[From Bill Powers (2005.01.13.0701 MST)]
Rick Marken (2005.01.12.1630)–
I think what I disagree with you
about is how much boiling down is
appropriate in an economic model. I want to boil down a lot more than
you
do.
In the Test Bed beta, I have boiled the system down to a consumer with
one goal for goods and another goal for savings, a manager with a goal
for inventory, a goal for investment reserve, and a goal for general cash
reserve, a plant that does the production and holds the plant inventory
and plant cash reserve and a household that receives goods into a
household inventory, and wages or capital income into a household cash
reserve,.
The manager is proposed to control plant inventory by adjusting prices,
and the plant cash reserve by adjusting capital distributions. The
consumer is proposed to control the household inventory by spending money
out of the household cash reserve, and the household cash reserve by
working for wages (the recipients of capital income do not work). Wages
in dollars pass from the plant’s cash reserve to the household’s cash
reserve. Work consists of producing goods at a certain productivity:
goods per hour worked. Wages are paid as dollars per hour worked. Goods
are sold at a price, so many dollars per good. The dollars pass from the
holusehold cash reserve to the plant cash reserve.
When this model runs you get a circular flow of goods and money in
opposite directions just like in TCP’s book. You can put leakage into it,
growth of population, growth in productivity, or any other factors you
think are important. If you don’t believe in leakage you can leave it out
and see what happens. If you think consumption is caused by income
(Keynes’ thesis) you can put that into the model and see what
happens.
All the arguments will come after people see what happens and don’t
believe the results. They will insist there’s something wrong with the
model if it doesn’t agree with their theory, and that will lead to more
careful construction of the model, including fixing the things they say
are wrong in it. This will focus arguments on the critical issues and
point out how to resolve them.
The main point of all this is to get economics on a model-testing basis
instead of an arena for flame wars, hotly defended prejudices,
superstition, and mathematical bumbling, its current condition.
This model needs to be expanded in several regards. One kind of expansion
would be to include multiple goods, multiple plants, and multiple
households, run by people with different settings for the assumed
reference levels, and possible different kinds of reference levels
(different strategies). In this way we could, for example, produce
supply-demand curves. If wage negotiations were included, we could
examine inflation. Adding banks would bring in effects of interest rates.
And so on.
If you were really going to
model the economy as interacting control systems
you would have to model (for the US) about 250,000,000 agents, each
controlling for hundreds of thousands of different variables (all the
goods
and services produced) by doing the hundreds of thousands of
different
things people can do to produce and consume these things. Of course
you
can’t do this. All modeling involves some degree of boiling down.
Yes. But the boiling down has to include everything that needs to be
included to create an explanatory model. You can’t, for example, just
assume that the economy will expand, and then create a model that will
behave that way. That’s modeling behavior, not modeling the system. You
have to allow for models that may sometimes expand and sometimes
contract, and include an explanation of what makes them do
that.
I think that, in the case of
economics, the boiling down (or aggregation)
should be done to a level that is both scientifically viable (in terms
of
accounting for the data) and relevant to economic policy decisions. I am
not
committed to a particular level of aggregation; I think what is
appropriate
will become apparent as the model development continues. My bias may be
to
go to a higher level of aggregation (boiling down) than you. But I bet
that,
if we both end up trying to model the economy at the same level (the
economy
of a nation, for example, rather than the economy of some segment of
a
nation, like a single household) we will end up at very similar levels
of
boiling down.
It’s legitimate to aggregate control systems when they all control
similar variables. You can aggregate, for example, working people who
control for saving money. Over the set of such people the amount
to be saved (the reference level) can range from zero to some maximum,
the loop gain likewise. But because they’re all controlling the same
variable, savings, you can aggregate them into a virtual control system
for purposes of predicting mass behavior – how much the economy saves
and how hard it tries to maintain the average level of savings by
adjusting spending and working. In my model, different managers may try
to control inventory at different levels, and do so by adjusting prices
with high or low gain, but such managers form a group that acts as a
virtual control system for the inventory of all plants managed in that
way.
Aggregate models will not predict very accurately because the actual
parameters have a wide range of values. To get more accurate models you
can create bins, with independent control systems having, for example,
weighted reference levels for the common controlled variable at the
center of each quintile. How many bins you use will depend largely on how
big your computer is and how fast it is. You just program for N bins, and
adjust N as appropriate. If you want total aggregation you set N = 1. I
was, the last time I worked on it, trying to set up the Test Bed that
way, so I could have P plants, H households, G goods, P prices, and so
on. The first test, of course, would be to see if the model still runs
properly with P = H = G = P … = 1. Then I would try setting them to 2
and see if everything still works. Then I’d set the numbers to 10000 with
appropriate parameter distributions and come back tomorrow to see what
happened.
“I” means, of course, “somebody”.
Best,
Bill P.