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Going with the flow: Can analog simulations make economics an experimental science?

27 June 2012

Turbulence ahead? Click to see an animation of how it develops

This month marks the centennial of the birth of mathematician Alan Turing, the “father” of modern computing and artificial intelligence. To celebrate the occasion, we’ll be publishing a series of articles on modelling and economics. Today’s article is from John Hulls, of the Cambiant Project at the Dominican University of California that uses a fluid dynamics modeling concept he developed to simulate economic performance. John is also an affiliate at Lawrence Berkeley National Laboratory, working principally in the area of environmental applications of the LBL Phylochip microarray technology.

Nobel Laureate James Meade related how, “Once upon a time a student at London School of Economics got into difficulties with such questions as whether Savings are necessarily related to Investments, but he realized that monetary flows could be viewed as tankfuls of water…” Meade’s support led to the young Bill Phillips’ creation of the Moniac, a sophisticated hydromechanical analog simulator, a cascade of tanks and interconnecting valves controlled by slotted plastic graphs representing the major sectors of the British economy. It was a fully dynamic simulator that, as Phillips explained in a 1950 paper, “will give solutions for non-linear systems as easily as for linear ones. The relationships need not be in analytical form if the curves can be drawn”.

Meade recognized the machine’s dynamic nature and the visibility of its flows as a powerful teaching tool. A favorite exercise at London School of Economics was to run an experiment on the impact of uncoordinated government intervention. One student (the “Chancellor of the Exchequer”) controlled taxation and public spending, a second managed monetary policy (“Head of the Bank of England”). Told to achieve a stable target level of national income while disregarding each other’s actions, they produced results that were invariably messy. Phillips used his machine to investigate many complex issues, leading to his applications of feedback control theory to economics and the Phillips curve showing the relationship between inflation and unemployment for which he is famous.

So why the current lack of analog simulations, which can reveal an economy’s dynamics yet are regulated by the physical laws of the analogy on which they are based? Julian Reiss examined the value of simulation as a means of economic experiment in a 2011 paper, defining the difference between mathematical modeling and simulation. He shows that only a tiny percentage of economic papers employ true simulations, despite its success in many other fields from aeronautics to population genetics. Yet the money is in developing highly constrained, complex mathematical models to interpret market statistics. One need only consider the financial sector, with trading algorithms stalking each other through a cybernetic market ecology, where the difference between the quick and the dead in making a trade is as little as a few microseconds, with billions of dollars to the survivors.

This “black box” trading ecology requires precise, highly constrained mathematical analysis of market statistics to build these algorithms, which obviously affect the pricing of financial instruments associated with the current Euro crisis. Yet, as Kevin Slavin points out, these algorithms, performing  around 70% of all securities trades in the U.S. market, all came together two years ago and, for a few minutes, “vanished” 9% of the entire value of the stock market, though no human asked for it. He says that we’ve turned these algorithms loose in the world, invisible to humans. We can only watch the numbers scroll on our trading screens, our only power “a big, red ‘Stop’ button.”  Some high-speed digital glitch, invisible to humans, caused the Flash Crash of 2010 (the subject of tomorrow’s article in this series).  Contrast this with the analog basis of Phillips simulator. A few small mistakes and leaks are inconsequential, but vanishing 9% of the market would leave large puddles on the floor.

Here’s where the power of simulation as a tool for experimentation really counts. It is worth watching the video of Allan McRobie, demonstrating Cambridge University’s restored Moniac, quickly adjusting valves and graphs to demonstrate multiplier effects, interest-rate impacts and business cycles. Best quote: “Let’s just shut off the banking sector for a moment….”. McRobie shows the many metaphors relating to economics and flow – liquidity, income streams, asset flow etc.- but notes that Phillips’ machine is a direct analog device tied to physical laws governing flow, not the mathematics of digital instruction defining Slavin’s stalking algorithms.

In a Dominican University Green MBA project to develop an analog economic policy “flight simulator”, we invoked the shade of Phillips and his stocks and flows, to show policymakers how resource utilization and environmental considerations affect economic performance. Instead of hydraulics, we used the flow over a specific cambered surface to drive the simulation, essentially a “wing” flying through an atmosphere of potential transactions, with the surface representing the structure of a given economy. The idea came from the serendipitous observation of the similarity between pressure distributions over an airfoil and income distribution, producing an analog where the principal forces on the surface and dynamic outputs have direct economic equivalents.  Results are shown with stocks and resources represented as altitude and potential energy by the kinetic energy of flow represented as velocity through the atmosphere of transactions.

The properties of the simulation’s cambered surfaces were validated by comparing output from varying the growth coefficient with U.S. income from 1979-2007, and comparing the overall force coefficients developed by the U.S. and Sweden over the same period vs. GDP.  The simulation displays all the economies’ characteristics including long- and short-term cyclic behavior, efficiency and stability, with relative income shown by one’s position on the cambered surface. The results are highly visible, shown in the project website video, which includes an analog replication of the “Crash of 87” and the collapse of the housing bubble, We also show that former U.S. Treasury Secretary Larry Summers assumed metaphor that “the U.S. is flying out of the recession dangerously close to the stall” is actually a direct analog.

The simulation, disturbingly, shows that there is a minimum velocity below which austerity will have negative effects, directly opposite to the intended policy, literally a region of reversed commands. Phillips’ Moniac simply runs dry, but our model shows that catastrophic stall is inevitable unless velocity is restored to the point where growth is possible.

Math models and economists’ other tools all count, but the profession must develop good simulations that let policymakers evaluate the potential consequences of their actions in an accessible, comprehensible and visible way.

Useful links

OECD economic outlook, analysis and forecasts

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