miscellaneous factZ

This January I met Alan Kirman at the Robinson Workshop on Rationality and Emotions. Over lunch we had a brief discussion about the difficulties of modern macroeconomics. I was therefore intrigued to see a new paper of his (co-authored with Peter Howitt, David Colander, Axel Leijonhufvud and Perry Mehrling) entitled Beyond DSGE Models: Towards an Empirically-Based Macroeconomics which was presented in January at the AEA conference (and looks like it will be appearing in the AER ‘Papers and Proceedings’).

The paper has much to say about the current state of macro, in particular the serious problems with DSGE (dynamic stochastic general equilibrium models) and where we should go from here. As the abstract puts it:

This paper argues that macro models should be as simple as possible, but not more so. Existing models are “more so” by far. It is time for the science of macro to step beyond representative agent, DSGE models and focus more on alternative heterogeneous agent macro models that take agent interaction, complexity, coordination problems and endogenous learning seriously. It further argues that as analytic work on these scientific models continues, policy-relevant models should be more empirically based; policy researchers should not approach the data with theoretical blinders on; instead, they should follow an engineering approach to policy analysis and let the data guide their choice of the relevant theory to apply.

It is worth quoting at some length from the paper in order to bring out the full ramifications of the story the authors tell:

Keynesianism Goes Wrong

With the development of macro econometric models in the 1950s, many of the Keynesian models were presented as having formal underpinnings of microeconomic theory and thus as providing a formal model of the macro economy. Specifically, IS/LM type models were too often presented as being “scientific” in this sense, rather than as the ad hoc engineering models that they were. Selective micro foundations were integrated into sectors of the models which give them the illusory appearance of being based on the axiomatic approach of General Equilibrium theory. This led to the economics of Keynes becoming separated from Keynesian economics.

The Reaction and a New Dawn (Rational Expectations and Neoclassical GE Models)

The exaggerated claims for the macro models of the 1960s led to a justifiable reaction by macroeconomists wanting to “do the science of macro right”, which meant bringing it up to the standards of rigor imposed by the General Equilibrium tradition. Thus, in the 1970s the formal modeling of macro in this spirit began, including work on the micro foundations of macroeconomics, construction of an explicit New Classical macroeconomic model, and the rational expectations approach. All of this work rightfully challenged the rigor of the previous work. The aim was to build a general equilibrium model of the macro economy based on explicit and fully formulated micro foundations.

But ‘Technical’ Difficulties Intervene

Given the difficulties inherent in such an approach, researchers started with a simple analytically tractable macro model which they hoped would be a stepping stone toward a more sensible macro model grounded in microfoundations. The problem is that the simple model was not susceptible to generalization, so the profession languished on the first step; and rational expectations representative agent models mysteriously became the only allowable modeling method. Moreover, such models were directly applied to policy even though they had little or no relevance. … [emphasis added]

But There Was a Reason For This: Other Stuff is Hard

The reason researchers clung to the rational expectations representative agent models for so long is not that they did not recognize their problems, but because of the analytical difficulties involved in moving beyond these models. Dropping the standard assumptions about agent rationality would complicate the already complicated models and abandoning the ad hoc representative agent assumption would leave them face to face with the difficulties raised by Sonnenschein, Mantel and Debreu. While the standard DSGE representative models may look daunting, it is the mathematical sophistication of the analysis and not the models themselves which are difficult. Conceptually, their technical difficulty pales in comparison to models with more realistic specifications: heterogeneous agents, statistical dynamics, multiple equilibria (or no equilibria), and endogenous learning. Yet, it is precisely such models that are needed if we are to start to capture the relevant intricacies of the macro economy.

Building more realistic models along these lines involves enormous work with little immediate payoff; one must either move beyond the extremely restrictive class of economic models to far more complicated analytic macro models, or one must replace the analytic modeling approach with virtual modeling. Happily, both changes are occurring; researchers are beginning to move on to models that attempt to deal with heterogeneous interacting agents, potential emergent macro properties, and behaviorally more varied and more realistic opportunistic agents. The papers in this session describe some of these new approaches. [emphasis added]

Some Closing Comments of My Own

So there you go: plenty of tough challenges and a big dose of humility. To some extent here it seems thing run on 30-40 years cycles: Keynesianism from 1945-1975, Rational Expectations DSGE from 1975-2005 and now we’re into the era of complexity and ‘loose’ tools with emphasis on empirics and heuristics rather than formal models. Whether this new approach will deliver more than the old is yet to be seen. After all, one reason that there are so many physicists getting interested in Economics and Finance is that the going is so hard in, e.g., condensed matter physics (superconductivity anyone …). If the economy really is so complex will we ever do any better at the macro scale than we do for the weather and if so will it not rely on some conceptual breakthrough rather than just doing using more hard-core dynamical systems theory and running more agent-based simulations?

That said, as the authors argue, the ’simple’ route isn’t working and the hardness of the path is no reason not to attempt it — an argument in many ways directly inverse to the traditional ‘drunkard-and-the-lamp’ approach in which we restrict our models, often beyond the point in which they remain relevant, in order to maintain analytical tractability. Thus, though cautious regarding what more ‘complexity-oriented’ methods can deliver, I am in wholehearted agreement with the authors that they justify much greater exploration.

Originally status would have developed from some kind of of stimulus-response setup:

    Beating Competitor
            |
            V
      Higher Status
            |
            V            
Better Access to 'Resources'
  (e.g. Food and Partners)
            |
            V            
  Higher Survival Rate /
    More Progeny etc
            |
            V            
  Development of Reward System(s)
   for these outcomes (Food etc)   
            |
            |  (short-circuiting
            |   as with e.g. sex)
            |
            V         
Development of Reward Systems
 for Success in Competition 
     (Higher Status)

So status now has two components:

1. Increase in status improves access to ‘basic’ goods we derive direct ‘utility’ from (food etc)
2. Increase in status provides direct ‘utility’ independent of any impact upon access ‘basic’ goods.

What about respect? It could be argued that respect is a ‘basic’ good directly equivalent to type (ii) status. However I’m not really convinced of this for two reasons. First, ‘respect’ is fundamentally different from ‘normal’ goods in that one can select what you respect (and whose respect you care about). Second, and more importantly, as just outlined above, the desire for ‘respect’ or ’status’ seems to me a ’secondary’ desire, which has come about via a short-circuiting of our basic reward systems for ‘primary/basic’ goods.

Leaving this aside, the crucial point is that type (ii) status results in a pure zero-sum game. Thus, reducing competition for it (perhaps by increasing compassion) might move us to a (more) positive sum situation. Furthermore, the clear distinction between type (i) and type (ii) allow us to separate out ‘competing to survive’ (which might be essential) and ‘competing (just) to win’. This seems an important distinction to make. After all, we can all accept that, in a whole set of situations, successfully competing may be crucial to obtaining the basic resources needed to survive. However as we get wealthier it would seem that this first aspect diminishes in importance and the second (less healthy) aspect of status looms ever larger.

This is a topic I’ve thought about quite a bit before[^1][^2] but on this particular occasion it arose from a discussion with a friend about the size of Cambridge colleges and the growth of the EU.

Having (many smaller) different competing organizations rather than (fewer/one bigger) organization is:

• Good because of variation: the average rate of improvement is proportional to the variance in current quality (cf. Fisher’s theorem for natural selection).
• Bad because lack of standardization means fewer economies of scale and scope and higher transaction costs (e.g. for trade) and greater free-rider issues across jurisdictions/organizations.
• Good because smaller means more responsive to the preferences of participants and fewer transaction costs (e.g. in monitoring and voting) and fewer free-rider problems within jurisdictions/organizations.
• Good because humans ‘feel’ better (more autonomous, more in control of their lives, understand better what is happening to them) within jurisdictions/organizations of a smaller size.

One interesting point is that simple prisoner dilemma type arguments arising from inter-state conflict (whether over territory or over the inter-country rules of the game for things like trade — consider the US vs. Burkina Faso in a bilateral trade negotiation) would imply that there’s is an escalation effect in country size (if you get bigger I want to get bigger). This would then imply that countries are larger than they should be for simple (i.e. ignoring fights with others) welfare maximization for citizens (cf. Christopher Alexander’s pattern for states suggesting a size of between 5-15 million citizens with the fact that almost all states are significantly larger than this).

[Later] The very day of writing this I came across a review of Alesina and Spolaore, The Size of Nations, while idly flicking through old JEL (March 2005) reviews. It appears from the review to make several similar points (not exactly surprising given how the ideas themselves are fairly obvious …):

“The nation-state is defined in terms of a monopoly of coercion and the legal use of force within its boundaries [ed: Weber’s definition]. The central tenet of the book is that the size of nations is determined by a trade-off between the benefits of economies of scale in providing public goods (e.g. defense) and the costs of heterogeneity in preferences over the provision of these public goods.”

“This raises the question why, instead of a unified nation-state, we do not observe a series of overlapping jurisdictions that best resolve this trade-off for individual public-goods. The authors argue convincingly that such a configuration would face prohibitive transaction costs and fail to internalize economies of scope. The nation-state monopolizes the provision of essential public goods (law and defense) and adopts a host of other function because economies of scope and transactions costs. Some functions are delegated to subnational levels of government, but subnational jurisdictions do not cross national borders.” [from Redding’s review, p.161]

[^1]: One particular early idea was whether one could ‘generalize’ some parallel computing ‘results’ such as Amdahl’s law to organizations. The diminishing returns of Amdahl’s law occur because only some portion of the program is parallelizable and hence adding more processors provides ever less speedup as one approachs the basic speed constraint set by the remaining serial part of the program. This problem will be made even worse if there is a need for intercommnication between processors (e.g. due to some part of the program having sequential dependencies as would the be the case where there are set of parallelizable tasks that need to be performed sequentially). Thus, while more processors allow for greater application of the divide-and-conquer effect (and therefore specialization and economies of scale) they may require greater transaction costs in terms of communication/synchronization between the processors. At some point the transaction costs become larger than the divide-and-conquer benefits and the system becomes slower. (This also has connections to the transaction costs theory of the firm, though, there the comparison is not between economies of scale and transaction costs but between transaction costs within the firm versus those outside of the firm — in the market.)

[^2]: A second point was on the empirical evidence on optimal size of such entities. One often hears comments about 5-12 being the optimal size for a team or 300-500 being the optimal size for a community (see e.g. Alexander et al’s A Pattern Language) but I’ve never yet come across (though I haven’t looked that hard) firm evidence on which these figures are based.

Consider a metal arm fixed by a pin. If it is hung vertically then the arm, no matter where it starts, will always end up in the same position. However, if you fix the arm (perfectly) horizontally it will stay forever in its initial position. The first case is ergodic: we converge independent of the starting point to some particular configuration; while the second is ‘path-dependent’ (or dependent on initial conditions): where you end up depends crucially on where you start. The question:

Is animal/technological/historical/linguistic evolution ergodic or path dependent?

More generally, how ergodic or path-dependent are the following processes?

• (Natural) Evolution
• Technological change
• Human history
• Communication systems such as natural languages
• Other symbol systems (e.g. games or mathematics)