## Thursday, September 9, 2010

### Endogenous Business Cycles and Randomness...

As I was re-reading Masanao Aoki's Reconstructing Macroeconomics: A Perspective from Statistical Physics and Combinatorial Stochastic Processes, I came upon (again) an insight regarding the stochastic nature of business cycles that I think is worth sharing.  The insight was originally Eugene Slutsky's.  The basic idea is that the simple summation of random variables can produce cycles.  A concrete example will help fix ideas.  Suppose we have the following random walk model:

Si-Si-1=ei=+/-1 for all i=1,2,... with S0=0

with the respective probability of either outcome (i.e., -1 or 1) equal to a half.   This is simply a model of "winnings" from tossing a fair coin (where heads wins $1 and tails losses$1)  The unconditional mean of this process is zero, which might lead one to expect that the process spends "most" of the time "near" its zero unconditional mean.  But this intuition would be incorrect.  Take a look at the following diagram of a sample path of 10,000 tosses of a fair coin:

For me, Slutsky's insight should be taken as a reminder that quite sophisticated behavior, including cycles, can be generated out of simple randomness.  I actually think that this insight is more general than even Slutsky might have been willing to admit.  Simple randomness is a major force in this world, especially in economic behavior.  We as economists tend to be too quick to assume that the sophisticated/complicated macroeconomic behavior that we see in the world must be the result of fairly (or extremely) sophisticated human behavior at the micro level.

Perhaps the macroeconomic behavior we observe is actually being driven by fairly simplistic humans operating by "rules of thumb" sprinkled with a bit of randomness...