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In Defense of the "Quants"

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.


autor

Mark R. Crovelli
é pos-graduado em ciência política pela Universidade do Colorado.

  • clark  14/07/2011 00:19
    "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."
  • Curt Doolittle  15/04/2012 20:02
    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



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