Risk Latte - Morgan Stanley and the Birth of Statistical Arbitrage

Quantity Theory of Money - the Fisher-Friedman Illusion!

Team LatteRahul Bhattacharya
17th January 2015


Irving Fisher of Yale in 1911 came up with the equation of money and laid the foundations of the quantity theory of money (the quantity theory of money did not originate with Fisher, he merely formalized the ideas espoused by some notable European political scientists such as John Stuart Mill and Simon Newcomb). However, he was the first to come out with a mathematical model (via a simple equation) of how the dynamics of money supply impacts the price of goods and services in an economy.

Fisher, like his predecessors in the field of economics, must have ransacked physics texts and re-discovered the gas equation, which is mathematically expressed as which was formulated in 1834. It states that for an ideal gas the pressure, , times the volume, , which the gas occupies is equal to a constant (R, is the gas constant) times the temperature, . And like his predecessors, he may have been obsessed with belief that the discipline of economics can be perfected by supplanting crude axioms with equations lifted from physics text books. Of course, I am perhaps exaggerating. Fisher's genius lay in the fact that he was able to figure out that a simple math equation with the form similar to the gas equation in physics can be applied to explain the dynamics of the flow of goods and services in an economy and how that relates to the supply of money.

Fisher's equation for money, which was a continuation of a strand of theory known as the Quantity Theory of Money, therefore, became encapsulated in following mathematical equation

Here M is the money supply, V is the velocity of money, P is the price of goods and services produced and is the volume of transactions of goods and services produced in the economy. This was gas equation of physics masquerading as the "equation of exchange" in economics. In simple English this means that the total amount of money in an economy multiplied by its velocity (how fast it circulates) is equal to the total spending.

This idea, this ludicrously simple mathematical formulation of an extremely complex process of that of how money supply in an economy impacts the economic growth and livelihood of millions, remained buried for almost five decades before it got resurrected by Milton Friedman in the mid nineteen fifties. Under Milton Friedman and the Monetarist school of thought that he founded with Anna Schwartz the Fisher equation became

Where, Q is the index of real value of final expenditures. In more understandable economic jargon, Q is the total quantity of goods and services produced in an economy. Therefore, money supply times the velocity of money is the economic output or the GDP of an economy.

Milton Friedman, became convinced that Fisher's equation of money was the holy grail of economics and that money supply the key to understanding practically all problems in economics. He invented a whole new school of thought, the Monetarist school of thought, based on the premise that "money matters", that the only thing that matters in an economy is the supply of money.

There was only one problem with the Fisher equation; a very fundamental problem and one which the Keynesians had pointed out long before Friedman's arrival on the scene. Nobody quite knew how this "velocity of money", V, behaved. At best, it was not constant and could vary substantially from one period to another. And if V is not constant then the equation of money runs aground.

Gas equation in physics works because R is a gas constant and hence how the change in temperature influences the pressure and volume of a gas can be studied. To be precise, the gas constant has a precise value (8.31 J/K mole).

What about the quantity theory of money? The Fisher equation works only if we assume that V is constant. In fact, the money equation implies that if V is constant then we can measure the change in P, Q and PQ by changing M, the money supply. However, is V is not constant then a change in M can be offset by a change in V in such a way that PQ does not change at all. And if that happens, then it would be pointless, for the economic policy makers, to target and tinker with the supply of money in the economy to influence the prices in the long run and both the prices and the economic output in the short run.

Milton Friedman, of course, understood this very well. Not only did he resurrect the Fisher equation he set out on a bold mission with his colleague to analyze the monetary history of the United States. His mission was to establish that the velocity of money was in fact very stable. He wanted to test the classical notion that V was stable and wanted to test this via empirical estimates. He concluded, after long and tiring research and quite a lot of fancy math, that the velocity of money, V, was indeed stable and was independently determined from T, the number of transactions in the economy.

And thus started a new strand of economics, the monetary theory or Monetarism as it came to be called. His ingenuity lay in turning the Fisher equation of exchange into a demand equation of money. He contended that inflation was a monetary phenomenon and is everywhere. Demand for money is fairly stable and therefore, the policy makers can play with the supply of money, and influence the prices and the output of the economy.

And this was possible, all this fancy math turning a simple gas equation like equation into a "cult-equation" of money was possible, because of a simple premise - of course, tested thoroughly by Friedman - that the velocity of money is constant, or at least very stable. But is it? Can such a hypothesis be asserted in the most general terms by looking at certain periods in history, no matter how long that period is? Friedman took a fairly large slice of time series of data while analyzing the movement of money in the United States. But then can that be turned into a universal truth? A universal truth is that a planet goes round the sun in an elliptic orbits. That holds true always and in all time frames. But to say that the notion of velocity of money being constant is a universal truth would be incorrect.

If the Federal Reserve starts pumping in a lot of money into the economy via the commercial banking system, then is there a guarantee that the banks will then in turn start lending it to their customers and the customers will then start spending and the economy will start to grow again? No, there is no guarantee.

Economics is at best a pseudo-science. And, here was, perhaps, the beginning of the one of the greatest illusions of all time, the illusion of money, the illusion of Fisher-Friedman hypothesis.


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