In the first post in this three post series, I gleaned a theory of the economic frontier from some of BK’s comments and offered a few of my own responses. In this post, I’ll expound my own theory.

Two general points. First, how the economic frontier advances is both enormously important for human welfare and quite mysterious. It is important because long-run economic growth will determine how well we can mitigate world poverty and deliver ever-improving lives to future generations. A tiny increase in the rate of advance of the economic frontier, say from 3% to 5%, would make our descendants a century hence almost an order of magnitude wealthier. Second, open borders would likely affect the rate of advance of the economic frontier. Before reading BK’s comments, I had pretty much taken it for granted that open borders would boost growth, at least in the short run, as people move from low-productivity countries to high-productivity countries. Based on Clemens (2011)  and Kennan (2012), the modal result of formal studies so far seems to be that open borders would double world GDP, and the assumptions on which this result is based are actually conservative in some ways, e.g., they don’t assume that everyone would migrate to where their marginal product is highest. Negative institutional/productivity side-effects of open borders on frontier countries would have to be very large to offset this, but such effects are not beyond the range of plausibility.

My theory, which I’ll call the “Endogenous Division of Labor” or “EDOL” model, was the topic of the second chapter of my dissertation, Complexity, Competition and Growth (but don’t pay $103, it’s available here for free). More recently, and I think more accessibly, I published a new version as an SSRN working paper here, under the title “Development as Division of Labor: Adam Smith Meets Agent-Based Simulation.” All the data is drawn from a simulation I wrote, which is introduced in this video, and I’ll be happy to send the simulation (as a runnable JAR file) if you’re interested in exploring its properties on your own. It’s not that user-friendly, but I’ll even be glad to give you a tutorial via Skype. I’ll also be glad to present it at academic conferences or seminars or whatever. I think it would lend itself to public presentation quite well, though I haven’t got the chance to transfer. I’m trying to publish it. So far, the Journal of Political Economy rejected it, with some harsh but useful feedback. I plan to submit a completely rewritten version to the Journal of Economic Growth. Any feedback is welcome.

So, down to business.

The first thing to mention about my model is that there are no institutions in it, and no government. It is purely about how markets work. You can say, if you like, that government is implicitly present, enforcing property rights and contracts. Second, as is typical in economic models, agents are homogeneous. There is no high IQ vs. low IQ distinction here: all inter-personal differences are assumed away.

On a more methodological note, the model is implemented using an agent-based simulation. I use the simulation as a substitute for the solving equations. In solving equations, an economic theorist impersonates a Walrasian auctioneer, equilibrating markets by finding a price vector that causes quantities demanded and supplied of every good to be equal. This method of economic theory has been objected to on the grounds of its lack of realism, but I object to it on the ground that it lacks generality. It cannot deal with nonconvexities. The simplest case that flummoxes a Walrasian auctioneer is the Triangle Economy, in which three agents have one x and one y and a utility function u=x^2+y^2. A price more or less than one would cause them all to want to buy the same good; a price of one would split them at random 3/0 or 2/1 in favor of one good or the other; but in any case, the market will not clear. The Triangle Economy is one of a huge range of cases where Walrasian equilibrium fails to exist, including the case with individual-level fixed costs of production in which I’m interested. For more technical details, see the paper.

The model starts by specifying the technology (Figure 1). Each good is a point in L0/alpha space, where L0 represents “how difficult to make” and alpha “how well-liked” a good is.

Figure 1: Specifying the technology

As a professor, I’ve become accustomed to showing students charts whose meaning seems obvious to me, but of which students find all sorts of ingenious ways of misunderstanding. Of course, the reason is that after years of looking at and manipulating and arguing from and through charts generally, and certain standard charts in particular, using them becomes “second nature” in a way that students can’t easily grasp. This chart, however, will not be very easy to understand even for trained economists. But let me try to explain.

L0 may be called, more technically, “labor fixed cost.” Its role lies in the production function, which, for each good i, is:

(1) M_i = L_i – L0_i

On the horizontal axis is “alpha.” This enters into the following utility function:

(2) $latex U = \left(M_T^\sigma + \displaystyle \sum_{i \in V} \alpha_iX_i^\sigma\right)^{1/\sigma}$

What equation (2) says is that there’s a taste for variety, so agents want to consume a wider range of goods in small quantities rather than a narrow range in small quantities; however, on the other hand, some goods are better liked than others, i.e., enter the utility function with larger coefficients.

In the Goods Space chart, each point in the chart represents a different good. Its vertical position represents how hard the good is to make, while its horizontal position represents how well liked it is. I have added extra information to the Goods Space chart by replacing neutral round dots with three types of marks representing different series, thus classifying the goods as:

(a) those for which active industries emerged in all four of a series of simulations with N=50, N=100, N=200, and N=500;

(b) those for which active industries emerged in either the N=50 or the N=100 economy; and

(c) those for which active industries emerged only in the N=200 or N=500 economy.

We see here the phenomenon of technological “low-hanging fruit,” goods which are well-liked and easy to make, being picked first. Later, the easiest technologies are already in use, so further progress depends on “high-hanging fruit” and is somewhat harder. This sounds like a pessimistic result, but as we will see, the EDOL model can yield optimistic results as easily as pessimistic ones. Note, in any case, that when the society runs out of low-hanging fruit, it doesn’t get poorer, it merely can’t grow as fast. The title of Tyler Cowen’s The Great Stagnation: How America Ate All the Low-Hanging Fruit of Modern History, Got Sick, and Will (Eventually) Feel Better uses the phrase “low-hanging fruit” in the same way, meaning not that we are destined to become poorer, but only that further growth may become harder.

How economies emerge in the simulator is too technical for a blog post, but here’s an overview. The model is inhabited by agents. Agents have a few skills, which get swapped in and out randomly when unused. They can self-supply some goods. They also have money and may have opportunities to trade. Because agents can’t make everything themselves, and because they value vareity, they may want to buy goods on the market, using their cash reserves but also earning more reserves by selling some of the goods they make at home. Because there are fixed costs to producing each good, it is inefficient for agents to make multiple goods themselves, and they usually specialize in a single good and buy everything else from the market. Trade is mediated by a retail sector. Retailers are founded by agents. Each retailer trades in only one good. It does not explicitly maximize profits, but instead adjusts prices in order to balance supply and demand over time while charging a markup to compensate its owner-operator. When the Simulator launches, there will be only agents, no retailers. Autarky. But soon retailers begin to be founded, and a division of labor emerges. A larger population makes it possible to overcome the fixed costs and transactions cost (i.e., retailer costs) of introducing a new good. Consequently, the variety of goods available increases, and productivity and living standards rise.

The EDOL Simulator is able to map a goods space into an aggregate production function linking output to capital and population. Let me unpack that. Start with a goods space, a level of “capital,” which augments labor according to the formula L=1+K^a, a<1, and a population. Set the model in motion. Let the retail sector emerge and the model equilibrate, i.e., the moving average of utility settles into some roughly stable level. Now vary the level of capital, and/or the population, and run to equilibrium again. Gradually data accumulates. What results is that from a goods space like that shown in Figure 2…

Figure 2

… you can derive a production function like that shown in Figure 3:

Figure 3

Some things to note here. First, the larger the population, the greater the payoff to capital. Capital allows more goods to be introduced, but this is less useful if the population is not large enough to supply labor and distribution for a wide variety of industries. Second, returns to capital at the aggregate level are much higher, especially in the N=500 case, than returns to capital in any given production process. In this case, the exponent on capital was 0.5, yet in the N=500 case, for k>3, a regression of the log of GDP against the log of capital yields an estimate of the aggregate production function as y=0.7*k^1.08. By allowing for the introduction of new goods, by inducing a more intensive division of labor, capital raises productivity so much that it output rises more than proportionately with capital. Third, the big lesson of the EDOL model is much the same as the big lesson of the first three chapters ofThe Wealth of Nations. It might be called a formalization of Adam Smith.

We can stop here and start listing some stylized facts the model can (help to) explain.

1. Why are there cities? Cities arise because they facilitate an intensive division of labor, raising productivity enough to offset the artificial scarcity of certain resources, especially land, which they induce. Of course, this is also why urbanization and development exhibit such a strong correlation.

2. Why is free trade so beneficial? Empirical studies such as Sachs and Warner (1994) and Dollar and Kraay (2001) find gains that seem larger than the neoclassical theory of comparative advantage, with its “Harberger triangles” of welfare increase, can explain. This is because countries that open themselves to free trade can plug into a global division of labor, finding new narrower niches of specialization while getting access to a wider variety of consumer, intermediate and capital goods.

3. How does the economic frontier advance? Doubtless, new ideas are important, but growth theory since Romer (1991) may have overstressed the role of R&D and invention. We can agree with Romer in characterizing the state of technology as a set of blueprints, but just because a good has been invented– just because the blueprint is available– doesn’t mean it’s economically viable. A lot of technological progress may consist of occupying, or exploiting, a goods space that technology had already mapped out. What makes a good economically viable is primarily the size of the market (population) and the availability of capital. The best way to promote technology may be, not to fund science or even to protect patents, but to liberalize trade, encourage savings and investment (down with Social Security!)… and open the borders.

4. Why “and open the borders?” Because it grows the market, which can make latent technologies economically viable. For one thing.

5. If science is so important to progress as economists claim, why do you sometimes meet these engineers and inventors who are beating their heads against the wall because they have brilliant ideas and can’t get the capital to fund them? Are these guys just deluded about the value of their ideas? Not necessarily. Engineers and inventors add blueprints to society’s reserve of technological knowledge. In other words, they populate the goods space. But society probably isn’t fully exploiting the goods space. There are probably a lot of latent technologies, things that technologists know how to do, but which can’t yet be run on a paying basis. Some frustrated may be quite right that they’ve invented a technology that could change the world. But the economy needs to develop further before that technology can be activated.

6. Why did Western Europe dominate the world so much in the 19th century? And why did East Asia experience such a spectacular rise in the late 20th century? There are a lot of candidate explanations for these ones, and several may be valid, but an important factor is access to the sea. Europe is a very strange continent in one respect: its ratio of coastline to surface area is extraordinarily high. It is full of peninsulas: Scandinavia, Denmark, Iberia, Italy, the Balkans, the Peloponnese. Plus the British Isles. In the age of sail, when water transport was far cheaper than the alternatives and no slower, easy access to the sea made it easier for Europeans to move goods and people around within Europe and to other parts of the world, greatly enlarging the market. East Asia, too, is notable for its peninsulas (e.g., Malaysia, Korea) and islands (Japan, Taiwan), and when containerized shipping lowered the cost of moving goods by sea in the late 20th century, East Asia was poised for an export-led manufacturing boom.

7. Why do US cities seem to specialize in certain industries, e.g., the Bay Area in high technology, Boston/Cambridge in higher education, New York in finance, Washington in government/lobbying/journalism, Houston in energy, Detroit in cars, Seattle in airplanes, LA in movies, Nashville in music? Economies of scale. These don’t just operate at the level of the firm. They can operate at a higher level. Alfred Marshall coined the term “external economies of scale” for this, but his explanation bundled a lot of things together. It may be true, it may even be important, that many benefits from being “where the action is,” so to speak, in a particular industry, are pure, disinterested spillovers. You might learn a lot about politics in DC just by hanging out at certain parties, from people who are talking just for the fun of it or to be polite, about what they know. But in other cases, the market size is what matters. You don’t want to run a full-service think tank in a town where only one person is informed about an important issue, say health policy, or foreign affairs. That person might die, or move away, or clash with the culture of your organization. They might also perceive that they’re a monopolist vis-a-vis your think tank– without them, you’ll have nothing to say on a key issue– and “hold you up,” demanding better terms. You want a deep labor market, so that everyone in your organization is easily replaceable. They, too, want a deep market, so that if your think tank treats them unreasonably they can move to another one. And so everyone assembles in DC. Similarly, screenwriters and actors and producer all want to live in LA. All this regional specialization makes the US economy more productive. And of course, open borders would allow that to happen at the global level. (More than it does already.)

8. What’s the deal with jobs? Why do they seem to be a peculiarly modern concern? There has always been work, but people haven’t always had jobs, exactly. In some parts of the world even today, the bad situation to be in is not so much to be jobless as to be landless, because subsistence agriculture is still the norm. If you have land, you have work: you work the land. Modern capitalist economies are different because they have much more complex and productive networks of specialization. Autarky is still an option in principle– an unemployed homeowner could dedicate himself to growing peas and beans in his backyard– but since its productivity is so negligible compared to occupying even the least favorable specialized niches in the economy– say, selling popcorn in a movie theater– that we don’t even take the autarky option into account. Farmers in advanced modern economies, of course, are no more autarkic than anyone else: they produce the vast majority of their food for others, relying on the larger economy for equipment, fuel, finance, and nowadays even the best GMO seeds to do so, and they enjoy a far higher living standard than subsistence farmers would.

I could extend this list further, but let me focus on one issue that will tie it back to open borders. I said in Part 1 that I had a fifth reason for being skeptical of BK’s ideas about why high IQ people are less productive in many regions where they’re in a minority. I’ll call it the automotive revolution, opaquely for the moment.

Transportation technology facilitates the division of labor. Improvements in transportation technology permit a more extensive division of labor. Today, there are five major modes of transport: air, water, rail, motor (vehicle), and pipeline (only for fluids). Air is by the far the fastest but also by far the most expensive. Water is by far the cheapest but also by far the slowest. Rail is much cheaper than motor, though more expensive than water, but it doesn’t have “last mile” capability. Goods shipped by rail usually have to go intermodally with trucks. For this reason, rail is likely to be slower than motor, even though the fastest trains go as fast or faster than the fastest trucks. Trucks dominate, carrying 70% of US freight by value.

But it was not always so. In the 18th century, shipping goods from London to Edinburgh by sea and by land took about the same time but was a couple orders of magnitude cheaper by sea. Since then, shipping has improved. Steamships are faster and more reliable than sailing ships. But land transport has improved much more, first with the advent of the railroad, second, even more importantly, with the automotive revolution. Consequently, it has become much less relatively important whether two places are connected by sea, and much more important whether they are connected by a road. Economic space has been drastically transformed. On land, economic distance is usually roughly proportional to physical distance now, obviously excepting off-road destinations. Meanwhile, for most purposes– since the speed of trucks is usually more important than the cheapness of ships– all economic distances over water are larger than equivalent physical distances over land would be.

The automotive revolution transformed the economy. It hollowed out many city centers, as people could live in quiet green suburbs while still benefiting from an intricate urban division of labor. The 1920s and 1930s probably saw the fastest productivity growth of the 20th century, in an important degree thanks to the automobile. Now, while probably almost every region of the world could make some use of the automobile, some places were better positioned to benefit from it than others. A big continental land empire like the United States was perfect. Once the highways were built, the common man could zoom from Chicago to New York in a (long) day. The division of labor could elaborate itself on a continental scale. Continental Western Europe, once it got the world wars out of its system, was well positioned too, as cars and trucks could drive from the toe of Italy to Granada or Normandy or Berlin or the northern tip of Denmark. The British Empire, by contrast, suddenly made much less sense, as its sea links lost economic importance. And Britain itself, as an island, was perhaps not as well served by the advent of cars as were France, Germany, and the Benelux countries. It saw three decades of relative decline after World War II, and the automotive revolution may have been partly to blame.

Now compare the situation of the white post-colonial diasporas in Rhodesia/Zimbabwe, South Africa, the Caribbean, and South America. The relative economic distance to Europe has suddenly increased. They are not well positioned to plug into Europe’s new automotively-enhanced economy. What matters now is the volume of economic activity in a given land mass, and this was everywhere inferior in the colonies to what it was in western Europe or even Great Britain, let alone the United States. So why were the European diasporas to some extent left behind economically, becoming less productive than their genetic kin in Europe? It might not be because they were in a minority, and a poorer/low IQ/less enlightened/whatever minority was making the rules. It might be because the automotive revolution favored big continental empires like western Europe and the United States, and to a lesser extent Japan, but certainly not Caribbean islands, or remote landlocked Rhodesia/Zimbabwe, or faraway Argentina and Chile, or Brazil with its population concentrated on the seacoast, or Spanish America where the elite had often lived in coastal cities and felt closer to Europe than to their own mountainous hinterlands.

In the next post, I’ll try to appraise IQ-based theories of the wealth and poverty of nations in the light of my own EDOL model, and vice versa. I don’t know where I’ll come down, because I need to read more Garett Jones and more of BK’s links.