The Comparative Advantage of Cities

Date December 16, 2013
Speaker Donald R. DAVIS(Kathryn & Shelby Cullom Davis Professor of Economics & International Affairs, Columbia University)
Moderator SAITO Yukiko(Fellow, RIETI)


Donald R. DAVIS's PhotoDonald R. DAVIS

In our research, we asked a question that is fundamental to understanding national and regional economies: what determines the spatial distribution of skills, occupations, and industries across cities? Each of these items varies with the size of the city. I will discuss the comparative advantage of cities at the levels of theory and data (Note1).

To start with some examples, first, the wood product manufacturing industry is a relatively low-skill occupation in the United States (average education: 12 years). One might think that big cities produce more of everything compared to smaller cities, thus as city size increases, population would increase as well as wood manufacturing. In that case, plotting wood manufacturing employment against city size would create an increasing graph. Or, one might assume that as a low-skilled occupation, there would be more of such employment found in smaller cities, creating a decreasing graph. As well, one might conjecture that there is a city size perfect for manufacturing wood products, so the graph would first increase with the population and then decrease. In actuality, our plot for 276 metropolitan areas (cities including their greater areas) of employment against city size, i.e., the log of employment in wood manufacturing against the log of the population size, is an ascending graph. The slope of the curve of the locally weighted linear regression, as a description of the increase in the graph, gives us an elasticity. That is, as the population rises by 1%, by what percentage does employment in wood manufacturing rise? These elasticities are key.

Machinery manufacturing (average education: 13 years), a higher skill industry, presents the same graph relatively, but the slope is steeper. This indicates that employment in machinery manufacturing rises more with a 1% increase in population size than in the wood product manufacturing industry. The computer and electronic products industry (average education: 14 years) rises even more steeply. The general trend is that larger cities have greater employment, but as you move from lower to higher skill, the elasticity of employment with respect to city size rises.

In our theory, the comparative advantage of cities is based on two elements, of which the first is the comparative advantage of individuals. By picking any two people and ordering them by skill, and taking any two activities or goods and ordering them by skill intensity, the more skilled individual of the two will be more productive relatively in producing the high-skill-intensive good.

In urban models, a tractable model is required, so there is often only one or two types of labor investigated in terms of individuals to reduce complexity. However, such limited types of labor are inadequate to explain modern labor markets, especially in the last 15-20 years. While increasing the types of labor makes it more difficult to create a substantively informative model, modeling an infinite number of types of labor is actually easier. Therefore, we have infinite types of labor organized by skill level.

The second aspect of the comparative advantage of cities is locational choices. Individuals need to make choices about where they want to live. People must be able to move freely to where they want when we create economic models in which the fundamental issue to be addressed is the location where people choose to live and produce goods.

Any urban model of a system of cities where people can move between cities requires two things. First, there must be an explanation about why people go to cities at all given that prices and rents are higher in cities. That is, we need an agglomeration force. The second need is a congestion force—an explanation as to why not everyone moves to cities.

The agglomeration force is called total factor productivity (TFP) or simply the "productivity of the city." Some locations make an individual more productive due to better infrastructure, access to ideas, a better labor market, etc. In our explanation determined within the model, it is the higher-skilled individuals who care the most about such productivity gains, namely, in the agglomeration economies that are driving cities, the benefits of agglomeration are stronger for those who are more skilled. Hence, higher skilled people are attracted relatively to larger, more productive cities.

As for the congestion force, why doesn't everyone go to cities? In the tradition of urban economics, the congestion force is standard. Considering one city at a time, there is the von Thünen model in which people have many reasons for wanting to be in different locations within the city, indicating spatial heterogeneity. Individuals care not only about which city they are in but also the location they live within that city. Each individual is willing to make trade-offs, for example, choosing a less productive city because he or she will be able to be in a better location within it, have a shorter commute, etc. In the case of Tokyo, an individual would be more productive compared to living in a smaller city, but he or she might live more remotely from the business district.

Traditional models have dealt very well with the case where every city produces every good or every city produces one tradable good, but they have not been able to deal satisfactorily with cities producing a subset of goods and different cities producing different proportions of goods. This trade-off makes it possible for us to create a model to solve this.

Within the city, another key point is that there are reasons why more skilled individuals are more willing to pay for the best locations. Large cities are skill-abundant in equilibrium, i.e., between any two skills, the larger city will have relatively more of the higher of the two than would a smaller city. Because of this fact and that individuals choose the sector in which they will produce in order to use their skills, skilled cities produce relatively more of the high-skill-intensive goods.

We set up a system in which cities all start out completely symmetric with no differences between them. Incidentally, this is the perspective of the new economic geography to which Masahisa Fujita has been a major and an absolute fundamental contributor. In this model, with many skills, it turns out to be true that large cities have a comparative advantage in high-skilled goods. Going back to the U.S. data, for 21 industries, the higher-skill industries see faster employment rises with city size than do the lower-skill industries. We also look into this relation concerning skills themselves and also in terms of occupations.

Next is the pairwise comparison test that relies on the mathematical property of log-supermodularity. We find that when selecting any two skills and any two cities and allowing individuals to move and live wherever they wish, the larger city has a relatively larger endowment of high-skilled people. This is log-supermodularity, the mathematical key and the analytic tool with which we worked.

I will discuss data later, but first I will discuss theory. Skills represent different types of individuals, of which some are more skilled than others, along a single spectrum. Likewise, skills are represented by educational attainment in the industry or in an occupation. Also, sectors are the industries or occupations.

Regarding the relation of our model to the existing literature, including the new economic geography which has been foundational in terms of reintroducing the concept of space back into economics, there are similarities and departures.

Some of the departures with our approach include the existence of perfect competition everywhere, the lack of internal scale economies, and the lack of space or cost of transporting goods between cities. Such simplifications make it possible to answer some questions that have been difficult to answer within the framework of the new economic geography, making ours a complementary approach.

Similarly to the new economic geography, cities start with no a priori differences in our model, and locations vary in their desirability within the city. In the von Thünen model, there is what is considered an indifference condition—there is heterogeneity within a city, but the prices adjust so that individuals are indifferent about where they live. However, in our model, individuals care about where they live, and different individuals care to different extents, with the highest skilled caring the most. The agglomeration mechanism (A(c)) basically states two points: all else being equal, larger cities are more productive, and conditional on what the size of the city is, having a more skilled labor force (j(ω)) is a weighting of the distribution of skill types. A more skilled workforce means the TFP is also higher. This is taken from the new economic geography as well.

Along with the infinite number of types of labor is an infinite number of goods. If one individual is more skilled than another, that person will have a higher relative productivity in producing goods that require higher skill. In terms of an individual's location within a city, delta represents the distance from the ideal location. This can be thought of as similar to the traditional commuting form in the von Thünen model, the Alonso-Mills-Muth form, i.e., the distance from the central business district.

The productivity of an individual depends on three factors: the city in which he or she lives, the location within the city, and who the person is and what sector he or she works in. For example, living on the outskirts means losing much time in commuting. ωis the skill-type of the individual. σis the sector in which the person lives. H(ω, σ) is the physical productivity of a person of skill-typeωwhen he or she produces in sectorσ, and that is log-supermodular. This connects with the Massachusetts Institute of Technology's (MIT) Arnaud Costinot's paper in regard to countries rather than cities. The difference is that Costinot assumes that the distributions of skills across countries satisfy log-supermodularity, namely, an assumption that some countries are more inherently skilled than others. Our model, allowing people to move to wherever they desire, satisfies this condition in equilibrium. Individuals try to maximize their income less the amount they have to pay for the location they select in the city they choose.

The early contributions to understanding many skills in many cities tended to have overly aggressive sorting. For example, all of the best people would be in Tokyo, and Osaka would only get the second best people. This is most likely not true; cities have more diverse sets of people than that. We wanted our model to show that Tokyo would have relatively more of the highest skilled people, but that it would also have people of all types, taking into account that individuals of the same skill type would be willing to live in more than one location based on their balancing of the pros and cons of the locations.

What we obtained is something that looks very much like the old "central place theory." The underlying theoretical mechanism is that large cities produce all of the goods that are produced in smaller cities plus additional items that are not made in smaller cities. We did not use any of the underlying assumptions of that theory. In our theory, the largest city produces all of the goods that are produced by any smaller city, and that trickles down in terms of city size, and the same takes place in terms of skills. For example, there are some people in Tokyo who are simply not found in Osaka, but all of the people found in Osaka (skill-types) exist in Tokyo, and Tokyo has every skill-type all the way down to the very bottom of the hierarchy of cities. In other words, larger cities have a strict superset of the skills and goods produced in smaller cities, thereby creating an urban hierarchy in terms of skills and sectors.

Now, I will discuss data. We looked at skill in the United States broken down into three groups: high school graduates, those with some college education, and those with a bachelor of arts degree (BA) or higher. We also broke down the data into nine skill groups, which may be unprecedented. Furthermore, we looked at 21 manufacturing industries and 22 occupations. Occupations include a wider range of educational levels and are probably a closer measure of our meaning of skill, as there are individuals with many different skills within an industry.

We start with the empirical results for the distribution of skills across the cities. Looking at the previously mentioned elasticity, we try to answer whether low skills rise with city size but not as quickly as medium skills and even less quickly than high skills.

From some linear regressions of log-skill type on log-population, all three skill groups rise whether we look at all people in the United States or only those who were born there. The vertical axis in the graph is population elasticity. Since it slopes upward, it can be interpreted that population elasticity is lowest in the "high school or less" group, in the middle for the "some college" group, and highest for the "BA or higher" group. Looking at the skill types divided into nine groups, however, there are deviations away from upward sloping, especially with the foreign-born population. Why do we see differences in the levels of matching between U.S. native born population and the foreign-born population?

One explanation may be found in the idea that the highest-skilled individuals really need the lowest-skilled individuals together with them in large cities, an idea pursued by Eeckhout, Pinheiro, and Schmidheiny, which they call "extreme-skill complementarity." An alternative view is that many of the lowest-skilled people in the United States are illegal immigrants. As larger cities are better than smaller cities for such people to avoid being noticed—and, once an enclave of theirs becomes established in a particular city, everyone wants to go there—the model neglects this.

It also might be possible that these deviations result from the model simply not having ethnic enclaves in it. The foreign-born population in the United States in the 20 years from 1980-2000 roughly doubled in its share of the overall population. In 1980, the foreign born accounted for a much smaller proportion of the total population, which meant that they were an even smaller proportion of the least-skilled population. And, for that year, the data fits very nicely.

More skilled occupations are found in larger cities, although there are a few outliers. Computer and mathematical occupations are overly present in large cities. Other outliers include education, healthcare, and social services which are non-traded occupations, making it very difficult to concentrate them in one place.

Industry data also matches well. Outliers in this category include apparel manufacturing which is overly present in the larger cities given its low educational attainment on average. However, this is a similar position to textile manufacturing in that both industries employ foreign-born, low-skilled people who come to live in cities as described above.

In conclusion, in terms of the theory, we extend the "system of cities" approach from urban literature to incorporate substantial locational heterogeneity within cities. From the international trade literature, we integrate the endogenous spatial distribution of skills with a high-dimensional theory of comparative advantage taken from Arnaud Costinot. We link the ordering of locations by skills to city size, thus there is a natural ordering. We predict the distributions of skills and sectors across cities, use log-supermodularity, and drive empirically implementable tests of the theory.

Looking at the data, the tradition in this literature is to compare two sizes of cities to two types of skills. We were able to go to 276 cities, nine skills, 21 industries, and 22 occupations. We can make specific predictions very closely tied to the theory and then look at the data. On the whole, especially in terms of elasticity tests, the data and theory fit well. Elasticities accord in 35 of the 36 comparisons of the nine U.S.-born skill groups. It is a consistent theory.

Thank you very much.


Q1: You said that you don't take into account levels and space, but given your theory and different subgroups, do you have an impression of a comparison toward emerging countries, which have a very strong drive towards major cities but very different setups in terms of skills?

Donald R. DAVIS
I really want to find the answer to that question. In this theory, we only looked at one country—the United States. Our agglomeration mechanism in principle states that city productivity is raised more by having higher-skilled people, and these people are better situated to take advantage of what the city has to offer. Is that only true of major developed countries? I don't have an answer, but my suspicion is this mechanism might be fairly general.

Q2: I would like to know about implications for policies in this paper. Assuming agglomeration benefits, then, maybe in the model, it is suggested that policies should force people to specialize in a particular sector in a particular city so that the productivity will be maximized. Is that the case in your model?

Donald R. DAVIS
You're basically asking if there are welfare implications to our model. Are cities too large? Not large enough? Too skilled? Not skilled enough? Which way should policy push this? Urban and regional literature has different answers to those questions. We have not yet explored the welfare effects of this. Let me tie that into the previous question about countries at different levels of development. China is expecting another 250 million people to move into the cities in the next 10 years. What is worrying is that it has a very strong government hand in encouraging development in particular regions, and, in particular, while our model is spaceless between cities, one concern is that China is pushing people too much into the more remote regions and that actually can be very costly—obviously, environmental costs—including lower productivity associated with the nature and locations of the cities. What is the single largest policy issue that we need to think about in the next decade or two? I would say it's the process of urbanization in the very largest countries. Models like this could be useful here.

Q3: Do you think creating special economic zones to attract a specific sector is a good idea?

Donald R. DAVIS
I have two answers. If what you mean by a special economic zone is a zone where you isolate all of the most innovative activity from the rest of your economy ….

No not really. I'm thinking about China and the idea of a high-tech special zone like the Zhongguancun Science Park. According to your theory, given a specific city size, specializing in a particular sector promotes increases in productivity.

Donald R. DAVIS
You mean the difference in the urban and regional literature between localization economies and general agglomeration economies. One is about the size of the city as a whole, and the other is about the size of the sector in which you work. These are very different things. A fair amount of empirical work on that has been done, and I don't find it to be conclusive yet. How to integrate this kind of model that preserves the simplicity of the log-supermodularity while still allowing the own-sector effects to take place was beyond what we were trying to do.

Q4: There is a lot of air pollution in Beijing, but people still go there and to Shanghai. Can you incorporate this kind of phenomenon in your model?

Donald R. DAVIS
People are moving, especially from the countryside, in spite of the hukou system that gives them only limited rights, because being able to move there is a tremendous income gain, compared to what they had before. Driving down the pollution to a tolerable level is hard in a country with a lower level of income. Also, there are some behavioral issues. If you are moving from the countryside, are you taking into account the long-term consequences of moving into a polluted environment? That might be a reason to look at government policy. One of the things China would like to do is to have growing engagement with a real international community, but it becomes very costly for them to get people. Furthermore, the quality of the people they can get will be lower than it would be if they had a better environment.

Q5. In our field, for a long time, we have had a very difficult problem of how to explain the hierarchy that exists in the system of cities. Big cities provide a wider range of products, services, and goods. You have just presented a very elegant theory that can answer the problem. In your framework, what are the welfare/policy implications? What might be better in the short-run and in the long-run for Japan? We are looking forward to the further development of your theory.

Donald R. DAVIS
We had a very general agglomeration mechanism—the "skills and scale" agglomeration—where larger as well as higher-skilled is better. But in Fujita, Krugman, and Venables, they discuss three agglomeration opportunities—three things you can exchange in a city, which are goods, labor, and ideas. At first, research on a general agglomeration mechanism was on the exchange of ideas. What hadn't been done was to look into the role of ideas in creating the system of cities of different types, and, in particular, there was the difficulty of moving beyond having only one type of labor. There was also an idea of costly idea exchange and using that as a foundation for a system of cities. The basic idea is extremely simple: in our occupations, we produce things and exchange ideas. Idea exchange increases productivity and can give rise to a hierarchy of cities. That hierarchy at equilibrium will have different skill types in different cities.

Q6. The United States is a big country, and you ignored space and trade. There are many small countries in the world, in Europe and Asia in particular, and different city sizes. Do you have an impression in terms of your research of when you include space and trade aspects?

Donald R. DAVIS
Our model is a pure cross-sectional model. There is neither an explanation of how the knowledge base of a country evolves over time nor about how they integrate across countries, although these are things we really want to know. You brought up a large number of important research questions. For example, why did Switzerland end up with finance and instruments in history? We have nothing to say about that in our theory.


  1. ^ For more detailed explanation on the topics discussed in the BBL Summary, please visit Dr. Donald Davis' site:

*This summary was compiled by RIETI Editorial staff.