Re: poly: On Simple Models (Was: Why interest rates may stay low)

Robin Hanson writes:
> >I just have some trouble with the notion that once you've made enough
> >assumptions that what comes out the other end is interesting in a
> >predictive sense and doesn't just become an interesting math problem
> >arbitrarily selected from the space of all math problems.)
>
> In virtually every field I'm familiar with, experts use simplified models
> to illustrate basic points both to novices, and to each other. If experts
> have done their job right, these basic points should continue to hold in
> more complex models, but the complexity gets in the way of illustration.

True enough.

However, most of the time these simplifications are pretty minor. "We
note that although the energy in this system is in fact more
complicated than this simple equation, a closer model differs from
this simplified one by only a few parts in a thousand and we're
dealing with a smooth model so the outcome isn't going to be very
different and the simplification is unimportant."

The simplifications you've made aren't even simplifications in many
instances (the real behavior is, based on observation, far simpler)
and the assumptions you are making are pretty big here.

> Perry, I don't see any indication that you are discriminating in your
> choice of assumptions to challenge, nor that it is possible to
> develop credibility with you. Nor even that you understand and disagree
> with my basic point. And you are not paying me to teach you this field.

I believe I actually understand the field pretty well for a layman.

Permit me to state what I feel is an underlying problem here.

Mathematical models of large scale human behavior can produce
interesting "large picture" result -- we can note the general
mechanism by which supply and demand tends to balance, we can see the
reasons certain kinds of cooperation are likely to arise, we can note
that free banking likely produces a superior result to central
banking, etc.

However, there is a temptation to do more than this. "Markets are
efficient, so we shouldn't expect any individual player to beat the
market in the long term" is one that we hear occassionally. "This
equation gives us the 'optimal' portfolio of securities" is another
rib tickler. "We can expect a small group of agents (NOT a large
agregate) to behave in manner X" is a third.

I am highly skeptical of any sort of mathematical economics that
pretends to be able to make overly precise predictions.

> My main point was just this: when there are not property rights in some
> investment, and the investment becomes more and more attractive as time
> goes on, the investment will happen near the time when it first seems to
> offer at least a "competitive" return, even if that investment would
> offer an even higher return if everyone waited. Do you really find
> this point implausible, and if so can you identify the *one* complexity
> you most want to see if my simplifed model is robust regarding?

I find the statement generally plausible in a rough sort of way. Of
course, the mechanisms you are postulating that would generate the
stated result are rather bizarre and resemble real venture capitalists
only in that they are far more complex and resemble the real thing in
almost no particulars. Furthermore, you're using a lot of great
ambiguous terms there.

What is a "competitive rate of return"? How does one measure this
rate? Why would we really expect the result to be radically different
if people have property rights in their investment?

Perry

PS You might want to try taking this a bit less personally.
Received on Tue Mar 3 20:32:34 1998