Back to Python and Markov Chains...

So I am back to programming in Python and working my way through Economic Dynamics: Theory and Computation.  I am in the middle of Chapter 4 at the moment and have just written some basic code for simulating the Markov-switching model of unemployment from Hamilton (2005).  I highly recommend a read of the paper.  It is fairly short, contains a neat little model, and after reading it I felt like I had a greater understanding of the dynamics of unemployment and the business cycle...

I will continue to work on the code over the holidays, and will push my it out to github for others to use...after I get my github repository set up!

Best network visualization that I have seen in a while...

Follow the link to read the story behind this image...if you look closely you will notice that there are actually no geographical borders plotted in this image...the "borders" emerge as a result of the geographical clustering of network connections between Facebook users...spooky!

Rational Addiction...

I have known drug users...and I would not describe them as having anything remotely approaching time-consistent preferences...

Theory of Value: Final Thoughts...

I have just finished reading the final chapter on uncertainty in Debreu's Theory of Value.  This final chapter which is very short, simply introduces the idea of contingent commodities and then sketches how the theorems and proofs in previous chapters go through in this more general case.

Instead of sharing my thoughts about contingent commodities, I thought I would post some of my over all thoughts about the book and about general equilibrium more generally...

After reading this book I feel like I have a much improved understanding of both the mathematics and the economics of general equilibrium theory.  For an aspiring academic economist, this is clearly a good thing.  Unfortunately, I do not feel like I have a better understanding of how real-world  economies generally behave.   This is clearly not a good thing. 

After reading, say Minsky's Stabilizing and Unstable Economy, I felt that I was better equipped to talk about issues of serious importance in modern, capitalist economies.  I do not feel that way after reading Theory of Value.  General equilibrium, in my view at least, is not supposed to describe real-world economies but instead serves as a kind of null model for how an idealized economy should behave.  Thus perhaps comparing Theory of Value and Stabilizing and Unstable Economy is not very fair. 

However, even as a null model of the economy, I think general equilibrium falls short.  Any null model of the economy, in my opinion, must allow for the possibility that individual optimization decisions are influenced by the decisions of other individuals in the economy.  In the real world, economic behavior is a very social activity and preferences and individual decisions are heavily influenced by others actions and beliefs.  In the real world, there is also lots of trades.  Perhaps even lots of "false trades" (by false trades I mean trades at non-equilibrium prices).  In GE no one trades until the equilibrium price vector has been calculated, and then they only trade once. 

Once one allows for the possibility that a single agent's decisions can impact the decisions (and/or influence the preferences) of other agents, then micro-dynamics may no longer average-out in the aggregate.  Once one allows for "false trades" each false trade alters the wealth distribution amongst the agents in the economy which then shifts the equilibrium to which the economy would have converged.  In this world "equilibrium" is a moving target.

None of the above critiques of GE are original, and I had encountered all of them prior to reading Theory of Value.  Despite my criticisms, I am still very glad that I read the book and would recommend it to anyone who plans on pursuing an academic career in economics... 

Theory of Value, Chapter 6...

Just finished reading Chapter 6: Optimum.  Debreu lays out the conditions necessary for the equilibrium concept described in the previous chapter to be an optimum for the economy, and under what conditions any optimum can be supported as an equilibrium of a private ownership economy. 

Convexity of individual consumer sets, and of the overall economy's production possibilities set plays is important role for proofs to obtain.  Although the convexity requirement on the production possibilities set is only required to prove that any optimum can be supported by a market equilibrium under a certain price vector.

Only other comment is to point out that, according to Debreu, optimums are in general not comparable to one another (except in trivial case where everyone is simply indifferent between the two optimums).  Although, it is not entirely clear to me how this squares with the idea of Pareto dominance which is sometimes used to eliminate some market equilibria.  To compare between two optimums would require, I think, being able to make inter-personal comparisons of utility...    

The Golden Rule...

"The golden rule of research is to carefully define your question before you start searching for answers..."

-probably many people

Unfortunately...I very often seem to disregard this rule, and start searching for answers to questions that I have not defined...this is a very inefficient search method.

Networks, cycles, and supply chains...

If you haven't already read it, check out this post on Stumbling and Mumbling...it is very similar in spirit to some things that James, Sean, and I have been talking about recently regarding network theories of complementarities in the production process and how this might generate business cycles...