The Vaults and Garden Cafe...

Coming at you, post-"Community Detection in Multi-Slice Networks," from the Vaults and Garden Cafe in Oxford...

Dr. Mason Porter gave a very nice and thorough seminar on applications of his method of detecting communities in multi-slice networks.  Applications ranged from financial networks to actual human brains (and everything in between).  The technique itself is deceptively simply:  one simply seeks the community partition that optimizes a well-known network quantity called modularity (where modularity is measured in terms of departure from some chosen null model).  However, actually implementing the technique can be extremely challenging.

I am interested in applying these techniques to international trade (which to Dr. Porter's knowledge has not yet been attempted).  To start, what I need is to find an appropriate null model for international trade networks.  I will then find a community partition that maximizes modularity relative to what one would expect given my null model.  Typically, null models are random network models...so which random network model is most descriptive on the international trade network?  What about Kronecker graphs?

The White Horse Pub...

I almost forgot...I had an excellent meal last night in the White Horse pub near Balliol College.  The pub itself was founded in 1591!  I had planned to go search out a good curry on Cowley St., but became distracted by a hand-scrawled chalkboard offering "Fresh Game Pie and Local Ale." 

So instead of a curry dinner...I had a rabbit, venison, and boar pie with potatoes.  I spent the remainder of my evening at the White Horse by the fire with two pints of a local ale called "The Village Idiot" and a newly purchased book: Marx: A Very Short Introduction...

Complexity Catastrophes...

On the train down to Oxford I read through almost all of the proceedings from the original Sante Fe Conference on economics as a complex system.  I found the following chapters to be particularly useful for economists:

1. The Evolution of Economic Webs, Stuart Kaufman
2. Persistent Oscillations and Chaos in Economic Models, Michele Boldrin
3. Self-Reinforcing Mechanisms in Economics, W. Brian Arthur
4. Computation and Multiplicity of Economic Equilibria, Timothy J. Kehoe
5. Rational Expectations, Game Theory and Inflationary Inertia, Mario Henrique Simonsen
6. The Global Economy as an Adaptive Process, John H. Holland

Of the above chapters, Kaufman's on the evolution of economic webs is by far the most thought-provoking.  I am particularly fond of his ideas on complexity catastrophes, as they parallel some of my own ideas on the dangers posed by overly dense connectivity in financial networks. 

Afternoon in Oxford...

After spending most of the early morning walking around Oxford trying to find a coffee shop that doesn't force you to pair for wifi service, I have now settled down to work on my international trade networks presentation in the Cafe Nero above the original Blackwell's bookstore...apparently the Blackwell's is close enough to Trinity College that I can access its eduroam wifi.

On a side note, I must say that  I am underwhelmed by the coffee shops that I have encountered in Oxford so far (with the exception of Green's Cafe)...Edinburgh wins easily using the coffee shop metric...

Are there any Oxford alums that are reading my blog? If so, suggestion regarding food, coffee, and pubs would be much appreciated...tonight I am going to go searching for a good curry over on Cowley St.

Edinburgh at Dusk...

Took this photo from the top of Arthur's Seat around 4:30 pm...

 

I am heading south to Oxford University tomorrow to attend a seminar on the evolution of community structure in multi-slice networks at CABDyN.

I have never been to England before (I do not count layovers at Heathrow), and I am excited about this first (of hopefully many) visits to Oxford University.

Computational Model of Trade...

Just need to jot down the specifics of an idea I had about a computational model of trade with endogenous network formation...

The world consists of an exchange economy with N agents arranged in a circle.  Each agent is described by the following parameters:

1. Parameter, r~U[0,1] describing their level of risk aversion.
2. Parameter, v~U[a,b] describing their vision.  This vision parameter tells how many agents to the left and right are in an agents neighbourhood.  Vision could also be the same fixed v for all agents to simplify things.  Assume that agent's have perfect information about the endowments etc of all other agents in their neighbourhood/vision.
3. Each agent is endowed with some amount of two goods sugar and spice.  Endowments could be distributed uniform on some interval.
4. Agent have the same utility function which takes the amount of sugar and spice as arguments, and also must include risk aversion somehow.  I am open to suggestions as to what utility function would be most appropriate.

Agents would then have to decide whether or not to trade (if they wanted to trade at all) at "home" within their neighbourhood/vision or "abroad" by linking up with some other agent about which they know nothing (except the distributions of risk aversion, vision, etc.).  Of interest to me are the following...

1. Do agents with higher levels of risk aversion trade at home more often? Do agents with less risk aversion trade abroad more often?
2. What type of trade networks evolve through this process? Network structure within time steps and network structure aggregated across time steps would be of interest.
3. What are the equilibrium properties of such a model?  Is there meaningful convergence?  If so, how fast?  Is the equilibrium Pareto efficient/Pareto optimal?

I wrote this down very fast, and no doubt left out details necessary to close the model, but I thought I better write it down lest I forget...

International Trade Network: A First Pass...

I will be presenting a talk on the structure of international trade at a networks workshop being held here at the University of Edinburgh.  What follows is a dump of my thoughts related to the subject which so far are largely based on my attempt to replicate recently published work on the structure of international trade network.

International Trade Network Data...
There are two principle sources of network data on international trade (that I have been able to find):

1. Prof. Kristian Skrede Gleditsch at the University of Essex:  Data are from 1948-2000 and the primary source is the IMF.
2. UN Comtrade: Data are from 1962-2009 and the primary source is of course the UN.  
3. There is a third data source, the Economics Web Institute, that I would like to dissuade people from using even though they use Prof. Gleditsch's IMF data (without going into too much detail, the Economics Web Institute, seems to use an inconsistent methodology to assign edge weights (trade values) to countries when converting from Prof. Gleditsch's raw .asc files to .xls workbooks). 

If you would like to hear the gory details on the data validity issues feel free to contact me.

Hierarchical Clustering and Trade Network Density:
For the moment I am simply trying to replicate the work of the Deem et al. (2010) paper (linked to above).  I have applied a average linkage hierarchical clustering algorithm to the OECD international trade network as outlined in their paper.  Below are some plots of the cophenetic correlation coefficient (CCC) and network density for the international trade network for OECD countries using two different data-sets.  The first plot uses data entirely from the UN Comtrade database.  NBER recessions are marked with gray bars.  I downloaded the data by hand from Comtrade (commodity code is SITC ver. 1 AG0) and then used a Python script to clean and reorganize the .xls spreadsheets into more manageable text files.  Statistical analysis is done using SciPy, network analysis (so far) has been done using NetworkX, and plotting has been done using Matplotlib.     

The plot below is the CCC and network density for the international trade network for OECD countries using Prof. Gleditsch's IMF data for 1948-2000 and then UN Comtrade from 2001-2009 (commodity code this time is SITC ver. 3 AG0). 

There are some differences between the two plots of the CCC (I have not yet tested whether or not they are significantly different nor have I tested whether or not the CCC jumps significantly during/after recessions...this is on my to do list!).

Still to come:

1. Dendrogram of identified clusters
2. Results of community structure algorithm applications
3. Weighted clustering algorithms and other graph measures

Basically I am just trying to learn to do network analysis using Python by applying the tools to an interesting topic...