Post by Nathan Smith (regular blogger for the site, joined April 2012). See:

At a family reunion in Alaska in August 2007, during a beautiful hike to a place called Exit Glacier, several strands of thought I had been mulling over came together and exploded in my mind. I was in a state of intense intellectual excitement. Without diminishing my enjoyment of the company and the beautiful scenery, I felt an urgent need to be somewhere else, namely, sitting in front of a stack of papers, scribbling equations. David Warsh’s book Knowledge and the Wealth of Nations had clarified for me the bottleneck that economic theory was in– that theory relied on a notion of “equilibrium” to close models which presupposed constant returns– and I saw the way out of it– implement market equilibrium by the interactions of agents in a computer memory instead of by solving systems of equations. Equations, and especially mathematical optimization, still had its place, for agents’ methods of maximizing utility subject to a budget constraint would be lifted lock, stock, and barrel from traditional methods… though more modifications were needed, as I learned the hard way. My first attempt (as a graduate student that fall) involved 90+ pages of code and was a complete fiasco. I got no results at all. Desperate after a failed presentation (though Professor Rob Axtell, sympathetic to my Herculean if futile efforts, asked for my code for an excuse to give me an A-), I went home and read Joseph Schumpeter’s Theory of Economic Development for inspiration. After an enormous amount of work, many rethinkings and failures, I succeeded, yielding a dissertation, Complexity, Competition and Growth (free version here), and helping me to land an academic job at Fresno Pacific University. So far, frustratingly, I haven’t managed to get what my dissertation chair called “a breakthrough” (I agree) into the academic journals, for whom, I suppose, the piece is intimidatingly eccentric and complex (and perhaps arrogant in its sweeping claims, though I can’t really scale them back much). Here’s my latest attempt, entitled “The Aggregate Production with Endogenous Division of Labor,” submitted last week to the Journal of Economic Growth.

This is connected with open borders because it is a theory of increasing returns and therefore of how economic activity tends to concentrate itself. Surely this is one of the most obvious facts about the economy. Economic activity is concentrated spatially: we call those places cities. Economic activity is concentrated temporally: we call the working day. Some theories of economic booms and busts– “coordination failure” models– see them, essentially, as a tendency for economic activity to concentrate itself in time, but I wouldn’t stress that too much. Of course, economic activity is concentrated in certain countries, too. We call those developed or rich countries; those where economic activity is not concentrated we call developing or poor countries. Certainly, the principle that makes people concentrate in cities is not the only principle at work in determining the wealth and poverty of nations. But it probably is one of the principles. In “Geography and Economic Development,” Sachs, Mellinger, and Gallup (1999) make a strong case that geography does much to determine the development, and one of the ways in which it does this is that it places landlocked places, places far from coasts and with poor access to the sea, at a disadvantage, because they can’t plug into networks of international trade.

Imagine what would happen if economic activity has a tendency to concentrate itself but people are not allowed to concentrate themselves. In the places where economic activity is concentrated, the ratio of economic activity to population will be high, and people will be rich. In the places where economic activity is not concentrated, the ratio will be low, and people will be poor. Of course, it’s never as simple as that. Economic activity can’t usually concentrate itself without people concentrating themselves to some extent. But it seems to be true that massive inequality tends to arise when mobility is restricted and people are not allowed to go where the jobs are, or where the high wages are.

Why does economic activity tend to concentrate itself? Adam Smith understood. The first three chapters of The Wealth of Nations are titled:

I. Of the Division of Labor, which begins by asserting that “the greatest improvement*17 in the productive powers of labour, and the greater part of the skill, dexterity, and judgment with which it is any where directed, or applied, seem to have been the effects of the division of labour.”
II. Of the Principle which Gives Occasion to the Division of Labor [namely, the human propensity to truck, barter and exchange]
III. That the Division of Labor is Limited by the Extent of the Market

When people live in close proximity, they can specialize more, and trade with more specialists. There are all sorts of jobs, and all sorts of services, which one can do, or hire, in New York City, that one can’t do, or hire, in a small town. Cuisine and culture are the most obvious, because here the consumer observes the benefits directly. Foodies and theater fans will fare much better in Manhattan than in Muncie, Indiana. But the same holds in business. If you want to run a think tank, there are big advantages to doing it in DC, where the pool of specialists is deep and rich, and you can find someone with experience privatizing electricity generation or someone who knows a lot about factional infighting in Tajikistan. A friend of mine worked as a professional trumpet player in Chicago, and made a decent living. Now, for the sake of his wife’s job, he lives in a small town in Maine. You can’t make a living by trumpet gigs there. Of course, what business there is might be easier to catch, because the competition is slight, too. But that means that if you want to hire a professional trumpet player, for an Easter service, say, or a wedding, it won’t be easy. It’s not just a matter of urban vs. rural or city vs. small town. I live in a medium-sized city, Fresno. The eating’s OK, but it has far fewer vegetarian options than DC. Classical music concerts take place every month or so, maybe. There’s a continuum, with the abundance of specialized jobs and the availability of specialized services steadily increasing as the city grows. More than that, cities themselves specialize, with LA specializing in movies, Houston in energy, Seattle in airplanes, Detroit in cars, Palo Alto in information technology, New York in finance and culture, Boston in higher education, Washington, DC, in politics and government.

Of course, there’s a downside to concentration, too. People may suffer from one another’s negative externalities– smog, car noise, light pollution, crime– but more importantly, the free goods of nature become scarcer. If you want to live on a large plot of land, that’s exorbitantly expensive in Manhattan. That said, Central Park is available to all, and I’ve often noticed that if you want to take a nice walk and enjoy greenery, it’s sometimes easy to do this in big cities, with their verdant parkland, than in the countryside, with its agriculture and fences. But the free goods of nature are also inputs to production, and for production processes wherein the free goods of nature are important, economic activity has to spread itself out through rural areas. Farming, in particular, has to be spread out over vast expanses of rural territory. Farmers need services– grocery stores, auto dealers, schools, hospitals– so other economic activities, besides farming itself, follow them. Tourists seek beautiful natural scenery, and economic activity follows them, too. Then there’s logging, and drilling for oil and gas, etc. The free goods of nature draw people to rural areas, small towns locate near them, big towns locate near small towns. Meanwhile, when large-scale economic activities don’t particularly depend on the free goods of nature, but also have relatively few synergies with other large-scale economic activities, it may not make sense to locate them in the same city, driving up land prices and giving rise to the usual negative externalities of urban life without important economic complementarities to offset these costs. All these reasons explain why we don’t all concentrate ourselves in one enormous city.

By the way, feel free to challenge me on this, but I think it’s fair to say that neoclassical economics, the mainstream paradigm in economics today, is largely blind to all this. To see why, think about a standard supply-and-demand chart, the central concept of neoclassical economics. Demand slopes down. Fine so far. Supply slopes up. Why? Because marginal costs rise when you produce more? Do they? It seems more typical, if anything, for prices to fall when suppliers can produce in bulk. In that case, however, it doesn’t make sense to view suppliers as “competitive” “price takers.” But neoclassical economics must impose price-taking, because it predicts what will happen in markets by solving a system of equations for the “market-clearing” price that equilibrates supply and demand. Without that device, it doesn’t know how to close a model. Of course, neoclassical economists know that economic activity tends to concentrate itself, and most of them probably understand clearly enough why, namely the benefits of specialization and trade. But when making formal models, they habitually write down production functions with constant returns to scale, thus ruling out an important role for specialization, trade, and the division of labor, and making the existence of cities suddenly mysterious. That was the challenge I set out to tackle.

In the latest iteration of my simulation-based economic modeling, I report a lot of results, but it’s hard to know the best way to elucidate their significance to lay readers, or for that matter to professional economists, who are in some ways in a better position to understand what my model does, but in some ways, not. In some ways, well-trained professional economists may even be at a disadvantage because they have to unlearn certain habits, such as looking for market-clearing prices and “interior solutions” and shunning “corner solutions,” increasing returns, and chaotic, imperfect competition. My work is very close in spirit to Adam Smith and the classical tradition, but from the neoclassical point of view it is definitely “heterodox.” Indeed, if I ever manage to publish versions of these results in both the academic journals and the popular press, it will be interesting to see whether professional economists or lay readers are more receptive. At any rate, the results of one simulation run are shown in the chart below:

Each point in the chart represents a simulation run, with the shape of the point roughly indicating total GDP. The curves represent “isoquants” derived from the production function I estimated from the data. This estimate involved regressing log GDP against log capital and log labor, which yielded the following:

where Y is income, K is total capital, and N is total labor. What matters here is not the precise values of the coefficient and exponents, which would vary randomly depending on the technological specifications, but the high degree of increasing returns that the production function exhibits. If such a production function describes the US economy, a doubling of the labor supply with no influx of new capital would only reduce per capita income of all residents slightly. In the model, capital’s share of income exhibits no tendency to be equal to the aggregate elasticity of capital. Returns on capital and entrepreneurial profits together generally comprised a little over half of income in the simulation, with the rest going to labor. When society’s capital stock increased, the return on capital fell, consistent with the neoclassical prediction, except much less precipitously. A tenfold increase in the capital stock would reduce the return on capital by less than half. Meanwhile, holding the capital stock constant, an increase in labor, holding the capital stock constant, tends to raise the return on capital almost in proportion to the increase in labor, while the effect on the wage of labor, though it is usually negative, is mild.

How is this possible? Because population growth leads to the introduction of new goods, the intensification of patterns of specialization and trade. If the lessons from this model cross-apply to the US economy, under open borders we would see the big cities get even bigger, and even richer in the variety of goods and services they have to offer, while many small towns would grow into big cities, and new towns would spring up– so there would be no shortage of small town life for those who prefer it, but there would be a wider variety of urban life available to city-lovers, including some cities bigger than any available now. (Not that new cities would be founded to surpass New York. Rather, New York itself would surpass what it is now, while other cities would become what New York was.) Wages wouldn’t fall much if at all for low-skilled workers. They might find new niches. Owners of other factors– land, capital, entrepreneurship– would enjoy new opportunities and rising incomes. Specialized jobs that don’t exist now would appear. Specialized jobs that currently exist only in, say, New York, would appear in other places. Foreigners would benefit too, not only from access to “public goods” or “institutions,” but from being able to plug into America’s complex division of labor. New patterns of specialization might emerge at the level of cities, with some cities becoming global rather than merely national hubs for this or that industry.

You can make a strong case for open borders from the standpoint of neoclassical economics. The case for open borders is largely the same as the case for free trade, except that instead of trading with people living abroad you trade with people from abroad now resident in your own country, likely in goods and services that, for whatever reason, can’t be traded internationally. But endogenous division of labor strengthens the case for both free trade and open borders.

Nathan Smith

Nathan Smith is an assistant professor of economics at Fresno Pacific University. He did his Ph.D. in economics from George Mason University and has also worked for the World Bank. Smith proposed Don’t Restrict Immigration, Tax It, one of the more comprehensive keyhole solution proposals to address concerns surrounding open borders.

See also:

Page about Nathan Smith on Open Borders
All blog posts by Nathan Smith