(Complex?) Thoughts on Heterogeneity and Complexity; Quality and Quantity

|Peter Lewin|

Considering the concept of heterogeneity throws light on the relationship between quantity and quality.

All observation and explanation proceeds on the basis of classification (categorization). Phenomena are grouped into categories according to our perception of their essential similarity (homogeneity). The elements of any category (class) might be different in some respects, but in all respects that ‘matter’ to us they are identical. Items within a particular category can be counted, quantified. The ability to quantify is crucially dependent on being able to count items in this manner. The number and type of categories (variables) is known and fixed. Thus, the arrival of a new category cannot be accommodated within a scheme of simple quantitative variation and must be considered to be a change in quality. Qualitative differences are categorical differences.

All quantitative modeling proceeds on the basis of the assumption that the individual elements of any given quantifiable variable are identical (homogeneous) and are different in some important respect from those of another variable. Variables are essentially distinguishable categories. In addition the elements of a quantifiable category do not interact with each other – else they could not be simply counted. Each element is an independent, identical instance of the class. (Most obvious is the case of ‘identical randomly distributed variables’). This does not preclude the elements themselves being complex – being the result of lower-level interactions, like identical molecules or biological cells, which are incredibly complex phenomena.

We may think of this in terms of structure. Structure implies connections/interactions. A structure is composed of heterogeneous items that are more than simply a list of those items. There is a sense of how the heterogeneous items work together to ‘produce’ something. (We see here how a capital-structure is both a metaphor for and a particular case of the phenomenon of complex structures in the world.) A structure is an ‘order’ in Hayek’s sense, in which it is possible to know something about the whole by observing the types and the ways in which they are related, without having to observe a totality of the elements. Structures are relational. Elements are defined not only by their individual characteristics but also by the manner in which they relate to other elements. These interactions are, in effect, additional variables.

Thus, though the elements of a quantifiable category may be unstructured, these elements may be composed of structured sub-elements. This is the basis of the phenomenon of modularity. Self-contained (possibly complex) modules may be quantified. This dramatically simplifies the organization of complex phenomena, as has been noted in a fast growing literature on the subject. Modularity is a ubiquitous phenomenon in both nature and in social organizations. It is an indispensable principle of hierarchically structured complex systems. The benefits of modularity in social settings include the facilitation of adjustment to change, and of product design, and the reaping of large economies in the use and management of knowledge (see for example work by Baldwin and Clark 2000, Langlois 2002, 2012) and it is clearly an aspect, perhaps the key aspect, of Lachmannian capital-structures. Capital-goods themselves are modules, which are creatively grouped into capital-combinations which constitute the modules of the (non-quantifiable) capital-structure.

Returning to the theme of the relationship between quantity and quality, quantitative modeling works when both the independent and dependent variables are meaningful, identifiable quantifiable categories that can be causally related. The model ‘works’ then in the sense of providing quantitative predictions. The inputs and outputs can be described in quantitative terms. But, when the outcome of the process described by the model is a new (novel) category of things, no such quantitative prediction is possible. Ambiguity in the type and number of categories in any system destroys the ability to meaningfully describe that system exclusively in terms of quantities. We have a sense then of the effects of heterogeneity. Variation applies to quantitative range. Heterogeneity (variety) applies to qualitative (categorical) range. Diversity incorporates both, but they are significantly different. Heterogeneity may not be necessary for complexity, but heterogeneity does militate in its favor. For example, compound interaction between quantitative variables (categories) can be an important characteristic of complex systems, but complex systems are likely to result from substantial heterogeneity, especially where heterogeneity is open-ended, in the sense that the set of all possible categories of things is unknown and unknowable.  

Heterogeneity rules out aggregation, which, in turn, rules out quantitative prediction and control, but certainly does not rule out the type of ‘pattern prediction’ of which Hayek spoke. In fact, erroneously treating heterogeneous capital as though it were a quantifiable magnitude has led to misunderstandings and policy-errors, such as the those associated with the connection between investment and interest rates - errors that could have been avoided with a better understanding of capital heterogeneity and its effects. The capital-structure is complex, but it is intelligible. We can understand and describe in qualitative (abstract) terms how it works and render judgment on economic policies that affect it. And, as a result of Hayek’s insights into complex phenomena, we have an enhanced appreciation of what is involved.

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Baldwin, C. Y and K. B. Clark (2000), Design Rules (Cambridge, Mass.: MIT Press).

Langlois, Richard N. (2002), ‘Modularity in Technology and Organization,’ in Entrepreneurship and the Firm: Austrian Perspectives on Economic Organization, N. J. Foss and P. G. Klein, 24-47. Aldershot: Edward Elgar,.

Langlois, Richard N. (2012), ‘The Austrian Theory of the Firm: Retrospect and Prospect,’ Review of Austrian Economics, forthcoming.

 

Comments

[Greg Ransom]

Nicely done Peter.

[Allan Walstad]

"All observation and explanation proceeds on the basis of classification (categorization)."

That's a "categorical" claim, one which I see no compelling reason to believe and which is not necessary to the valid (and well-understood among Austrians) points regarding the importance of capital heterogeneity and the failure of policy prescriptions that presume homogeneity.

If I look at the car speedometer and it says "60 mph" how is that observation usefully characterized as having proceeded on the basis of classification? How is any causal-realist explanation (such as "the thief was able to enter because the door had been left unlocked") to be said to have proceeded on the basis of classification?

[Alex Salter]

@Allan: I think the answer comes from unpacking higher-order concepts like "60 mph" and "the thief." Break them down into their constituent parts and you'll eventually get to the whole genus/differentia thing that is, unless I'm mistaken, the metaphysical basis for Professor Lewin's claim.

[Peter Lewin]

Yes Alex is correct. Unless you classify all of the unique things that you see into categories (classes), you cannot even begin to make sense of the world. All thought and language does this. The fact that these categories are shared with others, allows us to communicate. (Hayek's Sensory Order and many other works.)

[Jeffrey Friedman]

If you are going to post things that are this good, please give us the ability to print them out!

[Peter Lewin]

@Jefferey: I think this is directed at the hosts of this blog - since it is beyond my control. I think you mean they should provide a print-function link as many web sites do. That would be nice. Otherwise cut and paste works :-). Glad you liked the post.

[Roger Koppl]

Peter,

I'm not sure I know what your post implies for Austrian capital theory. If the capital structure is so complex, then perhaps the relatively simple models of Bohm-Bawerk and Jevons are suspect? But then what happens to ABCT? I think Hayek pretty much admitted that his theory of capital was a mess (Hayek on Hayek p. 142). He points favorably to Lachmann, but I'm not sure how that book supports ABCT.

[Barkley Rosser]

A very well-though and written post, Peter. Congratulations. My only substantive addition is to note that this matter of qualitative change is a very deep issue/question that is not easily resolved. How do we know when we see a qualitative change that we really are seeing one. There are plenty of classic and nice examples of phase transitions in the physical world that are pretty clear cut, such as the old Hegelian chestnut about the freezing and boiling temperatures for water under normal atmospheric pressure. But, to take an example that lurks beneath a lot of current discussions in economics of all sorts, have we seen a qualitative change in our economic system since the financial crash/crisis of 2008?

On capital theory, I second Roger Koppl's observation regarding Hayek and heterogenetity.

[Allan Walstad]

I tried plowing through Sensory Order several years ago, and of course it may be that I lack the candlepower to grasp the point. Nevertheless, I asked above, in regard to two very simple examples, how they are usefully understood as having proceeded on the basis of classification.

Alex Salter: "Break them down into their constituent parts..." Please demonstrate with regard to one or both of the examples. Do you think that people need to read Hayek's Sensory Order to understand that capital is heterogeneous, that how it fits together is vital, and that policies premised on homogeneity are missing something important? I don't see how anybody who questions the Austrian emphasis on heterogeneity is likely to be persuaded by the assertions with which Peter leads off his post.

[Peter Lewin]

Thanks Berkley, I need to think about this. The phenomenon of "category killer" is well-known in the marketing world, but it would be interesting to see how quality-quantity manifest in people's consciousness more generally.

@Roger: This is the trillion dollar question, one which I have asked and answered in different ways over the course of my career as an Austrian economist. I have said that it is possible (and inadvisable) to take the ABCT too literally. Hayek felt constrained to work within a formal framework - to provide a tangible model - so he constructed the triangle interest-rate story. In the middle period of his life he distanced himself from this particular form and spoke of cycles in much more abstract terms. He was particularly concerned about the effect of labor-union wage demands leading to economic policy that distorted the production structure. Here, the interest rate played a less mechanical role. Mises's approach was always to claim that the details of cycle were unique and complex.

So, I think you are correct. ABCT has drawn a lot of fire in its simplistic form - a form easy to discredit. But that form is not embedded in a world of complex phenomena. (I think Dick Wagner's work - starting with the Wheat-Chaff essay - is highly relevant here). The question of the effects of monetary expansive government spending has to be considered in the context of a complex world - a highly specialized, changing, dynamic economy.

A full answer would require (at least) another lengthy post (even longer than this has become), but, I will say just this. My current understanding of and appreciation for the ABCT proceeds on the basis of intuition and a set of empirical claims.

1. The market economy is inherently stable. This is a huge claim. In effect it means that the processes of the market are complex adaptive systems. I include in this the capacity to generate stable social institutions under the right circumstances as well as the capacity of the market process itself, functioning within the framework of facilitating social institutions (property, contract, money, ... ), to generate value-creation (economic growth) through investment and innovation. The latter can be better understood in the context of my post - innovation takes the form of the introduction of new "categories." We don't know exactly how the liberal social order achieves this stability and growth - this capacity for complex adaption - if we did we would not need the market, right? But things like network-effects provide some clues.

2. Inject into this a big-player (from whom did I learn that term?) policy of money-fiscal expansion. This adds to the noise of the system and disturbs its adaptive capacity - "distortion." Cognitive processes are relevant. Whence do economic agents get their signals in the market process? Clearly this adds an element to the loan market. An example is the dot.com boom-bust. Interest rates started to rise as the boom accelerated. The Fed injected money to keep down the price of loans, so as not to short-circuit the boom. But this obscured the "real" price of loans. In the absence of this, the loan-makers were forming a judgment about the viability of the projects they were financing - many of them involving high levels of innovation - and as book values started to rise became justifiably nervous. The Fed initiative essentially provided an underwrite to their fears causing them to gamble where they otherwise would not. This is not controversial. At the top of the boom everyone knew that it was unsustainable, they just did not know when it would burst and many did not want to get out too soon. People understood that many of the specific investments, whose profitability, depended on the lack of profitability of alternative specific investments (for example, new product offerings with specific standards)were losers and would have to be abandoned (bankruptcies, restructuring, asset sales, etc.), they just did not know which. (How could any government agent know? Keynesian policy suggests this type of thing does not matter).

3. This kind of story is augmented by a host of claims from the public-choice perspective and from the central-planning-calculation perspective. There are formidable knowledge and incentive problems attached to Keynesian policies. I guess another way of saying this is that discretionary government policies of this kind are not complexly adaptive. In stark contrast to decentralized agent-based actions, government agents proceed in a tainted, low-powered-incentive environment. Incentives are perverse in the sense of amplifying rather than dampening diversions, and signals about what to do are at best highly ambiguous. At some level the entrepreneurial public knows this.

4. The policy thus causes the cycle, influences its magnitude and prevents recovery.

I need to stop. This is the way I see it now.

[Peter Lewin]

To see much more on Hayek and heterogeneity go here:

http://www.utdallas.edu/~plewin/Hayek%20and%20Lachmann%20final.pdf

[Roger Koppl]

Peter,

Nice reply. And I think we are pretty much on the same page. Please allow me to pick up on one point, however.

I don't think the argument for laissez faire requires the claim that "The market economy is inherently stable." The issue is what the state can do about such instability as may exist. We probably have about the same opinion of the state's ability to stabilize the economy, namely that any such effort is likely to do more harm than good. And I think "Austrian" arguments help to show why. If we can't do much to stabilize the economy, then we need to ask about relief measures such as unemployment insurance. On this topic we might disagree, at least if I am not mistaken to think that you are more libertarian than I. I am totally for social insurance, just as Hayek was in The Road to Serfdom. But even if you don't like policies of that sort, you would probably concede that they are not such great departures from laissez faire and do not compare with some of the regulatory apparatus in the US.

Rather than asking if "the market" is or is not "stable," we should ask which policies promote stability and which reduce stability. Until we have the right policy mix to ensure a high degree of stability (or whatever), we should probably not abandon all welfare state measures. I kinda think that our maximal possible level of stability is not so high as to make the welfare state otiose. All that depends, of course, on my rejection of libertarian deontology in favor of a more consequentialist ethics. But I think you could be a pretty hardcore Rothbardian in ethics and still accept my point about the *relative* stability of different policy regimes. We should look at relative stability and eshew hard-to-prove statements about the absolute stability of "the" market economy.

[Peter Lewin]

@Roger: Hmm. Food for thought. I pretty much accept what you are saying. Yes I am definitely more libertarian than you. But I think our approach is the same. I am no Rothbardian. I am a Yeagerian consequentialist. I think we would differ on the empirical question and on where we put the burden of proof. My libertarian commitments are expressed in where i put the burden of proof. I always put it on those who would interfere in people's free choice. I consider the case for unemployment insurance to be, at best, unproven.

But, we libertarians, I believe cannot run away from judgements conditioned by the status quo. We cannot, as some do, simply reject all policy proposals on the basis that they are, by libertarian ethical standards, compromised. To state the obvious, the actual choices we face are not between the ideal and the imperfect; they are between what we must grade as degrees of imperfection. So, I find myself agreeing with much of what Milton Friedman said - for example on school vouchers, negative income taxes, privatization of social security, etc. even thosgh these are not my first-best alternatives. This is NOT a matter of ethics, or even ideology; it is a matter of strategy. I understand this means, for these policies to stand a chance of success, we must have different constitutional constraints, and that this faces the kind of incentive problems previously alluded to. Friedman hoped that simplification (replacing the thousands of entitlement programs by just one, simplifying the tax code, simplifying the health-care system, etc.) would provide support for the kind of constraints we need. But he, and I, and most people realize this is unlikely.

On the question of the "stability" of the market. OK, what you said. But, we have to be careful. I think there is a qualitative difference here. There are complex feedback mechanisms that work in the decentralized private sector that do not work in government - in fact, where the opposite type of feedback is at work. The market system is stable in the sense that it is peaceful (for the most part - non-coercive) and creates value. The government system is exactly the opposite. That is what I would claim.

[McKinney]

Peter, I really enjoyed your paper on Hayek and Lachmann. Although I find the epistemological and methodological aspects interesting, I prefer applied economics and the implications for it.

I agree that Lachmann took disequilibrium economics about as far as can be done with this caveat: he took it as far as can be expected for a general theory. Others have taken it further, but are not economists. They are professionals.

Skouzen in his "Structure of Production" suggests such when he points out that many professions exhibit marks of the Austrian business cycle theory without knowing it. For example, professional investors have long divided stocks into cyclical and secular. Cyclical stocks generally are capital goods/services produceers, Caterpillar being typical. Secular stocks tend to be consumer goods/services producers with Walmart as the example. Cyclical stocks are high beta and secular low beta. You make money in cyclical stocks and seek refuge in secular ones. Diversifying across asset classes is another example.

An investment advisor I follow actually uses a ratio of the price of Caterpillar to Walmart as an indicator of the direction of the market.

I know business people who invest only in the depths of a depression when businesses are failing and can be purchased for pennies on the dollar. They pile up cash during booms in order to buy during busts. One of my grandfathers had a sixth grade education but became financially well off buying foreclosed farms at auction during depressions and selling them in smaller parcels during booms.

I think dynamic economics is too large and complex for a general theory beyond what Lachmann developed. Any further progress has to happen in specific fields, such as labor, business or financial economics, and much of that has been done, as Skouzen suggests, by applied economists in those fields.

[McKinney]

Roger, Of course we have to ask why is the goal stability? Except for the occasional famine, medieval economics were stable. So were the economies of the USSR and China under Mao. Stability is not that difficult to achieve.

Of course no one wants such stability because it means grinding poverty. The real question is how to achieve increased wealth in as stable a manner as possible.

As for the welfare state measures, too often proponents of welfare measures imply that without the state those victims would simply starve to death. I'm not saying you think this, but that tends to be the tone of most discussions on the subject. Wages would be less sticky without unemployment insurance and therefore recessions might be shorter and less severe.

Of course, smarter monetary policy would limit the length and severity of recessions and make unemployment insurance less necessary.

[Roger Koppl]

McKinney,

Yes on all points, I think.

Stability is a goal, but not the only goal. Sure, yes.

Like you, I don't see where folks here in the US would be literally starving without "welfare," no. Although there seems to have been serious malnutrition among America's poor before LBJ's dubiously named "War on Poverty." And in general, I would not wish to minimize the sufferings of the unemployed. Think of the guy who just shot his ex-boss near the Empire State Building. Whatever might be going on in that particular case, certainly there are cases in which people turn desperate after losing their jobs. Unemployment relief pushes in the opposite direction, though at the cost, which you note, of wage stickiness.

As for monetary policy, you are certainly right IMHO to say that better policy makes for less frequent or severe recessions. I bet you would agree with me, however, that it is not so clear how good monetary *policy* can be. That is, without some sort of relatively rigid constitutional constraints on the monetary authorities, we probably cannot hope for that much wisdom or restraint in monetary policy. Better to have some sort of commodity standard or, for many countries, currency board, or something like that. Best to have "free banking" a la Horwitz, Selgin, White, and others.

[Troy Camplin]

What happens when positive feedback dominates in a complex (i.e., heterogeneous) system/process?

ABCT is a description of positive feedback in a complex/heterogeneous system/process. "Cheap money" acts as positive feedback. So I would argue that ABCT is (generally) correct precisely because capital is heterogeneous, and capital heterogeneity is one of the precise reasons why the economy is a CAS.

[Peter Lewin]

@Troy. There is probably a lot more that could be said about this. I think we know, more or less, why stable institutions emerge (looking back) - because of network effects - the signals that each individual gets push his behavior in the direction of more coordinated action (the more people accept a particular money, the more people accept it; the more people use a particular language, communication protocol, legal system, ..., the more people use it, and expect others to). Clearly something like this operates in the market process as well - Adman Smith's invisible hand - but, as far as I know, we don't have a good account of the details - except to assume that the price signals are accurate enough (Hayek 1945). But, in disequilibrium (inconsistent expectations), this may not be the case, in theory. And, more importantly, in the market process we NEED to be able to accommodate mistakes, and lots of them, if we are to have progress (trial and error). How come it works so well in practice? That is the true miracle :-).

[Joshua Wojnilower]

Peter,

Fantastic post and discussion. I look forward to reading your paper mentioned above.

Your thoughts complement well a post from Synthesis about chaos versus complexity. I combined thoughts from both here: http://bubblesandbusts.blogspot.com/2012/08/macroeconomics-could-benefit-from.html.

Hopefully economics will continue moving in the direction of applying complexity to understanding systems.

[Peter Lewin]

Thanks Joshua. I look forward to reading it.

[Troy Camplin]

PEter,

I'm curious what you think of these musings of mine on prices in a far-from-equilibrium process:

http://zatavu.blogspot.com/2012/05/bipolar-feedback-prices.html

[John]

One way I like to quantify what's happening to inter temporal prices is by trying to tease out the changes in inter temporal prices from different indices, my favorite by measuring the change of the CPI over the PPI. The Austrian story of consumer prices rising relatively during busts holds, though prices usually fall everywhere due to money destruction.

http://research.stlouisfed.org/fred2/graph/fredgraph.pdf?&chart_type=line&graph_id=&category_id=&recession_bars=On&width=630&height=378&bgcolor=%23b3cde7&graph_bgcolor=%23ffffff&txtcolor=%23000000&ts=8&preserve_ratio=true&fo=ve&id=CPIAUCSL_PPIACO&transformation=pc1_pc1&scale=Left&range=Max&cosd=1913-01-01&coed=2012-07-01&line_color=%230000ff&link_values=&mark_type=NONE&mw=4&line_style=Solid&lw=1&vintage_date=2012-09-01_2012-09-01&revision_date=2012-09-01_2012-09-01&mma=0&nd=_&ost=&oet=&fml=a-b&fq=Monthly&fam=avg&fgst=lin