[From Rick Marken (2003.02.07.1330)]
Bill Powers (2003.02.07.1037 MST)
Ah. This was very helpful. Thanks.
Rick Marken (2003.02.06.2200)--
>OK. I imagine the diagram could be better.
Then make it better. It's not much help as it stands. It is hiding errors.
I will do that. And I will try to present a better description of the model so
that you can get a better idea of what it is.
>I guess one thing I was trying to do was model at the aggregate level,
>the same level at which TCP was describing the behavior of the circular
>flow. The variables whose behavior I am trying to model are aggregate
>variables, like GNP. So the agents are really conceptual agents.
That's not an answer to my objection. If you want to see what the model
predicts about the growth of GNP, you don't make GNP a controlled variable
and give it an exponentially-rising reference level. If you do that, you'll
get out of the model precisely what you put into it, an
exponentially-rising GNP. That is exactly what TPC did: declared that
economic output depends on exponents, and then gave the impression that he
had proven that it rises exponentially. In other words, the way you're
going to prove that GNP rises exponentially is to make sure it rises
exponentially. What kind of modeling is that?
Actually, that's not quite what I did. It's true that the reference for GNP rises
at a constant rate but I wasn't trying to show that GNP rises at a constant rate.
I was trying to see if, within the context of the model, leakage would have an
effect on growth rate. It could have, just as a constant disturbance will result
in a constant offset of controlled variable from it's reference. In fact, it
turns out that d leakage/dt does have an effect on dGNP/dt in the model.
It would be like proving that
the outfielder runs along a curved path by giving him reference levels for
direction of running in X and Y that correspond to the curved path you
observe. In your baseball model, you at least show how the directions of
running are functions of error signals in some _other_ control systems than
the direction-of-running systems. The fact that they are curved _emerges_
from the operation of the model; there's nothing in the model that
specifies the curvature directly, as your rising reference level for GNP
specifies how GNP is to behave.
What bugs me is that you know better than this. You have never, to my
knowledge, made this mistake before.
Well, no wonder you're pissed. You just expect great things of me;-)
If I actually did this (putting conclusions in as assumptions) -- and I suppose
it's possible that I did -- then that certainly would be a huge mistake. I don't
_think_ I did it. I certainly don't think I came to any conclusions about the
behavior of the model after putting those conclusions into the model as
assumptions. But you never know. I might have. If so, it was the result of pure
stupidity, not nefarious intent.
Since you don't have Excel, I will try to write out the model as procedural code
and we can go over it and see if I did, indeed, put in my conclusions as
assumptions. I'm pretty sure I didn't; that's why I find your reply so
encouraging. I suspect I may be more guilty of poor communication than of stacking
the deck. But if I goofed up then I'm happy to correct the error.
>Individuals compare income (PQ' at the individual level) to expenses
>(P'Q' at the individual level). My PQ' - P'Q' controller is a
>representation of the aggregate control over their balance sheets
>exerted by many individuals.
So are they trying to make PQ' = P'Q'? That denies leakage right there; if
there is actually leakage of money from the system, it is impossible for
PQ' to equal P'Q', if I interpret those symbols correctly. Your model
contains no source of money to replace the leakage disturbance. so the
books clearly cannot balance.
Actually, money does enter the system automatically to make up for leakage. But
it does sneak in. Inventory also builds up until enough money comes back in to
make up for leakage. But I'll present the details of the model so you can judge
for yourself (and then you can explain to me what's wrong).
>The evidence I gave that the model is working properly (given what I
>wanted the model to do) is presented in Table 1, p. 169. This table
>shows that the model does what it was designed to do: produce behavior
>(of Q/Q' and inflation, at least) that matches the behavior of these
>variables, according to TCP's model, as a function of leakage.
But it does that only because you specifically made it do that. And there
has to be an error in your model, because Table 1 shows the rate of growth
increasing at a constant 13% a year, while in fact the amount of money
available for spending is decreasing at the assumed leakage rate. There is
no way that the rate of spending can be increasing according to the
indicated inflation rate while the rate of growth is remaining constant in
terms of goods purchased. The amount of goods may be increasing year by
year, but inflation is increasing faster, so there is a net loss of output
in constant dollars -- exactly as the Circular Flow model predicts.
I'll have to look at this. There is a net loss of output relative to potential
output in constant dollars. I'll have to explain what the model did.
> I'm sure I could have done a better job of
>validating the model. But the model did do what I built it to do.
So why didn't you just make GNP increase at 13% per year, so you could say
the model is correct, since GNP increases at 13% per year? Essentially
that's what you did by making the reference level increase 13% per year.
I wasn't trying to show that GNP increases at any particular rate per year. I was
looking to see if leakage would have an effect on the rate of increase in GNP.
> I
>agree that the discussion might have been too sketchy. But I don't know
>what detailed evidence (other than what I presented in Table 1) you
>would want to prove to yourself that this is a "proper" model.
Look at Econ004.pas. It's not complete and it may even be mistaken, but it
is a proper model. No behavior is simply assumed to happen and then made to
happen that way.
Again, I don't believe I did that. If I _did_ do it, then it was a result of
stupidity and I obviously have some important things to learn about modeling. But
I'll try to describe the model in more detail and then you can point out where I
did that. But I will say that I didn't put the increasing reference for GNP into
the model because I wanted to show that GNP increases at a constant rate. I put in
the increasing reference because I assumed that demand increases with population
growth. I wanted to see how the behavior of the demanded variable (GNP) would be
affected by variations in leakage. If anything, I assumed that the behavior of
the controlled variable would by affected by leakage. It was, but not in the way
described by TCP.
>I don't think your conclusion that "of course leakage had no effect" is
>correct. The increasing reference for GNP corresponds (somewhat) to
>TCP's intrinsic growth rate; I think it represents the growth in demand
>for GNP that results simply from population growth.
None of that is in your model, and your model can't really work for that
reason. Leakage has no effect in your model because you have not provided
any way for it to have an effect.
But leakage does have an effect -- on Q/Q' and inflation rate (as shown in Table
1).
> I constructed the
>model to mimic the behavior of TCP's model. And my model succeeds at
>doing that.
Except for the effect of leakage. Imitating the behavior is trivial. I can
construct a model for stopping a car by saying its velocity decreases
exponentially to zero. That duplicates the behavior of the real car. But
the whole point is how that result is achieved; the essence of the model is
in the how, not the what. Your model contains no how, or no valid how.
I _think_ you are wrong about this and I will try to prove it to you. But you may
be right. If so, that would be fine with me. I'm just trying to do it right.
> I thought that the effect of leakage on growth rate would
>"fall out" of the model. But it didn't, and that's how I discovered that
>TCP had put the effect of leakage on growth rate in as an assumption.
But you did the same thing: you assumed a constant growth rate by making
the reference level grow at a constant rate. Of course there was no way
leakage could have an effect on growth rate when you specifically set up
the model so _nothing_ could materially affect growth rate.
But d leakage/dt _does_ materially affect growth rate in the model
> In
>fact, _change_ in leakage does affect growth rate.
How could it? You show the growth rate in Fig. 1 as constant at 13% per
year.
There is a _change_ in growth rate (above and beyond that demanded by the
reference) that results from a _change_ in leakage. If leakage changes
continuously then growth rate changes continuously (with an average rate of 13%,
if that is the rate at which the reference for GNP changes).
But if your home projects
with modeling are to fare any better than the economic model, you should
consider very carefully what we're discussing here.
Well, I haven't given up on my economic model yet but of course I'll consider
carefully what we are discussing here. I want to learn. If I did what you say then
I've made a terrible mistake and I want to correct it. So if I give you a better
description of the model I hope you well help me understand what I did wrong. I'm
really not trying to put one over on anyone. This was an honest effort to build a
working model based on TCP's concept of the circular flow of goods/services and
money between aggregate producer and consumer. If I put conclusions in as
assumptions then it was a huge mistake. I don't think I did that but if I did then
please just explain it to me.
Your model works by
magic, and that is not how you have normally made models in the past. If
you don't figure out exactly where you went wrong, you could make the same
mistake again.
Great. At the moment I honestly have no idea where I went wrong (or _that_ I went
wrong). I don't think the model works by magic. I don't think I put conclusions in
as assumptions. But if I did I would like to learn about it so I don't do this
again.
Thanks
Rick
···
--
Richard S. Marken, Ph.D.
Senior Behavioral Scientist
The RAND Corporation
PO Box 2138
1700 Main Street
Santa Monica, CA 90407-2138
Tel: 310-393-0411 x7971
Fax: 310-451-7018
E-mail: rmarken@rand.org