## Thursday, September 1, 2016

### What Was, Is And Could Be Austrian Economics?

Ludwig von Mises

So-called "Austrian Economics" didn't start as a by-word for "libertarianism" (whatever that is). That's not to say it wasn't political. The elder Carl Menger was part of the generation that discovered the method of marginal analysis but he also was a close associate of Crown Prince Rudolf. But when the Austrian School was still young and vital, Austrianism was capable of having wide differences of opinion. Wieser, Menger's first student, was sympathetic to some varieties of socialism. Bohm-Bawerk (according to Wikipedia) invented income tax as an alternative to a production tax laden with perverse incentives. Bohm-Bawerk's student Schumpeter believed that breakdown of the capitalist system was necessary, but bad and to be prevented as much as possible. What happened?

Morgenstern & von Neumann

Part of the later seeming uniformity is due to the re-writing of the books to separate The Austrians from ... the Austrians. Nobody wants to remember that von Mises was chief economist for the Austrian Chamber of Commerce when the city was called "Red Vienna". Morgenstern - despite having written one of the first, best and clearest books on the dangers of using measured aggregates to guide policy (and, through this analysis, a precursor to rational expectations and random walk stock hypotheses) has been written out of the official Austrian history book. Anyone who went on to have a good career in economics has been all but abandoned by the Austrians: Abraham Wald (probably the most important non-famous economist) and the younger Karl Menger both attended and loved von Mises's seminars.

Otto Neurath

This was made possible by the intellectual environment that the Austrian economists lived in. Higher education and research in Red Vienna was unusually loose and - as a result - creative. When the economist von Mises got his doctorate, Freud was beginning his own discussion group. Freud's group included Herbert Graf, who produced Schoenberg's operas. When von Mises was dealing with reactions to his book Liberalism, Neurath and the rest of the Vienna Circle was doing the same for The Scientific Conception of the World. The time was ripe for loose collections of followers. And Ludwig von Mises was part of that.

Piero Sraffa

With that out of the way, I want to talk about what I understand to be Austrian economics. I make no attempt to reconcile it with the precise words of von Mises et. al.. I offer the following pseudo-reason tounge-in-cheek: One can argue that as a brute historical matter, the great Austrians did not completely understand their own system. So my obvious misunderstandings are going to be only following in that tradition. Once upon a time, after publishing what seemed to most like it would be the new big book on the macroeconomy (a useful phrase not yet then coined), Frederich Hayek was unable to answer his critic Piero Sraffa's simple question of why there is only one interest rate if capital is dis-aggregated. This question is easily answered (in fact, Irving Fisher had solved the problem before Hayek was born), which I take as evidence that Hayek did not understand the intertemporal equilbrium framework he proposed. Ludwig von Mises's approach to anything resembling disagreement or criticism was not to respond, but to spew bile and anger (hey, this approach seems to work for physicists), which leaves open the possibility that even if his formulation of Austrianism had a flaw, he wouldn't discover it.

Roger Garrison

As a result, I will be relying largely - but not completely - on Roger Garrison's easily understood and probably-not-entirely-stupid formulation from Time And Money. I thought this book was just the bee's knees, and anyone who likes pre-Lucas economics should check it out (preferably after you've read some less biased introductory stuff).

I will start where Garrison suggests but does not go, with a highly dis-aggregated production function. There are $$N$$ goods in the economy (let's not worry about innovation and entrepreneurship yet, we're gonna start with an "evenly rotating economy"). The production function is therefore is a vector function $$\vec{f} : \mathbb{R}^{+N} \to \mathbb{R}^{+N}$$. The quantity of outputs of each good is summarized in the vector $$\vec{Q_1} \in \mathbb{R}^{+N}$$ , the quantity of inputs of each good is summarized in the vector $$\vec{Q_0} \in \mathbb{R}^{+N}$$, the quantity of labor allocated to the production of each good is $$\vec{L} \in \mathbb{R}^{+N}$$, and the quantity of land allocated to each good is $$\vec{T} \in \mathbb{R}^{+N}$$. For each $$\vec{L}$$ and $$\vec{T}$$ fixed, I assume there is a unique stable growth path. I will assume these are fixed for the rest of this post and therefore ignore writing them over and over again. Around this stable growth path, the "means of production reproduce themselves" in Marxist language. I will call this the "golden path". That is,

$\vec{Q_1} = \vec{f}(\vec{Q_0}) \approx A \vec{Q_0}$

around the growth path for an all positive matrix $$A$$ (there are weaker conditions than positivity, I won't use them). By the Perron-Frobenius theorem, there is therefore a unique, positive, simple largest eigenvalue $$\lambda$$ with an all-positive eigenvector $$\vec{\lambda}$$. Obviously, the real interest rate is then $$r = \lambda - 1$$.

Every other eigenvector of $$A$$ has at least one negative component. One might think (with some allowance for vagueness and intuition) that any small deviation from the golden growth path will involve some eating of resources, which will eventually return the system to the golden path.

This is a loose, "Austrian" version of a Turnpike "Theorem". I put "Austrian" in quotes because a Marxist could accept it and "Theorem" in quotes because it isn't anything near a theorem. Let me pause to explain why I think it could be seen as Austrian. Let's say the initial quantity of goods $$\vec{Q_0} = a \vec{\lambda} + b \vec{v}$$, for $$a,b > 0$$ but $$b \ll 1$$. The initial quantity is "mal-distributed", the $$b \vec{v}$$ portion of the distribution is actually going to destroy some goods. But if the production function is iterated (i.e. the market is allowed to operate without interference), because $$\lambda$$ is the largest eigenvalue the system will eventually go back to the equilibrium growth path. This won't be caught by all aggregates (that is, non-negative scalar functions $$g(\vec{Q})$$ ), so using them to guide the economy might not be the best.

Trotsky

Let's pause for a moment. Now I think this is a good mathematical approach to von Mises's position, but I haven't yet captured the idea in its entirety. So far, there is nothing in the above that would ruffle the leather jacket of a loyal Communist leader. In order to complete this theory, one would need to describe the method by which final demand impute backwards to determine $$\vec{f}$$ and $$A$$. This imputation process is where the system becomes neoclassical and eventually perhaps distinctively Austrian.

Frederich von Wieser

The Austrian economist who completely developed this theory was Wieser. Through Frank Knight into Paul Samuelson, Wieser's method has been absorbed into mainstream theory as Linear Programming. There are many technical steps along the way, for instance, as Uzawa points out the opportunity costs of factors of production are not well defined in the general case (but downward opportunity cost - the shadow price of lacking a quantum of a factor - is, which allows him to save the theory). One of the victims of the explicit thinking through is probably "roundaboutness", "capital intensity" and other scalar measures of capital except as first order approximations. Dimension is conserved by continuous functions and Brouwer will not be mocked. Even when we aggregate, we must not do so willy-nilly.

Hayek Triangle

Well, then let's move to a more aggregated view. We measure aggregate output with some scalar function $$Y = g( \vec{Q} )$$. One good such function is $$g( \vec{Q} ) = min_i (Q)$$, $$g( \vec{Q} ) = \Sigma_i (Q_i)$$ another. According to our earlier view, if $$Q_0$$ is near the golden path, then after $$T$$ time units, $$Y = \lambda^T g(Q_0)$$, or just about. Since this is an aggregate, we can even look at real data. Let's look at a nice period of time with no recessions - the Clinton years (height of the New Neo-Classical Consensus)

Obviously, this isn't evidence of anything in particular, partly because the theory so far can fit everybody from Karl Marx and Joan Robinson through Paul Samuelson and Robert Solow all the way to von Mises and Hayek.

Hey yeah, what about that? So I sort of posited a capital theory that can be verbally described as maybe having some Austrian characteristics. What about the distinctive Mises Austrian macroeconomics - where is von Mises's idea that the dance of the dollar distorts capital structure and and is the sole cause of recessions/depressions/etc.? I've left out all discussion of money so far. It's been an "evenly rotating economy", if not a barter economy.

John Hicks

To continue further we need a money market and that for Garrison that means IS-LM. Garrison underrates the influence of his Keynesian schooling which he disliked as much as he overrates his Austrian enthusiasm which he liked. I think Garrison this gives the Austrian school more credit than they deserved by giving them the benefit of a post-war theory. The IS-LM analysis was not possible until after Keynes, General Equilibrium theory and probably much besides. Interestingly, IS-LM was invented by one of Hayek's students, the eclectic Sir John Hicks. I won't go into detail about IS-LM now, because I think that the Krugman description is basically right. One hitch for the uninitiated: most economists would say IS-LM is connected to the Keynesian Cross, but Krugman develops a model that works on nothing but neo-classical fundamentals and aggregation, so you might get confused if you use Krugman's advanced model and suddenly see someone object to a feature of the other model.

Irving Fisher

Hicks' IS-LM model is the second simplest possible money theory, but there is one simpler - the equation of exchange of Irving Fisher, Alfred Marshall etc.. This was the money model of the early neoclassicals, Mises very much included. When an Austrian tells you that printing money always leads to inflation and only inflation, they have this model in mind. I honestly doubt one could be "distinctively" Austrian with an IS-LM money model, and his use of this model explains to me why Garrison is able to approach Monetarist models when Mises and Hayek could not.

When I say "equation of exchange", I don't just mean $$M V = P Y$$ - where $$M$$ is the quantity of money, $$V$$ is the velocity of money, $$P$$ is the price level and $$Y$$ is real output - though that is part of it. I mean the pre-Keynesian, pre-Friedmanian classical and neo-classical understanding of those variables as functions of the deeper economy. This isn't quite what the Austrians thought, but one must begin at the beginning. That understanding is as follows:

The meaning of $$M$$ has remained unchanged and vague. The velocity of money $$V$$ is best understood as $$V = \frac{1}{k}$$, where $$k$$ is the portion of real output that people want to save (Garrison - and, well, everyone - represents this with a PPF curve). This is a deep and unchanging fact about human nature, society, etc. As before, aggregate output $$Y = g( \vec{Q} )$$. The price level $$P$$ adjusts more or less rapidly to changes in $$M$$. (Without a definition of the price level, one may not even talk about inflation.)

So the ultra-classical theory of money contains two variables and two constants. It could be better written $$\frac{M}{P} = k Y = const$$ - verbally, "The real amount of money is equal to the amount of savings, which is a constant.". The problem with this ultraclassical theory is in the second equation $$k Y = const$$. The problem is called the Lucas Critique, first pointed out by Keynes. There is no actual theory of which k is chosen, other than that it is related to something deep and immovable. Keynes pointed out that it should be affected by the interest rate, which is agreed upon by Garrison's PPF diagram. The point on the PPF diagram is decided by the IS-LM equilibrium. So one can see Garrison giving a Keynesian innovation to the Austrians for free isn't without consequence. Garrison's system fixes $$k$$ - and therefore $$V$$ - by using a general equilibrium framework in a way that was missing from pre-macro "macro".

Ludwig von Mises

Okay, okay. What does all of this have to do with Edler von Mises? Well, von Mises was not one of those who left the sentence "The price level $$P$$ adjusts more or less rapidly to changes in $$M$$." alone. In fact, von Mises believed that "price level $$P$$ ... less rapidly to changes in $$M$$.". Remember that the real interest rate is determined by the structure of the highly dis-aggregated production function - the capital structure. This is the same in all markets, including money. But von Mises believed that it was difficult for practicing capitalists to tell the difference between a temporary mistaken change in the money or bank interest rate and the underlying true interest rate. Some entrepreneurs mistakenly switch to a technique only viable at the bank rate of interest (which drives $$Y$$ up), but then get stuck when the interest rate inevitably returns to the unique real interest rate (which drives $$Y$$ down). Overshooting causes a boom-bust business cycle. The only thing that can be done during the bad times is to let the mistaken entrepreneurs liquidate and purge the unstable techniques. This, I think, completes the basic overview of what is distinctive about Austrian economics as I understand it.

So what is wrong with this, if anything? I can think of four objections:

First of all, it's hard to develop realistic examples of this kind of reswitching, since reswitching takes place in logical space and not temporal. That is, von Mises and the others (Joan Robinson etc.) treat the loans behind the choice of technique as if they were constant interest rate loans, then make the interest rate vary - it's no surprise that the outcomes are paradoxical! Why haven't modern banks innovated loans that are aware of the dance of the dollar (you can really tell I love saying that)? As far as I am aware, Austrians simply haven't thought this out very well, but I could be wrong - they write an awful lot of words.

Secondly, von Mises's system assumes that the government can fool people in predictable ways, but you can't fool all the people all the time. If the government tries to take advantage of the "drives $$Y$$ up" part of the Austrian business cycle during election years (and Austrians claim that they always will! They don't though), why can't people figure that out? A vague place for expectations is a huge flaw in any intertemporal system, and Austrians are all about how cool an intertemporal their system is. While on this subject, von Mises assumes that $$M$$ is determined willy-nilly, not by a policy rule. Both of these are considered severe limitations in modern economics, which has gone a long way to treat them (not long enough!).

Thirdly, von Mises seems to assume that it is obvious that the direction of causation is from the means of production onto the monetary superstructure (again, using Marxist language). But, if the Daishogun declares that on pain of death the inflation rate shall be 2% and the nominal interest rate will be 5%, then eventually the capital structure will move to make the real interest rate 3% and not the Daishogun. This, arguably, is what we are seeing in the Euro Area right now. In other words, von Mises was positing a particular institutional structure (perhaps strong neo-liberalism with skittish bankers) without being explicit about it. I don't know if this is a criticism, since Austrians feel that Austrian-style institutions would be a boon...

Fourthly, we can return to the theory of positive matrices in the dis-aggregated production function. Recall that all the vectors leading away from the golden path have negative entries. I interpreted this loosely as meaning mal-distribution eats away resources (or, at least, does not produce as fast). The golden path is unique in not doing so. Therefore, we might expect mal-distribution not to create a von Mises style boom-bust cycle, but rather a Friedman style plucking model. I'm not sure that this objection holds water on a mathematical level, but examining linear algebra and the theory of positive matrices would be worth doing.

Well, I'm sure much of this has been covered before and better, so I'd be happy to take any useful comments you might have. I'd be particularly interested in demolitions (or demonstrations) of the first and fourth objections, or even just a numerical working through of the fourth objection. I hope it is clear that I am not unsympathetic to Austrian Economics, even if I don't yet think that it is as all-fired great as Garrison does. The question in the title is one that I am asking you, not one that I want to explain!