To My Fellow Economists:
It is my understanding that Chaos Theory is normally explained first as “sensitive dependence to initial conditions.” However, what interests me also is the necessity for a “Non-Linear Equation or System of Equations” to exist. Or, to put it another way, if either “Additivity” or “Homogeneity” is missing, both being necessary to be a “Linear equation,” then it becomes “Non-Linear.” What all this gobbly gook means to me is that the Linear one is solvable while the Non-Linear one is dependent on the Initial Conditions. Or the way I see this the former has a Single Answer while the latter is one that it “Depends.”
So my question to my fellow economists is:
Is Micro Economics dependent on Linear Equations while Macro is finally realizing that it is only understandable in a Non-Linear system? I define Macro broadly to include the Financial Markets where Black-Scholes is a non-linear differential equation. Other Chaotic research efforts have involved stock market crashes, cotton & wheat pricing, as well as other macro aspects.
The implications for Macro are:
(1) Long term forecasts are rather foolish because of “Sensitivity Dependence.” This leads to the cliché: A good forecaster forecasts often.
(2) “Strange Attractors” lead to chaotic conditions that cannot yield reliable forecasts and, worse, the chaotic condition’s duration is unknown. However once it works its way through that a new “sort of equilibrium” will exist. I don’t know if I would go so far as to call this a paradigm shift but it fits the idea fairly well.
In summary, I now try to think of our global economy in a non-linear fashion and do believe we are in a “Strange Attractor Phase.”