I have not used attractors.  This is a very interesting question, and I am going to closely follow it. .

Hi Pahlaj,

Thanks for your interest and vote of confidence!

I'm not sure I follow. Even if we concentrate on fixed points that are attractors, a system that is sufficiently close will tend towards the sink and have a constant trajectory forever. That's how we define stable equilibria. Periodic and preperiodic (eventually periodic) continue to have a trajectory that varies, albeit regularly.

I've always been curious why, despite the enormous wealth of literature (not all of it any good) pouring out of various sciences on complex systems, nonlinear dynamical systems, etc., so few of the volumes or monographs I have are on economics (several have a section). That said, if you are interested in complexity theory as applied to economics you might find the following interesting:

Bruun, C. (2006).Advances in Artificial Economics: The Economy as a Complex Dynamic System (Lecture Notes in Economics and Mathematical Systems). Springer.

Schulz, M. (2003). Statistical Physics and Economics: Concepts, Tools and Applications (Springer Tracts in Modern Physics Vol. 184). Springer.

I'd be curious how you'd go about defining what seems to me (not an economist, and therefore at best tangentially familiar with economic systems in certain respects) to be a nonlinear process in terms of attractors/sinks.

Hi Andrew,

Thanks for sharing your views on the applicability of complexity to economics.  Yes there are some that may argue that importing physics or even cross-pollination of models has its limits. And we should be wary of efforts that stray off into abstraction. But I am concern more of how these models, especially the attractor concept in complexity science is useful as a means to understand far-from-equilibrium conditions (and multiple equilibria- not technically a point but a "locus of stability"- as is the case with the strange attractor), in the current context FDI. If we can't pinpoint a point we can always rely on phase portraits and the like: that is where attractors have their utility as classification schemes. A good and accessible survey/and attempt to marry complexity with economics (though others through the years have done so in their own small ways) be found in Eric Boinhocker's The Origin of Wealth: The Radical Remaking of Economics and What it Means for Business and Society.

Another book that is interesting and related to the shifting of the dominant paradigm in economics (the mainstream version is still very much entrenched in classical/Newtonian mechanics) but I did not get to read in detail is:Meme Wars: The Creative Destruction of Neoclassical Economics. Complexity science- which is born out of interdisciplinary thinking and multidisciplinary approaches provide a varied tool set for investigating the increasingly unpredictable economic landscape looming beyond the horizon.

http://www.amazon.com/The-Origin-Wealth-Remaking-Economics/dp/1422121038

http://www.amazon.com/Meme-Wars-Destruction-Neoclassical-Economics/dp/1609804732

Hello!

Do you have in mind the Working Paper No. 04-06,

The Chaotic Attractor of Foreign Direct Investment - Why China? A Panel Data Analysis, Frank S.T. Hsiao and Mei-chu W. Hsiao, May 2004,

am I right?

There is also a study entitled:

The CEEC as FDI Attractors - A Menace to the EU Periphery? Galego, Aurora; Vieira, Carlos; Vieira, Isabel, 2004.

and

Competitiveness Strategy in Developing Countries

A Manual for Policy Analysis, by Ganeshan Wignaraja, 2002 – 320 pages, Series: Routledge Studies in Development Economics.

In The Chaotic Attractor of Foreign Direct Investment - Why China? A Panel Data Analysis, China is considered a "strange attractor". In fact, there are two categories of "attractors": (1) major FDI destinations such as China, USA, the "big four" in the EU etc. as well as (2) FDI determinants as "attractors".

International organizations such as UNCTAD, World Bank and IMF consider

FDI attractors=variables as follows: natural resource intensity, size and growth potential of the host market, labour cost, human capital, economic stability, trade openness, income level, corporate tax rates, the quality of institutions, rate of return on FDI, "round tripping" etc.

Dynamical systems are moving from an equilibrium point to another, along with the evolution of own "attractors", new technologies, new competitors, that is why both categories of "attractors" (destinations and determinants) are changing.

Please consult also the UNCTAD statistics:

http://unctad.org/en/pages/DIAE/World%20Investment%20Report/Annex-Tables.aspx

I think it is important to map out FDI flows to different major FDI hosts from a double perspective: that of competitors for FDI and that of FDI determinants and their evolution in time.

Best,

Monica

I think my initial reply wasn't very clear, at least with respect to the applicability of a complex systems approach to economics. I mentioned a relative dearth in the amount of material I have on complex systems of one sort or another compared to those focused on economics. I did so not because I think that such an approach is ill-suited to economics, but the opposite: the economy is too complicated to model or study without the interdisciplinary tools provided by complexity and systems sciences. I would expect more of the works I have on complex systems to have sections related to economics or to be devoted to economics, given that I have e.g., The Mathematics of Marriage: Dynamic Nonlinear Models, Self-Organized Criticality in Astrophysics: The Statistics of Nonlinear Processes in the Universe, Power Grid Complexity, Biomineralization I: Crystallization and Self-Organization Process (Topics in Current Chemistry), Dynamics of Combustion Systems (2nd Ed.), and other books that involve a nonlinear dynamical/complex systems approach to things one wouldn't expect (compared to e.g., neurophysiology, climate science, systems biology, etc.).

There are countless works on the complexity of various kinds of social networks, on granular media, on biophysical signaling, ant colonies, bee colonies, swarming/flocking, cognitive development, and on and on, all of which use a complex systems approach. The titles above (particular the first) would seem far less likely to have any value than would a similar approach to economic theory. Yet for some reason I have found comparatively few works which are devoted to a complex/ dynamical systems approach to economics. This may simply reflect that the more I get away from my field, the less likely I am to look at the form the majority of literature in any field consists of: journal articles. But I am simply surprised by the relative paucity of monographs/volumes on economic theory from a complexity perspective. I don't see how it is possible not to use such an approach and get very far at all. Which is why I find your question intriguing and am interested in how you might go about answering it.

Hi Iulia,

Thanks for the many links to sources that you cite. I intend to check out the UNCTAD database, in light of your insights into attractors in FDI.

I have come across the source: "Working Paper No. 04-06,

The Chaotic Attractor of Foreign Direct Investment - Why China? A Panel Data Analysis, Frank S.T. Hsiao and Mei-chu W. Hsiao, May 2004."  

But unfortunately the authors intended it to be figurative/metaphorical of strange and chaotic attractors (though taking this connotation to models isn't all wrong), rather than looking at the science of it (i.e. dynamical systems, three -body problem etc.). Nonetheless I think those links and leads are indeed indications that there are emergent thinking that mirrors the trajectory of the question!

I tend to agree with Andrew that there are many technical works (of fundamental nature, relating to the hard sciences) on complexity, and comparatively less applied efforts in economics. Because people are either misled by the terms or stumped by its obtuse intricacies (e.g. "chaos" and "complexity" is not exactly what it means in the English dictionary). Ironically the "soft sciences" are the ones that are in greater need of formalism than the hard sciences, and complexity/dynamical systems offers an "open-source" toolset if you want to call it that.  

In the context of "round tripping" and dynamical systems, would you say that the concept of attractors applies more as a description for "competitors of FDI" (as Andrew refers to as, "tends towards the sink") as opposed to being an explanatory framework that reinforces the traditional "determinants" (e.g. political economy etc.)?

Best Regards

This may help in some dimension:

Article Negative Impact of FDI: A Co-integrated Approach

and this one..

Chapter Foreign Aid to Pakistan: Impact on GDP with least square estimation

And this..

Article Empirical Analysis of the Impact of FDI on Pakistan’s Curren...