[Part 6 of a series of articles and a section taken out of the longer essay “Do You Even Prax, Bro?” explaining Austrian methodology/epistemology. For previous articles in this series on Austrian epistemology/methodology, see herehere,herehere, and here.]

 

 

Why is it that critics complain about the lack of math in general among Austrians, but never name an actual mathematical proposition that Austrians should accept? Unfortunately, mainstream economics has taken it upon itself to completely conceal what’s being said, which leads to physicists and the like (that usually need to use math) to fling insults of “pseudoscience” at Austrians. The Austrian idea of economics, on the contrary, accepts intellectual humility. Do Austrians “reject” the use of math in economics? To be clear, the Austrian position is Austrians say economists can’t make quantitative predictions, on the grounds that there are no quantitative constants in human action. A consequence of this is that mathematical economic models are impossible. Because of that statement, half of the anti-Austrian crowd is running around looking for something mathy-looking that they can throw in our faces. “Isn’t this math? Looks like math to me. Isn’t logic basically the same as math? If I expand 1=1 creatively enough, it starts to look like math. $1.50 soda plus $1.00 candy bar= $2.50, math! Aha!”

Mathematics is indeed powerful, but there’s also a point where understanding is exceeded by obfuscation. This has nothing to do with a supposed “dogmatic” aversion to math.

 

Critics should not dismiss Austrians so quickly on this basis of “rejecting math.” First of all, most Austrian economists (if not even all) understand math and conventional economic theory for the simple reason that, being economists, they were force-fed this stuff during their training at university. For instance, Rothbard, who had a degree in math, states:

 

“Since knowledge in physics is never certain and absolute, positivists can never understand how economists can arrive at certain truths; therefore they accuse economists of being “a priori” and “dogmatic.” Similarly, cause in physics tends to be fragile, and positivists have tended to replace the concept of cause by one of “mutual determination.” Mathematical equations are uniquely suited to depicting a state of mutual determination of factors, rather than singly determined cause and effect relations. Hence, again, mathematics are singularly suitable for physics.

I have grave philosophic doubts as to whether the concept of cause can really be expunged from physics. But whether or not it can, it certainly cannot be from economics. For in economics, the cause is known from the beginning — human action using means directed towards ends. From this we can deduce singly determined effects, not mutually determined equations. This is another reason that mathematics is uniquely unsuited to economics.”  [1]

 

Second, quite a number of Austrian economists didn’t start out that way and converted at some stage during their career. In something like physics, a mathematical model can be shown to be false with an experiment or series of experiments. The problem with economics is that the “experiments” and evidence are always — and can only be — in the past. Economists have developed the illusion that they can use models that were shown to fit with the data in hindsight as a tool for predicting the future.

 

Third, Austrians did already provide ample epistemological discussions about why math is not suitable for modeling any human action at all. Mathematical models cannot be used in economics because subjective preference cannot ever be modeled well enough to make any accurate conclusions about an economy. People are changing preferences all the time. If you could somehow model human interactions perfectly, all you would learn is that any decision you make for those people based on your perfect knowledge would be identical to the decisions those people would already be making.

 

Fourth, Austrians fully recognize that there are indeed a lot of “ifs,” which makes modeling or predicting future behavior more or less impossible, especially if it is done on the basis of arbitrary historical data, with the additional difficulty of including all the variables that influenced historic events (especially the motivation behind certain actions). Economics, when undertaken properly, is a science of human action. In human action, there are no quantitative constants. Any formula you try to throw at it, therefore, is just something you made up and are not going to work out. If by sheer luck some number comes out tomorrow that vindicates your formula, next week it won’t do it again, because human beings are not protons.

 

Mathematical models can’t work to determine policy, because mathematical models can never be as accurate in determining what people desire as people just determining this for themselves.

 

To use math would, in most cases, be that you are able to definitively measure something, but when it comes to human action, as Mises put it, there are no fixed points, no fixed correlations that can be used as a yardstick. Even the relatively simple task of “measuring inflation” is forever trapped in an arbitrary world of the observer’s subjective viewpoint, not some objective measurement for all:

 

“The pretentious solemnity which statisticians and statistical bureaus display in computing indexes of purchasing power and cost of living is out of place. These index numbers are at best rather crude and inaccurate illustrations of changes which have occurred. In periods of slow alterations in the relation between the supply of and the demand for money they do not convey any information at all. In periods of inflation and consequently of sharp price changes they provide a rough image of events which every individual experiences in his daily life. A judicious housewife knows much more about price changes as far as they affect her own household than the statistical averages can tell. She has little use for computations disregarding changes both in quality and in the amount of goods which she is able or permitted to buy at the prices entering into the computation. If she “measures” the changes for her personal appreciation by taking the prices of only two or three commodities as a yardstick, she is no less “scientific” and no more arbitrary than the sophisticated mathematicians in choosing their methods for the manipulation of the data of the market.” [2]

 

As Hayek explained in “The Counter Revolution of Science,” hard sciences use a specific set of strict rules and controls, trying to eliminate the human factor, while economics, psychology, sociology, et cetera, all specifically are attempting to understand that human factor. Instead of trying to hide human action and motivation, those are central to their disciplines. Those soft sciences, therefore, should not engage in a pretense of knowledge, where they affect precision and certainty with their metrics and math, when it’s actually somewhat worse than flipping a coin.

 

Hayek clarifies this further in his UCLA interviews in which he speaks multiple times on math:

“[…] I limit the possible achievement of economics to the explanation of a type — One of my friends has explained it as a purely algebraic theory […] you get an algebraic formula without the constants being put in. Just as you have a formula for, say, a hyperbola; if you haven’t got the constants set in, you don’t know what the shape of the hyperbola is — all you know is it’s a hyperbola. So I can say it will be a certain type of pattern, but what specific quantitative dimensions it will have, I cannot predict, because for that I would have to have more information than anybody actually has.” [3]

 

One might suggest that math is not trying to explain the thought processes or any one person’s emotions, rather they’re just calculating or observing the manifestations of economic actors, mainly in the aggregate. Or that it isn’t used to explain human action, it just measures the manifestations thereof.

 

However, even there, there are no constants. If you say that, historically, the money supply went up by X and prices of eggs rose by Y%, sure, you have some data. But what does this mean?

 

One approach is to logically deduce laws and then apply them to explain the data. The other is to posit some strict mathematical relationship between various data points, such that one can supposedly predict — just like with gravity or electricity — the results of various changes in that data. But the latter is clearly absurd. Also, I can’t ignore the fact that measuring is not modeling, and economic models are intended to predict, not to measure.

 

But my real point is that manifestations of human action are … well, manifestations of human action, and if there are no quantitative constants in human action, you can’t use them to predict manifestations thereof. You can’t even build a wrong model without implicitly, illegitimately, and incorrectly assigning a constant value to what in reality is a variable, and one whose value is and always will be unknown until it’s too late to call your work a prediction, and even then you only know how the “real” value as manifested in a given actor’s action, not the actual value (which is unattainable because value is subjective), so even if you assume it doesn’t change you can’t use it to correct the assumptions that led to the previous predictions.

 

Mathematical models simply do not work. Human preferences change (and circumstances from environmental to accidents to random events) matter because these changes alter, sometimes significantly, the dynamics between economic actors in relation to the scarce resources they need in their efforts to satisfy their ends, and therefore alter the market signals other actors receive, which in turn alters their actions, and on and on in a constantly adjusting way. Why? Because we live in a constantly changing, dynamic world, not a static one. Mathematics are static and precise. If you base any mathematical equation on something you perceive at one moment in time, it’s relevance to any real world situation is with almost absolute certainty going to be irrelevant and useless in a very, very, very short time.

Very.

Economics is a lot of things, but for these very reasons, precise ain’t one of them. Economic models work fantastically in a completely static economy. Sadly, completely static economies are theoretical constructs.

 

In a way though, to be clear, we all use “math” in making our own determinations in things such as accounting, speculation, financing, grocery shopping, etc. Yet, as it has been shown elsewhere, this is not economics. None of this means that “math” is bad. However, the real question is whether or not what we are discovering is an objective truth. It’s not that Austrians believe math isn’t suitable for use elsewhere, such as day-to-day life for the Average Joe, it’s that Austrians recognize that economics is a soft science, far too imprecise for equations to make accurate, or even useful, predictions.

 

Which leads me to ask again, why is it that critics complain about the lack of math in general among Austrians, but never name an actual mathematical proposition that Austrians should accept? That is, an example of an equation capable of predicting economic outcomes. One example of what the Austrians say can’t exist and everyone else insists is all around us.

 

To elaborate, let us go over some mathematical propositions in economics, along with some objections, which have been raised to Austrians that can further illustrate the Austrian position:

 

  •     “I don’t get the Austrians position on math… so wait, are you denying 2+2=4? Whaaa?”

2+2 = 4 is logically true. Note the equation is made entirely of constants. No variables. Can you offer an equation that’s supposed to offer economic predictions, which is logically true? 2+2=4 regardless of your empirical evidence to the contrary or my lack of empirical evidence to support it. This cannot be tested empirically. It can no more be validated or falsified through experiment or observation than “no two straight lines can enclose a space.”

 

You can’t explain human action through observation. You can’t even directly observe action, properly defined. You can see me move, but you can’t see my purpose or the decision-making process that led me to this particular course of action as the best way to achieve my purpose. Or even that any of these occurred in my mind. You have to infer it. Through understanding, not observation.

 

  • “The claim that there are no constants in human action is entirely meaningless. If mathematical models cannot capture human action, then shouldn’t no models be able to? If we cannot make simplifying assumptions in our mathematical models that will capture economic relationships there is no reason we can make these assumptions when using the Austrian method”

This is correct and just the sort of thing an Austrian would (and does) say. Note the lack of quantitative anything – it’s entirely quantitative. Nobody has said anything like “If the price increases by 10%, demand will decrease by 8%.” To arrive at a conclusion like that, you would need to discover a quantitative constant in human action. The Austrian approach are thought experiments, not modeling. A representation of a qualitative relationship. Sometimes drawn with quantities filled in, but nobody pretends those quantities are known or meaningful – that’s only ever done as thought experiments.

 

And sure, even if you don’t represent the model in mathematical terms, merely explain what the mathematical model says, thus it can be modeled mathematically…. No, you can’t. If you try, it will no longer be correct. You could – and people do – draw supply and demand curves with actual prices and quantities on the axes, but every point on the curve with the possible exception of the point of intersection, which would be an observation of current conditions and nothing else, would be purely hypothetical, and any mathematical representation of those curves would be perfectly meaningless.

 

  • There are no constants in mathematics, only trends. Economists do not look for constants. They discover trends.”

No, speculators look for trends.  Some economists look for trends, because they think they can learn new economic truth from them. Real economists don’t.   There’s nothing wrong with looking at trends, extracting predictions and making trades based on those predictions which can vindicate them or not based on profit and loss. If you’re an economist looking at trends to establish or defend a theory, there’s no analog to profit and loss to expose your theory to anything that could compel you to abandon it. If you make a prediction based on it, and the prediction doesn’t work out, you’ll just take another look at the data and what do you know, find some other change that explains it, and your theory is as strong as ever. And math, it’s full of constants. You can’t do math without them. You can’t solve equations made entirely of variables.

 

 

  • “Let us say I take a job offer, and one pays $80,000 a year which I take over $60,000 a year, can’t I say I am better off by the difference? I use math here.”

This has to do with cardinal vs. ordinal ranking[4]. Obviously you can measure a difference between $60,000 and $80,000 but those are dollars, not preferences. You’ll always prefer $80,000 over $60,000, but a) not by 33%, and b) really not even at all — your preferences are about what you can buy with that money, not the money itself. Since money is always a means, and preferences are about ends, you ultimately just use money as a proxy for your preferences. Plus, a measurement isn’t a prediction.

 

  • “Austrians should accept the inverse relationship between price and quantity demand.”

How is this mathematical? All this says is that, ceteris paribus, if demand goes up price also goes up.  A mathematical statement would be an assertion like, “given an n% increase in demand, prices will increase by n*x%.” Price is inversely related to supply, qualitatively. You can’t predict the actual price of a good given a supply. You can only say that if the supply falls, the price will be higher than it would otherwise have been; or, that if the supply falls the price will rise, other things being equal. No math to be done there at all. And while demand responds to price changes can arguably be expressed mathematically, it can’t be predicted mathematically. And I say “arguably” for two reasons: you can never know actual demand across possible prices, so all demand curves actually drawn out are completely made up — you only know the direction of the curve (a qualitative relationship)… and second, that curve isn’t going to conform to a mathematical formula except occasionally and coincidentally, and you can never know when that has happened anyway, except after the fact.

 

  • “In mathematical economics, the Arrow–Debreu model suggests that under certain economic assumptions (convex preferences, perfect competition and demand independence) there must be a set of prices such that aggregate supplies will equal aggregate demands for every commodity in the economy.[5]  The Arrow-Debreu model assumes people have preference orderings, yet the actual results the model supplies do not depend on any specific allocation of preferences.”

So, assuming consumer preferences are defined by strongly concave utility functions (already wrong like 5 times), and that they are twice continually differentiable (wrong some more), that consumer demand for one good is independent of demand for any other good (easily disproved), and that perfect competition exists (fine as a thought experiment, but no).

So, what exactly does the theorem tell you? Absolutely nothing. Nothing follows from it, even if the literally impossible set of conditions it depends on is satisfied, which can never happen.

Or if I’m wrong – can you extract a policy recommendation from the theorem, or make an accurate price prediction based on it?

The Arrow-Debreu model also has erroneous nonsense assumptions like the mentioned “perfect competition” (among many others) and has a conclusion that is rejected by Austrian analysis. The non-mathematical logical approach does not, for instance, draw the conclusion that there exist prices where “aggregate supply = aggregate demand” – there could very well be a good brought to market that could never sell at any price.
Further, even if it were correct, this would not require any sort of mathematical analysis to demonstrate it. It would only require that one accept the truth of Say’s Law – that any one supplying a good to market is inherently demanding other goods in exchange, and that an exchange cannot happen without this holding true.

 

  • “How do I know what an increase in price is? Is 2$ more than 3$? How do I know the numbers are ordered? The only way to answer these questions is with math. If you accept the statement 2 < 3 you are accepting a mathematical proposition which is essential for economics to have any meaning.”

Sure, if this is coming down to what counts as math, and you’re saying “$3 > $2” is a specifically mathematical proposition, then OK, non-quantitative “math” can be useful in economics. But if you want to extract from that an assertion that quantitative modeling is therefore possible, you’ve made an illogical leap from a concession to a semantic dispute.

 

  • “Game theory is a branch of mathematics first developed by Emile Borel, and then popularized by the works of Von Neumann, Morgenstern, Nash etc. There is a plethora of economic questions game theory answers. “

Game theory is a branch of praxeology and it explores how people seek their ends under certain, usually contrived, circumstances, typically deliberately designed to maximize the likelihood of error or otherwise make it difficult to discover which course of action is most likely to serve those ends. The “correct” action is held to be the one most likely to bring about the outcome we assume the actor will prefer — he stays out of prison or gets a million dollars or doesn’t die or whatever. The fact that I can sometimes use math as a means to discover which course of action is best suited to my goals is irrelevant. Game theory should be considered to be a branch of praxeology rather than of mathematics, though of course math is used to compute the optimal set of choices for each player. Which is not to say it uses math to predict the actual choices of each player, which is why it’s of no use in economics. The (safe) assumption of game theorists is that each player will try to maximize his utility, that is, his “payoff” in the face of imperfect information either about the details of the “game” or about the decisions other players would make that might ruin his strategy. Take the prisoners’ dilemma, the classic example. Math is used to describe various possible strategies, to compute optimal outcomes etc., but it’s of no use whatsoever in predicting the actual choices of each player — human action, the stuff economics is made of.

 

Now, you may have noticed that some of the examples were (more or less) algebraic questions, where others were (more or less) models. To clarify, you can do things like algebra but that’s not what we mean by math when we say math isn’t useful in economics. Thus, when I ask the question at the base of this essay, it’s really a shorthand for “quantitative economic predictions are impossible because there are no quantitative constants in human action, thus mathematical modeling is impossible.” The “no quantitative constants” point is important because you can’t solve for anything in mathematics with an equation made entirely of variables. You need pi, for example, to work out the unknown attributes of a circle from the known attributes. There is no analog to pi in human action.

 

One of the biggest problems is assuming that any mathematical model can ever make accurate predictions about future human behavior. There are far too many factors that go into the market, and any of these could change at any given time. We can make observations about any given moment, but does our observation of it influence people’s attitudes and thus future outcomes? If we understand basic patterns we can say what is happening — for example, identifying a bubble (again, that’s qualitative)— but we cannot say exactly when this bubble will pop, how long prices will rise, which markets will be affected, etc. (all quantitative).

 

Other schools object to Austrians use of math or supposed lack thereof because mathematics supposedly has a use in simplifying abstract concepts with a more symbolic representation or conceptualization. Yet, I don’t think this is true. A mathematical formula is an assertion of fact, of some consistent quantitative relationship among variables. Mathematical notation simplifies the task of doing actual math, but equations don’t make abstract concepts concrete in any way that could be defended as correct.

 

Whether it is on the micro level or the macro level, economics studies purposeful human behavior, human reasoning in a world with scarce resources, limited time, and unlimited wants. Economics is a social science, not a math class. Humans have the ability to learn and adapt, while numbers do not. A number is always the same next week and twenty years from now. Learning is what separates a human actor from a proton. Formulas and numbers are not subject to change whereas we are.

 

 

Jeff Peterson II

We the Individuals

 

 

[1] A Note On Mathematical Economics by Murray Rothbard

http://mises.org/daily/3638

[2] Human Action by Ludwig von Mises Pg 222

[3] The UCLA Interviews with Friedrich Hayek

http://archive.mises.org/9657/the-ucla-interviews-with-friedrich-hayek/

[4] Cardinal Utility: It’s Worse Than You Thought by Kenneth A. Zahringer

http://mises.org/daily/5399/Cardinal-Utility-Its-Worse-than-You-Thought

[5] http://en.wikipedia.org/wiki/Arrow%E2%80%93Debreu_model