TWO natural rates of unemployment?

[6155GUASTELL@xxxxxxxxxxxxxxx]

Way back in January we were discussion the natural rate of
unemployment, the alternative hysteresis hypothesis, unit
root analysis, Bill Mitchell's work (and others') on same.

During that phase, with the help of PKTers shooting some
data my way, I did a near-instant analysis of the nonlinear
dynamics that could underlie US Unemployment rates 1948-1994.
In that process I isolated two plausible functions, one a
chaotic attractor (R^2 = .86, DIM = 1.43), and a Hopf
bifurcation (R^2 = .92, DIM = 1.98), both of which compared
favorably against a linear regresion of unemployment rates
over time (R^2 = .32).

Since then I have been exploring those functions further,
with the intention of using them to identify the "real"
natural rate of unemployment in the US. I came up with
two very different values.

1. Hopf model. Because this function had a negative
exponent, iteration was initialized with the average
u-e rate for 1994, then run until it was close to convergence
(48 iterations analogous to 12 years of real time).
All the usual assumptions and risks concerning ergodicity apply.
The natural rate obtained from this situation was 6.6% of the
workforce unemployed.

2. Chaotic attractor. Because this function had a positive
exponent, the method for find the epicenter of the attractor
is to multiply the exponent by -1t, and iterate backwards
in time to find the initial conditions that are most likely
to have produced the time series we observe. That value was
3.4% unemployment.

I would think these two natural rates would have very different
policy implications, no? Any thoughts from PKT are appreciated.

--Stephen Guastello