Friday, October 24, 2008

Insights(?) from math about the economy

Example 1 from Control Theory

The top figure is a plot of the Dow Jones Industrial Average for the past two months (from CNN Money). The figure under it shows a "ringing response" of an underdamped system to a step change in its forcing function. If we want the volatility of the stock market to be less in response to a major change in understanding of the market fundamentals, perhaps we need to increase damping in the system. That might involve regulation of trading institutions and reduction of speculation on market prices.

Example 2 from Complexity Theory

The prototypical situation of complexity theory is lots of actors interacting, making independent decisions based on locally available information. The prototypical insight from complexity theory is the existence of "emergent properties" that are visible in the ensemble but not (necessarily) to the individual actors, and certainly not deliberately planned by those actors.

The model might be applied to American society, and the huge level of debt (federal, state, corporate, consumer) might be thought of as an emergent property of their individual decisions. One might look for a state variable, characteristic of the individual actors to help explain the functioning of the complex set of actors. A metaphor might be temperature as a state variable in modeling of climate change, where global warming affects all the cells in the simulation of the global atmospheric system. The willingness to consume in excess of income might be considered such a state variable in a (complexity theory based) simulation of the economy. Many have suggested that there has been a wide spread increase in the willingness of Americans to go into debt, in short greed for immediate consumption and lack of concern for the future.

There should be means to set the temperature of the economy, to reduce the willingness of actors to accumulate debt for immediate consumption. One thinks of schools and churches, the media, and the government. The financial services industry in our capitalist system works on the basis of profit maximization of the individual enterprises, and has invented all sorts of new instruments to maximize those profits. The Great Depression resulted in regulation to assure that banks did not accept too much risk in the effort to maximize profits, but since the Reagan Revolution the U.S. government has been in the power of people who thought that such regulations were excessive; they did not impose limitations on risk on the new financial instruments that were being created, and the financial industry responded by inventing new instruments to avoid existing regulations.

One might infer that we need to get people to return to deferring immediate gratification in favor of investments which would yield long term benefits.

Example 3 from Systems Theory

A key principle of systems theory is the utility of defining a system of entities that interact strongly, separating it from a surround that includes entities that react much less strongly with the elements of the system that those elements do with each other.

The United States went through a long history, developing financial policies on the basis that the American economy would be a system and the economy of the rest of the world its surround. Monitary policy would be under the control of the Federal Reserve System, and fiscal policy would be under the control of the Federal Government.

In the aftermath of World War II and the Great Depression, the community of nations created the Breton Woods institutions (IMF, World Bank, etc.), recognizing that there were interconnections among national economies, in order to regulate the functioning of the international system. Essentially, the Breton Woods institutions managed a global economic system consisting of weakly interacting national systems. In the intervening period, Europe has recognized that the European economies are interacting strongly with each other. The European Union has created and is continuing to evolve institutions to manage the economy of Europe as an single integrated system.

Globalization and the rise of BRICs to comparable status with the G7 have changed the nature of the world. The current crisis seems to suggest that the assumption that national economies can be regarded as independent systems is no longer valid. That in turn would suggest that, as was done in Europe, the nations of the world consider a stronger set of global economic institutions to manage an increasingly interconnected global economy.

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