Exploring the Intersection of Quantum Mechanics and Economics: A 60-Year Analysis of Money Velocity and Economic Output

The classical equation of exchange, MV = pQ, has been a cornerstone in economic theory for understanding the relationship between money supply (M), velocity of money (V), price levels (p), and economic output (Q). This equation suggests a direct and linear relationship: the amount of money in circulation and its velocity should be proportional to the total economic output adjusted for price levels. This model has long been used to explain inflation, economic growth, and monetary policy. However, as the complexities of the modern economy grow, some have wondered whether these traditional models are sufficient or whether more advanced theories—perhaps even those rooted in quantum mechanics—might better explain certain economic behaviours.

The Theory: Does Quantum Mechanics Apply to Economics?

At the heart of this inquiry is the hypothesis that the economy, much like the physical world, may operate under different rules depending on the scale and context. In normal conditions, the economy might follow predictable, linear dynamics similar to Newtonian physics. However, during periods of significant upheaval—economic crises, for example—the economy could behave in a more complex, non-linear manner, akin to quantum mechanics where classical physics fails to explain phenomena at the subatomic level.

In an intriguing coincidence, the idea of squaring velocity (V^2) in our analysis parallels the famous equation from physics, E = mc^2. Just as E = mc^2 describes the energy (E) contained in a mass (m) accelerated to the speed of light squared (c^2), we are exploring whether pQ = MV^2 might similarly capture a deeper, more complex relationship in economics, particularly during times of crisis. Could it be that just as quantum mechanics governs the behaviour of particles at the subatomic level, V^2 becomes relevant in economics during times of extreme volatility or crisis, revealing a non-linear and more dynamic interaction between money velocity and economic output?

Analysing the Data: 60 Years of Economic Behaviour

We conducted an empirical analysis using data from 1964 to 2024, segmented into 5-year periods, to explore how well MV and V^2 correlate with pQ during different economic environments. The results were revealing:

Periods Correlating with MV (1964–1978, 2014–2018):

- In periods of economic stability, particularly from 1964 to 1978 and again from 2014 to 2018, we observed strong positive correlations between MV and pQ. This suggests that during these times, the economy followed the classical, linear dynamics predicted by the Quantity Theory of Money. The velocity of money had a predictable, direct impact on economic output and price levels, much like how Newtonian physics accurately describes the motion of large-scale objects.

Periods Correlating with V^2 (2004–2008, 2014–2018):

- Interestingly, during the periods leading up to major economic crises—specifically 2004–2008 before the financial crisis and 2014–2018 before the COVID-19 pandemic—V^2 exhibited strong correlations with pQ. This suggests that as the economy approached these tipping points, traditional linear relationships broke down, and non-linear effects became more prominent. The squaring of velocity may capture these accelerating or compounding effects, reflecting a shift from classical to quantum-like economic behaviour.

The Quantum Mechanics of Economic Crises?

These findings suggest a fascinating parallel between economics and physics. In stable times, the economy behaves predictably, much like how Newtonian physics governs the macroscopic world. However, as the economy approaches a crisis—analogous to the subatomic realm in physics—these traditional laws seem to falter, and more complex, non-linear behaviours emerge. Just as quantum mechanics takes over where classical physics fails, V^2 might better explain economic dynamics during extreme volatility or crisis.

What Does This Mean for 2024 and Beyond?

As we look to the future, particularly towards 2024 and 2025, the data up until 2024 does not suggest an imminent crisis of the scale seen in 2008 or during the onset of the COVID-19 pandemic. The weak correlation between V^2 and pQ in the most recent period suggests that the economy, while still adjusting to the aftershocks of the pandemic, is not currently exhibiting the heightened sensitivity that might indicate another major disruption.

However, it is essential to remember that economic conditions are constantly evolving. The weak correlation with V^2 does not guarantee stability but rather suggests that the economy may still be in a transitional phase. Continued monitoring of these relationships will be crucial as we move forward, especially given the complex and interconnected nature of today’s global economy.

The Caveats and the Road Ahead

It is important to note that this analysis, while insightful, is still rudimentary. The idea of applying quantum mechanics to economics is a novel and speculative approach that requires further exploration and validation. The correlations observed in this study are just one piece of the puzzle, and real-world economic behaviour is influenced by countless factors, including policy decisions, global events, and technological changes.

Nevertheless, the potential parallels between the laws of nature and the laws of economics offer a fascinating avenue for future research. If the economy indeed exhibits quantum-like behaviour during periods of crisis, this could open new ways of thinking about economic policy and crisis management, helping us better anticipate and respond to the complex challenges of the modern world.

As we navigate the uncertainties of the future, integrating insights from both classical and quantum perspectives might provide a more comprehensive understanding of the economy, enabling us to better manage the balance between stability and volatility in the years to come.

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Notes to the Components of the Equation:

1. Money Supply M :

   - Explanation: This feature represents the year-over-year percentage change in the M2 money supply, which is a broad measure of money supply that includes cash, checking deposits, and easily convertible near money. I used this as a proxy for M, recognizing that it is not the absolute level of M2 but its change, which still gives us a sense of how the money supply is evolving.

2. Velocity of Money V

   - Explanation:  Velocity V  was calculated by dividing the nominal GDP (in current dollars) by the money supply (M2). This gives us an estimate of how frequently money is circulating in the economy relative to the amount of economic output it supports.

3. Price Level p

   - Explanation: The Consumer Price Index (CPI) year-over-year percentage change was used to represent the price level. CPI is a commonly used measure of inflation, reflecting changes in the price level of a basket of consumer goods and services.

4. Economic Output Q

   - Explanation: The year-over-year percentage change in real GDP (chained dollars) was used to represent economic output Q. This measure adjusts for inflation, providing a more accurate reflection of real changes in economic production.

These components were used to analyze the relationships between MV and pQ and V^2  and pQ, over different periods, providing insights into how these relationships evolve in stable versus crisis periods.