There are two multipliers we teach in first year: the money multiplier; and the "keynesian" (Hawtreyan?) multiplier. Both are set aside as embarrassing reminders of childhood. Let me defend them both. They have a lot in common.

Alone again or, just me and the money multiplier, against the world of trendy sophisticates who have put aside such childish things. It brings out the reactionary contrarian in me. And the world needs more reactionary contrarians, to help provide negative feedback against the faddish bubble multiplier of popular theory.

Most of economics is about negative feedback processes. An increased demand for apples creates an initial excess demand for apples. But that in turn causes the price of apples to rise, which reduces quantity demanded and increases quantity supplied, eliminating the initial excess demand for apples. And the equilibrium change in quantity demanded is smaller than the original change in quantity demanded.

The money multiplier, and the keynesian multiplier, are rare examples of positive feedback processes. The equilibrium increase in money supplied is bigger than the original increase in money supplied. The equilibrium increase in output demanded is bigger than the original increase in output demanded.

The central puzzle of (short run) macroeconomics is to explain why market economies have fluctuations in the volume of trade. It is hard to identify shocks large enough to explain the trade cycle. Real Business Cycle Theory has tried, and in my opinion failed, to do just this. It would seem natural to look for positive feedback processes to help us understand why large fluctuations might result from small shocks. If the multipliers are large enough, the shocks might be too small to see. Fussing about whether the magnitudes of those multipliers are "stable" (unchanging over time) is of secondary concern. What matters is that those magnitudes are bigger than one. The "instability" of the magnitude of a positive feedback process can make that multiplier even more important in explaining fluctuations. We can ignore stuff that never changes.

You can't see the keynesian multiplier in New Keynesian models. That's because they have hidden it, or refused to look at it. But it's still there, in the Euler equation, and it's larger than ever. The marginal propensity to consume out of permanent disposable income is one, and so the keynesian multiplier is infinite in New Keynesian models. It's so big the New Keynesians have to assume it away, by turning into "classical" economists, and assuming (the representative agent expects) an automatic tendency towards "full employment" (aka the natural rate), even though nothing in their models justifies that ad hoc assumption, just to keep permanent income pinned down by the supply-side Phillips Curve.

Does permanent income determine permanent consumption, or does permanent consumption determine permanent income? Yes. As individuals, and in aggregate, we decide how much to save and invest, and our decisions affect our permanent income. But one person's spending is another person's income, and it is not unreasonable to ask, as Keynes asked, what, if anything, ensures that our (permanent) desired aggregate spending is sufficient to equal our (permanent) desired aggregate income? What, if anything, might adjust to ensure that Say's Law holds? And the answer is not "the rate of interest", because the rate of interest is a relative price, that only affects the demand and supply of present goods relative to future goods. It is a fallacy of composition to assume that, since the right rate of interest in each individual period can ensure demand equals supply in that individual period, therefore the right rate of interest in all periods can ensure that demand equals supply in all periods.

(And please don't be a knuckle-dragger and think of the keynesian multiplier as the fiscal policy multiplier. It is as much a monetary policy multiplier as a fiscal policy multiplier, and it's not even a purely policy multiplier. It multiplies anything that gets the ball rolling.)

New Keynesians adopted the monetarist tendency towards full employment, but they threw out the monetary forces that might actually get us there, and lost their own Keynesian heritage in forgetting Keynes' fundamental question to which the monetary baby was the answer.

Keynes' question only makes sense in a monetary exchange economy, where people both buy and sell all other goods for the medium of exchange. Another way to ask Keynes' fundamental question is to ask: "what, if anything, ensures there can never be an excess demand for the medium of exchange?" Because if there is an excess demand for the medium of exchange, then people will want to buy fewer goods than they want to sell.

It is no accident that New Keynesians deleted Keynes' fundamental question from their models, and deleted the medium of exchange from their models too. The two deletions are the same. Yes, if you ignore money, and assume market-clearing in future markets, then getting the right relative price in the current market (the right rate of interest) is all you need to get market-clearing in the current market.

The demand and supply of the medium of exchange matters. Central banks produce a medium of exchange, and commercial banks produce a medium of exchange too. If people can buy and sell goods using either media of exchange, and if excess demands for media of exchange matter, it makes sense to ask what determines the demands and supplies of both media of exchange.

"Banks create money!" chants the cultist. Yes they do. And one of the things the textbook money multiplier teaches the first year students is precisely that. An initial creation of money by the central bank results in a much larger equilibrium amount of money created by the banking system. Where did that extra money come from? From the commercial banks, of course. And commercial banks create that money despite each individual bank only lending out money that has been deposited in that bank, as long as they have less than 100% desired reserve-deposit ratios.

"Loans create deposits!" chants the cultist. Yes, they do. And one of the things the textbook multiplier teaches the first year students is precisely that. If the commercial banks did not expand their loans, they would create no new money on top of what the central bank created. But what the textbook also reminds us is that an individual commercial bank that creates a deposit by making a loan will very likely lose that same deposit to another bank when the borrower spends the loan and the cheque gets deposited in a different bank. It is exactly as if the individual bank had made the loan by giving the borrower central bank currency, which then gets spent and deposited in a different bank. The textbook cuts directly to the chase scene, which the cultist never gets to. Because the individual bank's incentive to make an extra loan is what matters, unless you assume all commercial banks collude to maximise joint profits, knowing that they are simply transferring base money between themselves when deposits get transferred between themselves.

And commercial banks, neither individually nor collectively, can create loans, unless they can persuade people to hold their deposits and not hold central bank money instead. Because they promise to redeem their deposit money for central bank money at a fixed exchange rate.

Is the stock of money exogenous or endogenous? Yes. The stock of money depends on stuff that is assumed exogenous in the model, like the inflation target, and various shocks. In that sense the stock of money is (trivially) endogenous, because it will change when that exogenous stuff changes. But that does not mean the stock of money responds only to changes in the demand for money, so there can never be an excess supply or demand for money and we can ignore the supply side. Money, as medium of exchange, is traded in all markets, and just because there is neither excess demand nor supply of money in one market does not mean it cannot be in excess demand or supply in all other markets. And the medium of exchange is not like refrigerators, because we buy money in order to sell it again, not just to hold it. Suppliers of money, unlike suppliers of refrigerators, can "force" us to buy more money than we want to hold, because each buys it planning to sell it again to someone else. And that excess supply of money causes P and/or Y to increase until the quantity of money demanded adjusts to equal the quantity supplied. Say's Law, paradoxically, only applies to money itself. The supply of money creates its own demand.

(And please don't be a knuckle-dragger and assume the money multiplier refers to the multiplier effect of an initial decision by the central bank only. Yes, the textbook usually illustrates the money multiplier with an example where the initial shock comes from the central bank, just as it usually illustrates the keynesian multiplier with an example where the initial shock comes from fiscal policy. But the money multiplier, just like the keynesian multiplier, multiplies anything that gets the ball rolling.)

How big is the money multiplier? Well, that depends, on many things. Most importantly, it depends on what the central bank is targeting. If the central bank is targeting a fixed rate of interest (no central bank in its right mind would do this, but let's just suppose), the money multiplier is infinite. Just like the keynesian multiplier in New Keynesian models. Some initial shock causes one bank to expand loans and deposits, which causes other banks to expand their loans and deposits too, and the central bank expands base money as the demand for reserves + currency expands, and so on, and the ball keeps rolling until something causes it to stop. And the only thing we ought to rely on to bring the process to a stop is the central bank itself, because it is more concerned with some vaguely sensible target like inflation or NGDP, and realises that sort of target is incompatible with a permanently fixed interest rate target and "supplying base money on demand", as the cultists say.

The two positive feedback processes in the first year textbook are very closely connected. Both multipliers are infinite when the central bank targets a rate of interest and everything just scales up across markets and time-periods. Providing the right policy answer to Keynes' fundamental question requires the central bank to not allow everything to scale up. A good central bank would ensure we never observe either multiplier process in action in the real world. If we observe random shocks to government spending creating a keynesian multiplier process we know the central bank has failed. If we observe random shocks to base money creating a money multiplier process we know the central bank has failed. But the central bank needs to know its enemies to ensure they never appear in the data. This is Milton Friedman's Thermostat.