The most objectionable and frustrating aspect of Austrian economics, to me, is the almost complete abandonment of formal mathematical models in their analyses.
To be clear, I am an empiricist and believe that the study of systems can only come about through careful experimentation, modeling, and formal mathematics. Mathematics, in my opinion, is the only objective measure by which we can analyse systems and trends.
I would concede that many of the macroeconomic models and experimentation in mainstream economics are weak and misused. However, I think any mainstream economist would agree with you and say that they are working hard to deal with the explosion of mathematical complexity in these kinds of analyses. They don't present their results as gospel, but they do formally state the models, meaning that they also formally state the assumptions being made.
Austrian economics, meanwhile, seems whole unscientific. Almost all Austrian economic systems eschew formal mathematics in favor of cute rhetorical devices. This book is a perfect example -- where are the mathematical models and formal reasoning? Formalism is good. Formalism is how we know what we are actually discussing and what we are trying to deduce. An example of how formalism is essential is Turing's PhD thesis. Without getting into details, Turing was trying to find the answer to a certain intuitive mathematical relation. What Turing found, however, was that there was no answer -- the statement itself could not be well-defined in a formal sense, meaning that it was not a good question.
This small example simply represents the large class of problems which can't be analyzed without formal breakdowns, simply because what seems interesting in rhetoric may be wholly untrue in a strict sense.
Rothbard, especially, seems guilty of my criticism. In a number of works he stated that he believed that historical analysis and modeling could never apply to economics and that all of economics could be explained by a priori relations. The troubling thing is that Rothbard should have known from physics and chemistry (and now somewhat formalized by statements about Turing machines and automata) that there can be underlying principles in mathematical systems and that can still be absolutely useless in analyzing the results of those systems. The three body problem, for instance, operates on very simple principles, but those principles are of almost no use in predicting the results of such a system.
So, in conclusion, I'm not saying that Austrian economics has no useful ideas, but what I am saying is that an underlying philosophy of many of Austrian economics' most celebrated evangelists is directly in conflict with my own. I don't believe that the right way to do economic or systems analysis is through rhetorical flourish or logical argument. These things are convincing on Internet boards but are not scientific and not well-defined. We should be trying to bring more science and formalism to economics, not less.
Austrians do not "eschew" mathematics nor empiricism, rather they reject the claim that what is commonly called empirical evidence actually is, and admit to the limits of empiricism in social sciences. Aping the physical sciences in some form of cargo-cult formalism is not only wrong, but leads to flawed conclusions.
Austrians assert that the only way to empirically know a person's preferences is through observing their choices. There is no objective meaning to graphs that rely on the assumption that people have these scales of numbers in their heads that say, "An apple is five utils, a banana is ten." The only meaning comes from decisions - either you prefer the apple to the banana, or you prefer the banana to the apple.
Austrians further assert that any macroeconomic model must be a result of (or at least 100% consistent with) valid microeconomic principles. A macroeconomic model which concludes something that is not explainable in terms of human decisions is necessarily wrong.
rather they reject the claim that what is commonly called empirical evidence actually is, and admit to the limits of empiricism in social sciences. Aping the physical sciences in some form of cargo-cult formalism is not only wrong, but leads to flawed conclusions.
Empirical evidence is exactly what it says it is and mathematics is exactly what it says it is. That's what makes them facts and mathematics. What you argue using those facts is completely different.
Austrians assert that the only way to empirically know a person's preferences is through observing their choices.
No they don't. Because then they could collect data on these choices, produce a model, and formally define it mathematically. This is the fundamental truth of falsifiable systems.
There is no objective meaning to graphs that rely on the assumption that people have these scales of numbers in their heads that say, "An apple is five utils, a banana is ten." The only meaning comes from decisions - either you prefer the apple to the banana, or you prefer the banana to the apple.
There are more systems of mathematics than ones based on continuous distributions. Consider the following definition:
forall people, exists pref : (fruit, fruit) -> {-1, 1} st. forall a,b in fruit => pref(a,b)
This is math. This formally encodes your statement. This is the kind of thing that Austrian economics should define and use. The fact that they don't is why I don't take them seriously.
Austrians further assert that any macroeconomic model must be a result of (or at least 100% consistent with) valid microeconomic principles. A macroeconomic model which concludes something that is not explainable in terms of human decisions is necessarily wrong.
So? I can both know that all quantum particles obey the Schrödinger wave function in all atomic structures and be completely unable to derive the properties of Si just from the wave construction of protons, electrons, and neutrons. Just because we know microeconomic models doesn't make them useful in a macroeconomic context.
"To be clear, I am an empiricist and believe that the study of systems can only come about through careful experimentation, modeling, and formal mathematics. Mathematics, in my opinion, is the only objective measure by which we can analyse systems and trends."
I think we have to be a little careful about approaching economics as a problem to be solved. Logic, math, and empiricism have their limits (even if they are the best tools we have).
For one thing, empiricism relies on being able to control the variables. But that's hard to do, because others can always refute the results by introducing other variables and factors.
And (as you point out) the possibilities explode so quickly that it's very difficult to reason purely based on logic from base principles. And there are humans involved, which makes it even more difficult (if not impossible).
I'm not criticizing logic and empiricism as tools. But I think they can very easily give a false confidence in the answers you get. You have to realize how small a piece of the problem space your logic actually covers; and how difficult it is to distill real world events into a nice clean, unbiased data set.
I would argue that mathematics can only give you false confidence if you fail to understand it completely. A sound formal mathematical definition holds all assumptions within the definition itself.
Note that I think that if you can't encode your theory in mathematics than it is non-predictive by definition. If it is non-predictive then I see no use for it in any real sense.
I hold all economic systems to the same level of critique, by the way. If your Keynesian system doesn't encode its assumptions and predictions in mathematics then it is by definition useless.
"I would argue that mathematics can only give you false confidence if you fail to understand it completely."
Yes, that's the problem. In economics, it's difficult to know what all of the relevant variables are and the basic inputs are not well-understood (like the behavior of people).
Even if you did create a perfect model, most of the assumptions would have to be nearly wild guesses, and probably even small errors in the assumptions would lead to wild errors in the result. And the resulting model would be so complex that I'm not at all sure it would even be useful for crafting policy.
Then, let's say we had a perfect and simple model that anyone could understand. Everything would be wonderful, right? No, you still have to collect all the relevant data for inputs, run the simulation, and then distribute the results to all of the relevant parties -- all before the economy plays out in real time.
So what actually happens with mathematical models is that people oversimplify, but because it has the aura of formalism they become very confident. There are always so many wild variables like wars or drought that it's easy to later dismiss any deviation from their model as "a special event" (e.g. an earthquake).
And what's the optimization target, by the way? The total number of shoes produced? Using GDP as an optimization target has a lot of known problems and embeds a lot of assumptions itself. And some people simply prefer living under a certain kind of economic system.
So, trying to approach economics from a purely mathematical standpoint is useless, in my opinion.
Applying mathematical models to human action is interesting, no doubt, but we are a long way off from anything approaching a hard science when it comes to economics. I'm certainly no economist, but economics in general seems to be more of a sociological problem than a mathematical one. I'm happy that there are two sides to the coin. I've delved into Keynes's General Theory a bit, and witness on a daily basis how that approach is fouled by the actions of humans.
Robert Murphy is an austrian economist who was trained by keynsians. He talks about the the difference in approach in this video:
http://www.youtube.com/watch?v=hkDYsRDah3I
Just because you use math dose not mean its more scientific, it just looks more like science. Hayek called this sientism. It does not make sence to use math-models in economics because its a social science, you cant model human behavior the same why you can with atoms.
There seem to be two issues at stake here. The first is whether mathematical models are appropriate and adequate to explain human behaviour. Here I have a lot of sympathy with Austrian arguments, but it's quite clear they overstate the case. Sure, economic models, like meteorological models, are rather looser and more speculative than Newtonian classical mechanics, but there are multimillion dollar industries that have grown up based on mathematical models of human behaviour; denying the obvious predictive power of at least some models of human behaviour seems akin to denying that one can make assumptions about natural selection because actions of lifeforms appear to be indeterminate. It's not like physical sciences are devoid of controversies over models either.
Hayek alluded to the problem of inferring a relationship between inflation and full employment from too small a sample, but Milton Friedman got a Nobel prize for predicting the breakdown of the relationship with an economic model. In the long run, economists might all be wrong about something, but at least most conventional ones they have the intellectual honesty to admit to the possibility theirtheories might be demonstrably false.
The second question is whether Austrian economists have something more compelling to offer than mathematical models. The answer, so far as I can tell, is no. They have A number of interesting ideas, many of which neoclassical authors have tried to develop as models rather than simply assert them as a priori truths. But praxaeology comes across as pure sophistry of the worst kind; Rothbard's "Praxaeology" paper might claim that it's intended to be a set of axioms where A implies B but he then goes on to provide an example which consists of rather elementary and mostly uncontroversial statements most of which simply dont imply each other at all
Sample: "that a man acts implies that he will make a difference...action therefore implies that man does not have omniscient knowledge of the future"
http://mises.org/rothbard/praxeology.pdf
Obviously, when it comes to more controversial statements it's necessary to stretch the definition of "imply" a little further in order to paint your pet theory as a priori truth. But even while discussing something as indisputably empirically true as human nonomniscience, that sort of woolly argument is enough to make even the most superficial mathematical model a lot more compelling.
In defence of bad application of math, it's less of a dead end than bad application of philosophy
To be clear, I am an empiricist and believe that the study of systems can only come about through careful experimentation, modeling, and formal mathematics. Mathematics, in my opinion, is the only objective measure by which we can analyse systems and trends.
I would concede that many of the macroeconomic models and experimentation in mainstream economics are weak and misused. However, I think any mainstream economist would agree with you and say that they are working hard to deal with the explosion of mathematical complexity in these kinds of analyses. They don't present their results as gospel, but they do formally state the models, meaning that they also formally state the assumptions being made.
Austrian economics, meanwhile, seems whole unscientific. Almost all Austrian economic systems eschew formal mathematics in favor of cute rhetorical devices. This book is a perfect example -- where are the mathematical models and formal reasoning? Formalism is good. Formalism is how we know what we are actually discussing and what we are trying to deduce. An example of how formalism is essential is Turing's PhD thesis. Without getting into details, Turing was trying to find the answer to a certain intuitive mathematical relation. What Turing found, however, was that there was no answer -- the statement itself could not be well-defined in a formal sense, meaning that it was not a good question.
This small example simply represents the large class of problems which can't be analyzed without formal breakdowns, simply because what seems interesting in rhetoric may be wholly untrue in a strict sense.
Rothbard, especially, seems guilty of my criticism. In a number of works he stated that he believed that historical analysis and modeling could never apply to economics and that all of economics could be explained by a priori relations. The troubling thing is that Rothbard should have known from physics and chemistry (and now somewhat formalized by statements about Turing machines and automata) that there can be underlying principles in mathematical systems and that can still be absolutely useless in analyzing the results of those systems. The three body problem, for instance, operates on very simple principles, but those principles are of almost no use in predicting the results of such a system.
So, in conclusion, I'm not saying that Austrian economics has no useful ideas, but what I am saying is that an underlying philosophy of many of Austrian economics' most celebrated evangelists is directly in conflict with my own. I don't believe that the right way to do economic or systems analysis is through rhetorical flourish or logical argument. These things are convincing on Internet boards but are not scientific and not well-defined. We should be trying to bring more science and formalism to economics, not less.