Batten proposes the following distinction between simple and complex economic systems: "By and large, simple economic systems are homogeneous and weakly interactive. Individual beliefs and expectations must be sufficiently uniform, and the level of interactions sufficiently weak or trivial, for us to be able to predict collective patterns of behavior with any confidence. ... By way of comparison, complex economies are heterogeneous and strongly interactive. They lie beyond the point where individual behavior can be discerned with any degree of confidence (see Figure 3.1). ... A complex economy is never additive. It behaves quite differently from what we'd expect by simply adding up these pairs, trios, and quartets of interaction. Self-organizing economies are not additive; they're emergent. This is precisely why some of the collective behaviors can't be predicted in advance."
This discussion by Batten blends the idea of "predictability" with possible factors (heterogeneous expectations, strong interaction effects, non-additivity) that might make prediction difficult. For reasons clarified below, a more rigorous and useful way to define the difference between "simple" and "complex" economic systems would seem to be to focus on the degree of predictability per se. A secondary issue then arises: Which system features (if any) systematically affect the degree of predictability? Proposed definitions for "simple" and "complex" systems along these lines are outlined below.
Suppose a dynamic economic system can be simulated subject to controlled experimental conditions. That is, starting from any feasible initial state, the system can be run multiple times and its observed outcomes recorded. Call the economic system simple if, starting from any given initial state, the observed outcomes of multiple runs of the system have a central tendency distribution, in the sense that there exists a unique "attractor" (most likely outcome) around which the observed outcomes tend to cluster. In this case, the system structure (the initial state) determines a reliable "point prediction" for the system outcome: namely, the unique attractor corresponding to the initial state.
In contrast, call an economic system complex if, starting from any given initial state, the observed outcomes of multiple runs of the system have a spectral distribution with two or more distinct attractors around which the observed outcomes tend to cluster. In this case, the system structure in and of itself does not determine a reliable point prediction of the system outcome.
Batten points to the following phenomena which he claims are indeed causing the global economy to become strongly interactive: Rising levels of international trade; Increased "foreign direct investment" (i.e., increased foreign ownership of domestically located productive assets); Rise of "multinational" (i.e., multi-country owned) corporations.
On pages 96-98 he discusses an example to support his thesis. He asks: Who actually stands to gain most from increased beef exports from America to Japan? He visualizes the possible relationships by means of signed digraphs (Figures 3.3 and 3.4).
Below I have combined and extended Batten's digraphs to a single signed digraph that more fully reflects Batten's accompanying text discussion. The following assumptions are made for illustration only, to illustrate Batten's points about possible complicating effects. (It would be interesting to see actual empirical data related to these effects).
The nodes of the modified digraph are as follows:
--------------------- JConsBeef --------------------- /|\ /|\ +1 | | +1 | | +1 \|/ -1 \|/ +1 -------------- X<------ JConsBA ----- JConsBJ ------> ProdBeefJ ------> | -------------- -1 | +1 +1 | +1 | | | | \|/ IncJRJ IncARJ ExpABeefJ | | | +1 \|/ +1 \|/ | -------------- +1 | ExpGrainAJ | -------------- | | \|/ +1 | --------------- +1 \|/ ProdBeefA -----------------------> ProdGrainA --------------- | +1 | +1 | +1 | | | \|/ \|/ \|/ IncGrainA IncARA IncJRA
Suppose that the U.S. government convinces Japan to eliminate the tariff on imports of American beef into Japan. Assuming this cut is immediately passed through to the retail level, it will decrease the yen price of American beef relative to the yen price of Japanese beef for Japanese consumers from 13 yen per pound to 10 yen per pound. All else equal, this should lead to an increase in JConsBA (Japanese consumption of beef imported from America). The issue is who ultimately gets helped and who ultimately gets hurt by this change? In particular, is America better off or worse off overall as a result of this Japanese tariff cut?
Batten claims that standard "partial equilibrium" international trade models tend to focus only on the chain consisting of the positively weighted links connecting JConsBA to ExpABeefJ to ProdBeefA to IncARA. This chain predicts that a tariff cut causing an increase in JConsBA will ultimately increase the income IncARA of American-owned cattle ranches, a good thing for America. Batten points out, however, that complicated network effects make it difficult to predict the overall impact of this tariff cut on the welfare of American citizens.
Specifically, the increase in JConsBA due to a cut in the yen price of American beef for Japanese consumers will have a negative impact on JConsBJ (Japanese consumption of beef produced in Japan) as Japanese consumers now substitute American beef for Japanese beef. This, in turn, will have a negative effect on ProdBeefJ, the production of beef in Japan. This will decrease the income of cattle ranches in Japan, hence in particular it will decrease the income IncARJ of American-owned cattle ranches in Japan.
In addition, the reduction in ProdBeefJ will decrease ExpGrainAJ (the export of grain from America to Japan) since not as much grain will be needed in Japan to feed cattle. This decrease in the amount of American grain needed to feed cattle in Japan will not be fully offset by an increase in the amount of American grain needed to feed cattle in America since at least part of any increase in beef exports to Japan will represent a switch of already existing beef production from American consumers to Japanese consumers. Consequently, the overall production ProdGrainA of grain in America will decline, which will decrease the income IncGrainA of American grain farmers.
NOTE: Realistically, for Japanese consumers to convince American beef producers to sell more beef to them in the short run, before American beef production can be increased to fully meet this increase in demand, the Japanese consumers will have to bid up the dollar price of American beef (thus discouraging American demand for American beef). However, the tariff cut gives Japanese consumers some leeway to do this while still ensuring they pay a lower yen price for American beef than before the tariff cut. For example, assuming the exchange rate X stays fixed at 2 yen per dollar, even if Japanese consumers bid up the dollar price of American beef from $5/pound to $6/pound, they will only pay 12 yen per pound of American beef, which is still lower than the 13 yen per pound they paid prior to the tariff cut. Note that any such rise in the dollar price of American beef would decrease the welfare of American beef consumers.
Finally, the income earned by cattle ranchers in America will increase due to the increase in ProdBeefA, the production of beef in America, but the overall increase in income to cattle ranches in America will be divided between IncARA and IncJRA, i.e., between the incomes of American and Japanese-owned cattle ranches in America.
The ultimate effect of the tariff cut on the welfare of American citizens (grain farmers, cattle ranchers, and beef consumers) is therefore ambiguous without further information regarding the timing and magnitudes of the indicated production and income changes.
QUESTIONS: How can these complicated network effects be more rigorously modeled? By an equation-based model? By an agent-based model? By some other approach? What are the advantages and drawbacks of each approach?
Notes:The graph theory terminology used below is explained above in the "Basic Concepts from Graph Theory" portion of these notes. For a more rigorous and detailed treatment of random graphs, see Bollobás (1985), Strogatz (2001), and Watts and Strogatz (1999). The first researchers to study how the connectivity of a random graph changes as a function of the number of its links were Erdös and Rényi (1960).
For any graph G, let R(G) denote the ratio of its size (number of links) to its order (number of nodes), and let M(G) denote the size (number of links) of its largest component. Batten notes that the plot of M against R for a sequence of random graphs G_0, G_1, G_2,... with steadily increasing R values reveals that the random graphs undergo a phase transition as R passes through the critical value R=0.50. Specifically, as depicted in Figure 3.6 (p. 103), the random graphs transit from being "nearly unconnected" to "nearly connected" at the critical value R=0.50, in the sense that the value of M undergoes a sudden dramatic increase.
M | | _ - - | - M=Size of| - largest | component| - | | - | | - | - |______________________________________________ R 0.50 R = Ratio of Links to Nodes
Batten describes the construction of the random graph sequence G_0, G_1, G_2,... as follows. Let N denote some suitably large integer (Batten selects N=20). Start with a completely disconnected graph G_0 having N nodes and 0 links. Choose two nodes at random from the nodes of G_0 and connect them with a link. The resulting graph has N nodes and one link -- call this graph G_1. Next, choose two nodes at random from the nodes of G_1 and connect them with a link -- call this graph G_2. And so forth.
For each graph G_i in the sequence G_0, G_1, G_2,..., plot M(G_i) against R(G_i). Batten claims that the resulting plot will lie along an S-shaped ("sigmoid") curve as depicted in Figure 3.6 (p. 103). At first the value of M will increase at a slow but slightly accelerating rate. However, as R approaches the critical value 0.50, the value of M will suddenly exhibit a substantial increase. As R continues to increase beyond 0.50, the value of M will increase at an ever diminishing rate as it approaches an upper bound.
Note: The graph theory and small-world network terminology used below is explained above in the "Basic Concepts" portion of these notes. A more rigorous and detailed treatment of the small-world network findings discussed below can be found in Strogatz (2001), Watts and Strogatz (1998), Watts (1999), and Wilhite (2001).
Batten points to several suggestive examples of socioeconomic systems exhibiting phase transitions as connectivity increases: for example, the formation of community common interest groups (e.g., voting blocs, political parties, unions, clubs); an audience watching a performer; traffic on city highways. He notes that he will discuss the traffic example in detail in his later Chapter 6.
At the time he wrote his book, Batten was apparently unaware of the attempts by Duncan Watts and Steven Strogatz to rigorously address his question through an analysis of small world networks (Watts and Strogatz, 1998; Watts, 1999). These authors explored a simple family of graphs G(p) that could be tuned by a parameter p to range all the way from a regular graph G(0) at p=0 (every node has the same number of links) to a random graph G(1) at p=1 (all links are randomly generated). For intermediate values of p, they discovered a range of "small world networks" G(p) displaying a number of interesting properties. The networks exhibited global reachability (similar to random graphs) yet had high degrees of local neighborhood clustering (similar to regular graphs).
More precisely, as detailed in Strogatz and Watts (1998, pp. 440-441), these small-world networks G(p) arise for an intermediate range of p values where the characteristic path lengths L(p) of the networks are almost as small as for a random graph yet the clustering coefficients C(p) of the networks are much greater than for a random graph. The small L(p) values result from the introduction of a few "short cut" links that connect nodes that otherwise would be very far apart. For small p, each short cut has a highly nonlinear effect on L(p), contracting the distance not just between the directly connected pair of nodes but also between their immediate neighborhoods, and between neighborhoods of neighborhoods, and so forth. In contrast, for small p, a link removed from a clustered neighborhood to form a short cut has at most a linear contracting effect on C(p). Thus, for small p, an increase in p causes L(p) to drop very rapidly while C(p) decreases only slowly.
After discovering this small-world form of network connectivity, Stogatz and Watts (1998) investigated its empirical significance. They found that small-world network architectures appear to characterize a wide variety of real-world networks as disparate as the neural network of the nematode worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration pattern of motion picture actors. They conjectured that one reason for the ubiquity of small-world network architectures might be enhanced signal-propagation speed, computational power, and synchronizability.
A number of ACE researchers have begun to consider small-world networks in relation to economic processes. For example, Wilhite (2001) uses an ACE model of a bilateral exchange economy to explore the consequences of restricting trade to small-world trade networks.
Specifically, Wilhite focuses on the trade-off between market efficiency and transaction costs under four types of trade networks: (a) completely connected trade networks (every trader can trade with every other trader); (b) locally disconnected trade networks consisting of disjoint trade groups; (c) locally connected trade networks consisting of trade groups aligned around a ring with a one-trader overlap at each meeting point; and (d) small-world trade networks constructed from the locally connected trade networks by permitting from one to five randomly specified short-cut trade links between members of non-neighboring trade groups. Given each type of trade network, traders endowed with stocks of two goods seek out feasible partners, negotiate prices, and then trade with those who offer the best deals.
Wilhite's key finding is that small-world trade networks provide most of the market-efficiency advantages of the completely connected trade networks while retaining almost all of the transaction cost economies of the locally connected trade networks. His findings also suggest that there exist micro-level incentives for the formation of small-world trade networks, since the traders who use this type of network tend to do well relative to the traders who do not.
As Strogatz (2001) notes, however, for social networks it is not enough to focus on the implications of a fixed or parametrically varied network architecture. Feedback mechanisms are at work in social networks that reduce the ability to predict system performance solely on the basis of initial structural conditions. For example, in social networks, the participants (nodes) might be able to preferentially determine their relationships (links) over time by means of adaptive choice and refusal of partners. In such cases, interaction networks might continually coevolve over time through the operation of intricate feedback loops: who I partner with today depends on the behaviors expressed by myself and my partners in past interactions, and how I behave today depends on whom I partnered with in past interactions.
The issue of evolving interaction networks will constitute one of the main topics of Section VII of the course, which focuses on the ACE modelling of markets with strong learning and network effects.
Batten asserts (p. 111) that "learning by interacting proves to be an adaptive process out of which a desire for cooperation emerges." As will be seen in Section VII of this course, this is too simplistic. Certain structural conditions promote cooperation; others do not. For example, basic market structural conditions (e.g., costs, capacities,...) and biases inherent in market protocols (e.g., who gets to bid first) can systematically advantage buyers over sellers, or vice versa, encouraging aggressive and predatory behaviors on the part of the advantaged group.