Re: Metastable oscillators

>>>>> "ben" == Benjamin J Tilly <" <[email protected]>> writes:

    ben> Stable versus unstable is a local criterion.  Stability does
    ben> not imply that the system won't fall over if it is stressed
    ben> properly, and most stable equilibria indeed can be forced to
    ben> fall over.

Of course you are mathematically correct.  That's why I mentioned the
"design range."  I know that open sets are "large" but if you tell the
engineers "it's stable as long as you stay within an open set
containing an 0.1-sigma tolerance of the mean" you'll get some funny
looks.

    ben> Note that there is also no real distinction between natural
    ben> and artificial equilibria.  Both tend to be only locally
    ben> stable, and both routinely go through catastrophic
    ben> adjustements.

The distinction I made _is_ a real distinction.  Many control systems
are intended to optimize something, and usually that requires banging
up against some constraint.  And there's nothing that guarantees that
a system behaves smoothly in a case where a moving constraint makes
the current "steady state" infeasible, as far as I know.

    >> There is as yet not even one generally accepted dynamical model
    >> embedding Nash equilibria.

    ben> Is the lack of a generally accepted dynamical model evidence
    ben> that it is hard to produce one that is mathematically
    ben> acceptable, or evidence that a dynamic system has sufficient
    ben> additional features that it is hard to agree on how much of
    ben> the system can be included/excluded?

It's evidence that it is all too easy to produce many dynamic models
that are mathematically acceptable.  However, not even "backward
induction" (dynamic programming) in pure strategies is entirely
uncontroversial on behavioral grounds!

    >> Consider: the markets where we insist on controlling prices
    >> (labor, housing, agricultural products) are precisely with ones
    >> with rather unsatisfactory quantity outcomes.

    ben> Actually with agriculture we control both price and quantity
    ben> - we guarantee a minimum quantity and then offer farmers
    ben> direct support of some kind for the resulting low prices.

That's just plain wrong.  We simply guarantee the farmers a high
price.  In some cases we also subsidize the consumers, but I know of
no program in which minimum quantities are guaranteed.  It's never
necessary.  There are "soil bank" programs which attempt to guarantee
a _maximum_, but they always fail when the farmers (who always feel
they're undervalued) both sell in the market (usually, but not always,
a different crop, often enough also soil-banked---they're the
overpriced ones, after all) and collect their redundancy payments too.

    >> And, of course, because in situations like the labor market
    >> neither price nor quantity volatility should be accepted
    >> without a fight.

    ben> s/should/will be/

    ben> People disagree wildly on the shoulds in this case, and the
    ben> position that you take is strongly correlated with your
    ben> overall political stance.

Speak for your own correlations.  You know my overall political
stance.  :-)

    ben> Um, this makes no sense to me.  Generally speaking, chaos is
    ben> not a sign of stability.  For instance the basic Hadley cells
    ben> in the Earth's atmosphere give rise to the permanent Jet
    ben> Stream.  However the actual trajectory of the Jet Stream is
    ben> unstable and chaotic.  It wanders over a restricted range,
    ben> but slight perturbations in its basic path are not
    ben> counteracted, they grow.

By mathematical definition, chaos is not stable.  I should have said
"there exists an attractor with bounds we can live with."

    >> I think maybe they should just let them alone, except for
    >> controlling inflation.  Inflation does not affect the real
    >> economy to a first approximation.  Therefore applying negative
    >> feedback to control inflation can probably be decoupled from
    >> nasty side effects in the real economy.  Not so if you actually
    >> try to control interest rates.

    ben> Predictable inflation rates may not affect the real economy
    ben> to a first approximation, but boy oh boy do the higher order
    ben> effects matter!  Consider the difference between inflation
    ben> and deflation to see what I mean.

Predictable inflation does not affect the economy in equilibrium at
all, except to the extent that people can't do division.  Only if the
inflation is unbalanced or unpredictable does it have effects.  This
is actually fairly well verified empirically for countries whose
historical inflation rates stay under 15%.

Deflation is another matter because it is basically impossible for
nominal interest rates to go below zero (holding cash is always an
alternative, and if it's not, the financial system implodes).

    ben> Sure, the possibility of bias is one that you have to fight,
    ben> but a possible cause of bias is not necessarily sufficient to
    ben> disqualify research.

In behavioral research, it sure as hell is.  I don't even trust my own
intuition about why people do things that don't seem to be derivable
from maximization of some obvious value.  That's why I do mathematical
economics as opposed to non-mathematical economics, or any other
behavioral science.

    ben> Arguing for inaction when appropriate actions seem to be
    ben> obvious is always hard.  It becomes harder still when
    ben> subsequent events demonstrate that action was, after all,
    ben> justified.  See British inaction in the face of the Irish
    ben> Potato Famine, motivated by the belief that intervention now
    ben> would just cause a later, larger famine.  Given the
    ben> subsequent history, this conclusion is dubious.

Huh.  Of course you have a citation on tap?

    >> [1] Of course natural systems also respond catastrophically to
    >> extreme conditions.  Eg, an avalanche.  However, the usual goal
    >> of control systems is to push things toward optimal solutions,
    >> which are by definition extremes.

    ben> Um.  Control systems are often designed to manage otherwise
    ben> predictable natural catastrophes.

Economic catastrophes are by definition man-made, and the goal of
economic control systems seems never to be containment of the
disaster, but rather to return to unsustainably high levels of pork
for everybody.

    ben> I am bothered by people who are so convinced of the rightness
    ben> of their rational models that they can comfortably disregard
    ben> the human consequences.  But I am also wise enough to not
    ben> lightly disregard their reasoning...

Milton Friedman, in person, even when speaking to a large audience,
was nowhere near as smug about the human consequences as he comes off
in his books.  He still was convinced enough of his models to advocate
never caving in to the temptation to "do good."  I think that he's
pretty representative of the breed.  It's the dialectical materialists
who have historically been explicit about neglecting human consequences.



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