The Various Versions of the Quantity Theory

This issue is vexing me at the moment, as I am writing an article in the course of which I am reviewing the different versions of the quantity theory as an explanation of inflation.

The following post is a work in progress, to help me summarise the history of the quantity theory.

In essence, the quantity theory comes in various versions, as follows:

I. Equation of Exchange Versions(1) Irving Fisher’s equation of exchange in his book The Purchasing Power of Money: Its Determination and Relation to Credit, Interest and Crises (1911) (Fisher 1911: 24–28, and particularly 27):

MV = PT,
where M = the money supply;
V = the velocity of circulation (or the number of times money changes hands);
P = the average price level;
T = the volume of transactions of goods and services.

Fisher also gave this form of the equation:

MV = ΣpQ.
where ΣpQ is the sum of the price multiplied by quantity bought of every good in the economy (Fisher 1911: 26).

But Fisher also thought that ΣpQ could be written as PT:

“We may, if we wish, further simplify the right side by writing it in the form PT where P is a weighted average of all the p’s [prices], and T is the sum of all the Q’s. P then represents in one magnitude the level of prices, and T represents in one magnitude the volume of trade.” (Fisher 1911: 25).

(2) Milton Friedman’s version of the equation of exchange in his paper “The Quantity Theory of Money: A Restatement” (1956):

MV = PY
where M = the quantity of money;
P = the price level;
Y = aggregate income or value of aggregate output;
V = velocity.

Under equilibrium conditions where Q = Y, it can be written as:

MV = PQ.

II. Cambridge Cash Balance Equation Versions(3) Alfred Marshall’s reformulation of the quantity theory as the cash balance approach in the 1870s. It is unclear to me whether Marshall already had an equation form of the quantity theory in the 1870s.

I have read that this was Marshall’s version of the Cambridge Cash Balance Equation:

M = KY
where M = aggregate money supply;
Y = aggregate real income;
K = the proportion or fraction of real income which people hold in the form of money/cash balances.

The value of money is then explained by the following equation:

where P is the purchasing power of money.

But where this was given in Marshall’s works is not yet clear to me.

It seems that the final form of Marshall’s version of the Cambridge Cash Balance Equation was given in his book Money, Credit, and Commerce (1923).

(4) Arthur C. Pigou’s version of the Cambridge Cash Balance Equation in his paper “The Value of Money” (1917: 52):

where P = the purchasing power or value of money;
k = proportion of R (real income) held in the form of money/cash balances;
R = aggregate real income;
M = aggregate money stock or money supply.

(5) J. M. Keynes’ version of the Cambridge Cash Balance Equation in A Tract on Monetary Reform (1923: 77).

The basic form that Keynes gives is this:

n = pk
where n = currency notes or other forms of cash in circulation with the public;
k = consumption units of cash on hand;
p = the index number of the cost of living.

There is also another version that Keynes gives in which he included bank deposits in the total quantity of money, as follows:

n = p(k + rk′),
where n = quantity of money, or currency notes or other forms of cash in public circulation;
p = the index number of the cost of living;
k = consumption units of cash on hand;
k′ = money people want to be available in banks in the form of their demand deposits or checking accounts;
r = cash reserves of the banks.

In this version, Keynes thinks that as long as k, k′ and r remain unchanged, if n rises, then p will rise too (Keynes 1923: 77).

At the time he wrote A Tract on Monetary Reform Keynes had no doubts about the truth of the quantity theory (Keynes 1923: 74).

(6) Marshall’s final formulation of the Cambridge Cash Balance Equation in Money, Credit, and Commerce (1923).

(7) Dennis H. Robertson’s version of the Cambridge Cash Balance Equation in Appendix A of the 1928 edition of his book Money (rev. edn. 1928: 150; later edition 1964: 150):

where M = the quantity of money;
k = proportion of T against which people hold cash or money balances;
P = the price level;
T = the total amount of goods and services purchased.

From this, it is easy to derive the standard form:

M = PkT

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Now the “original” version of the Cambridge Cash Balance Equation (or so I have been told) is usually written as:

M = kPT

and this seems to be Dennis H. Robertson’s version.

However, the standard form of the Cambridge Cash Balance Equation as used today is usually given as follows:

M = kPY or
M = k_d PY
where M = the quantity of money;
k or k_d = the amount of money held as cash or money balances;
P = the general price level;
Y = real value of the volume of all transactions entering into the value of national income (that is, goods and services).

The variable k was held to be equivalent, but superior, to Irving Fisher’s “velocity of circulation” concept V (which is why it is held that 1/k = V), because, unlike V, k is supposed to be empirically measurable.

M and P are causally related, if k_d and Y are constant (Thirlwall 1999).

It is interesting that, while Keynes had formulated his own version of the Cambridge Cash Balance Equation – no. (5) above – he had by 1933, as stated in a letter to Dennis Robertson, come to the view that no version of the Cambridge Cash Balance Equation had any serious use in economic analysis:

“In my present state of mind, however, I doubt that either version of the Cambridge equation is of any serious utility, and I can’t remember that I have ever come across a case of anyone ever using either of them for practical purposes of interpretation. Thus, whether my version is slightly better than yours, or whether I ought to yield to your criticisms, I am not prepared to put up a serious case in defence of either. All this section is really a survival of the time when I was trying to make some practical use of the Cambridge equation, an attempt I have long since given up.” (Keynes, Letter to Dennis Robertson, 3 May, 1933 in Keynes 1971: 18).

Finally, one should note that mathematical statements of the quantity theory were apparently already being given in the 19th century, as Irving Fisher noted:

“An algebraic statement of the equation of exchange was made by Simon Newcomb in his able but little appreciated Principles of Political Economy, New York (Harper), 1885, p. 346. It is also expressed by Edgeworth, ‘Report on Monetary Standard.’ Report of the British Association for the Advancement of Science, 1887, p. 293, and by President Hadley, Economics, New York (Putnam), 1896, p. 197. See also Irving Fisher, ‘The Role of Capital in Economic Theory,’ Economic Journal, December, 1899, pp. 515-521, and E. W. Kemmerer, Money and Credit Instruments in their Relation to General Prices, New York (Holt), 1907, p. 13. While thus only recently given mathematical expression, the quantity theory has long been understood as a relationship among the several factors: amount of money, rapidity of circulation, and amount of trade.” (Fisher 1911: 25, n. 2).

BIBLIOGRAPHY
Dimand, Robert W. 2002. “Patinkin on Irving Fisher’s Monetary Economics,” The European Journal of the History of Economic Thought 9:2: 308–326.

Fisher, Irving. 1911. The Purchasing Power of Money: Its Determination and Relation to Credit, Interest and Crises. The Macmillan Company, New York.

Fisher, Irving. 1920. The Purchasing Power of Money: Its Determination and Relation to Credit, Interest and Crises (rev. edn.). The Macmillan Company, New York

Friedman, Milton. 1956. “The Quantity Theory of Money: A Restatement,” in Milton Friedman (ed.), Studies in the Quantity Theory of Money. The University of Chicago Press, Chicago. 3–21.

Friedman, Milton. 1968. “Money: the Quantity Theory,” in D. Sills (ed.), International Encyclopedia of the Social Sciences (vol. 10). Macmillan Free Press, New York. 432–447.

Humphrey, Thomas M. 2004. “Alfred Marshall and the Quantity Theory of Money,” FRB Richmond Working Paper No. 04–10,
December 1, 2004
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2184929

Keynes, John Maynard. 1923. A Tract on Monetary Reform. Macmillan, London.

Keynes, John Maynard. 1971. The Collected Writings of John Maynard Keynes. Volume XXIX. The General Theory and After. A Supplement (ed. by D. Moggridge). Macmillan, London.

Laidler, David E. W. 1999. Fabricating the Keynesian Revolution: Studies of the Inter-War Literature on Money, the Cycle, and Unemployment. Cambridge University Press, Cambridge.

Marshall, Alfred. 1923. Money, Credit, and Commerce. Macmillan, London.

Marshall, Alfred. 1926. Official Papers (ed. by J. M. Keynes). Macmillan, London.

Newcomb, Simon. 1885. Principles of Political Economy. Harper, New York.

Pigou, A. C. 1917. “The Value of Money,” The Quarterly Journal of Economics 32.1: 38–65.

Robertson, Dennis Holme. 1928. Money (rev. edn.). Nisbet, London.

Robertson, Dennis Holme. 1964. Money (rev. edn.). University of Chicago Press, Chicago, Ill.

Thirlwall, A. P. 1999. “Monetarism,” in P. Anthony O’Hara (ed.), Encyclopedia of Political Economy: L–Z. Routledge, London and New York. 750–753.

A Gulf Separates Milton Friedman and most Austrians

And this video shows why.



Milton Friedman understood perfectly well that central banks are vital in modern market economies to stabilise fractional reserve banking, and he rightly blamed the Federal Reserve for not intervening properly from 1929 to 1933 to stop the financial collapse.

But, of course, for most Austrians – with the exception of the GMU Austrians and (probably) the radical subjectivists – central banks are an unmitigated “evil” and should not even exist.

The “liquidationism” of such Austrians actually entails not only that central banks should do nothing during recessions, but also that they abolish themselves.

In light of this, it is indeed no surprise that Rothbardian Austrians loathe Friedman.

Why is this of interest? Because over at Free Advice Robert Murphy posts a video of Arnold Schwarzenegger singing a paean to Milton Friedman in an attempt to show that all the “non-interventionist stuff in Friedman … is inconsistent with his fine-tuning monetary policy ideas.”

But it is no such thing. Milton Friedman had (from his own perspective) a coherent economic theory that accepted fractional reserve banking as part and parcel of capitalism (unlike Rothbardians), and that such a system needed a central bank to stabilise it.

There is no contradiction involved in followers of Friedman praising his Free to Choose (1980) book and television series and ideas on personal liberty, but accepting the need for a central bank and even some type of monetary policy, as Friedman did.

Post Keynesians on Milton Friedman

There is some discussion of Milton Friedman at the moment by Paul Krugman (here and here).

So in that spirit, I think some heterodox Keynesian views of Friedman are worth mentioning:

Thomas Palley, “Milton Friedman: The Great Conservative Partisan,” November 27th, 2006.

James K. Galbraith, “The Collapse of Monetarism and the Irrelevance of the New Monetary Consensus,” March 31, 2008.

One can also revisit Friedman’s debate with the Post Keynesian economists Paul Davidson and Sidney Weintraub (Davidson and Weintraub 1973), which, I think, makes profitable reading.

All in all, Thomas Palley has a nice summing up of Friedman’s monetarist doctrine:

“Monetarism’s most famous aphorism is that ‘inflation is always and everywhere a monetary phenomenon.’ This saying reflects Friedman’s polemical powers, capturing for monetarists what all sensible economists already knew. Inflation is about rising prices, and prices are intrinsically a monetary phenomenon since they are denominated in money terms.

Sustained inflation requires that the money supply grow in order to finance transacting at higher prices. For Friedman, this made villainous central banks the exclusive cause of inflation because of his belief that they control the money supply. However, the reality is that the private sector can also inflate the money supply through its own credit creation activities. Additionally, central banks (viz. the Bernanke Fed) may be compelled to temporarily accommodate inflationary private sector pressures to avoid triggering costly recessions. The implication is that inflation can have different causes, something Friedman denied. Sometimes inflation is caused by excessively easy monetary policy or large budget deficits financed by central banks. Other times it is due to private sector forces, including speculative booms and conflicts over income distribution.”
Thomas Palley, “Milton Friedman: The Great Conservative Partisan,” November 27th, 2006.

Moreover, attempts by central banks to actually control base money or the broad money stock, as under Margaret Thatcher and Paul Volcker, ended in miserable failure. Central banks soon turned to inflation targeting, and the idea of direct controls on money supply growth died a humiliating death.

This is no doubt what prompted John Kenneth Galbraith (father of James K. Galbraith) to say that “Milton Friedman’s misfortune is that his economic policies have been tried”!

UPDATE
Here are some further links:

Ramanan, “Nicholas Kaldor on Milton Friedman’s Influence,” The Case For Concerted Action, 13 July 2013.

“Milton Friedman’s Distortions, Part II,” Unlearning Economics, July 12, 2013.

“Milton Friedman’s Distortions,” Unlearning Economics, November 27, 2012.

BIBLIOGRAPHY
Davidson, Paul and Sidney Weintraub. 1973. “Money as Cause and Effect,” The Economic Journal 83.332: 1117–1132.

Milton Friedman on ABCT

Milton Friedman, the developer of the macroeconomic theory of monetarism, and himself a supporter of free market economics, was interviewed in Barron’s in 1998 (August 24), and gave his opinion of ABCT. Friedman’s comments are available on Mises.org:

“... I think the Austrian business-cycle theory has done the world a great deal of harm. If you go back to the 1930s, which is a key point, here you had the Austrians sitting in London, Hayek and Lionel Robbins, and saying you just have to let the bottom drop out of the world. You’ve just got to let it cure itself. You can’t do anything about it. You will only make it worse. You have Rothbard saying it was a great mistake not to let the whole banking system collapse. I think by encouraging that kind of do-nothing policy both in Britain and the United States, they did harm.”

Jeff Scott, “Business Cycles,” September 6, 1998.

While I don’t think much of Friedman’s monetarism, here he is quite correct.

In 1929, America faced a collapsing asset bubble. While the limited interventions of Hoover did very little to counteract the slump that followed, Hoover at least did not engage in large cuts to government spending (or at least did not try to balance the budget until fiscal year 1933). An “Austrian” policy of dismantling government and complete privatisation (anarcho-capitalism) or savage government spending cuts and abolition of the central bank (in some types of Misesian Classical liberalism) would have collapsed the US economy to an even greater extent than its contraction from 1929–1933.

To see how much harm deflationary austerity did, one only has to turn to what happened in Weimar Germany:

“Economic breakdown [sc. in Germany during the Great Depression] led to political upheaval which in turn destroyed the international status quo. Germany was the most striking example of this complex interaction. Without the depression Hitler would not have gained power. Mass unemployment reinforced all the resentments against Versailles and the Weimar democracy that had been smouldering since 1919. Overnight the National Socialists were transformed into a major party; their representation in the Reichstag rose from 12 deputies in 1928 to 107 in 1930. The deflationary policies of the Weimar leaders sealed the fate of the Republic” (Adamthwaite 1977: 34).

It is interesting that Friedrich von Hayek, to his credit, actually changed his mind on the effects of US deflation in 1929–1933, at least later in life:

“There is no doubt, and in this I agree with Milton Friedman, that once the Crash had occurred, the Federal Reserve System pursued a silly deflationary policy. I am not only against inflation but I am also against deflation! So, once again, a badly programmed monetary policy prolonged the depression” (Pizano 2009: 13).

In Hayek’s view, a secondary deflation had negative effects on the US economy after 1929 and his mea culpa is worth quoting:

“Although I do not regard deflation as the original cause of a decline in business activity, such a reaction has unquestionably the tendency to induce a process of deflation – to cause what more than 40 years ago I called a ‘secondary deflation’ – the effect of which may be worse, and in the 1930s certainly was worse, than what the original cause of the reaction made necessary, and which has no steering function to perform. I must confess that forty years ago I argued differently. I have since altered my opinion – not about the theoretical explanation of the events, but about the practical possibility of removing the obstacles to the functioning of the system in a particular way” (Hayek 1978: 206).

BIBLIOGRAPHY

Adamthwaite, A. P. 1977. The Making of the Second World War, Allen & Unwin, London and Boston.

Hayek, F. A. 1978. New Studies in Philosophy, Politics, Economics and the History of Ideas, Routledge & Kegan Paul, London.

Pizano, D. 2009. Conversations with Great Economists, Jorge Pinto Books Inc., New York.