Posts from — August 2007

Complex Adaptive Systems: An Introduction to Computational Models of Social Life (Princeton Studies in Complexity) (Paperback)

by John H. Miller and Scott E. Page

Princeton University Press (March 5, 2007), ISBN 0691127026, USD 24.95.

This book is a non technical introduction to the field of Complex Adaptive Systems (CAS) from the Santa-Fe perspective, which means it emphasizes the role of emergent phenomena such as scaling distributions in attempting to build models of the economy which are more closely aligned with economic reality than standard neoclassical, axiom driven, reductionistic models prevalent in the mainstream. The main point of CAS is to use computational methods to study `complexity’ in social systems no easily captured in standard modeling methodologies.

The Miller and Page definition of complexity is (pg. 9):

“Complexity is a deep property of the system…[a] complex system dies when an element is removed…[the] behavior of many complex systems emerges from the activities of lower level forces.”

Contrasting this with Foley, pg. 2, 2003, who defines complexity in a broader, more agent-friendly way in order to connect complexity-economics to classical theories of value, we see how the definition of this central concept is malleable:

“Complexity theory represents an ambitious effort to analyze the functioning of highly organized but decentralized systems composed of very large numbers of individual components. The basic processes of life, involving the chemical interactions of thousands of proteins, the living cell, which localizes and organizes these processes, the human brain in which thousands of cells interact to maintain consciousness, ecological systems arising from the interaction of thousands of species, the processes of biological evolution from which new species emerges, and the capitalist economy, which arises from the interaction of millions of human individuals, each of them already a complex entity, are leading examples.“

The book is intended as a primer for the field. Miller and Page provide a nice motivating in the first Chapter, showing how models of standing ovations require both agent-level and systems level perspectives to model the phenomenon correctly.

Having established that yes, there is a need for systems research of this kind, they move on to consider the implications of searching for emergence-type results in research, and the change in modeling methodology this implies. Miller and Page provide a nice caricature of their method on pages 40––42, but really offer us little in the way of methodological meat. An example of the fluff:

“A model requires choices of both the equivalence classes and the transition function, and the art of modeling lies in judicious choices of both” (pg. 40).

Of course this statement is correct, but the authors could be talking about any type of modeling––there is nothing really here to suggest the authors can provide a roadmap for young scholars trying to get to grips with exactly how one should go about modeling a system as complex. The next chapter is a nice description of emergence as a social and physical concept, but for me it doesn’t provide enough links to the deeper parts of the economic literature on the subject for the would-be CAS scholar.

In a text like this, I, the interested reader, should be able to get 2 or 3 seminal articles on emergent phenomena in the economics literature from a Chapter like this. In total, in Chapter 4, not including the admittedly very cool opening quotes, there are 2 references, neither to economically motivated examples of the modeling of emergence. They provide a theory of emergence using the weak law of large numbers as an example of what Shalizi and Moore (2006) call a `macrostate’, which is a good way to tell the story, but the next logical step to take is to Pareto and power-law-like phenomena in social systems, which are also macrostates, and that has to wait until section 9.6. Personally in this chapter I’d love to have seen references to interesting applications of emergent phenomena as a backup for the theory Miller and Page advance: writers like Leijonhufvud (1997), Tesfatsion, (2002), Fafchamps (2002), Chavas and Holt (1993), Krugman (1996), especially the first two Chapters), Young (1998), Arthur, (1989), Folmer, (1974), and anything by Jose A. Scheinkman (most of his papers are up at http://www.princeton.edu/~joses/wp.html).

Next up, Miller and Page give us their version of computational theory, or rather the theory of computational modeling as a productive enterprise. This is the only place where the book really disappoints me. There is a theory of computation, and Profs. Page and Miller are well aware of it’s existence (they use parts of it very well in Chapters 9 and 10). Rather than providing a primer to the theory of computability to the interested reader with economic applications in Chapter 5, they skirt the topic, largely relegating the problem of uncomputable functions in economic systems to a footnote on page 174:

“It can be proved formally that not all functions can be solved by a standard computer (that is, not all functions are “computable”). We leave it as an open question whether any of the functions are of most interest to complex adaptive social systems, such as the behavior of a typical social agent, are in this latter group.”

It has been formally proven recently by Velupillai (2006) that general equilibrium models don’t actually compute the solution to an Arrow-Debreu type economy, but there is more research out there on this topic, and it would be wonderful to have this research included in a second edition. CAS is about using computers and computational models to understand economic phenomena. Using the mathematics that underpin the digital computer (as Miller and Page do in later chapters) seems like a good idea, and a development of this theory can be found in Velupillai (2000). Thus a chapter on computability theory would be a welcome addition to the book.

Miller and Page write on page 65 that:

“The types of computational models we wish to focus on here are those in which the abstractions maintain a close association with the real-world agents of interest, and where uncovering the implications of the abstractions requires a sequential set of computations involving those abstractions.”

I think Miller and Page want to replicate the strategy of Borgesian map-making that characterizes much of Stephen Wolfram’s New Kind of Science approach to modeling phenomena, and in fact they do allude to Borges on page 33, but the real meat of a theory and method of complex adaptive systems slips us by in this chapter. The authors are distinguished economists whose reputations as computational social scientists put them in a position to be able to make methodological claims for

Throughout the book, the authors claim a varied intellectual heritage for CAS: Hayek, Schelling, Crutchfield and Li/Packard, Wolfram and his NKS approach, and Herbert Simon, who is normally credited with anything that includes agents with limited information. However, the theories of these great men aren’t tied in with the models we are shown in the later chapters, so one feels a bit disconnected from their contributions. This is to be expected in a general overview book, but I do wish someone would tie all the strands together in a coherent way. CAS, like any other discipline, needs roots in the intellectual firmament, and the best way to do that with integrity is to build a catalogue of antecedents, obviously avoid ing whig history as you go.

To the meat of the book. Chapters 7––11 show us applications of the theory of CAS. This set of Chapters is a fantastic, simple overview, and is a really excellent pedagogical showing us forest fire models, 1 dimensional Cellular Automata, and other models. In Chapter 9 we are shown lots of models with dynamic content, from Schelling’s Beach and its variant, the El-Farol/Minority Game problem, to the formation of cities (simple agglomeration models), to network (small-world & Pack) formation, and Schelling’s Segregation model, and Bak’s Sandpile model.

Section 9.6 is really the best part of the book for me. It is a discussion of Power Laws. The definition and example Page and Miller give on page 165 is so good I’m going to quote it in its entirety:

A system is subject to a power law when Prob[X=x] ~x^{-k}. If x is the number of occurrences of some event of a particular size, then a power law would imply that the likelihood of this event is proportional to the size of the event raised to the -kth power. Thus, if k=1, events of size 100 are 1/100th as likely as events of size 1. This implies that power-law governed systems are characterized by many small events and a few, rare, big ones.

They discuss the prevalence of scaling phenomena in different economic contexts, but don’t really tie the existence of power laws to the macrostate/emergent property search that CAS is really there to conduct.

Chapter 11 models the organization as an information aggregation mechanism, an agglomeration of nodes that funnels information into itself through these nodes to solve Boolean (TRUE/FALSE) functions. Surely this isn’t the best way to tell this story? Chapter 11 doesn’t really build on anything previously and is more of a non-technical synopsis of the authors’ work. Maybe more research will be done on this in this area soon.

Following Chapter 11 the book moves into concluding chapters and appendices.

The appendices are excellent notes to the researcher, guides and hints for best practice in CAS modeling, and an attempt to set out an agenda.

Personally, if I were asked to edit this book, following the usual motivating Chapters, I would have put the applications of the theory first, with the hints for modeling in Appendix A moved to the heart of the book, with worked examples of real (possibly open) research problems, showing how the Borgesian-map strategy can be used more effectively than standard reductionist approaches in certain contexts. The `manifesto’ for CAS modeling deserves a book in in itself. I enjoyed this book, and, while it is flawed in places, with patches of rigor and patches of simple (but accurate) description, I think it represents a significant step forward for CAS research. That the field is large enough to require a book such as this is heartening, and the authors are to be congratulated for their efforts.

Further Reading



Starred references are robbed from C.S. Shalizi’s Notebooks. http://cscs.umich.edu/~crshalizi/notebooks/soc.html.

“An Unholy Trinity : Labor, Capital and Land in the New Economy” (Duncan Foley)

CRS and Cris Moore, “What Is a Macrostate? Subjective Measurements and Objective Dynamics,” cond-mat/0303625;

http://arxiv.org/abs/cond-mat/0303625

Leigh Tesfatsion, Economic Agents and Markets as Emergent Phenomena, Proceedings of the National Academy of Sciences of the United States of America, Vol. 99, No. 10, Supplement 3: Arthur M. Sackler Colloquium of the National Academy of Sciences. Sackler Colloquium on Adaptive Agents, Intelligence, and Emergent Human Organization: Capturing Complexity though Agent-Based Modeling (May 14, 2002), pp. 7191-7192, http://links.jstor.org/sici?sici=0027-8424%2820020514%2999%3A10%3C7191%3AEAAMAE%3E2.0.CO%3B2-4

Edwardo Zambrano 2004 “The Interplay Between Analytics and Computation in the Study of Congestion Externalities: The Case of the El Farol Problem.” Journal of Public Economic Theory, 6(2), 2004, http://www.nd.edu/%7Eezambran/WebPapers/compufinal.pdf

Marcel Fafchamps (2002) “Spontaneous Market Emergence,” Topics in Theoretical Economics: Vol. 2 : Iss. 1, Article 2. Available at: http://www.bepress.com/bejte/topics/vol2/iss1/art2

* F. Clementi, T. Di Matteo, M. Gallegati, “The Power-law Tail Exponent of Income Distributions”, physics/0603061 = Physica A 370 (2006): 49–53

Jean-Paul Chavas; Matthew T. Holt Market Instability and Nonlinear Dynamics

American Journal of Agricultural Economics, Vol. 75, No. 1. (Feb., 1993), pp. 113-120.

http://links.jstor.org/sici?sici=0002-9092%28199302%2975%3A1%3C113%3AMIAND%3E2.0.CO%3B2-0

Laherrère and D. Sornette, “Stretched exponential distributions in nature and economy: ‘fat tails’ with characteristic scales”, The European Physical Journal B 2 (1998): 525–539

Clementi, M. Gallegati, “Pareto’s Law of Income Distribution: Evidence for Germany, the United Kingdom, and the United States”, physics/0504217

*Michael Batty, “Rank Clocks”, Nature 444 (2006): 592–596

Kevin E. Bassler, Joseph L. McCauley, Gemunu H. Gunaratne, “Nonstationary Increments, Scaling Distributions, and Variable Diffusion Processes in Financial Markets”, physics/0609198

A. Arenas, A. Diaz-Guilera, C.J. Perez and F. Vega-Redondo, “Self-organized criticality in evolutionary systems with local interaction,” cond-mat/0103496

W. Brian Arthur, Competing Technologies, Increasing Returns, and Lock-In by Historical Events, The Economic Journal, Vol. 99, No. 394. (Mar., 1989), pp. 116-131.

http://links.jstor.org/sici?sici=0013-0133%28198903%2999%3A394%3C116%3ACTIRAL%3E2.0.CO%3B2-R

“Individual Strategy and Social Structure: An Evolutionary Theory of Institutions” (H. Peyton Young)

“The Self-Organizing Economy” (Paul R. Krugman)

Oxford: Blackwell Publishers, 1996.

Leijonhufvud, Axel. 1997. “Macroeconomics and Complexity: Inflation Theory,” in The Economy as an Evolving Complex System II. Arthur, W. Brian, Steven N. Durlauf, and David A. Lane, eds. Reading: Addison-Wesley, 1997, pp. 321-35.

Folmer, H, 1974, Random Economies with many interacting agents. Journal of Mathematical Economics, 1/1, 51–62. doi:10.1016/0304-4068(74)90035-4

“The Algorithmic Foundations of Computable General Equilibrium Theory”,

Journal of Applied Mathematics and Computation, Vol. 179, #1, August, pp. 360-9, 2006. doi:10.1016/j.amc.2005.11.113

So I’ve been watching a TED talk a day, and here’s one of my favourites. Artist designs web apps that capture the zeitgeist. Here he is talking about it.

But check out the stuff he’s developed, especially We Feel Fine. Truly fantastic social science can be done with tools like this, tweaked for specific projects and research questions.

http://www.tenbyten.org/

http://www.wefeelfine.org/

• GLLAMM
  (tags: econometrics economics Research STATA statistics software MultilevelModels LatentVariables)
• Papadimitriou vs. Game Theory: Papadimitriou wins
  (tags: Algorithms Course mathematics networks Research gametheory)
• Econbrowser: Variation in Global Economic Growth
  Great Pic and commentary for EC3601
  (tags: EC3601)

• Eduardo Zambrano’s Research
  Interesting Guy, nice application of game theory to sociological considerations, Parsons and Polyani especially. Cited favourably in Miller and Page 2007.
  (tags: interestingpeople)
• Helping Africa export | vox - Research-based policy analysis and commentary from Europe’s leading economists
  (tags: Ec4333)
• Federal Reserve Bank of Minneapolis - Great Depressions of the Twentieth Century - Computer Programs
  he files below demonstrate how to calibrate the neoclassical growth model and then solve the model numerically, using data from Finland as an example.

  BaseCaseCalibration.xls calibrates model parameters and derives a sequence of TFP values in the ‘ca

  (tags: math Growth)

• Competition
  Nice Review Article for Ec4333
  (tags: EC4333,)

Frugalist » The Frugality Cheat Sheet: 147 Tiny Tips to Live Healthier, Happier, Greener and Better:

I’m sure you’ve heard it before: if you want to reduce the stress in your life you need to simplify your lifestyle. Of course, this is much easier said than done, because it’s the ants, not the elephants that seem to get the best of us every time. Instead of tackling the big problems that seem overwhelming, it helps to remedy the small problems first. A few small changes can make a significant impact to overall happiness. The following 147 tips, broken down into ways you can improve your life through your job, around the house, in financial matters, in your goals and beliefs, in romance, in your social life, and through your health and diet, will lead you to a healthier, happier, greener, and better lifestyle.

Fascinating blog entry by Mankiw today, in fact one of a string. I don’t agree with his economics, but he is a good writer.

The Sociology of Economics:

I received a letter from a blog reader that was so interesting I thought it was worth sharing with all of you:

Dear Professor Mankiw,

I’m a resident at one of the Harvard hospitals. In the past couple of years I’ve had the chance to attend a number of inter-disciplinary seminars where you have statisticians, physicians, sociologists, anthropologists, epidemiologists and economists present. I’ve been impressed with what your discipline has to say: in virtually every seminar the economists are able to say something useful. Without inflating your ego, I’ve also noticed that the economists present better papers and are less likely to be caught off-guard in a seminar. They are also more likely to discover problems in the work of others. I’ve been trying to educate myself on the economic way of thinking by reading your blog, Freakonomics, and now, by slowly reading your textbook. But clearly, there’s no substitute to being formally trained as one.

My question to you doesn’t concern economics, but more its sociology. So feel free to ignore this email. At the seminar that I attend most often, I’ve noted the following:

1. The economists are the most aggressive people in the room. They have little patience for introductions, motivation, or “being nice”. They want to spend the first 10 minutes trying to figure out the -entire- talk. If they’re not happy, they tend to disengage. I will note that they’re like this with each other also. Why are things this way in economics? There must be pluses and minuses to this way of interacting.

2. The economists are the only social-scientists in the room that are willing to argue with the statisticians. This could be that you are a more argumentative lot in the absence of substance, but also that you know something. I’m not qualified to tell who wins these disputes, but the statisticians seem to regard the economists with a high degree of regard. Why do you think that different disciplines view the importance of statistics differently?

3. There seems to no love lost between the economists and other social-sciences. Some of this has to do with the nature of interferce in the two disciplines: your colleagues are always concerned about confounders. Other disciplines like “to tell a story”; confounders are certainly of concern to them, but the issues of bi-directional causality, and omitted variables seem of second-order importance to them. As a physician, I share your colleagues view of the importance of “selection bias” (nice term, incidentally). Why do you think that different disciplines weight the role of confounders differently?

I posed these questions to one of the economists who regularly attends. His response (that I have permission to send to you) is as follows:

“In general, economists are smarter (we may be better looking too). It’s fashionable not to say such things, but I will bet that if you look at the GRE and SAT scores of incoming PhD students at BU, Harvard and MIT, the average economist will sit at a higher percentile than the average (non-economist) social-scientist. Given that all the other disciplines are trying to recruit students with higher scores, I’m not willing to believe the explanation that these disciplines value other attributes that aren’t measured in the GRE. Higher salaries in economics will tend to reinforce the “economists are smarter” phenomena. Smart people don’t have the time waiting for the less-smart to catch up. If we can finish up the seminar in 10 minutes, then why not do it?

“To this ex ante advantage, add the role of superior and more rigorous training. Economics graduate school is not for slackers. It’s like boot-camp in the Army. One example of this is that we are provided a much deeper understanding of statistics than every other social-science. Consequently, economists are able to publish in journals like JASA and the Annals of Statistics. No other social science is able to do this with the same frequency. This superior training, complemented by a generally higher comfort-level with mathematics is the principal reason for why economists will not shy away from statistics. I wish I had concrete evidence for my argument. At present, it’s indirect evidence. But this “economics know more stats” argument is another reason for why we are more aggressive; we are able to see the strengths and weaknesses of a study faster than others who’re not as fluent in the methods.

“Third, the set of advocates who are economists is quite small (I don’t know if this reflects treatment or selection). In general, economists are more likely to make up their minds about whether a particular policy works based on theory or data. They may have priors, but not the the sort of “do-gooder”priors that advocates have. One of the reasons that economists are so aggressive with the non-economists is that we want to expose all the priors immediately. In my view, a lot of non-economics social science is straight advocacy. There is an important role for advocacy. It may influence policy more than science. But the nature of advocacy is to simplify and ignore nuance and confounding. But our (economists) beef with advocacy isn’t its lack of nuance. We just get really upset when advocacy masquerades as science.

“Fourth, the economics job-market is just that — a market. This means that the best people are more likely to be at the best programs. In other disciplines there are more “bad matches” (good people at bad places). What this means is that Harvard and MIT’s economics departments are more likely to have the top economists than the Sociology Department is likely to have the top sociologists. This is important because what you’re seeing at the Harvard seminars is an exchange between the best economists and not necessarily the best sociologists. The best sociologists may be able to clobber a mediocre economist.”

I’m curious if you have some of your own observations to add to the above.

Best regards,

[name withheld]

These are fascinating questions. I see a lot of truth to the observations described in the letter. I have heard many others note, for example, that economists are generally more aggressive in seminars than other academics. I am not sure how to explain this fact.

To the hypotheses in the letter, let me add one additional conjecture, which is less charitable to me and my colleagues: Perhaps the skills that make a good economist are, for some reason, negatively correlated with the attributes associated with being an agreeable human being. That is, economics may attract people with a particular set of personality attributes, and perhaps these attributes are not the same set of attributes you might choose for your next dinner party.

This is not entirely conjecture on my part. For example, this study

“explores the relationship between student’s personality types, as measured by the Myers-Briggs Personality Type Indicator, and their performance in introductory economics. We find that students with the personality types ENTP, ESTP, and ENFP do significantly worse in Principles of Macroeconomics than identical students with the personality type ISTJ.”

What is this personality type ISTJ that excels in economics class? Check out this description, which say in part:

The ISTJ is not naturally in tune with their own feelings and the feelings of others.

Sounds like any economist you know?

• Economic journals on the web
  (tags: journal literature Research Economics Journals)
• Economics Bulletin
  Possible MLE submission forum
  (tags: MLE)
• Studies in Nonlinear Dynamics & Econometrics
  Great DS journal with free content and good turnaround time
  (tags: MLE)

This Blog is turning into a bit of a link and file dump for the summer while I get my act together on the research front.

Will Milberg has a blog page. Well worth checking out. Home « Professor William S. Milberg

• Don Coursey, Vernon Smith, Economic Experiments, and the Visible Hand: Library of Economics and Liberty
  Nice note on experimental economics
  (tags: exp_econ_book)
• Supply, by Al Ehrbar: The Concise Encyclopedia of Economics: Library of Economics and Liberty
  Supply, Mentioned in Smiths podcast
  (tags: exp_econ_book)
• Hayek, The Use of Knowledge in Society: Library of Economics and Liberty
  Very important article in economics, basis of CAS and Exp. Economics
  (tags: exp_econ_book)
• Buchanan and Thirlby, L.S.E. Essays on Cost, Hayek, Economics and Knowledge: Library of Economics and Liberty
  Another version of Hayek’s AER paper
  (tags: economics Systems information exp_econ_book)
• Vernon Smith on Markets and Experimental Economics, EconTalk Permanent Podcast Link: Library of Economics and Liberty
  Nobellist Smith’s description of his own contributions
  (tags: exp_econ_book)
• Table of Contents; Bohm-Bawerk, The Positive Theory of Capital: Library of Economics and Liberty
  brilliant early analysis of the theory of capital.
  (tags: exp_econ_book)
• The Space of All Possible Bridge Shapes
  Usingmathematicatbuildbridges
  (tags: NKS)
• visualcomplexity.com | A visual exploration on mapping complex networks
  Lovely Site, extremely informative about data presentation techniques
  (tags: Algorithm art Blogs Complexity Data Design Music Net Research statistics Thesis visualization networks)

• Wolfram Technology Conference 2007: Submissions
  submission

  (tags: conferences)