The Money Multiplier, RIP?

In case you haven’t heard, Simon Wren-Lewis tried to kill the money multiplier earlier this week. And if he succeeded, and the money multiplier stays killed, if it has indeed been well and truly buried, I for one shall not mourn its long overdue passing. Over the course of my almost thirteen months of blogging I have argued on a number of occasions that, contrary to the money multiplier, bank deposits are endogenous, that they are not so many hot potatoes that, once created, must be held, never to be destroyed. This view has brought me into sharp, but friendly, disagreement with some pretty smart guys whom I usually agree with, like Nick Rowe and Bill Wolsey, but I’m not backing down.

My view of bank deposits has also put me in the same camp — or at least created the appearance that I am in the same camp — with the endogenous money group, Post-Keynesians, Modern Monetary Theorists and the like, whose views I only dimly understand. But it seems that they deny that even the monetary base (i.e., currency plus bank reserves) is under the control of the monetary authority. This group seems to think that banks create deposits in the process of lending, lending is undertaken by banks in response to the demands of the public (businesses and households) for bank loans, and reserves are created by the monetary authority to support whatever level of reserves the banks desire, given the amount of lending that they have undertaken. The money multiplier is wrong, in their view, because it implies that reserves are prior to deposits and, indeed, are the raw material from which deposits are created, when in fact reserves are created to support deposits.

So let me try to explain how I view the money multiplier. I agree with the endogenous money people that reserves are not the stuff out of which deposits are created. However, there is a sense in which base money is logically prior to deposits. Every deposit is a promise to pay the bearer something else outside the control of the creator of the deposit. That something is base money. Under a fiat money system, it is a promise to pay currency. Under a gold standard, it was a promise to pay gold, coin or bullion. This distinction is captured by the distinction between inside money (deposits) and outside money (currency).

It is my position that the quantity of inside money produced or created in an economy is endogenously determined by the real demand of the public to hold inside money and the costs banks incur in creating inside money. Because banks legally commit themselves to convert inside money into outside money on demand, arbitrage usually prevents any significant, or even insignificant, deviation between the value of inside and that of outside money. Because inside money and outside money are fairly close substitutes, the value of outside money is determined simultaneously in the markets for inside and outside money, just as the value of butter is determined simultaneously in the markets for butter and margarine. But heuristically, it is convenient to view the value of money as being determined by the supply of and the demand for base money, which then determines the value of inside money via the arbitrage opportunities created by the convertibility of inside into outside money. Given the equality in the values of inside and outside money, we can then view the supply of inside money and the demand for inside money as determining the quantity of deposits and the interest rate paid on deposits. Under competitive conditions, the interest paid on deposits must equal the bank lending rate (the gross revenue from creating a deposit) minus the cost of creating a deposit, so that the net revenue (the lending rate minus the deposit rate) equals the cost of creating deposits.

What determines the value of base money? The monetary authorities (central bank plus the Treasury) jointly determine the amount of currency and reserves made available. The public (banks plus households plus businesses) have demands to hold currency when tax payments are due, demands to hold currency for transactions purposes when taxes are not due, and demands to hold currency as a store of value, those demands depending as well on the expected future value of currency and on the yields of alternative assets including inside money. The total demand for currency versus the total stock in existence determines a value at which the public is just willing to hold the amount currency (base or outside money) in existence.

This theoretical setup is analogous to that which determines the value of money under a gold standard. Under a gold standard the amount of gold in existence is endogenously determined as the sum of all the gold ever mined from time period 0 until the present. But in the present period the total stock can be treated as an exogenously fixed amount. The total demand is the sum of the monetary plus non-monetary demands for gold. The value of gold is whatever value is just sufficient to induce the public to hold the amount in existence in the current period. Given that all prices are quoted in gold, the price level is determined by the conversion rate of money into gold times the gold value of every commodity corresponding to the equilibrium real value of gold. The amount of inside money in existence is whatever amount of convertible claims into gold the public wishes to hold given the yields on alternative assets and expectations of the future value of gold.

The operation of a gold standard requires no legal reserves of gold to be held. Legal reserve requirements were an add-on to the gold standard – in my view an unnecessary and dysfunctional add-on – imposed by legislation enacted by various national governments for their own, often misguided, reasons. That is not to say that it would not be prudent for monetary authorities to hold some reserves of gold, but the decision how much reserves to hold has no intrinsic connection to the operation of the gold standard.

Thus, the notion that there is any fixed relationship between the quantity of gold and the amount of convertible banknotes or bank deposits created by the banking system under the gold standard is a logical fallacy. The amount of banknotes and deposits created corresponded to the amount of banknotes and deposits the public wanted to hold, and was in no way logically connected to the amount of gold in existence. Similarly, under a fiat money system, there is no logical connection between the amount of base money and the amount of inside money. The money multiplier is simply a reduced-form, not a structural, equation. Treating it as a structural equation in which the total stock of money (currency plus demand deposits) in existence could be juxtaposed with the total demand to hold money is logically incoherent, because the money multiplier (as a reduced form) is itself determined in part by the demand to hold currency and the demand to hold deposits.

So it’s about time that we got rid of the money multiplier, and I wish Simon Wren-Lewis all the luck in the world in trying to drive a stake into its heart, but somehow I am not all that confident that we have yet seen the last of that pesky creature.

PS I hope, circumstances permitting, tomorrow to continue with my series on Earl Thompson’s reformulation of macroeconomics. This post can perhaps serve as introduction to a future post in the series on alternative versions of the LM curve corresponding to different monetary regimes.