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23.09.2002, 15:17

Über Models - sehr interessanter Artikel, mises.org, (engl.)

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http://www.mises.org/fullstory.asp?control=1051
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Models: What Are They Good For?
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By Gene Callahan

[Posted September 23, 2002]

[img][/img] Many
large brokerage houses, as well as small boutiques, rely heavily upon
mathematical models in their day-to-day trading. Clearly, there is a market
for this kind of modeling, yet Austrian economists have generally held the
view that the neoclassical, mathematical approach to economics is a strictly
limited approach.

How can we reconcile the market success of mathematical
models of trading with the Austrian skepticism toward theoretical models
expressed in math? Let's examine this question.

The Limits of Models

Mises explained the fundamental gulf between economics and
mathematics in Human Action:

<blockquote dir="ltr" style="MARGIN-RIGHT: 0px">

"Logic and mathematics deal with an ideal system of
thought. The relations and implications of their system are coexistent and
interdependent. We may say as well that they are synchronous or that they
are out of time. A perfect mind could grasp them all in one thought….
Within such a system the notions of anteriority and consequence are
metaphorical only. They do not refer to the system, but to our action in
grasping it. The system itself implies neither the category of time nor that
of causality. There is functional correspondence between elements, but there
is neither cause nor effect. What distinguishes… the praxeological system
from the logical system is precisely that it implies the categories both of
time and of causality" (1998: V.1).

[/i]
Let us take a famous mathematical creation, the
Pythagorean theorem, as an example of what Mises is talking about. As is well
known to school children everywhere, the theorem says that there is an
immutable relationship between the three sides of a right triangle, where the
sum of the squares of each of the shorter legs equals the square of the longer
leg (a2 + b2 = c2). Mises is saying that this
type of relationship has a fundamentally different nature than do the
relationships implied by human action.

None of the legs of a triangle causes any of the
other legs to be a certain length. Neither Pythagoras's equation nor any of
the infinite number of triangles that it describes has any temporal
relationship to each other. Once we clearly conceive the concept"right
triangle," then the universe of right triangles, along with the
relationship of their sides and all other geometric facts about them, emerge
as the aspects of a completely timeless, ideal form. Although our limited
minds must approach these aspects piecemeal, their existence is simultaneous
with the very notion"right triangle," and none of these aspects are
prior to or stand in a casual relationship to any other aspect of the ideal
form.

Human action is different. Just as the idea of a right
triangle implies the Pythagorean theorem, the idea of human action implies
"before" and"after,""cause" and"effect."
We cannot make sense of human plans unless we understand that there is a past
which, for the human actor, provides the soil in which the seeds of action
might be sown, that there is a present during which the sowing will transpire,
and that there is a future in which the actor hopes to reap the fruit of his
action. Similarly, we must see that the actor hopes that his action will be
the cause of a desired effect, or he would not act.

<h3>The Neoclassical Overreach</h3>

Viewing the economy as if it were a mathematical form is
coherent if it is seen, for instance, as the study of a limiting state—equilibrium—that
the real economy may have some tendency to gravitate toward. Equilibrium
theorizing is the construction of an abstract economy in which economic
activity proceeds strictly according to an interrelated system of equations.
As such, it may or may not yield an increased understanding of certain aspects
of an actual economy.

But when taken as more than that--as, for instance, a
description of the real economy, a normative ideal to which the real economy
must measure up, or as a causative force generating economic actions--it
creates confusion. It eliminates from view real human choices, the very
phenomena that differentiate economic activity from all else going on in
experience.

Let us look at an example. In Steven Landsburg's
microeconomics textbook, Price Theory, he says:

<blockquote dir="ltr" style="MARGIN-RIGHT: 0px">

"It is important to distinguish causes from effects.
For an individual demander or supplier, the price is taken as a given
and determines the quantity demanded or supplied. For the market as a whole,
the demand and supply curves determine both price and quantity
simultaneously" (1999: 18).

[/i]

Landsburg is saying we must not think of prices as being
determined by the actions of individuals--individuals simply take prices as a
given. Instead, it is the abstract mathematical notions of supply and demand
curves that simultaneously determine what occurs in the market.

We can agree with Landsburg that it is important to
distinguish causes from effects. At the same time, we must contend that there
is a real confusion in Landsburg's presentation of cause and effect in
economics. If Landsburg wants to construct a mathematical model in which
individual market participants have no influence, but instead are moved by
equations describing intersecting curves, he is engaged in a coherent
enterprise, the value of which he would have to demonstrate by drawing our
attention to whatever insight it provides.

But in doing so, it is incoherent to explain how we arrived
at the equilibrium point by invoking producers' or consumers' decisions to
raise or lower their bids and asks, as Landsburg does. By hypothesis, such
explanations have already been excluded as causative factors in the model, so
to bring them back into play makes the whole enterprise self-contradictory.

In the real economy, as Landsburg acknowledges, prices and
quantities change as the result of human action. Where in a real economy can a
new price come from if not a human deciding to bid or ask above or below the
current market price? It is the striving of individuals to better their
circumstances, in the face of an uncertain future, that drives the market
process.

Landsburg is forced into his odd posture because, on the one
hand, he wishes to use mathematics as the basis for economics. On the other
hand, he wants his economics to describe the real world. His goals are at odds
with each other, because mathematical equations cannot take into account
creative human decisions based on the categories of cause and effect, before
and after.

What they describe is a world of timeless correlations from
which causation is absent. Human intentions play no part in the model, as the
model assumes all humans know everything relevant to their situation and can
only accept it as a given. Faced with the prospect of acknowledging the limits
of his model, Landsburg opts for eliminating human action from the economy,
but then slips back into considering human action when giving a verbal
explanation of the model.

The fact that supply and demand curves can give us a rough
picture of market behavior is an effect of human action, and certainly
not the cause of it. No one acts with the goal of bringing supply and demand
into balance. (Well, no one except Fischer Black, as we'll see later.) People
act in the market in order to profit, in the broadest sense of the word: they
exchange because they feel they will be better off after the exchange than
they were beforehand. That their search for profit tends to bring supply and
demand into balance is a by-product of their actual goals. As Hayek said:
"…the modern theory of competitive equilibrium assumes the
situation to exist which a true explanation ought to account for as the effect
of the competitive process" (1948: 94).

In other words, mathematical economics simply assumes that
prices do bring supply and demand into balance, without asking how we
could have found the prices that did so. Rather than a market process
that consists of a groping for"correct" prices, in equilibrium
models, everyone knows the price to trade at before trading can begin.

The neoclassical mistake is not the mere use of such models.
Seen for what they are, they may be useful. Instead, the mistake is the notion
that equilibrium constructs are good descriptions of the actual market, or
normative ideals to which we should compare the real market. In fact, they are
mental constructs that abstract out the most crucial part of economics--human
action--from the world, and treat the world of economics as if it consisted
only of quantities of goods and services.

<h2>So What Is It Good For?</h2>

But that leaves us with a puzzle: Just what are all of the
investment banks, trading companies, and so on doing spending so much money on
modeling? Are they just nuts?

From an Austrian perspective, it would be strange to find
large groups of businessmen who were wasting resources on a useless activity.
So are Austrians wrong about mathematics and economics? I don't think so,
because the Austrian arguments are sound as far as I can see, and what Peter
Boettke calls the"precise irrelevance" of much of modern economics
is good evidence that the arguments are sound.*

My own experience at the equity trading company led me to
think about that question a good deal. What I finally decided was this:
Mathematical equations can be useful for modeling the result of people
following through on previously made plans, for capturing"equilibrium-like"
phases of markets.

Analogously, we could say that once a player in a basketball
game decides to shoot jumper, we could use an equation that, based on the
initial force vector that the shooter chooses to apply to the ball, then
predicts the progress of the shot. Such an equation will be of little use,
however, in predicting whether the player will change his mind and pass
instead.

Similarly, the relative price of the two stocks in a merger
may move in line with the predictions of a mathematical model most of the
time. But if traders find out something that alters their perception of the
merger, the relative price of the stocks may differ greatly from the model's
prediction.

If rumors emerge indicating that the merger might fall
through, the relative price of the seller might plunge. Traders have to employ
their entrepreneurial judgment in an attempt to grasp how other market
participants will react to this news. Once this evaluation is completed, a new
risk factor for deal failure can be fed into the model and it may again
function reasonably well

Such a model cannot capture the change of perception in the
market, which is the beginning of the creation of a new plan. That is the
moment of human choice, as the plan must aim for one goal while setting aside
others, and choose some means to achieve that goal while rejecting others.
Mathematical economics models the equilibrium-like phases of markets, when no
plans are being created or revised.

<h3>Fischer Black and CAPM</h3>

Now, as I mentioned, no human has ever acted with the goal
of bringing supply and demand into balance… except Fischer
Black. For those of you who don't know of him, he
was one of the two creators of the famous Black-Scholes
option pricing model, and he also has contributed to other areas of finance
and economics, especially the
Capital Asset Pricing Model [CAPM], one of the most
famous models in finance. I take up Black here because his work is so well
known in this area.

I make him the exception to the rule because it seems he
really tried to live his life with the goal of bringing about a general
equilibrium, or what Austrians might call the evenly rotating economy. (See
Mehrling, 2000.)

Perry Mehrling (ibid: 5-6) says:

<blockquote dir="ltr" style="MARGIN-RIGHT: 0px">

"From [Black's] point of view, economic growth
appears as a process of increasing sectoral differentiation and increasing
temporal roundaboutness, a process with no apparent end in sight. What we
observe as accumulation of capital, physical and human, is just the form
that the process takes."

[/i]

So, again, we see that the actual concrete choices people
make, the individual items of physical and human capital they choose to
accumulate, are seen as the happenstance"forms" of a"process,"
in the same way that concrete decisions to buy and sell are seen as the
outcome not of human choice but of mathematical curves. Since Black wanted to
create mathematical models that captured economic events, he had to
take such a view--as we saw above, mathematics inherently can't deal with
human action.

In Black's model, all security prices are explained by
considering only the rate of interest and the price of risk. Of course, any
model must simplify like that, as it's not possible to have a model in
which the input is"everything." Such a model would have to be as
complex as the entire universe!

Whatever parameters a model includes, however, as more
people employ it, those parameters not included will tend to move away
from equilibrium pricing. Let's say that I know of some firm with a great
R&D department. Well, having a great R&D department is not a parameter
in CAPM, so it is not taken into account by those trading using CAPM. As more
people employ CAPM, that great R&D department will become more and more
underpriced, and the profits I can make by buying the firm will increase. No
such model could"achieve" equilibrium, as that would result in a
state where no one is profiting. But it is precisely the desire to profit that
drives human action.

<h3>The Evenly Rotating Economy</h3>

What Black was hoping to achieve was an economy without true
economic profit--all investors would receive simply the market rate of return.
Mises pointed out the absurdity of an economy without profit when he discussed
the evenly rotating economy--roughly what mainstream economists call general
equilibrium.

The evenly rotating economy is an economy where the price
and quantity of all goods is in balance. There are no price fluctuations, as
everyone already knows what everyone else wants to buy and sell, and how much.
Such an"economy" is an endless cycle of the same events being
repeated. The same number of babies is born each year, and that number exactly
equals the number of people dying. The same goods are manufactured each year
and demanded in the exact same quantities. No harvest ever fails, no business
ever goes bankrupt, no new products are ever introduced, and no person's
tastes ever change.

Such a world could not possibly exist, but it can be helpful
to create the image of such a world for use as a mental tool. By introducing a
single change into our mental construction, we can isolate what the effects of
that particular change would be, apart from the welter of complicating data
that exists in our real world.

Why isn't such a world possible? For one thing, we no longer
have any motive force driving the market process. Why watch the stock market
when it never goes anywhere and everyone achieves the same return? Why search
for a better price for a good you want if you already know that everyone
offers the same price?

David Friedman (1996: 9-10) presents a nice analogy to the
stock market by discussing supermarket checkout lines. If we were in an
equilibrium-always world, all checkout lines would be equally fast, and there
would be no benefit to assessing their length--everyone would pick one at
random. But if that were the case, there would be no driving force tending to
equalize the speed of the lines, and they would become wildly imbalanced at
times!

In the real world, the weather and animal populations change,
resources are depleted and discovered, tastes change, learning occurs, and
change is omnipresent. In the real world, entrepreneurs hoping to profit from
such changes are the force driving prices toward equilibrium.

There is a further conceptual problem with a world where
everyone traded stocks using the same model. Whenever the model said"sell,"
everyone in the market would attempt to sell. Who would they be selling
to? Exchange is driven by differences in opinion as to the value of various
goods, and a"market" where everyone has the same valuation of all
goods is nonsensical, as there is no exchange in such a market.

<h3>The Use of Mathematical Models in the Social
Sciences</h3>

As I mentioned, the above considerations do not lead me to
believe that it is useless to examine the mathematical aspects of markets.
Political philosopher Terry Nardin calls statistical studies in the social
sciences"disguised descriptions" of customs, traditions, and
practices. A particular model may work fine, as long as there are no major new
alterations of those circumstances. (How large is"major"? The
answer depends on how far off can you afford to have your model be!)

Karen Vaughn makes what I take to be the same point:

<blockquote dir="ltr" style="MARGIN-RIGHT: 0px">

"In the first case [of action without a significant
alteration in the social context], we try to explain a set of choices and
their consequences within an established culture and an established
market--within a given set of institutions. Because there are established
institutional parameters, we can make informed theoretical predictions about
the outcome of any action. In the second case [where new practices are being
formulated], we are asking questions about the process of market creation
and institutional change brought about by the discovery of new knowledge or
the perception of previously unimagined opportunities. With changing
institutional parameters brought about by discovery or changing perceptions,
we can predict very little even in principle, since we cannot know in
advance what is going to be learned or perceived [i.e., what new practice
will be adopted]."

[/i]
<h2>Employing Models</h2>

So, if you're going to employ models as an aid to investing,
what rules of thumb might the above considerations suggest?

First of all, speculating in any market involves
entrepreneurship, whether done employing mathematical models or not. As Mises
(1998: XIV.7)
formulates the notion,"The term entrepreneur as used by catallactic
theory means: acting man exclusively seen from the aspect of the uncertainty
inherent in every action. In using this term one must never forget that every
action is embedded in the flux of time and therefore involves a speculation."
Mises notes that:

<blockquote dir="ltr" style="MARGIN-RIGHT: 0px">

"Like every acting man, the entrepreneur is always a
speculator. He deals with the uncertain conditions of the future. His
success or failure depends on the correctness of his anticipation of
uncertain events. If he fails in his understanding of things to come, he is
doomed. The only source from which an entrepreneur's profits stem is his
ability to anticipate better than other people the future demand of the
consumers. If everybody is correct in anticipating the future state of the
market of a certain commodity, its price and the prices of the complementary
factors of production concerned would already today be adjusted to this
future state. Neither profit nor loss can emerge for those embarking upon
this line of business" (ibid.: XV.8).

[/i]

Someone using mathematical models for investing is betting
that his models are going to be better able to anticipate future market
conditions than are the efforts of others to do the same.

Here are some principles of using financial models that
emerge from these considerations:

<ul>
~ You must have reason to think that you've discovered an
existing pattern before others have. Therefore, if"everyone"
knows about a model, forget about it. The disappearance of the"Dogs
of the Dow" effect once it became widely known is an example of this.
The technique consisted of buying the 10 Dow stocks with the highest
dividend yield and holding them for at least a year. After it became
popularly known, it underperformed the market in 1998 and 1999, had a
mediocre return in 2000, and lost money in 2001.
~ You must constantly watch for the pattern dissipating,
because eventually it will. Either market conditions will change, or
others will start to perceive the outlines of your model. The profits you
are earning are always temporary. You must watch the results of the model
carefully, to see when its applicability begins to fade.
<li dir="ltr">A corollary to the above: Be prepared to
innovate and find new patterns if you want to keep playing. Never stop
trying to develop, or trying to find from others who have developed, new
models, even while the old ones are still making profits.
~
<div style="MARGIN-RIGHT: 0px">
Finally, never trust anyone--including yourself--who says
he has a universal system for trading securities. Such a system implies
that we will arrive at the evenly rotating economy, or at least a
financial-market-wide equilibrium. As we saw above, it also implies all
market participants attempting to buy or sell at the same time.
</div>
</li>
</ul>
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<hr align="left" width="33%" SIZE="1">
</div>

Gene Callahan, who writes frequently for Mises.org, is
author of Economics
for Real People from the Mises Institute. See his
Mises.org Articles
Archive and send him MAIL.
His book is available through Mises.org or Amazon.com.
Read more about Callahan's book at Economics
for Real People.

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* That does not mean I think economic reasoning must by
empirically tested -- I agree with Say, Senior, Mises, Robbins, Knight,
Rothbard, Hoppe, and others that fundamental economic reasoning is a
priori. I merely would add that mistakes in a
priori reasoning are possible, and that empirical
results widely divergent from what one's a priori
reasoning indicates should occur do not disprove
one's theory, but they are a sign to check one's theory carefully. The
converse, that events are proceeding as one's theorizing leads one to suspect
they should, similarly does not prove
one's theory, but it can increase one's confidence in it.

References

Friedman, D. (1996) Hidden Order: The Economics of
Everyday Life, New York: Harper Collins.

Hayek, F.A. (1948)"The Meaning of Competition" in
Individualism and Economic Order, Chicago, Ill.: The University of
Chicago Press: 92-106.

Hoppe, H. H. (1995) Economic Science and the Austrian
Method, Auburn, Ala.: Ludwig von Mises Institute.

Landsburg, S. E. (1999) Price Theory & Applications,
Fourth Edition, Cincinnati, Ohio: South-Western College Publishing.

Mehrling, P. (2000)"Understanding Fischer Black,"
working paper presented to the NYU Austrian Colloquium.

Mises, Ludwig von ([1949] 1998) Human Action,
Scholar’s Edition, Auburn, Ala.: Ludwig von Mises Institute.

Nardin, T. (2001)"Oakeshott's Philosophy of the Social
Sciences," Presentation to the First Annual Michael Oakeshott Association
Conference, London School of Economics.

Vaughn, K. I. (1982)"Subjectivism, Predictability, and
Creativity: Comment on Buchanan," in Kirzner, Israel, ed., Method,
Process, and Austrian Economics: Essays in Honor of Ludwig von Mises,
Lexington, Mass.: D.C. Heath and Company, pp. 21-29.

Hirscherl 23.09.2002, 15:42 @ --- ELLI ---	Re: ;-) irreführender Titel, ich habe mich schon über Mises.org gewundert....
	-->[img][/img] Der Wunsch war wieder mal Vater des Gedankens.

Über Models - sehr interessanter Artikel, mises.org, (engl.)

Re: ;-) irreführender Titel, ich habe mich schon über Mises.org gewundert....