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Tuesday, May 13, 2008

The Evolution of the "Economic Web"

One of the editors at Scientific American brought this to my attention, and he is hoping to receive feedback. This is part of their "Edit This" series. The idea is that they post a draft of an article they plan to print in a future edition of the magazine, then incorporate feedback into the the print version:

Tell us your reactions to the arguments made in this piece. Your feedback will be incorporated into a version of this article that will appear in a future print issue of Scientific American.

The article itself, "which is sure to raise the hackles of some members of the economic community," argues that economists cannot explain the relationship between innovation and growth, and proposes a "grammar model" as an alternative to traditional growth models:

The Evolving Web of Future Wealth, by Stuart Kauffman, Stefan Thurner, and Rudolf Hanel, SciAm: ...Perhaps the most stunning feature of the economy over time is the explosion of goods and services. Yet contemporary economics has no adequate theory to understand this explosion or its importance for economic growth and the evolution of future wealth.

My first reaction was that we do have models of variety and growth:

Optimal Product Variety, Scale Effects, and Growth, by Henri L.F. de Groot and Richard Nahuis: ...Product variety is an important determinant of economic welfare. Following the seminal work by Dixit and Stiglitz (1977), and Spence (1976) the welfare effects of variety have been analyzed from various angles.[1] ... With the presence of economies of scale in production, producing a small variety saves resources that can be used to extend the production volume. Hence a trade-off arises... It turns out that the market supports too low product diversity. Subsequent studies addressed the optimality question in the presence of growth. In a dynamic context, reduced variety not only saves resources that can be used for extending the produced quantity, but potentially also to increase the rate of growth. Grossman and Helpman (1991, chapter 3) analyze welfare in a model of endogenous growth. In their analysis, there is (continuous) growth in product variety resulting from investment in R&D. The more labour an economy allocates in the R&D sector, the less labour remains for producing consumption goods. The question here is one of growth in variety versus volume of consumption goods. The optimal trajectory entails more rapid growth of variety than the market equilibrium sustains, as firms ignore the contribution of their knowledge creation to a common ’knowledge pool’. Grossman and Helpman (1991) also analyze a quality ladder model. ... Here innovative effort aimed at quality improvement might be suboptimal high or low, depending on the size of the quality step. Van de Klundert and Smulders (1997) develop an endogenous growth model in which, contrary to Grossman and Helpman (1991), R&D is an in-house activity aimed at improving quality. Besides quality growth, variety is also determined endogenously. ...

The studies discussed so far assume that variety has a direct effect on consumers’ welfare as consumers have a love for variety. Another branch of literature looks at the productivity effects of increased product variety...

And as footnote 1 notes, "In the overview..., we have no pretension of being exhaustive," so this is by no means all of the work on this topic. But these models don't, as far as I know, explain how new innovations and variety arise, and that is one of the things the Scientific American article is trying to do (though I'm not sure it is fully successful, the model produces broad statistical relationships that predict how frequently innovations ought to occur, but is not precise about the types of innovations that will arise). Back to the article:

Economic growth theory is highly sophisticated about the roles of capital, labor, human capital, knowledge, interest rates, saving rates and investment in existing economic opportunities, or investment of savings in research to find novel goods and services. Yet the major conceptual frameworks that undergird contemporary economics (competitive general equilibrium, rational expectations and game theory) share a crucial failing. They assume that all the goods and services (as well as the relations between them) and all the strategies for engaging with them in a local or global economy can be "pre-stated"—that is, known in advance. In reality, novel goods and services may constantly enter markets, thereby requiring economic actors to develop ever more novel strategies: all the relevant variables cannot be pre-stated.

Thus standard growth theory misses an essential feature of this "economic web" of goods and services. Even more important, as we shall explain, it ignores the role that the structure of the economic web itself plays in driving the creation of novelty and the evolution of future wealth. ...

The ways goods and services come to be used together in the real economy may not be describable in advance... Because it is impossible to identify all the preadaptations and potential economic uses for goods and services, it is impossible to finitely prestate all the possibilities for them. This conclusion has profound significance: it means that predicting future innovations is fundamentally incalculable, even on the basis of probability because no probability distribution can be assessed without knowing the range of possible outcomes. (And beyond economics, this principle may have equally radical consequences for much of the rest of science [see sidebar].)

Decision theory—the tool of management that suggests making optimal choices by summing discounted future values over the probability distribution of all possible outcomes—is of limited usefulness, as are businesses' five-year plans. ... Business, like life in general, is an art wherein we must use reason, intuition, emotion, metaphors, models, case studies and more to guide ourselves. Business is not a calculus. Thus, economics can only partially be a calculus, and a much broader conceptual framework is needed.

The Economic Web A screw and a screwdriver are complements, used together to create value by, say, fastening two boards. A screw and a nail are largely substitutes: loosely speaking we can use one where we use the other. Now imagine all 10 billion or more distinct goods in the contemporary global economy as points in a large three-dimensional space. Join complements by green lines and substitutes by red lines.

This network is the economic web. We do not know its structure, but it exists. It evolves over time, although we know little about how. Do statistical laws govern its evolution? Are firms located near the center of the web (say, automobiles or computers) in a strategic situation different from those on the periphery, such as hula hoops?

The web of complements to a good forms a mutually self-reinforcing and cross-reinforcing subnetwork that enhances its own economic growth. For example, with the car came its complements, among them gasoline, paved roads, motels, fast food restaurants and suburbia. In turn suburbia gave rise to an enormous number of consumers of automobiles, gasoline, paved roads and so on. We might call such mutual cross-enhancement "collectively autocatalytic,"... In economic terms, we might call them collective webs of mutually positive "externalities" between complementary technologies. ...

In contrast, consider the hula hoop, which appears to have few complements. It may have made money for its producers, but it sparked no lightning in the form of complementary technologies or products that collectively drove an explosion of wealth. The hula hoop could come and go with little effect on the economy.

The preceding observations show why we must come to understand the structure, evolution and roles of the economic web. Of course, it is people who invent novel goods and services, but the structure of the web itself singles out where invention and investment are likely to yield a profit and drive growth.

Two further features of the web make us suspect that the diversity of the economic web drives its own growth autocatalytically. First,.... The more goods and services that exist in the economy, the more recombinations among them are possible. ...

Second, new goods and services typically enter the economy as complements or substitutes for existing goods and services. Call the set of goods and services that are complements or substitutes to a given good or service its economic niche. As the web grows, does it create new niches faster than it creates new goods and services? The general answer is not known, but the very large number of complements to the automobile and computer noted above, with their mutually cross enhancing externalities, suggest that the average number of new adjacent complements and services created per new good or service is greater than 1.0.

If so, then the growth of economic niches is indeed autocatalytic. The more goods and services that exist, the higher the diversity of the economic web and the faster the creation of new economic niches. Thus the very diversity of the economic web is almost certainly a major factor in creating the conditions for its own further expansion.

We do not yet know whether that is so, nor whether the average number of novel niches created per new good has changed since 50,000 years ago. Economic historians can discover the truth. But in the meantime, we note that these issues are not yet part of economic theory, and may be major, largely overlooked factors. If so, they may have practical implications and deserve detailed examination.

An Algorithmic Model There are profound reasons that the structure and growth of the economic web is not part of current economic theory... What algorithmic model can describe unforeseeable Darwinian preadaptations in the economy? There may be none.

The hope of finding a mathematics that could describe and predict how novel goods and services unfold as the economy evolves into its adjacent possible thus seems precluded, at least at present. But even if the growth of the economy is not algorithmic, an algorithmic approach may still be of use in finding statistical features of model economies for comparison to the real one. Crucial here is the enlargement of the current framework: a concept is needed to mathematically tame the "adjacent possible."

One such approach is a "grammar model" that represents goods and services with binary symbol strings... Within our model, the number and diversity of the strings can stand for renewable resources, appearing each year. Symbol strings can act on one another to create new symbol strings. ... A "grammar table" lists all the pair rules for these transformations. This arrangement can simulate a simple economic production function.

Intuitively, one sees that if the starting (and renewable) number of strings is small, that their diversity is low and that the grammar table has few pair rules, symbol strings will probably not be able to act on one another and few novel symbol strings will be created. We call such behavior subcritical. A subcritical economy cannot generate a growing diversity of goods and services. On the other hand, studies show that as the number of pair rules, resource strings or both increases, the system can abruptly transit into a supercritical domain where a large—perhaps unending—diversity of symbols strings may be generated. We call this explosion of goods and services supracritical. ...[...continue reading...]

Quick reactions are dangerous, but I'm going to do it anyway. It's not hard to believe that when there are a lot of complementary objects in close proximity, they can be combined in many, many ways, some of which will be highly valued. It's also believable that what can be produced from novel combinations depends upon what already exists, i.e. there is path dependence to use the term from economics for this. That there is a critical number of connections required for innovative activity also seems reasonable.

But the web does not form exogenously, and the underlying economics has a big impact on its evolution. For example, agglomeration economies induce firms with complementary goods to locate close to each other - when a manufacturer comes to town, a company that produces packing materials for shipping the good may open nearby, and these decisions, when made by many firms, concentrate human and physical capital in close proximity, and this can set the stage for further innovation. (People with substitutes will also locate strategically, usually far apart but not always). What seems to be missing from this from my quick reading of it is the main topic of the research - the economics - and how price and expected profit signals determine how the web is organized, which innovations are pursued, etc. The decisions of agents, where to locate, what goods to buy, which ideas to pursue, determine the structure of the web. It is not an exogenous process that can be imposed upon the economic system, and the endogenous evolution of the web seems to me to be the important - and unanswered - question.

In a way we mathematically benefit from our profound ignorance of the real economic web's detailed structure because it forces us to model the catalytic network as basically random.

But is it "basically random"? That's where my questions begin.

    Posted by on Tuesday, May 13, 2008 at 12:33 PM in Economics, Science | Permalink  TrackBack (0)  Comments (43)

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