Savings and Investment

From[Bill Williams 21 March 2004 4:00 PM CST]

[From Bill Powers (2004.03.21.0626 MST)]

Bill Williams 20 March 2004 6:30 PM CST --

>You are probably tired. Why not give it a rest for a while and rethink

>the problem. Maybe you can come up with some basis for a discussion other

>than one which starts with you win and I lose.

Excellent idea. Let's both do that.

I will attempt to do my best-- and it really isn't that difficult for me.

Despite all that has transpired I do have a profound admiration for what

you've managed to accomplish. In particular your treatment of time and

causation in the Appendix to BCP seems almost unique-- at least in
psychology.

I've said this before, but I think it is worth repeating. For one thing the

way you treat time and causation in the appendix to BCP provides at least

a potential basis of agreement from which to start this discussion.

It might be helpful if you would explicitly confirm or reject this as a

basis for discussion.

My concern might seem unnecessarily theoretical for many people, but I

am convinced that a solid understanding of control theory applications

to human behavior requires an understanding of the implications involved

in two different conceptions of time and causation.

One is the period sequence notion that is characteristic of the

"reflex-arc" or behaviorism. The other is an analysis of behavior

in terms of a simultaneous equation of time rates. I think Dewey

had something of understanding of this in his treatment of behavior

as a "circle of coordination." But, he didn't have anything like

the conceptual or the computational resources to actually implement

this conception.

It is this simultaneous equation conception that I am convinced

is the proper mode of analysis for control theory. The

implementation of this conception using computer programs has to be

done carefully in order to preserve the proper treatment of time

and causation. At least this is my conviction. I think it is one

that you share, and I would guess that is an understanding in

common with Bruce A, and Richard K, and Martin Taylor, and

Wolfgang. And, perhaps others who don't come to mind.

And, if I may make a complaint about BCP it would be that the

Appendix on the analysis of a control process ought to have

been much, much longer. Perhaps one of the things that might

result from this thread might be an explicit and more extensive

treatment of the issues which were treated so briefly in the

Appendix to BCP.

The material below on economics was written before reading your recent post.

I've read your discussion-- which displays a detailed familiarity with
Keynes'

treatment of income. I want to re-read and study what you say giving it more

time before commenting at any length or with a measure of confidence. But,

the initial impression that I get from a first and rather hurried reading

is that you are attempting to trace income flows through time. In doing

so, I get the impression that your are treating savings are the source

of funds for investment. (In the Keynesian system the causation runs

from money created by banks to finance investment to the creation of

savings.) But, I want to say that my impression is gained from a

quick reading, and I want you to treat it as a conjecture on my part.

After a more careful reading I might come to a different conclusion.

But, it my initial reading is close to your actual position then it

would helpful for you to confirm or reject my initial conjecture.

      Text written Friday, modified somewhat Sunday

   My description of the process involved in the

aggregate economy and the investment savings

identity may and probably will appear bizarre.

And, I am not all that confident that it will

be all that intelligible or helpful. I have

recently looked at a couple of what I thought

were very good explanations of the point I am

making here-- that in the aggregate investment

is equal to and causes savings. Ordinarily text

book expositions present this Keynesian insight

in a style that is so gradual and low key that

I am sure that many students are never disturbed

by its novelty-- and the fundamental relationship

probably escapes their notice altogether-- which

may be what is intended-- if that is many or most

instructors in economics are aware of the deeper

intellectual cross currents involved.

It might be a good idea to consider the following

without feeling a necessity to either accept or

reject the argument for the moment. And, although

I've re-read what I've written carefully in an

attempt to avoid errors in detail, the exposition

may contain errors in expression or even-- though

I hope that I've avoided substantive errors. In

rereading, I've made some changes, but I have

retained what may be tiresome or annoying

repetitions.

       A digression:

One of the results that might come out of this

exercise is a model which would contain the detail

involved in a correct configuration. As it is now

it is necessary to get all this stuff into ones

head. And, it ordinarily takes years for a student

to do this-- if they ever do it properly. With a

proper model this effort of building a stable

system in one's head would be removed.

     Return to main exposition:

Then after consider what, and or, how I describe

the system in the following, you might consider

how Bruun treats the same issue or issues.

However, it may be that until you see the

implications of the contrast between the Orthodox

and the Keynesian conceptions illustrated by your

own working model you may not be inclined to credit

the Keynesian position. You are inclined to have

far more confidence in a simulation than in a

sequence of verbal arguments.

     The Presuppositions

What seems to be involved, or even required, in

understanding the Keynesian position is a gestalt

switch from the familiar micro relationship or

definition of savings, to a very different aggregate

relationship. One of the shifts involved is a shift

in the definition of saving, and the process that

generates saving. For the individual saving is the

result of an excess of money income over money

expenditure. In the aggregate income is equal to

expenditure so applying the micro conception of

saving generates what may seem to be a strange

conclusion. And, the conclusion is that savings

(in the aggregate meaning of the term) are equal

to the creation of money.

Of course, individuals are not allowed to make

their own money. But, governments and banks

can make all they wish to for next to nothing. The

expensive really doesn't amount to much beyond the

care required to keep track of the accounting

involved.

Perhaps it is a reluctance on the part of banks to

admit that they are making money out of nothing that

creates a something of veil of confusion that obscures

what is actually going on. Such a reluctance may also

be the source of the otherwise difficult to explain

policy of government borrowing and paying interest

on the loan of money, that could have simply been

printed. There is a life time of complications and

controversies involved. I thought it was fascinating

as a student, until I realized that it had already

been discovered before I was born, and had in the

meantime, I thought, become a bit tiresome. But, the

tiresome business involved a process in which things

were becoming more complex and more confused rather than

becoming better understood.

   The central paradox which is generated by attempting to

think about how aggregate income is determined, it seems to

me, involves two misconceptions. The first is to conceive

of aggregate savings such that savings is equal income minus

expenditure. ( This involves a transposition of a micro

conception to a macro context-- but the habituations

involved make this transposition difficult to avoid.

And, the second is to attempt to track the flow of money

through the economy in a time sequence. Such as assume

such and such level of income for the consumer, then the

consumer purchases so much, and saves so much. Then a

bank acts so as to make loans of such and such volume,

and then the entrepreneur spends such and such. Tracking

the income and expenditures this way through time, it

seems to me, is just what you, quite correctly in my

view, recommend against in the Appendix to BCP.

The problem, or one of the problems, with attempting to

track income flows is that unless one is extra-ordinarily

careful the effort is going to go in the ditch when the

accounting identities involved in a macro context are

ignored. I don't believe that it is impossible to follow

the "flow" of income and do so in a way that reaches

the "correct" result. More than a year ago I spent a

couple of days using odd and otherwise idle moments to

see if it could be done. And, I think that I got to a

point where, if I took it slow and was careful I could

do it. But, the impression I got was that tracking the

income through time in a period sequence sort analysis

was an artificial sort of student's exercise-- the sort

of thing that was possible only if one knew the answer

in advance.

Usually, or overwhelmingly, what is going to happen is

that a mistake is going to take place either a

transposition of a micro relationship (a substitution of

micro specification of saving ) or getting the temporal

relationships confused. (See your Appendix from BCP)

In the aggregate, however, income and expenditure are the

same thing. As a result the only way in which savings can

be generated is by the creation of more money. And, more

money can be created (not by efforts to save by individuals)

but rather by either government, or banks.

Ordinarily when thinking about money there is a tendency

to attempt to "follow the money" around a circuit. This

tendency almost always leads into misconceptions as a

result of adopting a periodic sequence approach to

analysis. When combined with a transfer of the microeconomic

assumption that savings can be increased by increasing

income and/or reducing expenditure the result is an error

that can be very difficult to discard.

Compare what you say BCP

"The most common beginner's error in analyzing how a control

system works is to trace the effects of an abrupt disturbance

step by step around the closed loop. Such analysis are

almost qualitative, and therefore do not reveal the

quantitative difficulty created by that approach." p. 280.

However, if one starts from the point of view that in the

aggregate what one agent sells another agent buys, then

sales (in the aggregate) are equal to purchases. Or, that

income is equal to expenditure. When viewed in this way it

is clear that savings can not be generated by increasing

income or reducing expenses. The only way that savings ( in

the aggregate) can be generated is by creating more money.

One way to do this is for a bank to create a loan. It might

seem that the bank would have to have money on hand to make

the loan. However, as it turns out this isn't necessary.

In the United States there is this idea that a bank ought

to have a "reserve" of money to "back up" the loans that

are being made. It is my understanding, although I don't

know the details that this mythical conception of bank

"reserves" is not shared by other cultures, or at least

all other cultures.

And, the direction of causation runs in a direction that

might seem to be backwards-- from loans to savings,

rather than from savings to loans. As a result of the

loan there is an increase in money and as a logical result

there is an increase in savings. So, investment (based

on the loan or more accurately the creation of bank money)

creates savings.

Maybe the only thing difficult about this explanation is

that there are two, at least, quite distinct meanings

assigned to the one term "savings." And, the emotional

weight that is attached to the term results in it being

easy to equivocate and inadvertently slip from one meaning

to the other.

There is also the possibility of equivocation in regard to

investment which may be defined either as the purchase

of plant and equipment or as the purchase of stocks,

bonds or some other form of paper. In the case of

"profit" there are at least three ways of slipping

about. 1) income minus expenses, 2) division of

income, or 3) the change in the price of an asset or

capital gains.

The causal story begins with the purchase of an item of

newly created equipment and the result is an increase in

the supply of money or savings.

I've thought that there is something of a similarity

between the explanation of how investment generates

savings, and how conceptually a sufficiently slow

disturbance to a control system generates not a response,

but rather the phenomena of control. And, the control is

a rather strange phenomena in that nothing, or nothing much

(the disturbance is divided by /(gain + 1) ) happens.

Viewed from the standpoint of a behaviorist is very strange.

   "If a control system is known to be dynamically stable, the

rules of thumb presented earlier can be applied without taking

time into account, provided only that one adopts a time scale

on which the outputs of the control system appear to change

immediately in response to a disturbance. On that time scale,

delays within the system are negligible." p. 282.

From the standpoint of the orthodox economists, the Keynesian

system might seem to run in reverse. Rather than savings

making investment possible, investment generates savings.

Let me know if this is helpful.

Also, it might help if you would describe the impression you

have of Bruun's dissertation.

Over all I was impressed with the dissertation. And, it isn't

really fair of me comment only upon aspects of the work with

which I do not approve. However, I will do so anyway.

1) I find Bruun's use of rule based agents very troubling. And,

   the reports of the behavior that the program generates looks

   to me more like noise and chaotic instabilities rather than

   a plausible behavior.

2) Bruun's treatment of time in terms of a period seems like

  it avoids actual errors. The accounting seems OK to me--

  but I haven't studied this with the care that would be more

  prudent before making comments.

3) Bruun's treatment of user cost and price indexs is candid,

   and while I don't neccesarily agree with her conclusions

   about what to do about the problems, I think her description

   of the problem involved is useful.

4) My general impression is that Bruun in the dissertation may

   have bitten off more than she could cope with. Is it your

   impression that the simulation that she created is one that

   can be readily modified and improved?

In closing, perhaps you could state your impression concerning

the following question. In you thinking which direction does

causation take? Is it from savings to investment, or from

investment to savings? Or, is there some other alternative

that is central to the determination of the level of income?

I am pleased to start the discussion from a basis, as I

understand it, that neither of us necesarily has to be a

loser.

Bill Williams

[From Bill Powers (2004.03.21.1519 MST)]

Bill Williams 21 March 2004 4:00 PM CST --

I think your exposition will be helpful to both of us, though clearly there
is still a way to go before we arrive at that pure and crystal-clear
description of the system that we will know is right when we see it. The
following, I fear, may lead to remarks to the effect that asking Bill P. a
question is like trying to get a drink from a firehose. There is just a lot
to say.

As you have seen, the problem of time is paramount. The way it is handled
in systems analysis is to describe processes that take time to be carried
out. One such process in economics is referred to by the term "income." The
problem is that this term has two meanings: it can indicate a flow, or it
can indicate a sum that has accumulated over time. Both are needed to allow
time to be introduced correctly.

I don't know the standard symbols to use, so I'll just use programming-type
mnemonics instead of single-letter variables (a practice that helps me
remember what the variables are, anyway). Let's say that the flow meaning
of income is represented as a variable called "IncomePerHour". As long as a
person is working, or a producer is selling goods, there is a flow of
income to the person measured as IncomePerHour.

A steady value of IncomePerHour is received into an account. We don't need
to give this account any suggestive name like "savings", which would
probably just muddy the water. Instead, we can just say that there is a
variable called IncomeAccount, the value of which is the sum of all the
hours or days of flow of IncomePerHour into this account. We can say, for
now, that

IncomeAccount = IncomePerHour * ElapsedHours.

In general,the money in IncomeAccount is being used for expenditures at the
same time it is accumulating (this begins to introduce the ideas about time
that you discuss). The value of the variable IncomeAccount is reduced when
there is a flow of money _out_ of this account. For uniformity, we can
express the expenses in a similar way, as an hourly flow, giving us a
subtractive term:

IncomeAccount = IncomePerHour * ElapsedHours - ExpensesPerHour * ElapsedHours,

or

IncomeAccount = (IncomePerHour - ExpensesPerHour) * ElapsedHours,

Remember that the name "IncomeAccount" stands for a number, the cumulative
total of all inputs to and outputs from the account. The inflow and the
outflow are simultaneous, not sequential.

Note that if the flow of income equals the flow of expenses, the value of
IncomeAccount remains constant. The constant value might be high or low,
depending on the flows that occurred prior to input and output becoming equal.

Now we have to introduce the transition from this incremental description
to something more like the continuous description used in differential
equations. This is done by dividing the "ElapsedHours" variable into many
time segments much smaller than an hour, and summing a much larger number
of segments to get the final value of IncomeAccount. This allows us to
handle flows that change during the computation period. Using "dt" to
represent the smaller length of time; we have

IncomeAccount = (Inc1 - Exp1))*dt + (inc2 - Exp2)*dt + ... (IncN - ExpN)*dt
  where Inc and Exp are short for income and expense flows.

During one hour, we will have many of these short periods of combined
inflow and outflow. If dt is picked as 1/60 second, then there will be 3600
such periods per hour. This means that income and expenditures can vary
quite rapidly while their simultaneous cumulative effects on IncomeAccount
are accurately computed.

This can be carried even further. Suppose we say there is another source of
inflow to IncomeAccount: the rate of borrowing (BorrowingPerHour), and
several more outflows: LaborExpensePerHour, EquipmentMaintenancePerHour,
CapitalDistributionsPerHour, InsuranceExpensesPerHour, and
CapitalPurchasesPerHour. Notice that they are all flows measured in
quantity of money per hour. We can simply add them all up, with minus signs
for the outflows, and say that

IncomeAccount := SumOfAllFlowsPerDt*ElapsedTime.

I'm leaving out the initial values of the cumulative variables, for simplicity.

All of these variables can be changing at the same time; our
nearly-continuous summation process will accurately keep track of the net
effect on the magnitude of the variable IncomeAccount, which will change
every dt seconds if the inflows do not precisely balance out the outflows.

What we have done, by introducing this concept of IncomeAccount, is to
write the differential equation for part of the economic system. An
essential part of it is this cumulative variable which has a value that is
the time integral of the sum of a related set of flow variables.

We can do a similar thing with the goods being produced, in as much detail
as we please. Suppose we have a variable called ManHoursWorkedPerHour (note
that we are once again using rate variables). If we multiply this by the
WagePerHour we will get (part of) the cost of production as
ProductionCostPerHour, which, being a rate variable, we can enter into the
computation of the producer's IncomeVariable as one of the expense rates.
Also, we can multiply ManHoursWorkedPerHour by a productivity factor,
GoodsProducedPerManHour, to get GoodsProducedPerHour, another rate
variable. We can sum the GoodsProducedPerHour into a new cumulative
variable which Keynes calls FinishedGoods (or would have done if he had
programmed computers) and which I have been calling Inventory. Note that
productivity and Inventory both have to be computed for each kind of good,
because the units of measure are number of goods rather than monetary value
of goods (as opposed to the standard practiced of converting all quantities
to money)..

At the same time that goods are accumulating in inventory according to
GoodsProducedPerManHour and productivity, goods are being sold at the rate
GoodsSoldPerHour (computed for each different kind of good). Inventory, as
a cumulative variable, is thus (for each good),

ChangeInInventory = (GoodsProducedPerManHour - GoodsSoldPerHour)*dt

during each small period dt, and accumulated over whatever elapsed time is
of interest.

The goods are sold at a price Pg, different for each good and probably
changing with time as well. This means that we can calculate the rate
variable we called IncomePerHour by multiplying the rate at which each good
is sold by the price for that good,.So we can say

ChangeOfIncomeVariable = SumOf(SaleRates*PricePerGood)*dt.

Now for the kicker. The above computations involving the summing of
positive and negative flows and other rate variables are ALL carried out
during EACH small interval dt. In effect, they are all done simultaneously,
within the same time interval dt. Since dt is a very small period of time,
the cumulative variables don't change very much during any one interval. If
prices are changing, we may compute all the values of the cumulative
variables 100 times before the price has changed by one percent, and during
that time, productivity, number of man-hours worked per hour, and number of
goods sold per hour may also have changed by small amounts.

The result is that we will see changes in Inventory, IncomeAccount, and
CostPerHour (of production) all happening at the same time.

Finally, we can expand this picture to include a consumer, who receives the
CostPerHour rate variable, putting the flow into a consumer account from
which money is simultaneously withdrawn to spend on goods. There can be
another consumer who receives capital distributions and doesn't work (the
owners, drawing profits, would be among those). Exactly the same approach
is used: flow variables with variable positive and negative values
accumulating in cumulative variables that represent consumer inventory and
consumer money accounts. Of course the number of specialized agents we put
into the model depends on how much detail we hope to include.

It may seem that the cumulative variables are superfluous -- why not just
convert the incoming rates into outgoing rates? In fact they are vital:
without them, you can't make a simulation operate properly.

To relate this approach to modeling to the Keynsian (or any other) system,
we have to realize that we are modeling the system at a lower level of
abstraction than Keynes uses. There is no "value" or "profit" or
"investment" or "savings" in this model -- there are only stocks and flows
of money, goods, and I suppose labor. The model works because of the ways
these variables are related, not because of the way we classify or describe
them. To create a translation into more normal economics terms, we have to
examine the variables in the model to see what the various abstract terms
refer to at this concrete level. When we model the actors in this scheme,
the managers and consumers, we will have to translate terms like
"propensity to consume" and "marginal disutility of labor" into terms of
specific perceptions and reference levels, to convert to PCT terms.

Best,

Bill P.

From[Bill Williams 21 March 2004 9:30 PM CST]

I can readily agree to everything you say in
[From Bill Powers (2004.03.21.1519 MST)].

But, then I can not recall my ever having found fault with your modeling
methodology.

So, now what?

Bill Williams

I know that both Bill Williams and Bill Powers are not in agreement
with my approach to economics and systems, but here's my take on this
investment/savings issue:

Saving is a store of value to the saver. It can be in the form of
cash, and hidden under the bed, or it can be invested. Investment
means giving it to somebody else to use to make a profit with.

Investment is a preferred way of saving because the savings has the
potential to grow.

The transferred money in an investment is used to pay for work, thus
it is beneficial for the economy as a whole (ignoring the possibility
that the work could be wasteful).

Banks can multiply the amount of work they can create with invested
money by providing loans that far exceed the money invested. This may
seem unethical, but, in a business sense, what they are doing is to
create a situation that allows them to spread the risk of the
invested money. This also has a multiplier effect to create more work
in the economy than the investment could do alone.

As I understand it, Keynes' main contribution to economic theory was
to recognize the benefits of this multiplier effect. He realized that
the creation of money could be used to ramp up an ailing economy.
i.e., create work.

To analyze the situation in terms of cash flows is not possible
because what you are dealing with is a dynamic, complex system that
is full of non-linear effects. Such systems cannot be accurately
modeled or predicted.

What Keynes was proposing, when he recommended that governments
create money, was to destabilize an economy that was in depression,
so that it might settle into a new steady state where the economy
would be providing a greater level of employment.

In fact, this policy was forced upon governments because of World War
2, where money had to be created to get people to work for the war
effort. This had the effect of initial total instability (chaos), but
with the economy later settling into a steady state that resulted in
economies achieving continuous growth for decades.

The point is that economic systems cannot be analyzed by observing
and tracking the details of individual transactions. Systems are
dynamic and can only be understood in terms of complexity theory -
where it is assumed that detailed analysis is not possible and
systems can jump unpredictably into different steady states.

It is for this reason that Keynes' theories fell out of favor,
because they cause instability - only a good thing if the economy is
stuck in a rut.

Peter Small

Author of: Lingo Sorcery, Magical A-Life Avatars, The Entrepreneurial
Web, The Ultimate Game of Strategy and Web Presence
http://www.stigmergicsystems.com

···

--

From[Bill Williams 22 March 2004 9:00 AM CST]

In my, for the time being anyway, irenic mode, I will say that I agree with
the "big picture" aspect of your conception of Keynes' theoretical position.
If I may say so you are a bit unusual for a "right winger" (in the
non-pejorative sense) in taking what I perceive as a somewhat sympathetic
view of Keynes and his _General Theory_.

If you are not aware of it, I should tell you that Bill Powers and I while
we both might disagree with you, may not entirely agree with each other in
regard to Keynes and the _General Theory_.

What Bill Powers is engaged in is an attempt to construct something similar
to a general equilibrium simulation of the economy. I don't doubt that such
a thing is possible, but I have had doubts about practicality, and the cost
to benefit ratio, and applicability of the exercise. There is, as they say
a "history" involved here, and as one of the deeply "engaged" participants
in that history my telling the story, if at this point, I wanted to tell the
story, might to subject to bias.

There is one point at which I would disagree with you. You speak of people
saving, and then putting their money into a bank and then the bank loaning
out this money, and beyond that creating more loans than they have money in
the vault. However, in the Keynesian analysis the direction of causation
runs in the reverse direction. Banks make loans, and increase in money
generates savings. The idea that banks should have a reserve of money in
the vault is a sort of folkway, in Veblen's terms a piece of "picturesque
misinformation."
What we actually pay a bank for is judgement. The money created costs next
to nothing. A bank that stays in business is one that, among other things,
makes the right judgements about who to loan money to. The right people pay
the money back and then some.

So how, for a right winger, do you come to what I would regard as fairly
functional views concerning Keynes? For a right winger you views are not
all that typical.

Bill Williams

[From Bill Powers (2004.03.22.0749 MST)]

So, now what?

Well, first I should clear up at least one loose end that was left in my
rush to get everything down on paper.

“Flow” or rate variables and “stock” or cumulative
variables are related in a program by the time-integration
statement

CumulativeVariable := CumulativeVariable + RateVariable1dt +
RateVariable2
dt and so on.

A rate variable is expressed in units of quantity per unit of time.
Multiplying that by a time interval (dt) cancels the time unit and leaves
only a quantity, which can then be added to the quantity represented by
the cumulative variable.

I didn’t really make all of that clear in the sketchy equations I wrote
yesterday.

Also, I tried to make the global nature of a program iteration clear, but
it will bear repeating. Basically, all parts of the economic system are
active at precisely the same instant. A simulation program must, because
computers can do only one thing at a time, share its time among all the
processes that are going on. This is done by advancing time in tiny
steps, and updating every equation in the whole system on each step,
doing all the computations that turn the state of a set of input
variables into the state of an output variable for each part of the
system. Only after all of the system equations have been evaluated do we
allow time to advance by one more increment “dt.” This can mean
evaluating dozens or even hundreds of equations during one iteration of
the program, before letting time increase by one increment dt.
Fortunately, computers are so fast nowadays that the program can still be
run at many times the real-time speed. (the Little Man program runs a
little faster than real-time speed, yet each iteration involves several
thousand program steps)…

This has nothing to do with any actual time delays in the real system.
All that real time delays do is make one part of the system work with
input data that came from another part of the system at some time in the
past. While the receiving subsystem is working with that old data, the
originating subsystem is, at exactly the same time, producing more output
effects that will reach the receiving system some time in the future. The
point is that every part of the system is in continuous operation, all
parts producing outputs at the same time, regardless of the age of the
input information it is using.

Real time delays are introduced into a simulation using a circular
buffer. On a given iteration, data is entered into the buffer using an
input pointer, and the output data is taken from the buffer using an
output pointer. Then both pointers are incremented by one (wrapping
around if they reach the end of the buffer). The output pointer lags
behind the input pointer by a number representing the time lag. The
buffer size is dictated by the maximum lag that is anticipated to be
needed. Obviously, the size of “dt” used in the simulation must
be small enough so that all real time delays are longer than, say, 10 of
the dt intervals (if you want to express time delays with an accuracy of
no worse than 10%).

Another form of lag is introduced by the time integration. But we can
leave that for another time.

OK, back to the question, what next?

The important thing that a simulation does is to force all parts of the
system to be related to each other properly all of the time. Because
there is at least one closed loop here, this means that it is no longer
possible to think in terms of changing one variable or parameter and
looking at its effects on another variable. Any variable that is changed
very quickly has an effect on itself, and the result of this can be
highly counterintuitive until you get used to these feedback effects.
Likewise, changing any parameter changes the way the local variables are
related, but because of the feedback connection the result can be quite
different from expectations – for example, the output variable might end
up changing very little, while the input variable changes the opposite
way, counteracting the effect of the change in the parameter. We see that
in negative feedback control systems all the time.

Keynes’ General Theory is partly about the mechanics of the economy. but
mostly it is about the psychology of the human agents who operate the
system. Yet when the human agents react to events by taking action, they
act through the mechanics of the system, and those actions can have
unforseen effects because of the multiple loops in the mechanical
connections. An example is a union leader who calls a strike for higher
wages, with the result of closing the company down and reducing all the
wages permanently to zero. Again, Keynes had an inkling of such things
when he talked about short-term versus long-term effects of entrepreneur
decisions. But he never really saw the closed-loop phenomena. In the
1930s, hardly anyone knew about them.

For example, Keynes speaks of changes in employment resulting from
changes in producer income. I don’t at the moment recall the exact
example, but the point is that a change in employment inevitably changes
the customer purchasing power which changes the rate of purchases which
changes the “causal” variable, the income. If the change in
income is in the same direction as the original change, we have positive
feedback and the potential for a disastrouns runaway. Therefore no simple
analysis based on local cause and effect can reveal what the actual
consequences will be. Keynbes had an inkling of this, particularly in
relation to delays in the feedback, but he lacked the tools to see the
analysis all the way through. Those tools came into full use only after
Keynes died.

There is another aspect of simulations that is very important. Listen to
Charlotte Bruun (from “Agent-Based Keynsian
Economics”):

5d07a7.jpg

One of the ways I am introducing multiple representative agents is to
distinguish between managers and consumers. Keynes spoke of “the
community,” but it was evident that this was the community of
entrepreneurs, with non-business consumers existing mainly as a
stimulus-response device for converting wages into comsumption, and of
course as a pool of labor. If we make the consumers into controlling
agents, with goals of their own, then we can have an economy that is both
M-C-M and C-M-C, in Keynes’ terms. The entrepreneurs view life as the
process of using Money to produce Consumption as a way of making more
Money (hence MCM), while the consumer takes the opposite view: that the
purpose of money is to provide for consumption of things the consumer
needs or desires. The economy results from an interaction between these
two – often conflicting – views.

We can also have an economy in which different entrepreneurs work
according to different principles, not just one kind operating according
to the sort of reasoning Keynes proposed.

As to what we can actually do next, I think we have to develop the
sketchy model called econ004 into something more elaborate, perhaps in
cooperation with Bruun who has produced a model of considerable
complexity, but without control system agents. We need a bank in it, we
need to add more ways in which producer income is spent (on maintaining
productivity, for example – that is, investment). We may need to add
more classes of consumer-agents to make the model interesting
enough.

I await your evaluation of my proposed explanation of Keynes’ equivalency
of savings and interest. If you agree with it, or can find suitable
modifications to make it agreeable, we can put that subject behind us.

Best,

Bill P.

From[Peter Small 22 March 2004]

Bill Williams asked:

So how, for a right winger, do you come to what I would regard as fairly
functional views concerning Keynes? For a right winger you views are not
all that typical.

Because I spent some time with an investment company in the City of
London, where Keynes was regarded as the anti Christ. I was his
defender.

Apart from that, I'm a fan of the group of thinkers that were around
in Keynes' time. That included Hilbert, Godel, von Neumann, Turing,
out of which emerged computers, quantum mechanics, game theory etc.
There is a common thread to all of their ideas, which is also
reflected in Keynes work.

Peter Small

Author of: Lingo Sorcery, Magical A-Life Avatars, The Entrepreneurial
Web, The Ultimate Game of Strategy and Web Presence
http://www.stigmergicsystems.com

···

--

From[Bill Williams 22 March 2004 11:00 AM CST]

I’ve read through your posting

[From Bill Powers (2004.03.22.0749 MST)]

I’m a bit pressed for time today, but I don’t see that I have any questions or objections to anything so far.

It does however, occur to me that what you seem to be doing in the last two post is extending the comments that appear in the Appendix to B:CP.

You are providing a through very elementary ( or elemental ) exposition of how to handle the time/causation issue correctly. Economics is providing the context for the exposition, but i think what you are saying ought to be a part of part of the education of future control theorists, and I am not aware of where these concepts are explained in a readily accessible fashion. I caught on to the issues involved as a result of studying with a professor who understood the issues and then rooting about in a university engineering library. So, I would encourage you to consider what you are posting as a first draft of what I have long thought was needed as a basic document explaining a theoretical method that is a basis for all the rest of control theory.

I’ll try to post a comment on your earlier posting later today. If you are so inclined you might comment on the way in which Bruun handled time and accounting relationships. I didn’t study what she did that closely, but it seemed to me that she didn’t make any actual errors. But, did she really need to make is so complex?

Bill Williams

5d07a7.jpg

···

----- Original Message -----

From:
Bill Powers

To: CSGNET@listserv.uiuc.edu

Sent: Monday, March 22, 2004 10:27 AM

Subject: Re: Savings and Investment

[From Bill Powers (2004.03.22.0749 MST)]

So, now what?

Well, first I should clear up at least one loose end that was left in my rush to get everything down on paper.

“Flow” or rate variables and “stock” or cumulative variables are related in a program by the time-integration statement

CumulativeVariable := CumulativeVariable + RateVariable1dt + RateVariable2dt and so on.

A rate variable is expressed in units of quantity per unit of time. Multiplying that by a time interval (dt) cancels the time unit and leaves only a quantity, which can then be added to the quantity represented by the cumulative variable.

I didn’t really make all of that clear in the sketchy equations I wrote yesterday.

Also, I tried to make the global nature of a program iteration clear, but it will bear repeating. Basically, all parts of the economic system are active at precisely the same instant. A simulation program must, because computers can do only one thing at a time, share its time among all the processes that are going on. This is done by advancing time in tiny steps, and updating every equation in the whole system on each step, doing all the computations that turn the state of a set of input variables into the state of an output variable for each part of the system. Only after all of the system equations have been evaluated do we allow time to advance by one more increment “dt.” This can mean evaluating dozens or even hundreds of equations during one iteration of the program, before letting time increase by one increment dt. Fortunately, computers are so fast nowadays that the program can still be run at many times the real-time speed. (the Little Man program runs a little faster than real-time speed, yet each iteration involves several thousand program steps)…

This has nothing to do with any actual time delays in the real system. All that real time delays do is make one part of the system work with input data that came from another part of the system at some time in the past. While the receiving subsystem is working with that old data, the originating subsystem is, at exactly the same time, producing more output effects that will reach the receiving system some time in the future. The point is that every part of the system is in continuous operation, all parts producing outputs at the same time, regardless of the age of the input information it is using.

Real time delays are introduced into a simulation using a circular buffer. On a given iteration, data is entered into the buffer using an input pointer, and the output data is taken from the buffer using an output pointer. Then both pointers are incremented by one (wrapping around if they reach the end of the buffer). The output pointer lags behind the input pointer by a number representing the time lag. The buffer size is dictated by the maximum lag that is anticipated to be needed. Obviously, the size of “dt” used in the simulation must be small enough so that all real time delays are longer than, say, 10 of the dt intervals (if you want to express time delays with an accuracy of no worse than 10%).

Another form of lag is introduced by the time integration. But we can leave that for another time.

OK, back to the question, what next?

The important thing that a simulation does is to force all parts of the system to be related to each other properly all of the time. Because there is at least one closed loop here, this means that it is no longer possible to think in terms of changing one variable or parameter and looking at its effects on another variable. Any variable that is changed very quickly has an effect on itself, and the result of this can be highly counterintuitive until you get used to these feedback effects. Likewise, changing any parameter changes the way the local variables are related, but because of the feedback connection the result can be quite different from expectations – for example, the output variable might end up changing very little, while the input variable changes the opposite way, counteracting the effect of the change in the parameter. We see that in negative feedback control systems all the time.

Keynes’ General Theory is partly about the mechanics of the economy. but mostly it is about the psychology of the human agents who operate the system. Yet when the human agents react to events by taking action, they act through the mechanics of the system, and those actions can have unforseen effects because of the multiple loops in the mechanical connections. An example is a union leader who calls a strike for higher wages, with the result of closing the company down and reducing all the wages permanently to zero. Again, Keynes had an inkling of such things when he talked about short-term versus long-term effects of entrepreneur decisions. But he never really saw the closed-loop phenomena. In the 1930s, hardly anyone knew about them.

For example, Keynes speaks of changes in employment resulting from changes in producer income. I don’t at the moment recall the exact example, but the point is that a change in employment inevitably changes the customer purchasing power which changes the rate of purchases which changes the “causal” variable, the income. If the change in income is in the same direction as the original change, we have positive feedback and the potential for a disastrouns runaway. Therefore no simple analysis based on local cause and effect can reveal what the actual consequences will be. Keynbes had an inkling of this, particularly in relation to delays in the feedback, but he lacked the tools to see the analysis all the way through. Those tools came into full use only after Keynes died.

There is another aspect of simulations that is very important. Listen to Charlotte Bruun (from “Agent-Based Keynsian Economics”):

5d07a7.jpg

One of the ways I am introducing multiple representative agents is to distinguish between managers and consumers. Keynes spoke of “the community,” but it was evident that this was the community of entrepreneurs, with non-business consumers existing mainly as a stimulus-response device for converting wages into comsumption, and of course as a pool of labor. If we make the consumers into controlling agents, with goals of their own, then we can have an economy that is both M-C-M and C-M-C, in Keynes’ terms. The entrepreneurs view life as the process of using Money to produce Consumption as a way of making more Money (hence MCM), while the consumer takes the opposite view: that the purpose of money is to provide for consumption of things the consumer needs or desires. The economy results from an interaction between these two – often conflicting – views.

We can also have an economy in which different entrepreneurs work according to different principles, not just one kind operating according to the sort of reasoning Keynes proposed.

As to what we can actually do next, I think we have to develop the sketchy model called econ004 into something more elaborate, perhaps in cooperation with Bruun who has produced a model of considerable complexity, but without control system agents. We need a bank in it, we need to add more ways in which producer income is spent (on maintaining productivity, for example – that is, investment). We may need to add more classes of consumer-agents to make the model interesting enough.

I await your evaluation of my proposed explanation of Keynes’ equivalency of savings and interest. If you agree with it, or can find suitable modifications to make it agreeable, we can put that subject behind us.

Best,

Bill P.

From[Bill Williams 22 March 2004]

From[Peter Small 22 March 2004]

There is also the suggestion in the title that Keynes selected-- _The
General Theory_, which contains an echo of Einstein's work, non-Euclidian
geometry and so forth.

However, as best I know Keynes was not that familiar with the sciences.

Bill Williams

[From Bill Powers (2004.03.22.1007 MST)]

Peter Small (2004.03.22) --

The point is that economic systems cannot be analyzed by observing
and tracking the details of individual transactions. Systems are
dynamic and can only be understood in terms of complexity theory -
where it is assumed that detailed analysis is not possible and
systems can jump unpredictably into different steady states.

This is not completely true, as I think you'll agree on reflection. We can
certainly model and simulate systems that behave chaotically under the
right circumstances -- and behave regularly under others. This is done all
the time by chaos theorists. Chaotic behavior is not random; it's simply
unpredictable by any normal means.In my "Crowd" program, for example, there
is a collision-avoidance control system in every active agent on the
screen. When the agent approaches an isolated obstacle, it must turn either
left or right to avoid it. But the more precisely the agent approaches the
exact center of the object, the less able we are to predict whether this
perfectly lawful and regular system will turn left or right. This is a
typical chaotic situation in which very small changes have inordinately
large effects -- the "butterfly effect."

I chickened out and put a small random dither into this control system, to
avoid situations where the moving agent would simply slow down more and
more, and take longer and longer to fall off to one side or the other when
approaching nearly dead-center collisions. But when the agent is travelling
through a random scattering of obstacles and interacting with other moving
agents, the behavior becomes truly chaotic. Nevertheless, since we can
initialize to the computer to _exactly_ the same set of starting
conditions, we can reproduce the same chaotic behavior! We couldn't measure
a real physical system accurately enough to do that, but it works with
simulations. And the simulation did generate patterns of movement and
position that were very accurate representations of what real people in
real crowds did.

So my point is that if the simulation is done correctly, any chaotic
characteristics of the system will show up, just as they do in simulations
of nonlinear oscillators as the driving forces increase. This would mean
that we can't predict the detailed behavior of individuals any more, but we
could still predict what the envelopes of behavior patterns would be, just
as we can predict that certain coupled nonlinear oscillators will generate
figure-eight patterns in phase space.

If the real system shows chaotic behavior, we can produce a simulated
system that will show at least the same class of chaotic behavior, if not
the actual details values of the variables.

Incidentally, one of my oldest friends, Harry Rymer. got his doctorate back
in the 1960s developing an analysis of something called "Almost-periodic
functions." With this analysis, he was able to predict that certain
three-body gravitational systems would appear stable for long periods of
time, and then suddenly eject one of the members of the system. The orbits
in these systems would never repeat, yet they would remain within envelopes
for a long time. Sound familiar?

Best,

Bill P.

[From Bill Powers (2004.03.22.1040 MST)]

Bill Williams 22 March 2004 11:00 AM CST

I've read through your posting

[From Bill Powers (2004.03.22.0749 MST)]
I'm a bit pressed for time today, but I don't see that I have any
questions or objections to anything so far.

It does however, occur to me that what you seem to be doing in the last
two post is extending the comments that appear in the Appendix to B:CP.
You are providing a through very elementary ( or elemental ) exposition
of how to handle the time/causation issue correctly.

Yes, and I'm sorry for going over details that you're already familiar
with. However, I want to get it said, and since I'm cc-ing to Charlotte
Bruun, it's not entirely repetitious.

  Economics is providing the context for the exposition, but i think what
you are saying ought to be a part of part of the education of future
control theorists, and I am not aware of where these concepts are
explained in a readily accessible fashion.

Right. In B:CP I was really just working them out, and didn't have a very
advanced understanding. I'd like to write something like what you
recommend, but it's getting harder to contemplate projects like that, and I
still suffer a considerable inferiority complex concerning any attempt to
commit Higher Mathematics where real mathematicians might see it. I think
my best bet is just to try to wind down gracefully and encourage others
with a longer future to take up the torch.

At least I can write about these things on the net for future reference.

I haven't really grasped Bruun's model as a whole yet, so I can't comment
on how she handles time. I discovered only today that I have a succinct
guide to her simulation: look in Appendix A of her thesis, p. 182. That
should help make sense of things.

Best,

Bill P.

From[Bill Williams 22 March 2004 1:45 PM CST]

···

[From Bill Powers (2004.03.22.1040 MST)]

########################################################

I've pasted in a passage from 21 March 2004 6:26 MST

However, this does not mean that the amount of money held in liquid cash
form or its equivalent is equal to the amount of money spent on the
purchase and upkeep of physical production machinery, buildings, or raw
materials -- physical assets. If we think of savings as actual cash held
back and not spent, and of investment as the actual purchase and upkeep of
capital machinery, then savings is clearly different from investment: cash
that is saved is not spent for investment; what is spent on investment is
not saved. The sum of cash held back and cash spent on investment remains
the total amount taken from income in addition to costs of production, of
course. But that, apparently, would be a nonstandard usage of these terms,
even though it is a common usage.

I hope this is an acceptable solution to the controversy over savings and
investment.

#######################################################

Unfortunately your interpretation does not solve the problem. In the above
you are attempting to trace the flow of money. You are thinking of saving
as being the residule-- the money "not spent." But, the way the system is
set up savings are equal to the money created during the time slice
considered. Savings is equal to money in the system at time 1 minus
money in the system at time 0. When a bank creates a loan for a business
the bank is creating checking deposit money for the purchase of capital
equipment. Considered as the money value of the capital equipment the
loan is Investment. When the calculation of the change in money in the
system is made money time 1 minums money time O the change in money
in the system can be treated as saving.

Try and discard the notion (for purposes of macro analysis) of saving as
money not spent or as saved out of income. I haven't taught macro theory
in a class room for 25 years or more. And, anyway you are rather different
than a freshman student. But, it sems to me that if you would start with
the
transaction between the banker and the businessman that creates the
funds for investment then the relationship might pop into place.

So, the banker makes a entry into an a checking account for the
businessman to use to purchase equipment.

The bank records the loan as an asset.

The business man records the loan as a debt.

But, the equipment that is purchased is carried as an asset on the
business's books.

So, in various places the loan is carried as a monetary asset (the bank's
books) a debt ( on the bussiness's books) and an asset (the title to the
equipment) on the bussiness's books.

While everyone is jotting this down, the newly created money enters
the economy into the hands of the firm and workers who created the
equipment. It doesn't matter what they choose to do with this money,
spend it save it whatever, the money created by the banker has entered
the system. Where it goes doesn't matter-- it is in and stays somewhere
in the system. When saving is measured by money in the system time 1
minus money in the system time 0 , this difference is counted as saving.
And, the source of the saving is the loan created to finanance the
investment. And, therefore saving is equal to investment. And, the
process of creating the loan and the resulting saving happens
simultaneously.

Hope this explaination works. Feed back from lurkers, either on the CSGnet
or privately would be appreciated.

Bill Williams

[From Bill Powers (2004.03.22.1324 MST)]

Bill Williams 22 March 2004 1:45 PM CST --

Thanks for a very lucid discussion of the savings/investment situation. The
key seems to be in the idea of "money in the system," which implies a
totally aggregate representation. The location of the money in the system
makes no difference if there is only one entity.:

While everyone is jotting this down, the newly created money enters
the economy into the hands of the firm and workers who created the
equipment. It doesn't matter what they choose to do with this money,
spend it save it whatever, the money created by the banker has entered
the system. Where it goes doesn't matter-- it is in and stays somewhere
in the system. When saving is measured by money in the system time 1
minus money in the system time 0 , this difference is counted as saving.

That makes it clear that what I have been calling saving is not what the
"official" term means, though your use of the term "save it" above is not
quite consistent with the main definition you're using for saving. So I
need a word to designate the quantity of money that I have been calling
"saving," which is a reserve of cash kept by both the plant managers and
the consumers -- a "pad" as it were, that takes up the slack when income is
low and is built up again when there is a temporary surplus of income. The
total amount of money in the system remains the same as long as new money
is not coming in, or as long as money is not being destroyed by loans being
repaid (I think you agreed once that repayment of money takes money out of
the system). Since that is true in econ004, it would seem that this model
conforms with your definition of saving, while at the same time providing a
place for money reserves to be kept. [I explained this to myself shortly
after this paragraph, but I leave it as is to show the progression]

I think you also commented once that there is no real "flow" of money --
that is, money doesn't really exist "between" people. It is always in
someone's hands. When a transaction takes place, money disappears from one
person's possession and simultaneously appears in another person's
possession. The metaphor of a flow is misleading. Is this correct?

If it is, then I think I have located the problem with savings. I have been
using the term so that "money saved by A" means nothing more than "money in
the possession of A." As long as A's bank accounts contain the same total
number, A is saving that much money. [This was the big AHA]

This makes me think we should abandon the flow metaphor and stick strictly
to the "rate" idea. Money disappears from one acount at some rate, so the
total in the acount declines, and appears in other accounts so the total in
them increases. The total rate of increase has to equal the total rate of
decline, with constant total money. All money, then, is "saved," whether we
speak in the aggregate or in terms of multiple agents.

I haven't found a similar resolution for "investment." I've seen the word
used to mean strictly the purchase of capital equipment (as a verb) or as
the capital equipment that is purchased (as a noun). Both seem to imply
that money is not invested until it is converted into physical means of
production. That would mean that all the money in the producer's possession
could remain unspent, or it could be converted to physical means of
production, so that would be a basis for distinguishing between savings and
investment even at the aggregate level. Can you straighten that out for me?

If this treatmenty of what I formerly called saving is acceptable, we can
say very simply that when one agent ceases to spend money, the money
remains in the agent's account. That's what I have been calling "saving" or
"reserve." In the aggregate, of course, the total amount in all acounts is
all the money there is at the moment, and the only way it can change is for
money to be created or destroyed. By the same token, there can be no
transactions in the aggregate: money and goods remain in posession of the
whole, so there is no change in quantities of either, or in their location.

Oops, I forgot about production and consumption. In the aggregate, raw
materials are still being transformed by labor into finished goods which
are being consumed or are depreciating. But neither money nor goods can
"change hands" when there is only one entity, so there are no transactions..

Actually, all the macroeconomic discussions I have seen break the whole
system down into different entities that interact in various ways.
Otherwise there wouldn't be much left to say, would there?. The trick is to
make the entities large enough that we are not back to microeconomics.

Best,

Bill P.

From[Bill Williams 22 March 2004 7:10 PM CST]

[From Bill Powers (2004.03.22.1324 MST)]

Bill Williams 22 March 2004 1:45 PM CST --

Thanks for a very lucid discussion of the savings/investment situation.

The

key seems to be in the idea of "money in the system," which implies a
totally aggregate representation. The location of the money in the system
makes no difference if there is only one entity.:

There is a sense in which there is "only one entity" However, while
retaining
the "one entity" aspect it is possible to keep track of different accounts
within the entity. It is sort of like the law in electronics (Polish
sounding name
begins with a K) that the sum of currents flowing into a node is equal to
zero.

>While everyone is jotting this down, the newly created money enters
>the economy into the hands of the firm and workers who created the
>equipment. It doesn't matter what they choose to do with this money,
>spend it save it whatever, the money created by the banker has entered
>the system. Where it goes doesn't matter-- it is in and stays somewhere
>in the system. When saving is measured by money in the system time 1
>minus money in the system time 0 , this difference is counted as saving.

That makes it clear that what I have been calling saving is not what the
"official" term means, though your use of the term "save it" above is not
quite consistent with the main definition you're using for saving.

Well, the main definition, and really the only specification is ( money in
the
system time 1 minus money in the system time zero ) . People sometimes
talk about money being horded. When you ask them what they tell you that
by hoarding the mean people are holding onto the money. If you ask them,
"then isn't it true that all the money is being held all the time?" They
become
annoyed. So, how can there be an increase in hoarding when all the money
is always being held onto. Nickels that fall down the drains in the street
are
an exception but this doesn't amount to much.

But you are right, I by accident engaged in the dreaded equvocation. I
shifted from defining saving as money time 1 minus money time 0 to
savings equals income minus expenses. It is, all to evidently, easy to
do..

So I
need a word to designate the quantity of money that I have been calling
"saving," which is a reserve of cash kept by both the plant managers and
the consumers -- a "pad" as it were, that takes up the slack when income

is

low and is built up again when there is a temporary surplus of income.

You could call it "money holdings." I am not sure if there is a standard
terminology.

The

total amount of money in the system remains the same as long as new money
is not coming in, or as long as money is not being destroyed by loans

being

repaid (I think you agreed once that repayment of money takes money out of
the system).

It depends. If the "money" being repaid is a loan that was made out of
"cash money" then there is no change in total money when the loan is paid.
If the loan that is being repaid is a loan that was made by a bank creating
money
to make the loan then paying it back reduces the stock of money.

Since that is true in econ004, it would seem that this model

conforms with your definition of saving,

It isn't really _my_ definition, since it has been use before I ever gave it
a thought.

while at the same time providing a

place for money reserves to be kept. [I explained this to myself shortly
after this paragraph, but I leave it as is to show the progression]

I think you also commented once that there is no real "flow" of money --
that is, money doesn't really exist "between" people.

Right. My old professor used to say, you almost never see any money that
isn't being held.

It is always in

someone's hands.

Yes.

When a transaction takes place, money disappears from one

person's possession and simultaneously appears in another person's
possession. The metaphor of a flow is misleading. Is this correct?

It really is. I think it is important to start with the "transaction" as
the basic
unit in the analysis.

If it is, then I think I have located the problem with savings. I have

been

using the term so that "money saved by A" means nothing more than "money

in

the possession of A."

Right.

As long as A's bank accounts contain the same total

number, A is saving that much money. [This was the big AHA]

I am not sure. In reading this, and applying the definition savings is
equal
to money time 1 minus money time 2 then the number I get for "saving"
if I understand what you say is zero. The quantity of money held stays the
same-- again if I understand what you ment. Therefore saving would equal
zero.

This makes me think we should abandon the flow metaphor and stick strictly
to the "rate" idea.

I would think so.

Money disappears from one acount at some rate, so the
total in the acount declines, and appears in other accounts so the total

in

them increases. The total rate of increase has to equal the total rate of
decline, with constant total money. All money, then, is "saved," whether

we

speak in the aggregate or in terms of multiple agents.

OK. All money is "saved" in the sense that all money is held. But in terms
of
saving defined as money time 1 minus money time 0 the saving is zero--
since the total money involved does not change.

I haven't found a similar resolution for "investment." I've seen the word
used to mean strictly the purchase of capital equipment (as a verb) or as
the capital equipment that is purchased (as a noun).

So there is a rate of purchase K/t or the amount K.

Both seem to imply

that money is not invested until it is converted into physical means of
production.

I would prefer to talk in terms of a transaction. A loan is created. The
new
bank money is transfered to the creators of the capital equipment, and the
capital is transfered to the business doing the capital investment. It
seems
to me that saying money is being "converted" into capital might be
misleading.
But, I am fairly confident about what you mean.

That would mean that all the money in the producer's possession

could remain unspent, or it could be converted to physical means of
production, so that would be a basis for distinguishing between savings

and

investment even at the aggregate level. Can you straighten that out for

me?

I am not sure what you are saying in the above. My reaction as I read it
is--
at any given time none of the money is spent in the sense that looking at an
account you could be told how much money is in the account, but how could
you tell whether the money in the account had been spent or not? Are you
possibly drifting into equvocation here? I think the rule should be when
ever t
here seems to be a possiblity of confusion apply the definition-- saving (in
the
macro sense) is equal to money time 1 minus money time 0.

If this treatmenty of what I formerly called saving is acceptable, we can
say very simply that when one agent ceases to spend money, the money
remains in the agent's account. That's what I have been calling "saving"

or

"reserve." In the aggregate, of course, the total amount in all acounts is
all the money there is at the moment, and the only way it can change is

for

money to be created or destroyed.

Yes.

By the same token, there can be no

transactions in the aggregate: money and goods remain in posession of the
whole, so there is no change in quantities of either, or in their

location.

I think it might be better to say there are no _net_ transactions, in the
sense
that sales minus purchases has to equal zero. However, you can add up
total sales and get a number representing what people have sold. I think
this would count as an aggregate measure of sales. If in the same
circumstance
you added up total purchases you would get the same number. But the volume
of transactions could increase or decrease.

Oops, I forgot about production and consumption. In the aggregate, raw
materials are still being transformed by labor into finished goods which
are being consumed or are depreciating. But neither money nor goods can
"change hands" when there is only one entity, so there are no

transactions..

I don't see why not. The "one entity" in the macro analysis is really the
aggregate
balance sheet--

         the one entity is really a set of books

And, this "one entity" is not an agent in the sense that the macro accounts
are
merely numbers-- the macro accounts don't by themselves percieve, experience
error or have causal powers to do anything. The Accounts contain things
like total
sales, total purchases, total consumption spending, total investment
spending.
Now there are lots of "agents" doing the consuming, the investing and what
not.
But the identities of these agents get wiped out when the totals are added
up.

And, as you go on to say,

Actually, all the macroeconomic discussions I have seen break the whole
system down into different entities that interact in various ways.
Otherwise there wouldn't be much left to say, would there?. The trick is

to

make the entities large enough that we are not back to microeconomics.

I would rather say, that you could break down the analysis into entities as
small
as you wished or needed to, as long as when you perform operations on the
accounts representing these entities the operations you carry out are
consistent with the context. As an example, you could keep track of the
spending
of every person in the economy. Based on the definition of a transaction,
you
could be confident that what one person generated as an expense while
shopping
would be an to some other person. Then you could group each person
within a class or occupation and track what happens to money. If you saw
that
one group's holdings of money was increasing you would suspect that either
money was being created, or that some other group was experience a decrease
in the quantity of money in their accounts.

I think you've got it.

Something you might think about, when I was writing a sentence just above in
my first effort I said, "some other group was losing money." Of course,
"losing
money" isn't actually what would be going on to any significant extent.
Rather
through transactions the group would be spending more money than they were
receiving. But, never-the-less it was easy enough to slip into
equivocation and
say "losing money." Not all such slips are as obvious, not all slips get
caught,
and not all slips are as harmless.

So, beware. Equivocation happens.

Bill Williams

[From Bill Powers (2004.03.23.0657 MST)]

Bill Williams 22 March 2004 7:10 PM CST --

There is a sense in which there is "only one entity" However, while
retaining the "one entity" aspect it is possible to keep track of
different accounts within the entity. It is sort of like the law in
electronics (Polish sounding name begins with a K) that the sum of
currents flowing into a node is equal to zero.

All I can think of right now is "Thevenin's theorem" which I can't even
recall. You're speaking of a conservation law.

Your way of defining savings makes it into a rate variable: change in a
quantity per unit time. However, the term savings is also used to represent
the quantity itself at a given time -- in this case, the total quantity of
money in existence. In fact you have to be able to measure the quantity at
specific times in order to compute the rate of change. I suppose something
similar happens with the term "investment," so investment can mean amount
spent on capital equipment per unit time, or total amount of capital
equipment in existence at a specific time. We need some standard way of
saying which kind of variable we're talking about.

I'm not quite sure how you answered my question on investment. Is
investment measured in terms of capital equipment, or in terms of its money
equivalent? Since the point is to acquire and maintain the physical means
of production, I would guess that it is the physical equipment (and all
that goes unto maintaining and using it) that matters. Any money equivalent
can only be an estimate. Also, if we think completely in aggregate terms,
there is no market for capital equipment: to whom or what would it be sold?
The whole economy already owns all the capital equipment, and could sell it
only to itself. Keynes varifies this by saying that in the aggregate, the
expense A1 must disappear -- A1 is the amount spent by one entrepreneur on
purchasing finished output from another entrepreneur -- it's a "wash," he says.

People sometimes talk about money being horded. When you ask them what
they tell you that by hoarding the mean people are holding onto the
money. If you ask them, "then isn't it true that all the money is being
held all the time?"

I'm not sure that argument holds water. It's not just a matter of holding
or not holding, but of how much is held and for how long. Just as an
extreme example, suppose that somehow one firm managed to acquire and hang
onto all the money that exists. The economy would cease to function,
wouldn't it? So there can be degrees of hoarding, ranging from harmless to
destructive. I think the point is that if one hangs onto money, never
spending it on goods or services, it ceases to circulate and represents an
_effective_ loss of the money from the whole system.

In econ004, you can set it up so that one consumer begins to accumulate
more and more of the existing money. The result is that one or more of the
other entities in the system runs out of money and has to borrow to supply
consumption needs (this is similar to your argument about the Giffen
Effect, in which there are biological constraints that determine what is
consumed, quite aside from economic considerations). If the other entities
can't qualify for loans (they are basically bankrupt with no assets) all
they can do is die.

If the "money" being repaid is a loan that was made out of
"cash money" then there is no change in total money when the loan is paid.
If the loan that is being repaid is a loan that was made by a bank creating
money to make the loan then paying it back reduces the stock of money.

Right, I understood that but it's good to keep in mind. In Econ004, which
has no bank, there is a constant store of money which simply passes around
from one entity to another while goods (and labor) flow the other way. A
negative balance of cash can be allowed (by setting "CreditAllowed :=
True"), in which case one entity can transfer money it doesn't have to
other entities, while running a negative balance. No interest has to be
paid so this can go on indefinitely. Needless to say, that feature must be
modified.

You haven't yet commented on my proposition that new money becomes a
permanent part of the economy when bank loans are defaulted, while the bank
that created the loan actually can end up with a profit after the loan is
written off (the interest that was paid, for example). I mention this
because I'm trying to work up to putting banking function into the model,
and need some way to know if it's working right.

When a transaction takes place, money disappears from one
person's possession and simultaneously appears in another person's
possession. The metaphor of a flow is misleading. Is this correct?

It really is. I think it is important to start with the "transaction" as
the basic unit in the analysis.

In econ004, it is not exactly the starting point, but it is present in
every loop. I trust you mean a process in which one thing is exchanged for
another: money for goods, or labor for money.

> This makes me think we should abandon the flow metaphor and stick strictly
> to the "rate" idea.

I would think so.

> Money disappears from one acount at some rate, so the
> total in the acount declines, and appears in other accounts so the total in
> them increases. The total rate of increase has to equal the total rate of
> decline, with constant total money. All money, then, is "saved," whether we
> speak in the aggregate or in terms of multiple agents.

OK. All money is "saved" in the sense that all money is held. But in terms
of saving defined as money time 1 minus money time 0 the saving is zero--
since the total money involved does not change.

This is where the difference between rate variables and cumulative
variables has to be kept clear.The _quantity_ of money saved at a given
time is the sum of all previous rates of saving times the interval over
which each rate was maintained. I save 2 dollars per day for 3 days, and 10
dollars per day for 2 days, which works out to a total of 26 dollars saved.
The saving rate varies, while accumulating to a total quantity of savings.
Careful use of terminology is clearly critical.

> Both seem to imply
> that money is not invested until it is converted into physical means of
production.

I would prefer to talk in terms of a transaction. A loan is created. The
new bank money is transfered to the creators of the capital equipment, and the
capital is transfered to the business doing the capital investment. It
seems to me that saying money is being "converted" into capital might be
misleading. But, I am fairly confident about what you mean.

Again, careful use of terminology can make all the difference here.
"Capital," I presume, means money when you speak of transferring it to the
creators of the capital equipment, but the capital equipment itself is not
money: it is machinery, buildings, supplies, maintenance, and so on. The
"conversion" I spoke of applied only to the step of tranferring money to
those who create the capital equipment and getting the capital equipment in
return -- as you say, a transaction. The capital equipment can be converted
back into money by putting it on the market and actually selling it, but
until this is actually done, the money equivalent is unknown because it
depends on the price at the time of the transaction. Of course to speak of
buying and selling or any transaction, we must have at least two entities

I am not sure what you are saying in the above. My reaction as I read it
is--at any given time none of the money is spent in the sense that looking
at an
account you could be told how much money is in the account, but how could
you tell whether the money in the account had been spent or not?

I think we can say that spending money means removing it from the account
and making it appear in a different account. So spending requires at least
two entities to exist; in a purely aggregate description of the system
where only global totals are considered (as in "total amount of money in
existence"), there is no spending. All we have left is a total population
working to make things or perform services and consuming the result. An
interesting concept. Who benefits from introducing money?

> By the same token, there can be no
> transactions in the aggregate: money and goods remain in posession of the
> whole, so there is no change in quantities of either, or in their
> location.

I think it might be better to say there are no _net_ transactions, in the
sense that sales minus purchases has to equal zero.

But for a sale to exist, there must be a buyer and a seller; the buyer must
take money from cash holdings (which thereby decrease) and transfer it to
the seller (whose cash holdings increase), and the seller must take goods
from inventory and transfer them to the buyer with similar increases and
decreases of holdings. If we are considering only totals, all these
transfers begin and and in the same place and there are no changes in
holdings to measure.

  However, you can add up total sales and get a number representing what
people have sold. I think this would count as an aggregate measure of
sales. If in the same
circumstance you added up total purchases you would get the same
number. But the volume
of transactions could increase or decrease

I don't think that in a pure macro model transactions are visible. .

> Oops, I forgot about production and consumption. In the aggregate, raw
> materials are still being transformed by labor into finished goods which
> are being consumed or are depreciating. But neither money nor goods can
> "change hands" when there is only one entity, so there are no
transactions..

I don't see why not. The "one entity" in the macro analysis is really the
aggregate balance sheet -- the one entity is really a set of books And,
this "one entity" is not an agent in the sense that the macro accounts are
merely numbers-- the macro accounts don't by themselves percieve,
experience error or have causal powers to do anything. The
Accounts contain things like total sales, total purchases, total
consumption spending, total investment spending Now there are lots
of "agents" doing the consuming, the investing and what not But the
identities of these agents get wiped out when the totals are added
up.

OK, this and your following comments are adding up to something important
about simulating the economy. Charlotte Bruun has said similar things.
Simulations are actually a bridge between microeconomics and
macroeconomics. A purely macro model is hardly possible -- it has no parts
to interact with each other. All you can do is write down the totals and
that is all you can say. To say anything, to predict anything about the
economy, you must analyze the total system into interacting parts. Only
then can you talk about transactions and other interactions, and begin to
predict phenomena beyond what has been observed, and thus learn something.

In Econ004, I have broken the total economy down into just three parts
(each containing some more detailed parts, including broad classes of human
agents), interacting only through interfaces among the major parts. This is
not enough parts yet to represent the entire economy, but with the addition
of a banking entity and a government entity we would probably be covering
most of it (unless you can think of another sector). The totals would still
add up to the same totals we would see in a macro description, but now we
can see how their components are distributed. Bruun's model has more parts,
including a financial part that may turn out to be as important as the
rest, so she may be ahead of us.

Whatever the case, I think we can see more clearly where this enterprise is
taking us. The idea is to find a level of analysis which is detailed enough
to capture the main features of the interchanges of money and
goods/services that take place, but not so detailed as to become
incomprehensible, and not so global that we can't see anything happening.
As a first step, I should think we would want to limit the number of
entities as much as possible, figuring that when we understand the system
in terms of its largest major components, we can always go on to analyze
the components further and add more detail to the model.

I need to add one more thing. While I am very interested in the economics
applications of PCT, and while I think I have something to contribute
regarding the methodology of modeling (as Bruun refers to it), I am
basically a control theorist and not an economist. I am trying to help
launch the boat into the right body of water and in the right direction,
but I know my limits and will probably not actually be aboard for the
cruise. I expect real economists to be in charge of the actual navigation,
not to mention selection of the destination.

Just in case you wonder what I am getting out of this.

Best,

Bill P>

[From Bill Powers (2004.03.23.0657 MST)]

Bill Williams 22 March 2004 7:10 PM CST --

>There is a sense in which there is "only one entity" However, while
>retaining the "one entity" aspect it is possible to keep track of
>different accounts within the entity. It is sort of like the law in
>electronics (Polish sounding name begins with a K) that the sum of
>currents flowing into a node is equal to zero.

All I can think of right now is "Thevenin's theorem" which I can't even
recall. You're speaking of a conservation law.

Your way of defining savings makes it into a rate variable: change in a
quantity per unit time. However, the term savings is also used to

represent

the quantity itself at a given time -- in this case, the total quantity of
money in existence. In fact you have to be able to measure the quantity at
specific times in order to compute the rate of change. I suppose something
similar happens with the term "investment," so investment can mean amount
spent on capital equipment per unit time, or total amount of capital
equipment in existence at a specific time. We need some standard way of
saying which kind of variable we're talking about.

I'm not quite sure how you answered my question on investment. Is
investment measured in terms of capital equipment, or in terms of its

money

equivalent? Since the point is to acquire and maintain the physical means
of production, I would guess that it is the physical equipment (and all
that goes unto maintaining and using it) that matters. Any money

equivalent

can only be an estimate. Also, if we think completely in aggregate terms,
there is no market for capital equipment: to whom or what would it be

sold?

The whole economy already owns all the capital equipment, and could sell

it

only to itself. Keynes varifies this by saying that in the aggregate, the
expense A1 must disappear -- A1 is the amount spent by one entrepreneur on
purchasing finished output from another entrepreneur -- it's a "wash," he

says.

>People sometimes talk about money being horded. When you ask them what
>they tell you that by hoarding the mean people are holding onto the
>money. If you ask them, "then isn't it true that all the money is being
>held all the time?"

I'm not sure that argument holds water. It's not just a matter of holding
or not holding, but of how much is held and for how long. Just as an
extreme example, suppose that somehow one firm managed to acquire and hang
onto all the money that exists. The economy would cease to function,
wouldn't it? So there can be degrees of hoarding, ranging from harmless to
destructive. I think the point is that if one hangs onto money, never
spending it on goods or services, it ceases to circulate and represents an
_effective_ loss of the money from the whole system.

In econ004, you can set it up so that one consumer begins to accumulate
more and more of the existing money. The result is that one or more of the
other entities in the system runs out of money and has to borrow to supply
consumption needs (this is similar to your argument about the Giffen
Effect, in which there are biological constraints that determine what is
consumed, quite aside from economic considerations). If the other entities
can't qualify for loans (they are basically bankrupt with no assets) all
they can do is die.

>If the "money" being repaid is a loan that was made out of
> "cash money" then there is no change in total money when the loan is

paid.

>If the loan that is being repaid is a loan that was made by a bank

creating

>money to make the loan then paying it back reduces the stock of money.

Right, I understood that but it's good to keep in mind. In Econ004, which
has no bank, there is a constant store of money which simply passes around
from one entity to another while goods (and labor) flow the other way. A
negative balance of cash can be allowed (by setting "CreditAllowed :=
True"), in which case one entity can transfer money it doesn't have to
other entities, while running a negative balance. No interest has to be
paid so this can go on indefinitely. Needless to say, that feature must be
modified.

You haven't yet commented on my proposition that new money becomes a
permanent part of the economy when bank loans are defaulted, while the

bank

that created the loan actually can end up with a profit after the loan is
written off (the interest that was paid, for example). I mention this
because I'm trying to work up to putting banking function into the model,
and need some way to know if it's working right.

>When a transaction takes place, money disappears from one
> person's possession and simultaneously appears in another person's
> possession. The metaphor of a flow is misleading. Is this correct?
>
>It really is. I think it is important to start with the "transaction"

as

>the basic unit in the analysis.

In econ004, it is not exactly the starting point, but it is present in
every loop. I trust you mean a process in which one thing is exchanged for
another: money for goods, or labor for money.

Might as well try to define, at least a first cut, transaction. It is an
economic
action that transfers money from A to B in exchange a transfer off goods or
services from B to A. Perhaps there is more that need to be included in
this
but, perhaps this will do for now.

> > This makes me think we should abandon the flow metaphor and stick

strictly

> > to the "rate" idea.
>
>I would think so.
>
> > Money disappears from one acount at some rate, so the
> > total in the acount declines, and appears in other accounts so the

total in

> > them increases. The total rate of increase has to equal the total rate

of

> > decline, with constant total money. All money, then, is "saved,"

whether we

> > speak in the aggregate or in terms of multiple agents.
>
>OK. All money is "saved" in the sense that all money is held. But in

terms

>of saving defined as money time 1 minus money time 0 the saving is zero--
>since the total money involved does not change.

This is where the difference between rate variables and cumulative
variables has to be kept clear.The _quantity_ of money saved at a given
time is the sum of all previous rates of saving times the interval over
which each rate was maintained. I save 2 dollars per day for 3 days, and

10

dollars per day for 2 days, which works out to a total of 26 dollars

saved.

The saving rate varies, while accumulating to a total quantity of savings.
Careful use of terminology is clearly critical.

Absolutely !!!!

> > Both seem to imply
> > that money is not invested until it is converted into physical means

of

> production.
>
>I would prefer to talk in terms of a transaction. A loan is created. The
>new bank money is transfered to the creators of the capital equipment,

and the

>capital is transfered to the business doing the capital investment. It
>seems to me that saying money is being "converted" into capital might be
>misleading. But, I am fairly confident about what you mean.

Again, careful use of terminology can make all the difference here.
"Capital," I presume, means money when you speak of transferring it to the
creators of the capital equipment, but the capital equipment itself is not
money: it is machinery, buildings, supplies, maintenance, and so on. The
"conversion" I spoke of applied only to the step of tranferring money to
those who create the capital equipment and getting the capital equipment

in

return -- as you say, a transaction. The capital equipment can be

converted

back into money by putting it on the market and actually selling it, but
until this is actually done, the money equivalent is unknown because it
depends on the price at the time of the transaction. Of course to speak of
buying and selling or any transaction, we must have at least two entities

Right, I didn't that there was any conceptual problem, but any novelty in
terminology may send the analysis into the ditch.

>I am not sure what you are saying in the above. My reaction as I read it
>is--at any given time none of the money is spent in the sense that

looking

>at an
>account you could be told how much money is in the account, but how could
>you tell whether the money in the account had been spent or not?

I think we can say that spending money means removing it from the account
and making it appear in a different account.

Yes.

So spending requires at least

two entities to exist; in a purely aggregate description of the system
where only global totals are considered (as in "total amount of money in
existence"), there is no spending. All we have left is a total population
working to make things or perform services and consuming the result. An
interesting concept. Who benefits from introducing money?

There are conjectural accounts, just so stories, and using a control theory
perspective it might be possible to develop a better explaination of how
and why money developed. However, until you asked the question, I hadn't
thought of seeing if, using control theory, developing such an explaination
would be worth the effort or not.

Without attempting a comprehensive description of the theory and history
of money, which is interesting enough on its own account, in the recent
discussions their is tendency to say that "modern money" is what ever the
state requires in payment of taxes. the transaction between the state and
other econmic agents regarding taxes is unique. This isn't a voluntary
exchange. But, the fact that money is the only thing that will satisfy the
state's billing the other economic agents with demand for payment is now
thought to be the process that determines what will be the "high powered"
money in the economy.

I suppose I might as well make a stab at the functions of money. The chief
one obviously is that you can buy stuff that you want using money. And, you
can pay off debts using money. And, to feel secure having money on hand
is a way of commanding resources in an uncertain future that is better than
trying to store up goods for anticipated future needs. This is true most
of
the time as long as the state is stable, and in the absence of culture wide
ecological disasters. And, of course, money transactions are much more
efficient than barter.

> > By the same token, there can be no
> > transactions in the aggregate: money and goods remain in posession of

the

> > whole, so there is no change in quantities of either, or in their
> > location.
>
>I think it might be better to say there are no _net_ transactions, in the
>sense that sales minus purchases has to equal zero.

But for a sale to exist, there must be a buyer and a seller; the buyer

must

take money from cash holdings (which thereby decrease) and transfer it to
the seller (whose cash holdings increase), and the seller must take goods
from inventory and transfer them to the buyer with similar increases and
decreases of holdings. If we are considering only totals, all these
transfers begin and and in the same place and there are no changes in
holdings to measure.

Yes, total holdings haven't changed. But, maybe here is the place for
something
like the idea of flow. If you had only one store that sold all the
consumer goods
you cold stand at the door and count the money being taken inside in
exchange
for the goods being taken out.

> However, you can add up total sales and get a number representing what
> people have sold. I think this would count as an aggregate measure of
> sales. If in the same
>circumstance you added up total purchases you would get the same
>number. But the volume
>of transactions could increase or decrease

I don't think that in a pure macro model transactions are visible. .

I am not confident that I see what you mean??? The state for one, can
demand
that a person or a firm produce records of transactions. And, we have the
various measures of transactions provided by the national income accounts,
but perhaps you have something else in mind???

> > Oops, I forgot about production and consumption. In the aggregate, raw
> > materials are still being transformed by labor into finished goods

which

> > are being consumed or are depreciating. But neither money nor goods

can

> > "change hands" when there is only one entity, so there are no
>transactions..
>
>I don't see why not. The "one entity" in the macro analysis is really

the

>aggregate balance sheet -- the one entity is really a set of books And,
>this "one entity" is not an agent in the sense that the macro accounts

are

>merely numbers-- the macro accounts don't by themselves percieve,
>experience error or have causal powers to do anything. The
>Accounts contain things like total sales, total purchases, total
>consumption spending, total investment spending Now there are lots
>of "agents" doing the consuming, the investing and what not But the
>identities of these agents get wiped out when the totals are added
>up.

OK, this and your following comments are adding up to something important
about simulating the economy. Charlotte Bruun has said similar things.
Simulations are actually a bridge between microeconomics and
macroeconomics. A purely macro model is hardly possible -- it has no parts
to interact with each other.

Right.

All you can do is write down the totals and

that is all you can say. To say anything, to predict anything about the
economy, you must analyze the total system into interacting parts.

Sure. And, people talk about things like two, three and more "sector"
models.

Only

then can you talk about transactions and other interactions, and begin to
predict phenomena beyond what has been observed, and thus learn something.

In Econ004, I have broken the total economy down into just three parts

These are : workers, managers and the capital income folks ?

(each containing some more detailed parts, including broad classes of

human

agents), interacting only through interfaces among the major parts. This

is

not enough parts yet to represent the entire economy, but with the

addition

of a banking entity and a government entity we would probably be covering
most of it (unless you can think of another sector). The totals would

still

add up to the same totals we would see in a macro description, but now we
can see how their components are distributed. Bruun's model has more

parts,

including a financial part that may turn out to be as important as the
rest, so she may be ahead of us.

Whatever the case, I think we can see more clearly where this enterprise

is

taking us. The idea is to find a level of analysis which is detailed

enough

to capture the main features of the interchanges of money and
goods/services that take place, but not so detailed as to become
incomprehensible, and not so global that we can't see anything happening.
As a first step, I should think we would want to limit the number of
entities as much as possible, figuring that when we understand the system
in terms of its largest major components, we can always go on to analyze
the components further and add more detail to the model.

Right. And, I would think a Banking sector, followed by Government might be
the
priority.

I need to add one more thing. While I am very interested in the economics
applications of PCT, and while I think I have something to contribute
regarding the methodology of modeling (as Bruun refers to it), I am
basically a control theorist and not an economist. I am trying to help
launch the boat into the right body of water and in the right direction,
but I know my limits and will probably not actually be aboard for the
cruise. I expect real economists to be in charge of the actual navigation,
not to mention selection of the destination.

Just in case you wonder what I am getting out of this.

Actually I hadn't been thinking about that not at least recently. Of course
the topic of what people "get out of what they do, and what they put into
what they do, is for an economists, an endlessly facinating subject.
Bascially I see you as a guy who, above all else, likes to figure stuff out.
That isn't all you are, but I think it comes way before other
considerations.

Bill Williams

I've got meetings this after noon, which are about to start, so this is
pecked
in, in a rush. But, I have a sense that you had some concerns about
defining
investment. At its most concise investment in the Macro sense is an
increase
in the quantity of capital. dK/dt . In the sense of transactions a businss
when
it purchases plant and equipment is "investing"-- investing in a "real
sense."

When a day or so ago I re-read the appendix to B:CP I noticed that some of
what I thought you had said there wasn't actually there. I had thought that
you
had explained how useful it is to define relationships in terms of equations
of
time rates-- but when I re-read the appendix what I didn't see was a
discussion
of how defining terms in the form [ dK/dt = the rate of investment ]
makes
life so much simpler. The discussions of modeling you posted recently seem
to start in a sense down stream of this point.

···

----- Original Message -----
From: "Bill Powers" <powers_w@EARTHLINK.NET>
To: <CSGNET@listserv.uiuc.edu>
Sent: Tuesday, March 23, 2004 9:35 AM
Subject: Re: Savings and Investment

[From Bill Powers (2004.03.24.0728 MST)]

Bill Williams (2004.03.24) --

Might as well try to define, at least a first cut, transaction. It is an
economic action that transfers money from A to B in exchange a transfer
off goods or services from B to A. Perhaps there is more that need to be
included in this but, perhaps this will do for now.

This is already part of Econ004. When a purchase/sale transaction takes
place, four things happen:

1. The number of goods bought is subtracted from the seller's inventory.

2. The number of goods bought is added to the buyer's inventory.

3. A quantity of money equal to the number of goods bought times the
selling price is subtracted from the buyer's cash account or reserve.

4. The same quantity of money is added to the seller's cash account or reserve.

These four thing happen in the same iteration of the program, the same
"instant" of time. A similar exchange happens as labor is traded for wages.
So unless I have left out some feature of transactions that is important,
I think your recommendation has already been implemented.

In the model, we actually speak of the rate at which transactions take
place, in transactions per unit time. What I refer to as "a" transaction in
the four steps above is actually a large number of transactions happening
simultaneously. If we take, for example, the number of goods of a given
type being transferred per unit time, and multiply that rate by dt, an
interval of time, we get a quantity of goods subtracted from one inventory
and added to another at one instant The same goes for the money: the money
is being transferred at a rate determined by the rate of exchange of goods
times the price per good, which converts to the rate of transferring
dollars. Multiplying that rate by the time interval dt gives the quantity
of money subtracted from one account and added to the other during the
interval dt.

This is how we let time flow continuously while a series of discrete
events, transactions, is taking place. This automatically takes "volume" or
"velocity" into account, since we are lumping many transactions among many
parties together and measuring rates of "flow" (which as you suggest might
still be a useful idea if not taken literally with dimes and quarters
flying through the air).

There are conjectural accounts, just so stories, and using a control theory
perspective it might be possible to develop a better explaination of how
and why money developed. However, until you asked the question, I hadn't
thought of seeing if, using control theory, developing such an explaination
would be worth the effort or not.

That remark seems to have lodged in my mind because this morning I awoke
realizing why I have been so bogged down in moving Econ004 toward at least
Econ004a. The other half of your remarks that stuck in mind mind comes
later so I'll wait a minute before talking about it.

> I don't think that in a pure macro model transactions are visible. .

I am not confident that I see what you mean??? The state for one, can
demand that a person or a firm produce records of transactions. And, we
have the various measures of transactions provided by the national income
accounts, but perhaps you have something else in mind???

Yes. To compute a transaction you have to observe a decrease in goods one
place and an increase in another place, accompanied by similar increases
and decreases in money accounts. If there is only one quantity to observe,
either of goods or of money, there is no change and therefore there is no
transaction. You have to be able to see a buyer and a seller as different
entities.

I have broken the total economy down into just three parts

These are : workers, managers and the capital income folks ?

Yes, the workers being the wage-income folks.

> we can always go on to analyze
> the components further and add more detail to the model.

Right. And, I would think a Banking sector, followed by Government might be
the priority.

That is the second half. Last night I thought, "OK, good, now we can start
actually putting the Bank into the system." And this morning I awoke
thinking "But what do we need a Bank for?" As I envisioned how the bank
would be set up to make loans, charge interest, keep books, pay its
employees and managers, and so forth, I realized that there is nothing in
the current model that could make any use of a Bank. The present model
coasts along on a constant supply of money which never gets larger or
smaller, but just moves around from one place to another, eventually
reaching a steady equilibrium distribution. Whatever the GNP or GDP is, it
never changes.

I have a few vague ideas, but I'll put the question to you. What is there
about an economy that requires banking functions to be carried out? Before
we can put a bank into the model, we have to do something to the model that
makes it need banking functions. This obviously has a lot to do with the
question you raised about the origins of money, but let's assume that money
exists as a medium of exchange, but that banks don't exist (this is where
the model is now), and see what would require at least borrowing and
interest to come into being. If you can put your finger on that, I can
change Econ004 to reflect the features you suggest, and _then_ we will be
able to add the banking functions and get Econ005.

Best,

Bill P.

P.S. I've been cc-ing these posts to Charlotte Bruun, who may be too busy
to get involved here (or not see enough reason to do so yet), but I wanted
to say she is certainly free to chime in if she wishes.

FromBill Williams 24 March 2004 12:46 PM CST]

Nothing I read in

[From Bill Powers (2004.03.24.0728 MST)]

seems to me to Indicate any area of disagreement. so I see if I can explain
why banks are a good idea, such a good idea that banks seem to emerge even
in socialist states.

If one accepts that a market reflects the choices of consumers and producers
in a fairly efficient way then it makes sense to have choices about
investment reflect market realities. I am saying "If" here because I don't
necessarily accept the idea that the "market" is always right. But, leaving
my reservations aside, the idea of banking -- in the sense of an firm that
is allowed to create money does seem to work rather effectively. I won't go
into all of the other functions that usually go along with the money
creation function. Basically what you have in a bank is an economic agent
who makes a living by making judgments about what loans ( money creations )
can be made that can and will be paid back over time. In the United States
we have a mythology about banking reserves, but basically the bank function
generates money out of nothing more than good judgment and a public
reputation that if the bank officer says Joe is OK, then Joe gets to
purchase a new steel mill, then you can accept a check from Joe. After a
bunch of sad experience the banking function is regulated, and regulated
fairly strictly. But, things sometimes slip by like the savings and loan
scam. As I understand it when the regulation that resulted in the savings
and loan scandal past the people paying attention said, "Well, if it is
heads I win and tails you (the rest of us) lose, then the parties on." And,
we all of us, more or less got robbed. But, basically the main -- the
commercial banking part-- works fairly well. At least now it works fairly
well, there was an era 1870 -1930in which there was a lot of instability in
the system, most of which was fixed by a lot of regulatory restriction and
establishment of the Federal Bank. If you follow this history I think it is
possible to pick out practices that are required to keep people from turning
banks into private fountains of money and other self-dealing scams.

Basically what banking does is allow an economic agent and the bank agent
through an agreement, and a transaction to create a loan which consists of
new money to be used for some purpose and simultaneously a debt. In a
sense the net effect might seem to be zero because the money created is
offset by a debt that is of the same amount. But, when the money is
sloshing about in the economy the people looking at their bank balances are
only concerned with the money side and not the debt side of the loan. It
wouldn't work if people were able to create money for themselves. And so
the function is made a specialty of people who can create money and loan it
to others. The auditors do keep an eye on banks to attempt to prevent them
from doing just creating loans for themselves for private purpose. You may
remember how that Burt Lance under Carter was in the habit of using his bank
to make loans to himself. This seems to be a minor folkway in the rural Deep
South.

Banks are also disciplined by the market. When you have banks in
competition some of the possible element of arbitrariness tends to be
reduced. If one bank rejects your loan application you can go to some other
bank and see if they think your loan is something they want to do. Not
that it works perfectly, cultural and other prejudices aren't entirely
ironed out by market forces.

There is, I suppose of course, a lot of mysticism about banking. After all
the idea that some people get to create money, and that they do it out of
nothing is a rather startling idea. Bankers and other people with vested
interests in how things are would rather not have this stuff discussed
candidly. But, despite thinking of myself as having a "critical"
orientation, I think the way the banking function works as a private
function that is rather strictly regulated, is probably better than the
alternatives. The separation of powers in this case seems to work to some
extent. At least I am not confident that turning to the state to conduct
the banking function-- the money creation loan making side -- would work as
well. Although some state banking for example the Reconstruction Finance
Corporation seems to have provided money for small business and especially
small technology companies that venture capital investment banking was not
incline to consider.

In my view the acceptance of private commercial banking is so widespread,
that you might as well include it in your model as a standard feature of
market economies. There is a mass of institutional detail involved in
keeping banks on the up and up. And, here may be something to think about.
If all of the economic agents in an economy are of an unrestricted
self-regarding profit maximizing type the standard market economy (including
in this commercial banking) can not function. At least some of the agents
have to function according to some other standard that sheer profit
maximizing-- your auditors, your accountants, your assessors, police, judges
and so forth have to be more or less ethical and law abiding. Otherwise the
costs involved in trade are going to be so high that the extent of the
market-- in time and in space -- is going to be very limited. It seems to
me this is an effect that could be modeled. And, the effects observed in
simulations might be, in a sense, confirmed by cross cultural historical
observations.

Has the definition of investment been sorted out to your satisfaction?

Bill Williams

[From Bill Powers (2004.03.24.1456 MST)]

Bill Williams 24 March 2004 12:46 PM CST --

If one accepts that a market reflects the choices of consumers and producers
in a fairly efficient way then it makes sense to have choices about
investment reflect market realities. I am saying "If" here because I don't
necessarily accept the idea that the "market" is always right. But, leaving
my reservations aside, the idea of banking -- in the sense of an firm that
is allowed to create money does seem to work rather effectively.

OK, I appreciate these introductory remarks and accept the idea that the
creation of money in a well-regulated way is better than the old way of
minting your own. I want to pry something out of you at a deeper level,
however, which I'm sure you can come up with.

The question is this: how must I change Econ004 so that it _demands_ some
agency that can create new money? Right now, it works just fine with an
initial stock of money that never increases or decreases. That is obviously
not realistic. What can happen in a network of transactions that means it
_needs_ more money in order to function? I'm not talking about individuals
trying to get rich -- they could do that in Econ004 by somehow getting more
of the existing money for themselves, leaving less for the rest and thus
getting that nice feeling of "I'm better than you." The total amount of
money would remain the same.

Incidentally, if you arbitrarily increase the amount of money in Econ004,
all that happens is that prices increase until everyone is consuming
exactly as much as before. Pure money inflation, I guess. So minting your
own money is not an answer to the new money problem.

What I'm after is an idea of what can happen in an economy that means it is
not going to work very well much longer unless some new money shows up. As
I said, I have some ideas, but I'm trying to get your ideas without
planting anything in your mind, to see if you'll come up with anything
similar or will find something else I hadn't thought of (not that I've had
any startling new ideas). We don't need to justify a banking system or the
way it's run; the banking system may be the best way to create new money.
But why do it?

···

==========================================================

I don't want to divert you from this main question, but one day I'll be
asking another one, although the model may provide an answer before that.
You say

Basically what you have in a bank is an economic agent who makes a living
by making judgments about what loans ( money creations ) can be made that
can and will be paid back over time.

This, I think, is going to prove to be an interesting puzzle. The bank
wants to know its loans will be paid back, but if all the loans were in
fact paid back to all the banks, there would be (it might seem) no money
left in the system and it would stop. It seems that it is _necessary_ for
loans to be made at least at the same rate they are paid back, and when you
ask where the interest is going to come from it seems that the amount of
outstanding loans has to increase continuously. Money is indeed created out
of nothing, but it's not given away. Books are kept and interest is charged.

We can take the view that interest is simply the payment to the bank for
its services. That payment then re-enters the economy by being distributed
to various consumers as wages, salary, and capital distributions (including
profit). No problem there. But there is the lingering question of repaying
more money than was lent, which means repaying _more money than was
created_. You can shuffle this pea around under as many different walnut
shells -- banks -- as you please, but interest means that you always need
more money than was created in the system. Doesn't it?

I have a hunch that the answer is going to be related to my question of
creating _permanent_ new money through bankruptcies. There seems to be a
lurking conclusion that to keep this system running, it is necessary for
competition to destroy some businesses. There is not actually enough money
to go around as it is set up now, and can't be enough without some unspoken
phenomenon to make up the shortfall.

==========================================================

That is a problem for the future. Right now the question is why new money
ever has to be created, since just pouring more money into the system won't
have any significant effects on it (in isolation from other systems) as it
is. When you find the answer to that question I will know how to change
Econ004 so as to provide something for a bank to do -- and then I can put
the bank in.

Best,

Bill P.

From[Bill Williams 24 March 2004 8:30 PM CST]

[From Bill Powers (2004.03.24.1456 MST)]

I have been thinking about the issue you consider in the savings thread
today. And, I've ben thinking about what to say. What seems to be needed
is a basic premise about why things happen in an economy, and particularly
in a money economy. You've encountered Marx's statement about the
difference between the motivation of a capitalist-- which is to use money to
obtain more money. ( My first impluse was to say "use money to make more
money." Must guard be ceaselessly on guard against equvocation! ) And,
Marx also in contrast described the non-capitalist class as supplying labor
to get money so as to get commodities. There may be some truth in this.
But, money is a very special sort of good for all people in a market
capitalist society.

I have come to the conclusion that the overwhelming condition of most people
in contemporary society is a situation in which the desired level of
consumption is greater than the budget availible to support consumption
purchases. Not a novel idea I will admit. But, it is an idea that can be
modeled using control theory. Set the reference level for consumption above
the actual level for the budget. Then set up two control loops one for
consumption and a second loop for the budget. To resolve the conflict
between the two looops include an integrating term in the control loop for
the budget. Obviously this leaves out stuff. But, it seems to me to be a
fairly accurate description of how the bulk of the population have organized
their lives.

Does this seem to be approximately accurate to you?

Second, you mention that when you add money to your system what happens is
that prices go up. I've been thinking about a control theory theory of
prices recently. There has been a lot of interest recently concerning the
fact that prices do not behave the way they ought to given the neo-classical
conception of economic behavior. A lot of transactions now are not
bargaining transaction- rather they are "fixed price transactions."
Usually the seller sets a price and that is that. But, even for prices that
are ordinarily bargaining prices the way these prices behave is not the way
they should behave acording to orthodox theory. People around here find the
possiblity of explaining what they call "sticky prices" a lot more
interesting than the Giffen stuff. Using control theory a reason prices
might be "sticky" is that once a price is set, that price becomes something
like a peace treaty. Who ever wants to change the price is doing something
like declaring war. I haven't modeled this yet, but the idea is appealing
to me, and there isn't really any current alternative out there to explain
why prices should be sticky.

It just occured to me why Econ4 would react to more money by a price level
increase. As I understand it Econ4 does not include a specification of the
non-money side of the economy. The way you are approaching modeling
economy means that you encounter issues that are ordinarily left implicit.
So, to explain the capacity of the economy to generate income you need a
theory. In the production function income is usually assumed to be the
result of a combination of land, labor, capital (equipment) and technology.
Some technology is owned ( patent rights) but most technology is freely
availible, And, without explicit financing technology seems to grow.

Anyway, you need something like a supply curve and shifts in the supply
curve to come closer to a plausible system. In the late 19th century there
was a long period of declining prices. Agricultural productitivity was
increasing rapidly, so was industrial p;roductivity. And, the money policy
was tight. I haven't been thinking about the supply side-- so it make take
a few day, or longer, for me to think of how this should be modeled.

A possible way of thinking about this is to assume an exogenous ( outside
the market at least) increase in the state of the art in production
technologies. This wold create the opportunity for entrpreneurs to buy
equipment that the new technology makes possible. This sets in motion a lot
of possiblities depending upon the strength of the factors involved.

Actually econ4 now behaves the way the Chicago school people think the real
economy behaves. What is needed is a supply side that would push the price
level down. A technological enthusastic culture would be expected to
generate a rapid increase in technology, while an anti-technological culture
would be expected to generate a slow growing or stagnate technology. This
rate of technological change might be one of your fundamental variables.
The explaination for the setting for technological change would be cultural.
A culture that was technological enthusiastic would know more about Veblen's
matter of fact world. And knowing more about this matter of fact world,
would be in a better position to combine existing understandings to create
new understandings. The attitude toward technology is one of the most
fundamental traits of a culture and economicly is decisive.

So, what about dtech/dt as a sytem variable?

Bill Williams