn't know existed, would that cause a recession?"
But that would cause a change in PSST. Wouldn't the adjustment period be falsely viewed as a recession? ( as a rise in the real price of, let's say oil, be viewed falsely as inflation as it was in '70's?)

[Dan]

Isn't this a complicated way to say that Say said that supply creates it's own demand. However, money creation can't create it's own demand because it is costless to produce.

[JW Mason]

I am writing a post on this now, but I don't think this is correct.

Or rather, I think it is correct as a characterization of how some (many? most? almost all?) economists think, but I don't think it follows logically.

The problem is that the term "interest rate" gets used in two distinct ways. In much of economic theory, "interest rate" means the rate of exchange between goods in two different periods. In equilibrium, the same rate should be incorporated into any trade with an intertemporal component.

But in policy discussions, and in general in discussion of the economy around us, "interest rate" means the coupon or yield on a bond or other debt contract. And while there is SOME relationship between these two prices they are certainly not the same, and there is absolutely no reason to single out the bond yield as the "interest rate" of theory, as opposed to the home price-rent ratio, or the profit rate, or the deflation rate, or the ratio of the college wage premium to tuition costs, or any other price with an intertemporal component.

For monetary policy, there really isn't (or anyway shouldn't be) any assumption that the "interest rate" set by policy, and its effect on current demand, has anything to do with the intertemporal substitution rate at all.

I am thinking about buying a home. i could buy it by taking out a mortgage. If I decide to do so, then I expect the flow of housing services I get from the house will exceed my debt service payments in all periods. And on the bank's side, the transaction simultaneously creates an asset and a liability. If they think the loan is worth making, they expect the payments from the asset (the mortgage) to exceed their costs in all periods. Nobody has given up any expenditure in any period. There is no intertemporal component to this transaction at all.

Lose monetary policy makes these sorts of transaction more attractive, and increases the amount of housing produced in the present. This raises present output and demand. But there is no intertemporal exchange being made.

[Mark A. Sadowski]

Off Topic.

This past weekend I expanded my Granger causality tests to more thoroughly cover four zero lower bound episodes when the monetary base was significantly expanded (i.e. when there was QE): 1) US from May 1933 to February 1937, 2) US from July 1937 through November 1941, 3) Japan from March 2001 through May 2006 and 5) the UK from April 2009 through September 2013. Note that since Japan only started QE in earnest in April 2013 I have not included this episode yet because the period is too brief. The time periods were selected based on the level of interest rates. The US periods in the 1930s are when the 3-month T-Bill yield was 0.29% or less. The Japanese period was selected based on when the call rate was 0.1% or less. The UK period was selected based on when the bank rate was 0.5% or less. The most recent US episode is when the federal funds rate dropped below 0.25%.

I shall review the test results for the US over December 2008 through September 2013 and then cover each of the other four periods.

1) US December 2008 - September 2013

The monetary base Granger causes loans and leases at commercial banks at the 5% significance level. The M1, M2 and MZM money multipliers each Granger cause loans and leases at commercial banks at the 5% significance levels. These results are the exact opposite of what Accomodative Endogeneity predicts.

The monetary base Granger causes 5-year inflation expectations as measured by TIPS at the 1% significance level. The monetary base Granger causes the PCEPI, the real broad dollar index, the 10-year T-Note yield (the impulse response is significantly *positive*), the S&P 500 and the DJIA at the 5% significance level. In addition the 10-year T-Note Granger causes the monetary base at the 10% significance level.

2) US May 1933 - February 1937

For the US during the 1930s I used the Friedman and Schwartz M1, M2 and M3 money supply measures (M4 was not available).

The monetary base Granger causes loans at Federal Reserve System member banks at the 5% significance level. The M2 and M3 money multipliers Granger cause loans at Federal Reserve System member banks at the 5% and 10% significance level respectively. This is the exact opposite of what Accomodative Endogeneity predicts.

In addition the monetary base Granger causes commercial bank deposits at the 5% significance level.

3) US July 1937 - November 1941

M1, M2 and M3 Granger cause loans at Federal Reserve System member banks at a 5%, 10% and 5% significance level respectively. This represents a partial rejection of Accomodative Endogeneity.

However, commercial bank deposits Granger cause loans at Federal Reserve System member banks at the 10% significance level which is the opposite of what one might expect if Accomodative Endogeneity were true (i.e. that "loans create deposits").

4) Japan March 2001 - May 2006

Japan has two measures of lending counterparts to broad money: 1) "loans and discounts" and 2) "loans and discounted bills". Japan has four measures of broad money: M1, M2, M3 and L.

There is bidirectional Granger causality between the monetary base and lending (both measures) at the 1% significance level.

M1 granger causes loans and discounts at the 5% significance level. There is bidirectional Granger causality between M2 and loans and discounts at the 1% significance level. There is bidirectional Granger causality between M3 and loans and discounts at the 1% significance level. Loans and discounts Granger cause the M1 money multiplier at the 5% significance level.

Loans and discounted bills Granger causes M1 at the 1% significance level. M2 Granger causes loans and discounted bills at the 1% significance level and loans and discounted bills Granger causes M2 at the 5% significance level. There is bidirectional Granger causality between M3 and loans and discounted bills at the 10% significance level. There is bidirectional Granger causality between the M2 money multiplier and loans and discounted bills at the 10% significance level. The M3 money multiplier Granger causes loans and discounted bills at the 10% significance level and loans and discounted bills Granger causes [the] M3 [money multiplier] at the 5% significance level. There is bidirectional Granger causality between the L money multiplier and loans and discounted bills at the 10% significance level.

All of this together is broadly supportive of Structural Endogeneity. However the sum of "deposit money" and "quasi money" (the deposit component of broad money with the sole exception of CDs, which was not available for the entire period) Granger causes both measures of lending at the 1% significance level which is the opposite of what one might expect if Accomodative Endogeneity were true.

In addition, the monetary base Granger causes the Nikkei 225 at the 10% significance level and there is bidirectional Granger causality between the monetary base and the sum of deposit money and quasi money at the 5% significance level.

5) UK April 2009 - September 2013

The UK's measure of broad money is denoted M4. In addition the BOE also estimates M1, M2 and M3 measures according to Euro Area standards. The lending counterpart of M4 is denoted M4Lx.

M1 Granger causes M4Lx at the 10% significance level. This represents a partial rejection of Accomodative Endogeneity.

The monetary base Granger causes 5-year inflation expectations as measured by inflation-linked gilts at the 1% significance level. The monetary base Granger causes the real effective exchange rate of the pound sterling and the industrial production index at the 5% significance level. The monetary base Granger causes the deposit component of the Euro Area measures of broad money at the 10% significance level. In addition the deposit component of M4 Granger causes the monetary base at the 10% significance level.

[Edited by NR to fix typos. See Mark's comment below]

[Min]

From some web searching it appears that the discovery of new land did not throw European economies into recession in the 16th century.

"In short, this of this century {1540-1660} as the century of dislocation in general, and of roller-coaster shifts between inflation and recession at more local levels, with profound effects on just about every aspect of European economy and society." -- Skip Knox ( http://europeanhistory.boisestate.edu/reformation/economics/overview.shtml )

[JW Mason]

We can think of the total expected return on any asset, which is equalized in equilibrium as being: y + l - d - c- r + g - i , where y is the the yield, l is the liquidity from holding the asset, d is the depreciation rate, c is the carrying costs, r is the risk, g is the expected capital gain or change in relative price, and i is the pure rate of time discount. Monetary policy is operating mainly on l, with some effect on r and g. By increasing the supply of liquidity, and also perhaps reducing some risk perceptions and raising expected price rises on tangible assets, it is encouraging away from provision for the future in financial form, and toward provision for the future in the form of tangible goods. The latter stimulates present demand, the former does not. But, again, the intertemporal substitution rate doesn't come into it.

A paper like Samuelson 1958 is brilliant but the world of pure consumption loans it models has no relevance for discussions of monetary policy.

[JW Mason]

Oops, that should be:

encouraging SUBSTITUTION away from provision for the future in financial form, and toward provision for the future in the form of tangible goods.

[anon]

Nick, the "problem" in your model is of course that you simply assume a halving of the money supply, for whatever reason. The intuition I'm talking about clearly relies on the supply of money being stable in some sense, so that all changes occur via the demand for money, reflecting precautionary/store-of-value reasons. I think even Mill might agree with that - he only really considers shifts in the supply of "broad" money (due to changing business perspectives), not what we might call the monetary base. And it's easy to see how these shifts might even out across time, in some sense.

[Mark A. Sadowski]

Correction on Japan:

“The M3 money multiplier Granger causes loans and discounted bills at the 10% significance level and loans and discounted bills Granger causes M3 at the 5% significance level.”

should read

“The M3 money multiplier Granger causes loans and discounted bills at the 10% significance level and loans and discounted bills Granger causes the M3 money multiplier at the 5% significance level.”

[Nick Rowe]

Jacques Rene: I think there's some sense to the PSST approach, if there's a sudden unexpected increase in supply. Yes.

Dan: "Isn't this a complicated way to say that Say said that supply creates it's own demand."

Supply creates its own demand. There cannot be an excess supply of all goods. To me these are equivalent versions of Say's Law.

"However, money creation can't create it's own demand because it is costless to produce."

It's got nothing to do with being costless to produce. If money were costly to produce, and we reallocated resources away from producing other goods and into producing more money, it still wouldn't increase the demand for money automatically.

JW: "Or rather, I think it is correct as a characterization of how some (many? most? almost all?) economists think, but I don't think it follows logically."

What I am trying to do here is to characterise how many/most/almost all economists think, and say it's illogical. But for different reasons than you.

Yes, there are many different interest rates and rates of return, and they will differ by term, risk, liquidity, and different measures of expected inflation. But if I sell apples today, buy some asset with the proceeds, then sell that asset next year, and buy apples next year, the nominal rate of return on that asset, minus the inflation rate on apples, will give me the relative price of present vs future apples. If monetary policy causes all real one-year yields to move in the same direction, even if by different amounts (which I think is what many/most/almost all economists believe), you get the result I'm criticising here.

You lost me on the later bit.

Mark: interesting stuff, even though I have my doubts about Granger causality.

Min: but when they found the new land, didn't they also find a lot more gold too?

JW: Agreed that samuelson 58 isn't really about monetary policy. It could be understood as a model of fiscal policy, and the optimal debt/GDP ratio, in a world of perfectly flexible prices.

The "mainstream" (God I really shouldn't use that word) Neo-Wicksellian approach says that central banks set "the" rate of interest, and that the Marginal Rate of Substitution between present and future consumption, and the Marginal Rate of Transformation between present and future consumption, both adjust in response to changes in that rate of interest. Just as the MRS and MRT between labour and gold would adjust if the money price of labour were sticky and the central bank set the money price of gold.

anon: OK, but I see a doubling of the demand for money as equivalent to halving the supply of money. Both would cause an excess demand for money, and a violation of Say's Law.

Mark: I edited your previous comment to fix that typo.

[nemi]

@JW Mason; "We can think of the total expected return on any asset, which is equalized in equilibrium as being: y + l - d - c- r + g - i , "

Does this not describe the price that you are willing to pay for an asset, and does the fact that this has nothing to do with the intertemporal substitution rate not follow from the basic Fisher separation theorem (unless you are liquidity constrained, which you are likely to be in the real world, and if the financial markets work perfectly, which they are unlikely to do in the real world)?

[JW Mason]

The "mainstream" (God I really shouldn't use that word) Neo-Wicksellian approach says that central banks set "the" rate of interest, and that the Marginal Rate of Substitution between present and future consumption, and the Marginal Rate of Transformation between present and future consumption, both adjust in response to changes in that rate of interest. Just as the MRS and MRT between labour and gold would adjust if the money price of labour were sticky and the central bank set the money price of gold.

Right. And I am saying that this is wrong. Because the interest rate set by the central bank and the intertemporal rate of substitution enter into different, basically disjoint sets of prices.

The adjustment that happens as a result of a change in monetary policy brings the supply and demand for balance-sheet liquidity into balance. Yes, the intertemporal rate of substitution will presumably be affected by a change in policy, just as all other relative prices will, but that's not the margin policy operates on.

Nemi: I'm not sure what you mean. Can you explain?

[Nick Rowe]

JW: you are starting to sound like a monetarist!

[J.V. Dubois]

Neat! I know that you posted somewhat similar things before, like saying that excess supply of goods does not automatically mean excess demand for bonds + peanut theory of recessions and all that. But this is a fresh angle that did not occur to me before. I really don't know how you do it to come up with this stuff but keep it comming. I hope DeLong reads it as he seems to be quite interested in Says law so maybe this will get through to him to provoke some interesting response.

PS: I am a little bit sad that your last few posts on New Keynesyan models did not provoke any response. I had nothing to add but it was still interesting. I hope you will bring it back from time to time because it needs to be responded to.

[Nick Rowe]

JV: Thanks! Yep, there's not really anything new in this post I haven't said before. I'm pulling previous ideas together. But sometimes it helps to look at the same things from a different angle.

[Jacques René Giguère]

We did discover new lands : America with the caravelles, and now China with Post-Malaccamax container ships. The second discovery meant the destruction of the western working class.

[Ritwik]

"Any economist who says that an excess supply of goods today means that the real interest rate must be too high is implicitly invoking Say's Law."

Walras's Law, not Say's, correct? Hidden parameters are total income/unemployment. And if income/unemployment adjusts faster than the real interest rate, you have an inter-temporal recession without violating Walras's law.

[Dan]

I think a simpler point needs to be made here. Leave interest rates entirely out of it for a moment.

Why does supply create its own demand: because supply has costs. If you want to supply more oil, you have to buy oil rigs, pay workers, lease land rights. All of those costs become income to someone else (or to oneself if you are lucky and make a profit).

If too much energy becomes available, the price goes down. Why does the economy not slow down? Because, the relative price of another good has gone up and people will on the margin go and start supplying the higher priced good (lets say cars in this example that become more attractive as energy prices fall) and in the process generate costs which are someone else's income - life goes on and Say says (correctly) that supply creates its own demand. And the world is happy because in total, the economy expands even though the price of somethings have fallen due to over supply.

So why does Says law not work all the time? It seems to be true but: Says law will not work if the good whose relative price has gone up can be produced with no costs - therefore without generating income for someone else (or profit for oneself).

Says law doesn't work when an economy uses a money that is cost-less to produce AND at times in that economy when money becomes the good that is desired on the margin. Obviously the global financial crisis caused just such a situation.

Here are some interesting conclusions that may follow if this story is correct:
This explains why Fiscal policy is necessary - money is being demanded - it is being supplied without creating income - this obviously creates a lack of demand. If the government is creating the money, its only natural that they should take the other side and create the income as well.

What to do with interest rates becomes more curious - One possible response to this situation (if you don't want to take the obvious one and just use fiscal policy to create the demand from the cost-less supply of money) would be to make money really unattractive by raising interest rates. I think this is why people are getting confused about the interest rate situation right now (SW). Of course, that gets messy because it will at the very least cause short term disruptions on the demand side for interest rate sensitive activities.

[Nick Rowe]

Ritwik: Walras' Law is normally taken to mean:

Sum P(Qd-Qs) over all goods + Md-Ms = 0

It is more reasonable than Say's Law, but still wrong IMO.

Say's Law leaves out the Md-Ms bit.

Dan: Say's Law has nothing to do with costs of production. Imagine a pure endowment barter economy, where all goods fall from heaven. Say's Law would work fine.

[Dan]

But Nick, that gets me back to the same place. If goods fall from the sky and presumably then all goods are consumption goods everyone has income (in the form of heavenly goods) but not all goods are the same (presumably) so I want to swap part of my heavenly goods with yours - thus creating some measurable economy. But this only works if the goods keep falling ie. if there is income and if both of us are equally endowed (so to speak). what if the heavens only drop goods on you and not me - supply won't be able to create a trade because I don't have an income (in this case in the form of heavenly goods).
I just don't see how Say's law doesn't depend on the daisy chain of my costs being someone else's income, and as soon as I take some action that stops the daisy chain the whole thing stops. This is the same situation with saving/investment It's great if I save and you invest, but what happens if I save and you don't invest.
Aren't these two of the basic points Keynes made? Says law does work, but doesn't have to; I does equal S, but doesn't have to.

[Nick Rowe]

Dan: suppose, every year apples and bananas fall from the skies (or trees). But half the people get only apples, and the other half get only bananas. So I supply half my apples to you, demanding bananas in exchange.

[Nick Rowe]

And if nothing drops on you, you have nothing to supply and nothing to demand in exchange.

[Dan]

Here's a possible way to ask my question.
In your original post you conclude that "If there's an excess demand for money, some mutually advantageous trades won't get made, and Say's Law will fail, both across space and across time."

Can money be substituted for any other item and the statement still hold true, or in a barter economy, what would make Say's law fail, or is there something unique about money that makes that only true for money, and if so, what.

Presumably the issue is a general failure as specific adjustments are taking place all the time.
My conjecture is that it's only true for money, and the reason is that money is unique in that it is cost-less to produce. Or in our land of banana's and apples - a day when someone gets bananas and no one gets apples, the supply of bananas has not created any demand.

[Nick Rowe]

Dan: here's my old post on the subject

[Dan]

"The individual can always get more money by buying less other goods even if he can't get more money by selling more other goods."

That works, though I'll have to reflect on it for awhile to really digest it. It feels close to saying money is cost-less.

This all reminds me of my suspicion that Econ could be improved by discarding 'equilibrium'.

[Dan]

Ughh...
I still keep coming back to money breaking the my expense is your income daisy chain being the problem.
Reading this this morning reminded me:
"Back in 1936 ... Keynes argued that increased government spending was needed to restore full employment. But then, as now, there was strong political resistance... So Keynes whimsically suggested ... the government bury bottles full of cash in disused coal mines, and let the private sector spend its own money to dig the cash back up. ..."