On the Obsolescence of Fisher’s Equation and the New Concept of Monetary Velocity

31 Août 2025 , Rédigé par Jamel BENJEMIA 31/08/2025 Publié dans #Articles

The English-translated article by Jamel #BENJEMIA published in #Le_Temps on Sunday, August 31, 2025.

On the Obsolescence of Fisher’s Equation and the New Concept of Monetary Velocity

By Jamel BENJEMIA

There are equations that shine with the clarity of textbook examples, like shards of intelligence glazed onto the page, only to vanish once exposed to the crude exigencies of life. Fisher’s equation, MV = PY, is one of these. Formulated in a 1911 pamphlet entitled The Purchasing Power of Money, it was said to hold the universal key: multiply the money stock (M) by its velocity (V), and the perfect identity between prices (P) and production (Y) was revealed. An algebraic beauty, a promise of rigor.

But by 1933 history had proved him wrong. With the arrival of the Great Depression, Fisher could no longer deny the shortcomings of his own construct. In The Debt-Deflation Theory of Great Depressions, he described the infernal mechanism that dismantled his equation: falling prices weighed down debts, which produced bankruptcies, which triggered banking panics and an accelerating deflationary spiral. Later, Friedman and Schwartz documented a collapse in velocity of more than 30 percent between 1929 and 1933 in A Monetary History of the United States.

Thus, the formula, so elegantly simple in its theoretical statement, became in practice a stalled engine, a theoretical rocket unable to launch into the atmosphere of crises.

The Illusion of an Imaginary Linearity

The ostensible power of Fisher’s equation lay in its simplicity; but this very simplicity concealed its weakness. Fisher assumed velocity to be fixed, obedient, mechanically determined. In truth, velocity is a moving target. It depends on confidence and fear, on the architecture of banks, on collective behavior, on that psychological alchemy that cannot be quantified.

Modern econometric models (VAR, PVAR) confirm this fragility. When crises erupt, circuits jam, balance sheets absorb liquidity, households hoard, firms postpone projects, and banks ration credit. Currency flows decelerate, then stagnate, and finally freeze. Expanding the money supply no longer produces proportional effects: beautiful algebra collapses under the leaden weight of reality.

1929: Frozen Blood

The Great Depression was the first shipwreck of Fisher’s identity. Money did not so much circulate as congeal, like clotting blood. Between 1929 and 1933, velocity collapsed by 30 percent. Not every bank failed, but every transaction was paralyzed by fear. Fisher had to face the harsh truth: his beautiful equation had lost its predictive force.

The economy, wounded, folded in on itself. The pulse of money slowed, like a breath held too long. The equation MV = PY, once meant to serve as a compass, had become a mute gauge.

Japan in the 1990s: The Rocket Nailed to the Ground

Sixty years later, Japan offered another illustration. Prices crashed after the collapse of its real estate and stock market bubble; banks staggered under mountains of bad loans; companies froze their investments. The Bank of Japan opened the floodgates, slashed rates to zero, and inundated the economy with liquidity. According to Fisher, this should have been enough to revive growth.

Yet nothing happened. The fuel was there, but the rocket remained nailed to the ground. Households hoarded, banks withheld credit, and firms concentrated on repairing their balance sheets. Velocity crumbled, confidence dissolved. What seemed at first a short pause became a long purgatory. Money accumulated like a stagnant river, incapable of feeding growth: it became nothing more than dormant fuel.

2008: Money Without an Ocean

The global crisis of 2008 confirmed the pattern. The Federal Reserve launched its “unconventional” monetary policy, injecting more than $4 trillion into the system. Yet instead of rising, velocity fell by 17 percent between 2007 and 2014.

The Financial Times captured it in 2014 with a striking phrase: “money creation looked like a river that no longer reaches the ocean.” Liquidity swelled bank balance sheets and inflated financial markets, but it never reached households. As in Japan, the rocket gathered thrust but remained trapped by psychological gravity.

The Historical Constant of Instability

History—whether 1929, Japan in the 1990s, or 2008—repeats the same refrain: velocity is not a constant, but a social thermometer. It rises with confidence, quickens with hope, and freezes with fear. Anderson, Bordo and Duca, in a 2023 ECB study, showed that velocity has been “structurally weakened” after every crisis, held back by banking and regulatory transformations.

Toward an Organic Equation

To move beyond Fisher’s blind spot, one must accept a central truth: money does not follow linear mechanics. Its path is uncertain—logarithmic, asymptotic, dependent on expectations. In this spirit, I propose the following formulation:

V(t)=Vc . ln(M0/Mr)⋅e−λA(t)

M0 : injected money supply
Mr : retained, hoarded, unproductive money
A(t) : negative expectations (mistrust, uncertainty)
Vc : confidence constant

The negative sign before λA(t) in the exponential e−λA(t) plays a clear role: it represents the dampening effect of negative expectations on velocity.

If A(t) (negative expectations, distrust, uncertainty) increases, then the term −λA(t) decreases further, which makes e−λA(t) shrink. As a result: velocity V(t) contracts.
Conversely, if A(t) is low or zero (stable confidence), then e−λA(t) approaches zero and the exponential tends toward 1, leaving velocity at its maximum potential.

This mirrors the principle of exponential decay in physics: the minus sign embodies a braking force, an invisible gravity weighing on motion. Here money becomes a rocket whose thrust depends on confidence, whose inertia comes from dead weight, and whose trajectory is slowed by the density of the psychological atmosphere.

The Rocket Metaphor

This analogy was inspired by the film Hidden Figures and by the story of Katherine Johnson, a Black mathematician who, in segregated America, wielded Euler’s equations with serene majesty, tracing with exactitude the closed parabolas and elliptical orbits of spaceflight. For her mastery of orthonormal algorithms anchored in Euclidean coordinates, she earned the deep respect of her superiors and of the nation itself.

It is no accident that she was nicknamed “the human computer,” so precise were her calculations.
And yet the rocket, despite exact equations and abundant fuel, could not leave the ground. Trapped by gravity, it stayed still.

So it is with modern money. Fed with billions, it should take flight; yet at each crisis it remains stuck, bolted to the launch pad. 1929, 1990, 2008: so many aborted launches, so many rockets unable to pierce the atmosphere of uncertainty.

Rereading Tsiolkovsky, the father of astronautics, the analogy becomes dazzling: just as a rocket’s thrust depends on the ratio of initial to final mass, monetary velocity depends on the ratio of injected to retained money. And just as gravity restrains ascent, distrust and negative expectations stifle circulation.

Inhabiting the Equation

From Fisher to Friedman, from 1990s Japan to the 2008 crash, the evidence converges: MV = PY is obsolete in times of crisis. Velocity is not a constant; it is a breath, a fragile respiration.

My dynamic formula offers a different grammar: that of an economy conceived as a social rocket. Charged with fuel, it only rises if confidence provides the thrust and dead weights do not suffocate its path.

Crises have made this clear: 1929 froze velocity; 1990s Japan revealed the weight of hoarding; 2008 showed the sterilization of liquidity. But history also teaches the opposite: Weimar in 1923, Hungary in 1946, today’s Venezuela. In these cases the rocket is not stuck—it explodes, carried away by uncontrollable velocity.

Stagnation or hyperinflation, the lesson remains the same: money is not a mechanism but a moving trajectory, not a fixed identity. It is something the economist must learn to inhabit.

The hesitation of one of my professors before Fisher’s equation taught me this: economics is not a number, but a rebellious breath—and no figure will ever contain it.