Wicksell's Cumulative Process

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(1898, 1906)

"A general rise in prices is therefore only conceivable on the supposition that the general

demand has for some reason become, or is expected to become, greater than supply. This

may seem paradoxical, because we have accustomed ourselves, with J.B. Say, toregard

goods themselves as reciprocally constituting and limiting the demand for each other. And

indeed ultimatelythey do so; here, however, we are concerned with precisely what occurs,

in the first place, with the middle link...Any theory of money worthy of the name must be

able to show how and why the monetary or pecuniary demand forgoods exceedsor falls

short of the supply of goods in given conditions"

(K. Wicksell,Lectures on Political Economy, Vol.2, 1906: p.159-60;

Emphasis in original)

We can see this differently. Say'sLaw says that real aggregate demand (Yd) is derived from real

aggregate supply (Ys), thus Yd = Ys at all times. Yet, in a Walras' Law constraint, we must remember

that:
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(Yd - Ys) + (Md - Ms)/p = 0

where Md and Ms is money demand and supply respectively. Thus, by Say's Law, left side falls to zero,

and thus Md = Ms at all times: there can never be excess or insufficient money supply necessary to make

the Quantity Theory work. We can look at this in terms of investment and savings. Now, by definition,

Yd = C + I + G where C is consumption, I is investment and G is government spending and Ys = C + S

+ T where S is savings and T is taxation, then assuming a balanced government budget, (G=T), to claimthat Say's Law states that Yd = Ys at all times is the same as saying that I = S, i.e. investment is equal to

savings at all times. Our Walras's Law constraint becomes:

(I - S) + (Md - Ms)/p = 0

which is identical to our previous constraint. However, again, by Say's Law, I = S so that necessarily Md

= Ms, i.e. money demand is always equal to money supply.

This way we can see the force of Wicksell's criticism of Say's Law and its inoperability in a theory of

money. Say's Law is in essence "dichotomy" as it separates the real and monetary sides completely - i.e.

disequilibria in money markets cannot spill over into disequilibria in goods markets. But then, Fisher's

whole story of the Quantity Theory arising from a "bidding war" for goods as a result of an excess supply

of money ispreciselywhy Fisher contradicted himself: as Wicksell claims, you cannot simultaneously

assume Say's Law and the Quantity Theory. This fundamental insight of Wicksell's was resurrected in the

Patinkin Controversyof the 1950s and 1960s.

Wicksell's solution is to make investment independent of savings so aggregate demand is free to rise

above or below a given aggregate supply. This breaking of Say's Law is done via "finance" or "credit".

Wicksell's process has its roots in that of Henry Thornton(1802). Recall that the start of the Quantity

Theory's mechanism is a helicopter drop of cash: an exogenousincrease in the supply of money.

Wicksell's theory claims, indeed, that increases in the supply of money leads to rises in price levels, but

the original increase is endogenous, created by the relative conditions of the financial and real sectors.

With the existence of credit money, Wicksell argued, two interest rates prevail: the "natural" rate and the"money" rate. The natural rate is the return on capital - or the real profit rate. It can be roughly considered

to be equivalent to the marginal product of new capital, therefore let us simply call it r. The money rate,

which we shall refer to as i, in turn, is the loan rate, an entirely financial construction.

Credit, then, is perceived quite appropriately as "money". Banks provide credit, after all, by creating

deposits upon which borrowers can draw. Since deposits constitute part of real money balances,

therefore the bank can, in essence, "create" money. This idea was put simply in later years by Dennis

Robertson:

"By a wave, apparently, of the bank's magic wand the farmer and his men [the borrowers]

have been enabled to live for six months at the expense of the rest of the community: the
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bank has give them a claim on the community's real income of food and clothing and tools

and cinema shows. And for rendering this service to the farmer the bank charges him

something called 'interest'. Our first impulse surely is to cry out on the whole proceeding as a

piece of fraudulent legerdemain."

(D.H. Robertson,Money, 1922: p.71)

Indeed it might be considered a "sleight-of-hand". But, as Robertson and Wicksell go on to note, without

this type of "fraud" one remains constrained by Say's Law- and this is inconsistent with the implied

"bidding war" mechanism of the Quantity Theory. It isfinance, Wicksell argued, which liberates

investment from a given supply of saving to become the wild card that can take aggregate demand above

(or below) aggregate supply - a maneouvre which anticipates and influences Keynes(1936).

Wicksell's"cumulative process" works as follows. Put simply, the finance demand for money is set by the

difference between the money and natural rates of interest. Let us propose that the natural rate is greater

than the money rate (i.e. r > i). In short, the marginal product of capital is greater than its cost.

Consequently, it will be to the advantage of every entrepreneur to borrow funds from the bank and invest

it in capital. That means I > S, i.e. finance investment will rise above savings as the bank, by its "magic

wand", can create the deposits upon which borrowers can draw. In short, the money supply increases as

a result.

Now one may accept that investment is independent of savings - at least initially. Banks, after all, give

credit out first and then verify if the funds are available. Thus, like Keynes and unlike modern

Neoclassical economics, Wicksell does not think investment is constrained by savings. But eventually,

surely, the savings have to come eventually to equality - the goods market must eventually clear. Keynes

had his multiplier to do this. What did Wicksell have?

Wicksell actually had no self-correcting mechanism other than a reserve constraint. The logic works as

follows: when r > i, then I > S. This extra investment demand then bears down on the capital goods

industry. Assuming full employment, the extra demand for capital goods by loan-backed entrepreneurs

cannotbe met by the makers of capital goods. On the contrary, the extra volume of demand will have to

be siphoned off by raising the price of capital goods. But just as they rise in the capital goods industry, so

too must they rise elsewhere - including consumer goods and, as a result, wage demands by workers.

A spiral ensues, a "cumulative process" whereas prices will rise and rise without limit as long as loan-

backed entrepreneurs keep borrowing from the banks and coming to market. And they will continue

doing so as long as the natural rate of interest (the marginal product of capital) remains above the money

rate of interest (the loan rate). Thus, the demand for loans will continue accumulating, and the banking

system's deposit creation forthcoming, indefinitely - with savings never really catching up. Money supply

will expand endogenously without limit and prices will rise also without end.

[Note: thus we get what Keynes(1930) called the "Gibson Paradox": the fact that Wicksell's theory tells

us interest rates and the price level move in opposite directions but empirical evidence contradicts this;
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Wicksell(1906: p.202) claimed to have resolved it by noting that the money rate lags behind the natural

rate.]

Will this cumulative process ever end and the goods market brought back into equilibrium (i.e. I = S)?

Two reasons can be given to ensure that it will. Firstly, the process ends when banks decide to raise their

loan rate to equate the natural rate. Theoretically, this will eventually happen given the limited supply of

reserves. Since each deposit, by law or prudence, must be backed by a certain amount of "reserves" (i.e.cash, gold or central bank liabilities), then new deposits will be created as long as the banks can find the

reserves to back them up. The moment the banks run out of their own reserves, they will have two

options: either they stop making loans or try to purchase reserves on the money market. Both options

lead to rising loan interest rates.

A second reason for the ending of the cumulative process was actually not thought of by Wicksell but

only much later. Indeed, we can argue that the process should be brought to an end quicker before the

reserve constraint is reached by recognizing that the marginal product of capital (the "natural rate") reallyrefers only to that on newcapital. Expressed in monetary terms, then, the rise in the inflation implies that

the "costs" of new capital goods have risen - consequently, the attractiveness of investment should

diminish. In modern terms, the marginal efficiency of investment (MEI) curve would shift down - notdue

to falling marginal efficiencies of capital but rather to rising supply price of capital, i.e. marginal adjustment

costs. In other words, inflation should alsoeat away at the natural rate so that as the cumulative process

gathers pace, there will be a decline, in real terms, of the natural rate. Thus, loan demand collapses. This

second effect, by and large ignored by Wicksell, provides a self-adjusting mechanism to the system. It is

no longer necessarily the case that inflation can only be stifled by the banks, feeling a reserve crunch,

moving the money rate up to the natural rate, as Wicksell posited, but also we can consider the

corresponding decline of the natural rate to meet the money rate as a result of inflation.

Thus, the cumulative process is not without end. Interest rates on the loan market will clear up the mess.

Nonetheless, the fundamental result of Wicksell's story, then, is that the dichotomy (short-run neutrality) is

very much broken. Primarily, Wicksell regarded that the disparity between the natural and money rate

arises largely because "the normal rate rises or falls whilst the loan rate remains unchanged or only tardily

follows it" (Wicksell, 1906: p.205). In other words, the root cause of inflation and deflation is realand

not monetary.

We should qualify this statement: Wicksell(1898: p.167; 1906: p.204-5) did accept the possibility of

exogeneous money supplies while Irving Fisher(as we saw with his credit cycle (Purchasing Power of

Money, 1911) and also in his Theory of Interest(1930: p.330-6)) did accept that of endogeneity, but

both regarded the alternative to be more common. For Wicksell, an exogenous increase in the supply of

gold, for instance, does lead to a rise in reserves which might lead to a collapse in the money rate of

interest below the natural rate as banks have greater ability to make loans.

Nonetheless, adhering to Wicksell's main thesis, the disequilibrium engendered by real changes leads

endogenouslyto an increase in the demand for money - and, simultaneously, its supply as banks try to
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accommodate it perfectly. Given full employment, (a constant Y) and payments structure (constant V),

then in terms of the equation of exchange, MV = PY, a rise in M leads only to a rise in P. Thus, the story

of the Quantity Theory, the long-run relationship between money and inflation, is kept in Wicksell.

However, the story is told in an entirely different and enriched way. Primarily, Say's Lawis violated and

abandoned by the wayside. Namely, when i However, real aggregate supply does constrain. Inflation

results because capital goods industries cannot meet new, real demands for capital goods byentrepreneurs by increasing capacity. They may try but this would involve making higher bids in the factor

market which itself is supply-constrained - thus raising factor prices and hence the price of goods in

general. In short, inflation is a real phenomenon brought about by a rise in real aggregate demand over

and above real aggregate supply.

Finally, the endogenous creation of money, and how it leads to changes in the real market (i.e. increase

real aggregate demand) is fundamentally a breakdown of the Neoclassical tradition of a dichotomy

between monetary and real sectors. Money is nota "veil" - agents do react to it and this is not due tosome irrational "money illusion". However, we should remind ourselves that, for Wicksell, in the long run,

the Quantity Theory still holds: money is still neutral in the long run, although to do so, we have broken the

cherished Neoclassical principles of dichotomy, money supply exogeneity and Say's Law.

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Wicksell's Cumulative Process

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