The Free Thinker

The attachment is a draft introduction to a book I'm thinking of writing as a dissertation.  Feedback is very welcome.  Thanks.  Download Prometheus and the Invisible Hand - Intro

Recessions in a Simulated Economy

I've just been getting some results from an economic simulation.  Here's a chart:

The data is based on running my economic simulation with 2000 agents, for 500 turns.  My goal was to produce a "circular flow" economy, which is always in motion at the micro level-- firms are being founded, and dissolved; goods are being produced, sold, consumed; agents are optimizing consumption, getting jobs, sometimes going into businesses, or exiting it to become wage earners again-- yet exhibit a rough macro-level stability.  The economy always seems to operate at around 80% of capacity (where "capacity" is defined as the maximum that could be produced if all workers were employed and all firms were operating at the efficient scale).  Well, not at first: it takes a little while for it to hit its stride.

What I find interesting is that my simulated economy seems to have recessions.  That was not part of the plan, and it's not part of what I'm planning to explore for my current project-- maybe later.  But it's very interesting.  Unemployment is generally around zero, then shows big spikes.  It seems to be driven by inventory overshooting: firms decide they have enough, and start to sell it off.  The real wage (not shown) drops when unemployment is high, as you'd expect.

There's no government in this model.  No technological change.  But also no "market clearing": firms are searching for the right price level through trial and error.  Whatever the reason, that seems to be enough to cause recessions.

Prometheus and the Invisible Hand

My excuse for not posting lately is that I've been absorbed by (obsessed with) a computational model I'm developing.  Perhaps foolishly, I signed up for a class in which I committed to producing a model that implements the ideas that will hopefully turn into my dissertation.  On the plus side, I'll have a big head start on my dissertation.  On the minus side, it's a very ambitious class project, and there's not much "deliverable" between zero and a fairly advanced stage of development, where the importance of what I'm doing should become visible to someone not versed in the theoretical and technical arcana of what might be best described as a nascent sub-field (which might someday be called "agent-based endogenous growth theory").  So I've been in an ecstasy, or frenzy, or agony (who knows?!), first of epic calculus/algebra problems, in which I made embarrassingly many false turns and ran into lots of dead ends-- it's not quite the case of the engineer who makes one wrong calculation and the bridge falls down, but I know how he feels-- and then of coding Java to distribute firms on a map, to make a GUI (graphical user interface) so that the user can try out different parameters, and so on.  I'm nowhere near there yet.  Meanwhile, there are classes, assorted tasks for professors, and plans to spend next summer in St. Petersburg at a think tank...  All in all, I feel like a juggler who is always on the brink of losing control, of missing one movement and watching the whole elaborate dance of levitating balls crash to the ground.

But since I'll have to do so at some point, I might as well try to convey what it is I'm trying to do.  Adam Smith founded the discipline of economics by writing The Wealth of Nations, a massive work whose impact can mostly, however, be boiled down into two simple, but earth-shakingly powerful, concepts: 1) the division of labor (cum specialization and gains from trade), and 2) the "invisible hand" of the market.    

The latter insight is, today, usually conveyed using demand and supply charts like the one shown on the left.  Smith did not have the benefit of graphical economics and had to explain the insight in words, applying it to hundreds of different cases.  An economics professor today will simply say that the "market clears" at the intersection of the demand and supply curves.  The stories about how the price gets to the market-clearing value tend to be highly plausible but, at the same time, a little vague.  What is clear is the case when the price will not converge to the market-clearing price, namely: monopoly.  If there is only one supplier, not constrained by credible threats of entry from other potential suppliers, the monopolist can increase profits by setting a higher price.  Oligopoly-- when there are several suppliers in an industry-- can be modeled in different ways: there is a "Bertrand model" according to which two suppliers drive the price down to the market-clearing level, and a "Cournot model" which generates an intuitively appealing result, that prices gradually converge to the market-clearing price as the number of firms rises to infinity, from some questionable assumptions about how markets operate.  None of this fits with the idea of the "invisible hand."  Monopoly and (maybe) oligopoly are situations of market power, in which the price arises from deliberate decisions by identifiable economic actors.

But most economic models jump over this to the case of "perfect competition," in which all agents are "price takers," which have no power to set the price but must charge whatever prevails in the market.  The idea is that if a firm tries to charge (even a penny!) more than the market price, it will lose all its business, and if it charges less it will fail to cover its costs and go broke.  Presumably no market realizes this ideal but many come close.  Prices must arise somehow, but none of the agents feels like he is setting them; they all feel that forces outside their control, perhaps mysterious forces that no one clearly understands, are driving the changes in the price. 

The trouble is that Adam Smith's insights, if taken to the limit, become contradictory: the "invisible hand" is at odds with the division of labor.  Suppose we carry the division of labor to a logical extreme, so that every single person has a single ultra-specialized job which no one else does.  In that case, there can be no competition!  If no one else does what I do, so no one can compete with me, how can I be a perfectly competitive price-taker?  Everyone is a monopolist.  To put the problem in more standard language, the division of labor is an increasing returns to scale argument-- because "the division of labor is limited by the extent of the market"-- while the invisible hand is a constant returns to scale argument.  The core growth model of modern macroeconomics, the Solow model, assumes from the outset that economies of scale have been exhausted and that society has an aggregate production function with constant returns to all factors of production (that is, capital and labor), jointly.  For a hundred years what Austrians call the "Walrasian" (a.k.a. neoclassical) tradition in economics has been gradually refining the assumptions surrounding efficient markets and perfect competition, producing theorems which routinely serve as inputs into other economic models, yet which depend on, and arguably are fatally vitiated by, assumptions such as constant returns to scale.  The power of Walrasian economics is that it is mathematically tractable.  It generates models that can be reduced to systems of equations and published in journals.  The Austrian school, which has resisted the Walrasian approach, has produced brilliant thinkers but has been left out of the mainstream because their scruples impede their ability to make mathematical models, forcing them to rely on verbiage and rhetoric.  This has made some of them-- Hayek, Schumpeter-- famous public intellectuals, but has marginalized the Austrian school within an increasingly rigorous-- with "rigor" being understood as closely linked to mathematical modeling-- discipline.  Yet the requirement of constant returns for normal market-clearing means that Adam Smith's division of labor insight has been neglected.

Computer simulations can do a lot of things that analytical models-- models that can be reduced to equations-- can't.  What got me started in agent-based endogenous growth theory was David Warsh's book Knowledge and the Wealth of Nations, a sort of intellectual history in economics with a focal point in the publication of "Endogenous Technological Change" by Paul Romer in 1990.  That, and my work with an aspiring start-up, Loft Aeronautics, last summer, which (a) led me to do a lot of research into the economics of transportation and thus economic geography, and (b) was a fascinating glimpse of entrepreneurship from the inside.  I wanted to model how an entrepreneur decides whether to produce a new good, something that isn't possible under the traditional Cobb-Douglas consumption and utility functions.  It turns out that minor modifications to the Cobb-Douglas production function make it amenable to the introduction of new goods (and also backwards-compatible, generalizable to the past when currently-available final and intermediate goods were not available).  The model rapidly moves beyond the range of analytical tractability, but I had a vague idea how one could specify and "solve," or perhaps not that-- the term either acquires a different meaning or becomes meaningless-- but at any rate study, the model using computers.  It turned out that my school, George Mason, has one of the leading specialists in computer-based (more specifically, "agent-based," because the modeling technique involves creating arbitrarily large numbers of agents in a computer and programming and then observing their interaction) economics, Robert Axtell.  So I've been pursuing it ever since.

Confused?  Not surprising: I don't fully understand it myself, I'm still working on it.  At some point I should be able to offer illustrative computer programs which, however, will still require heavy theoretical, even philosophical, support.  But a word on the title of the post: Prometheus and the Invisible Hand occurred to me the other day as a book/dissertation title.  Economists don't typically write books for their dissertations: more typical is to write three articles.  But I think it would make sense to buck the trend and publish this as a book.  I could distill it into articles, but it's a book-length idea.  Or rather, it's the germ of a research program of whose influence on the discipline I have a vaguely grandiose notion-- even if it turns out to be a lot smaller than I envision it could still become a significant sub-field-- and even the germ is a book-length idea.  But also, I want to integrate the modeling approach with economic history.  Prometheus, of course, is the figure from Greek mythology who stole fire from the gods and gave it to man (and was cruelly punished for it...); in modern times he lingers as a highfalutin symbol for technological progress.  What I want to do is (a) to integrate technological progress and the operation of markets at the theoretical level using computational and agent-based approaches that transcend the limitations of the traditional analytical approaches, and then (b) to show how phenomena observed in the simulations play out in the actual history of technology (and thus I could realize a bit of a long-ago dream of being a historian).

Since I've had dozens of book ideas and never written, let alone published, a book, it's possible this is all vainglory.  Still, it's exciting.

An Agent-Based, Spatial, Endogenous Growth Model

Apologies to regular readers for posting something rather drier and more technical than the usual fare on this blog, but I wanted to post a sketch of the model that I hope will become my dissertation.  It's a model of economic growth and technological change.

Increasing Returns

The first chapters of Adam Smith’s The Wealth of Nations contain two powerful and intuitive ideas, which however have proven proven challenging to model formally: (a) specialization and gains from trade, which is closely related to the ideas of increasing returns and economies of scale, most vividly illustrated in Smith’s account of a Pin Factory, (b) “the division of labor is limited by the extent of the market,” which in Smith is explicitly a geographical concept: large cities allow more division of labor than small towns, which in turn allow more than villages, etc.  By contrast, contemporary economic models generally assume constant returns to scale.

Technological Progress

Division of labor and increasing returns are linked in several ways to another old-new idea in economics: the importance of knowledge and the introduction of new goods to economic progress.  Knowledge itself is characterized by increasing returns—ideas are “non-rival” and, once developed, can be spread at low cost—and developments at the technological frontier often open new possibilities for division of labor (a concept akin to introduction of new goods since newly subdivided tasks can be thought of as new goods) and economies of scale.  Paul Romer has played the leading role in mainstreaming the economics of “endogenous growth,” so called because it seeks to endogenize the (in)famous “Solow residual,” the portion of growth which, according to the Solow model, is not explained by capital and labor, and so is attributed to “technology.” 

In Romer’s model of endogenous growth, entrepreneurs invest in research to develop designs for new goods.  Oddly, in Romer’s model, there is nothing exogenous in the invention/discovery of new goods at all: given a certain investment in research, new varieties will always be invented, and these varieties enter symmetrically into production functions: every design is as useful as every other, and none ever becomes obsolete.  One of the goals of the model I am developing is to capture the notion that the possibilities for technological advance are exogenous, out there, not knowable in advance.  We discover them, we do not make them.

Did the Automobile Destroy the British Empire?

I just thought of a theory that might make a maddeningly interesting dissertation...

Might the automobile explain the dissolution of the British empire?  When the British empire first began to take shape, ocean-going ships were by far the cheapest mode of cargo transport.  Well, they still are.  But.  Surface transport was far more expensive than ocean shipping, and it was also not much faster.  Think of having to carry mail and freight overland by horse and carriage.

If water transport is both cheaper and as fast or faster than surface transport, trade patterns will naturally be predominantly maritime.  Factory production will be located along coastlines, and manufactures will be shipped first of all to other coastlines.  Inland, pre-industrial modes of production will be more competitive with factory production, because greater economic distance will undermine the opportunity to benefit from economies of scale.

If trade is predominantly maritime, a maritime empire makes sense.  It can create value by enforcing contracts and facilitating exchange.

Beginning in the 19th century, a new, much faster and bulkier form of surface transport developed: the railroad.  That would seem to undermine the logic underlying the British maritime empire, because more trade would be oriented overland.  In practice, it didn't, of course: the British empire did good business building the railways.  But then, it took quite a while to build the railroads, and longer for the economic and cultural effects of the railroads to play out.

In the 20th century, the automobile came along, a machine with access characteristics far superior to those of the railroad.  (That is, trains go to the station; cars go everywhere there's a road.)  This caused a strong increase in the efficiency of surface transport of both people and cargo, relative to the maritime alternative.  The result should be to reorient trade away from far-flung maritime connections to closer-to-home surface connections.  The British empire would therefore become less harmonious with trade networks, and its economic raison d'etre would be considerably eroded.  By contrast, the United States, with its contiguous territorial landmass, would have its economic integrity reinforced by the new technology.

Could be right, or not-- I'd have to study it a lot more.  Certainly an interesting possibility.

Immigration and the Harberger Triangle

I just had a brain-wave for a dissertation topic. In a debate on immigration at EconLog, anti-immigration commenter Tino responds to my argument that the consumer-surplus benefit to natives from immigration outweighs the effect on natives through the tax-and-transfer system even if the latter is negative (though I don't think it is):

7. “but it's pretty clear they overwhelm the pocket-change redistribution that immigrants cause through the tax-and-transfer system, even if those did (contrary to fact) hurt the native-born.”

More evidence of bias! Borjas estimate of gains from trade to Americans is 10 billion per year. The lowball estimate of the tax-and-transfer estimate of low skilled immigrants is 90 billion per year.

Now, I've seen this Borjas analysis. It's based on a method of estimating the gains from trade known as the Harberger triangle. The Harberger triangle, however, tends to yield quite low estimates of the gains from trade. Most trade economists today think the gains from joining in trade and globalization are much bigger-- and certainly empirically "globalizing" countries have a much bigger growth advantage over non-globalizers than Harberger triangles can explain.  So trade economists have constructed various models to show why this might be the case.

What I could do is revisit Borjas's estimates of the gains of trade from immigration by applying more up-to-date international trade models to the analysis of the gains from immigration. Probably this would lead to much larger estimates of the gains from immigration, but (if I do it) we'll see.