As I, at least, see it, there are four big questions in the debate over “Say’s Law”:

  1. Is Walras’s Law–the claim that at any price factor the excess demand for all commodities taken together must adept zero–a good way to think about macroeconomics in general, or do we have to jump to Clower-Leijonhufvud-Malinvaud rationed-equilbrium approaches?
  2. Does it therefore immediately provide a refutation of the naïve Say’s Law claim–the claim that there is no such thing as a “general glut”, as an excess demand of commodities as a whole and of labor–via John Start Mill’s observation that, in Walras’s Law terms, an excess demand for money is an excess supply of commodities in general plus labor?
  3. Did the people whom Keynes claimed really believed in their hearts-of-hearts in “Say’s Law” from Say to Pigou actually do so?
  4. If (2) holds, how do we make sense of 2008-2014 (and of other episodes) given that an excess demand for money should show itself in high interest rates, as people dump interest-earning assets to try to build up their stocks of liquid cash money?

Four big questions. Five related posts in dialogue with each other that shed some light on them:

David Glasner: Who’s Afraid of Say’s Law?: “There were two famous objections made to Say’s Law:

first, current supply might be offered in order to save for future consumption, and, second, current supply might be offered in order to add to holdings of cash. In either case, there could be current supply that is not matched by current demand for output, so that total current demand would be insufficient to generate full employment…. The savings argument goes back to the nineteenth century, and the typical response was that… the shortfall in consumption demand would lead to an increase in investment demand driven by falling interest rates and rising asset prices…. Keynes proposed an argument about liquidity preference and a potential liquidity trap, suggesting a reason why the necessary adjustment in the rate of interest would not necessarily occur….

The argument that the existence of money implies that Say’s Law can be violated was widely accepted…. Oskar Lange… introduced a distinction between Walras’s Law and Say’s Law (“Say’s Law: A Restatement and Criticism”)…. Lange showed that Walras’s Law reduces to Say’s Law only in an economy without money. In an economy with money, Walras’s Law means that there could be an aggregate excess supply of all goods at some price vector, and the excess supply of goods would be matched by an equal excess demand for money. Aggregate demand would be deficient, and the result would be involuntary unemployment….

One of my regular commenters, Tom Brown, asked me recently whether I agreed with Nick Rowe’s statement: “the goal of good monetary policy is to try to make Say’s Law true.” I said that I wasn’t sure what the statement meant, thereby avoiding the need to go into a lengthy explanation about why I am not quite satisfied with that way of describing the goal of monetary policy.

There are at least two problems with Lange’s formulation of Say’s Law. The first was pointed out by Clower and Leijonhufvud…. Lange’s analysis was based on the absence of trading at disequilibrium prices…. In a real-time economy in which trading is routinely executed at disequilibrium prices, transactors may be unable to execute the trades that they planned to execute at the prevailing prices. But when planned trades cannot be executed, trading and output contract, because the volume of trade is constrained by the lesser of the amount supplied and the amount demanded…. If transactors do not succeed in supplying as much as they planned to supply at prevailing prices, then, depending on the condition of their balances sheets, and the condition of credit markets, transactors may have to curtail their demands in subsequent periods….

Paul Krugman: HearSay Economics: “David Glasner has another interesting post on the history of economic thought, this time on Say’s Law–which, at least since Keynes, has come to be identified as the doctrine that shortfalls in overall demand aren’t possible, because money has to be spent on something….

Keynes structured the early chapters of his General Theory as a debunking of this proposition; Glasner calls it a “misdirected tirade”. But Keynes was right…. I understand that you can argue about whether that’s what Say himself really meant; you can also argue about whether the “classical” economists Keynes takes on, men who believe in this version of Say’s Law, really existed.

But you know what? I don’t much care. The fact is that the fallacy Keynes called Say’s Law was and is a powerful force in economic discourse, seriously hampering our ability to respond rationally to economic troubles.

Do you want to assert that nobody important believes in Say’s Law? How about Eugene Fama and John Cochrane? Fama:

The problem is simple: bailouts and stimulus plans are funded by issuing more government debt. (The money must come from somewhere!) The added debt absorbs savings that would otherwise go to private investment. In the end, despite the existence of idle resources, bailouts and stimulus plans do not add to current resources in use. They just move resources from one use to another.

Cochrane (link to original is dead):

First, if money is not going to be printed, it has to come from somewhere. If the government borrows a dollar from you, that is a dollar that you do not spend, or that you do not lend to a company to spend on new investment. Every dollar of increased government spending must correspond to one less dollar of private spending. Jobs created by stimulus spending are offset by jobs lost from the decline in private spending. We can build roads instead of factories, but fiscal stimulus can’t help us to build more of both.1 This is just accounting, and does not need a complex argument about “crowding out.”

And here’s Brian Riedl of Heritage:

The grand Keynesian myth is that you can spend money and thereby increase demand. And it’s a myth because Congress does not have a vault of money to distribute in the economy. Every dollar Congress injects into the economy must first be taxed or borrowed out of the economy. You’re not creating new demand, you’re just transferring it from one group of people to another. If Washington borrows the money from domestic lenders, then investment spending falls, dollar for dollar.

So we don’t need to settle the debate about what, say, Pigou actually believed. The fallacy Keynes did battle with is very real, held by people in positions of great influence, right now.

Brad DeLong: Kenneth Rogoff’s Hooverismo…: “But… But… But…

About the Rogoff argument: If markets stop buying government debt, then they are buying something else: by Walras’s Law, excess supply of government debt is excess demand for currently-produced goods and services and labor. That is not continued deflation and depression, that is a boom–it may well be a destructive inflationary boom, and it may be a costly boom, but it is the opposite problem of an deflationary depression

So, by continuity, somewhere between policies of austerity that that produce deflationary depression due to an excess demand for safe assets and policies of fiscal license that produce inflationary boom caused by an excess supply of government debt, there must be a sweet spot: enough new issues of government debt to eliminate the excess demand for safe assets and so cure the depression, but not so much in the way of new issues of government debt to produce destructive inflation, right?

Why not aim for that sweet spot?

Certainly Cameron-Osborne-Clegg were not aiming for that sweet spot, and the John Stuart Millian using the government’s powers to issue money and debt to balance supply and demand for financial assets and so make Say’s Law true in practice even though it is not true and theory?

Brad DeLong: National Review Strikes Again!: “Mark Thoma us that the know-nothings at National Review are launching hit pieces on Ben Bernanke. Mark attempts the task of cleaning out the entire stable. I’m just going to deal with the first piece….

John Tamny on Ben Bernanke and the Federal Reserve on NRO Financial: Bernanke asked how much demand in the latest quarter “appears to have been satisfied out of inventories rather than from new production.” But supply-siders don’t even consider this–they don’t because they know that products are ultimately bought with other products. “Demand” will always exist, as human wants are unlimited. But what Bernanke deems “demand” is in fact producers offering up their surpluses for those of others. In the supply-side model, what Bernanke sees as a fall in aggregate demand is in fact a fall in production–something supply-siders agree results from governmental meddling along the lines of excessive taxation, regulation, and unstable money…

Bernanke’s point is that in the second quarter households, the government, and investing businesses bought one-half percent more goods and services than U.S. producers made and U.S. businesses (net) imported. Thus inventories are now below levels that businesses think they need to run their operations efficiently. In the next several quarters, therefore, businesses are going to ramp up production in order to build their inventories back to a comfortable level. This is an important thing to notice. It is not a contentious or a disputed point–except to the likes of John Tamny.

Tamny is enraged that Bernanke is thinking about fluctuations in employment and capacity utilization at all. We, Tamny says, “don’t even consider this” because “‘[d]emand’ will always exist, as human wants are unlimited…. [W]hat Bernanke sees as a fall in aggregate demand is in fact a fall in production…” Let us not comment on the fact that Tamny is too stupid to notice that what Bernanke is talking about is not a fall but a rise in aggregate demand: that’s just too embarrassing for words. Let us, instead, comment that Bernanke is talking about a fact about the world–that spending was larger than production in the second quarter. And Tamny’s response is that that fact doesn’t exist: because “products are ultimately bought with other products,” spending cannot be anything other than equal to production. In Tamny’s world, theory proves that fluctuations in unemployment and capacity utilization are logically impossible.

Now there was an economic theory that held that fluctuations in unemployment and capacity utilization were logically impossible: that supply was automatically equal to demand. That theory is called “Say’s Law,” after nineteenth-century French economist Jean-Baptiste Say. That theory wrong: there are fluctuations in unemployment and capacity utilization. And because that theory is wrong, we have the Federal Reserve. One way to think about the Federal Reserve’s mission is that it’s job is to try to make sure that spending is matched to production–to make Say’s Law true in practice, even though it is not true in theory.

Bernanke’s attention to the details of aggregate demand is, of course, on of the reasons that he is exceptionally highly qualified to chair the Federal Reserve.

Nick Rowe: Worthwhile Canadian Initiative: Money, interest, employment, and luck: “Monetary disequilibrium theorists must face this question: ‘If this recession was caused by an excess demand for money, how come interest rates are so low? Doesn’t an excess demand for money mean an excess supply of bonds and rise in interest rates?’

[Warning: this post is long, rambling, and unclear. I ought to tear it up and write a couple of shorter and clearer ones. I may do that later, when (if) I get my head clearer. Read at your own risk. Maybe skim it first.]

Despite all my brilliant theoretical proofs of the metaphysical necessity of monetarism–how a general glut can only be caused by an excess demand for the medium of exchange–Brad DeLong has got the perfect comeback: “OK, the 1982 recession was caused by an excess demand for money, as shown by the very high interest rates. But the recent recession must have been caused by an excess demand for safe assets in general, otherwise we wouldn’t be seeing interest rates on safe assets near zero.” (He didn’t actually say those words, but he might have done.)

So I’m going to sketch a simple model where an excess demand for money causes a recession but no rise in (real or nominal) interest rates.

The basic idea is simple. An excess demand for money causes unemployment for the “unlucky”. The unemployed can’t borrow (nobody will lend to the unemployed), and can only spend down their money balances by buying from those who are “lucky” and remain fully employed. The lucky employed get the money that used to be held by the unlucky unemployed. So nothing changes for the employed. And the unemployed are shut out of all markets, so can’t affect the equilibrium. And if unemployment causes expected deflation, nominal interest rates will fall via the Fisher effect.

[Warning to lefties: before you get too excited by this model, remember that the distribution of money is not the same as the distribution of wealth. This model is much closer to Milton Friedman than to Karl Marx.]

Before getting started on building the model, I need to talk about loanable funds vs liquidity preference, the ISLM model, and take a sort of cheap shot at Paul Krugman to illustrate my point. (It would be a cheap shot if I didn’t admit it were a cheap shot, if you can handle the Liar Paradox.)

Digression on loanable funds vs liquidity preference and ISLM and Paul Krugman and stuff:

The price of apples (if it is flexible) is set in the apple market to equilibrate the demand and supply of apples. If there’s an excess demand for apples it rises; if there’s an excess supply of apples it falls.

OK. So where is the rate of interest set? What market? What are the demands and supplies it is supposed to equilibrate?

Liquidity Preference says it is set in the money market, to equilibrate the demand and supply of money. Which is totally stupid, because there is no money market. Or rather, in a monetary exchange economy every market is a market for money plus one other good. When finance guys talk about the “money market” they are really talking about the market for short-term loans. When you lend someone money, you get an IOU in return. That IOU is a bond. So when we talk about “the money market” we are really talking about the bond market. So let’s call the thing by its proper name. The “apple market” is the market where money is exchanged for apples; the “bond market” is the market where money is exchanged for bonds.

But isn’t the “bond market” just another name for the market in “loanable funds”? If so, what the hell is the difference between the liquidity preference and loanable funds theories of the rate of interest?

Another way of describing the loanable funds theory is to say that the rate of interest adjusts to equilibrate desired savings and desired investment. OK. But since (closed economy) national savings is defined as Y-C-G, we can do some trivial math and re-write S=I as C+I+G=Y. So loanable funds says that the rate of interest adjusts to equilibrate desired consumption plus desired investment plus desired government spending to desired sales of newly-produced goods? In other words, loanable funds says that the rate of interest adjusts to equilibrate the output market?

Which is weird. Sure, the demand for output may depend on the rate of interest. But can we jump from that to saying that the rate of interest is set in the output market? Can we say that an excess demand for output will put upward pressure on the rate of interest? The rate of interest is the (reciprocal of) the price of bonds, not the price of output. The demand for apples may depend on the price of pears. But we don’t say that the price of pears is determined in the apple market.

The ISLM model was supposed to reconcile the liquidity preference and loanable funds theories of the rate of interest. IS shows the loanable funds answer, as a function of Y; LM shows the liquidity preference answer, as a function of Y. In the short run, with M/P fixed, Y adjusts until both curves give you the same answer. In the long run with P and hence M/P flexible, and Y fixed by the LRAS curve, M/P adjusts until the two curves give the same answer.

But the ISLM is trying to reconcile two opposing theories of the rate of interest, neither of which make any sense.

Here’s my cheap shot at Paul Krugman:

Paul says (H/T Brad De Long):

Now equilibrium in a three-good model can be represented by drawing curves that indicate combinations of prices for which each of the three markets is in equilibrium.

No it can’t. At least, not if one of the three goods is called “money”. In a barter economy, with n goods, there are n(n-1)/2 markets. So if n=3 that means three markets. But in a monetary exchange economy with n goods (including money) there are (n-1) markets. So if n=3 that means two markets.

Paul also says:

Although there are three curves, Walras’ Law (if all markets but one are in equilibrium, that market is in equilibrium too) tells us that they have a common intersection, which defines equilibrium prices for the economy as a whole.”

But Walras’ Law is wrong in a monetary exchange economy. It only works in a Walrasian General Equilibrium model with a single market in which all n goods can be traded for each other and no agent is ever unable to buy or sell as much as he wishes. That’s very different from a model of a monetary exchange economy used to explain excess supply recessions where people can’t sell as much labour as they want.

This is a cheap shot because lower down Paul says:

Sixty years on, the intellectual problems with doing macro this way are well known. First of all, the idea of treating money as an ordinary good begs many questions: surely money plays a special sort of role in the economy.

Yes. Money does play a special role. For one thing, money does not have a market of its own. It is traded in every market against every other good; and all the other goods are traded only against money. For a second thing, if we lump all output into one good, we have to recognise that every agent is both a buyer and a seller of that good. We sell our own output for money; and use money to buy others’ output. We don’t barter our own output for others’ output.

So let’s start from scratch.

A sketch of my model:

There are three goods: backscratches; bonds; and money. There are two markets: the output market, where backscratches are traded for money; and the bond market, where bonds are traded for money. The rate of interest (aka the price of bonds) is perfectly flexible. It adjusts instantly to excess demand or supply for bonds, so the bond market always clears. The price of backscratches is sticky, or fixed if you like, in terms of money. So the market for backscratches may not clear.

People must trade, because you can’t scratch your own back. And you can’t barter backscratches, or trade them for bonds (promise to pay later) because you can’t see a person’s face when you are scratching his back. (OK, so cook up your own silly story for the microfoundations of monetary exchange).

That makes the output market very different from the bond market. Each agent is either a buyer of bonds or a seller of bonds. But each agent is both a buyer and seller of output.

All agents are identical, except: agents differ by “luck”. Luck is distributed along a continuum. In the event of an excess supply of backscratches, where demand is only 60% of supply, the luckiest 60% of agents will be able to sell as many backscratches as they want, and the unluckiest 40% will be able to sell none.

Unlucky agents, who are unemployed, are unable to access the bond market. Everyone knows they are unemployed, and therefore unlucky, so they cannot borrow money from lucky agents because they might stay unemployed and not be able to repay the loan. (OK, this assumption could be relaxed a bit, but shouldn’t affect the results too much).

In advance of a recession, agents don’t observe their own luck, so all agents are identical ex ante, and the unlucky won’t save more than the lucky.

Start in full-employment equilibrium. All agents are buying and selling backscratches for money. But no bonds are traded, because all agents are ex ante identical. In full-employment equilibrium, it’s a representative agent model.

Now let’s shock the model.

Shock 1: This example is very contrived, but is also the simplest. Assume that a fire destroys all the stock of money held by the unluckiest half of the population. In this example, the unlucky are doubly unlucky. They are unlucky in the market for backscratches, and they are unlucky in the fire too. What happens?

In the new equilibrium the economy carries on exactly the same as before for the lucky half of the population, while the unlucky half of the population is shut out of all markets, and so has no effect on the equilibrium. The rate of interest initially stays the same.

The unlucky unemployed have no money, so can’t buy backscratches. They will want to borrow money, but nobody will lend to them, because they are unemployed. They want to sell backscratches, but the lucky employed are already buying as many backscratches as they want from each other, and the unlucky are at the end of the queue supplying backscratches, so the demand runs out at the halfway point. The fire that destroyed their money might as well have destroyed them too, in terms of how it affects the equilibrium in the luckier half of the economy. Except:

Of course, the excess supply of backscratches will slowly cause the price of backscratches to fall (assuming it’s sticky but not stuck). Given long enough, this fall in the price level will increase the real money supply by enough to restore full employment. But in the meantime the expected deflation will lower the equilibrium nominal rate of interest.

Shock 2: Now assume half of each agent’s stock of money gets destroyed by fire. (So, unlike Shock 1, the unlucky agents are only unlucky in the market for backscratches, not in the fire.) What happens?

Initially, each agent will respond in three ways. He will supply more bonds. He will supply more backscratches. He will demand fewer backscratches. All to try to rebuild his stock of money. But since the stock of money is fixed, they must collectively fail.

Since there is an excess supply of backscratches, some agents near the unluckiest end of the spectrum will be unemployed. They cannot sell backscratches to earn income. They cannot sell bonds to tide them over till the recession ends. They can slowly run down their stocks of money, which is earning 0% interest. Or they can sell some of that money to buy bonds, to earn positive interest, then slowly run down that stock of bonds. Either way, the money once held by the unemployed will, immediately or over time, end up in the pockets of the employed.

What does the new equilibrium look like?

To a first approximation, the equilibrium in Shock 2 will look exactly the same as the equilibrium in Shock 1. The only difference between the two shocks is a small change in the distribution of wealth. The unlucky half of the population is slightly better off, and the lucky half of the population slightly worse off, in Shock 2 than in Shock 1. At the previous equilibrium rate of interest, the unlucky unemployed will want to buy bonds with money, and the lucky employed will want to sell bonds for money. So both the demand and the supply of bonds will increase relative to Shock 1. This small change in the distribution of wealth will have an ambiguous effect on the rate of interest, compared to the equilibrium in Shock 1. And that effect will be small anyway, since stocks of money are such a small part of total wealth.

So, in Shock 2 as in Shock 1, the initial impact of the excess demand for money will be to leave the rate of interest (approximately) unchanged. And since the excess supply of backscratches will eventually cause expected deflation, the nominal rate of interest will fall.

Relaxing the key assumption:

What happens when we relax the assumption that the unemployed cannot borrow by issuing and selling bonds? The unemployed would want to borrow to smooth their consumption stream over time, and will be able to pay back the loan if the recession is short-lived. But the IOUs (bonds) they issue will be riskier, and will have to pay a higher rate of interest, than the safe bonds issued by employed agents. That might be a way to reconcile my model with Brad DeLong’s theory that the recession was caused by an excess demand for safe assets. But, I would want to insist that it was the recession that caused previously safe bonds to become unsafe, and the recession was caused by an excess demand for money.