Daniel James Sanchez’s recent article on Mises.org offers
a fascinating analysis of the use of probability and mathematical modeling in
the financial markets.[1] The article is highly critical of the use of
probability and mathematical modeling for the purpose of predicting future
economic conditions or future prices in the market.
That the article should take this critical
position is completely unsurprising, given the orthodox Austrian perspective on
probability theory that Mr. Sanchez utilizes to make his argument. Unfortunately, the article’s sweeping
criticism of the use of probability theory for the purposes of predicting
future economic conditions does not hold up under closer inspection.
Mr. Sanchez
bases his criticism of the use of probabilistic methods in the economic sphere
primarily on Ludwig von Mises’s famous distinction between so-called “class”
and “case” probability. Mises held that
numerical probabilities can legitimately be assigned to “classes” of events and
phenomena, whereas singular cases are not open to any type of numerical
probabilistic evaluation. Mises based
his claim on the observation that the relative frequency method for generating numerical
probabilities can only be utilized for of “repeatable” events or phenomena.[2]
This claim may seem completely
unobjectionable to Austrians who have become accustomed to Mises’s famous
distinction, and it may appear to have profound methodological and
epistemological implications, but in reality the claim is quite banal and
question-begging, as I have attempted to demonstrate elsewhere.[3]
Mr. Sanchez’s article offers an excellent
illustration of just how question-begging and banal Ludwig von Mises’s
distinction between “class” and “case” probability really is. In the first place, Mr. Sanchez’s article is
concerned to determine whether it is epistemologically and methodologically
justifiable to assign numerical probabilities to singular and complicated
economic events, as was increasingly done by the “Quants” over the past two
decades. The answer to this question
that Mr. Sanchez arrives at, citing Ludwig von Mises’s famous distinction
between “class” and “case” probability, is that it was not legitimate
for the Quants to assign numerical probabilities to these events, because they
lacked the necessary “class knowledge” to do so. They were “gambling,” according to Mr.
Sanchez, and nothing more.
A closer inspection of Ludwig von Mises’s
distinction between “class” and “case” probability, however, reveals that Mr.
Sanchez’s claim is baldly question begging.
Ludwig von Mises’s distinction between “class” and “case” probability is
simply a distinction between those situations in which a relative frequency can
be calculated and those situations where it is not possible to calculate a
relative frequency. Mr. Sanchez
recognizes as much when he writes that “The most important thing to note about
this distinction is that class probability has to do with frequency, and
case probability does not.”
This means that both Mr. Sanchez and Ludwig
von Mises are assuming from the outset that probabilities are always and
necessarily relative frequencies.
And the only justification they provide for believing that probabilities
are always relative frequencies is that certain situations are amenable to the
frequentist method (i.e., “class” probability), while others are not (i.e.,
“case probability). In other words, they
are assuming the very thing they are attempting to prove. They are assuming that numerical
probabilities must be relative frequencies in the process of trying to prove
that numerical probability cannot be applied to singular cases, such as
singular economic events. This is a
textbook case of begging the question.
It would be one thing for Ludwig von Mises
and Mr. Sanchez to pick out and criticize certain instances where the relative
frequency method for generating numerical probabilities was being
misapplied. I am certain that there were
many “Quants” who misapplied the relative frequency method over the past two
decades, for example. But Mr. Sanchez
goes far beyond that, following the lead of Ludwig von Mises, and claims that no
numerical probabilities can ever be applied to singular economic events. This sweeping claim is not justifiable based
upon the argument that he has provided.
Neither Ludwig von Mises nor Mr. Sanchez
provide us a reason, for example, why it would be epistemologically or
methodologically inappropriate for the “Quants” to employ “classical” or
“combinatorial” methods for generating numerical probabilities for economic
events.[4] Nor do they provide us with a reason why it
would be inappropriate for the “Quants” to employ some other non-frequentist
method for generating numerical probabilities.[5] On the contrary, they simply condemn the
entire application of numerical probability to the economic world, simply based
on the banal observation that no relative frequencies can be calculated in that
realm.
The root of the problem here is that neither
Ludwig von Mises nor Mr. Sanchez makes an attempt to define probability.[6] They start from the observation that relative
frequencies can be calculated in some instances, while they cannot be
calculated in others, as if this were a definition of probability in itself. Recognizing that uncertainty plays a role in
both the study of human beings and natural phenomena, they admit that
“judgment” and “psychological insight” play a critical role in predicting the
future state of the human world, but they nevertheless persist in completely
condemning the use of a numerical scale to measure that uncertainty.
This bizarre condemnation of the use of a
numerical scale to measure man’s uncertainty, “judgment” and “psychological
insight” could be completely eliminated were they to adopt a subjective
definition for probability. A subjective
definition for probability simply asserts that, in a world where every event
has a cause of some sort, a numerical probability is simply a measure of some
man’s (or some men’s) uncertainty about what will or will not occur.[7] There is thus no reason why man cannot use a
numerical scale to describe how certain or uncertain that he is that something
will or will not occur. This is just as
true of the economic world as the natural world.
Both Ludwig von Mises and Mr. Sanchez appear
to be extremely concerned that the use of probability theory in the realm of
economic forecasting will lead to a concomitant neglect of the relevant
thymological and praxeological insights that truly matter for making accurate economic
forecasts. While this is a valid concern
in general, and Mr. Sanchez rightly points out that this was a primary failing
of the “Quants,” it does not justify ejecting the entire corpus of probability
theory from the sciences of human action.
In fact, because both Ludwig von Mises and Mr. Sanchez conceive of
probability as a frequency alone, they unintentionally ascribe more gravity to frequentist
probabilities than they deserve. If
probabilities are conceived as nothing more than measures of human uncertainty,
as the subjective approach demands, then there exists ample room to criticize
all sorts of probabilistic methods and applications from a praxeological
perspective. If, on the other hand, one
conceives of probabilities as “objective” relative frequencies, and thereby
ascribes more epistemological weight to them than they deserve because they are
supposedly “objective,” one unintentionally bolsters the case of dogmatic
positivists and empiricists, like many of the “Quants,” who worship at the alter
of these supposedly “objective” methods.
The adoption of a subjective definition puts the methods and the
probabilities they generate on the shaky “subjective” epistemological
foundation that they deserve.
In conclusion, while Mr. Sanchez’s article is both fascinating and
valuable in terms of outlining Ludwig von Mises’s theory of probability, such
as it is,[8] it
does not justify the wholesale condemnation of the application of probability
in the sciences of human action.
[1] Daniel James Sanchez, “What Mises
can Teach the Quants,” Mises
Daily,
Friday, June 10, 2011
[2] The relative frequency
method for calculating probabilities, (which was first developed by John Venn
in the 19th century, but was popularized by Ludwig von Mises’s
brother, Richard von Mises in the 20th century), involves calculating the relative frequency
at which a certain type of event occurs in repeated trials. If a coin is flipped ten times, for example,
the relative frequency method for calculating the probability of flipping a
head would be to divide the number of times a head comes up by the total number
of tosses. For a more thoroughgoing
technical explanation of the relative frequency method, see page 23 of Robert
A. Crovelli’s “An
Analysis of the Basic Concepts in Applied Mathematics. For a more complete critique of the relative
frequency method, see Mark R. Crovelli, “On the
Possibility of Assigning Probabilities to Singular Events: Or, Probability is
Subjective, Too!” Libertarian Papers 1, 26 (2009).
[3] Mark R. Crovelli, “A Challenge to
Ludwig von Mises’s Theory of Probability,” Libertarian Papers 2, 23
(2010).
[4] For a succinct discussion
of the “classical approach” to generating numerical probabilities, see page 23
of Robert A. Crovelli’s “An Analysis of the Basic
Concepts in Applied Mathematics”
[5] For an explication of the
“subjective approach” to generating numerical probabilities, see Ibid, loc.
cit.
[6] For an elaboration of this
claim with regard to Ludwig von Mises, see Mark R. Crovelli, “On the
Possibility of Assigning Probabilities to Singular Events: Or, Probability is
Subjective, Too!” Libertarian Papers 1, 26 (2009).
[7] For more on the subjective
definition of probability, see Crovelli (2009) and Mark R. Crovelli “Why the Definition of Probability Matters,”
Mises Daily,
Wednesday, January 26, 2011.
[8] See Crovelli (2010) for an
argument that Ludwig von Mises did not truly develop a full-blown theory or
definition of probability.
Nota: as visões expressas no artigo não são necessariamente aquelas do Instituto Mises Brasil.
“the use of probability and mathematical modeling for the purpose of predicting future economic conditions or future prices in the market.”
That quote reminds me of science fiction writer Issac Asimov, a Russian/American author and professor of biochemistry at Boston University who wrote a story about People who tried to predict the future using mathematics.
The Foundation Series, from Wikki:
“The premise of the series is that mathematician Hari Seldon spent his life developing a branch of mathematics known as psychohistory, a concept of mathematical sociology (analogous to mathematical physics). Using the laws of mass action, it can predict the future, but only on a large scale; it is error-prone on a small scale. It works on the principle that the behaviour of a mass of people is predictable if the quantity of this mass is very large … The larger the number, the more predictable is the future.”
There is also a difference between the context Mises is working from (a managed economy) and that in which an investor works from, or that which the federal reserve uses in order to determine interest rates. The precision necessary in Mises’ context is far higher than the precision necessary in the super-aggregates used by investors or the federal reserve.
If, Mark, that is your objection, then I agree. I do not know what Sanchez’s context addresses. If it’s Mises’ then he’s correct, otherwise he’s wrong. But I cannot tell if this is a disagreement or the fact that the two of you are talking past each other.
The proper critique of the DSGE Model is that it encourages, over time, the creation of fragility in the economy by policy makers and throughout the financial system.. (per Taleb.) It assists in the formulation of bubbles, and exacerbates risk.
As far as I am able to tell, models help explain data. And the Quants are solving for the same thing that we (micro/austrians) are, but from the top down instead of the bottom up. THe difference being that we prefer to create stability in an economy, and the quants encourage the entire system to create instability.
The remaining objection is that it’s just another way to perform an involuntary transfer: redistribution. I”m not so sure I”m against that however. I’m against fragility.
–Curt