Information as Infrastructure: The Growth of English Cities, 1861 to 1961

Curtis J. Simon
and Clark Nardinelli
Clemson University

I. Introduction

We investigate the relationship between the population growth of cities and their initial level of human capital. We argue that if human capital generates external economies, cities whose industries use information more intensively should grow faster, other things the same. In our first (1992) paper, we found that American cities that employed higher proportions of highly skilled professionals grew faster over periods of 50 and 100 years over the period 1880-1980. This result suggested that the availability of information services drove the typical city's long-run population growth. If the connection between information and city growth is not merely a curious attribute of the American data, it should hold for other nations. In this paper, we examine the growth of 79 English (and Welsh) cities between 1861 and 1961. We find that English cities grew faster, the higher the employment share of business professionals in 1861, holding constant the city's size in 1861.

That we are able to corroborate our findings for America using data from England is valuable not only because replication is important, but because England's urban system was already mature in 1861, the starting year of our study and a reasonable date for the end of the first industrial revolution. In contrast to America's urban system, which had barely reached adolescence, the relative growth of English and Welsh cities mostly reflects the competition between existing cities for rural and between-city migrants.

Our findings provide support for theories that identify specialized human capital as the engine of economic growth. In Lucks (1988), for example, externalities arise from higher levels of human capital due to spillovers of knowledge. In Roamer (1987), increasing returns in the production of intermediate capital goods give rise to a wider variety of capital services. We think that it is plausible to model intermediate information services in a similar fashion. It is plausible that external economies are strongest within a city because the costs of acquiring and exchanging information, especially the costs of the frequent exchange of small bits of information are lower within a city. Indeed, Backer and Murphy (1992) argued that specialization and the division of labor are more often limited by the costs of coordinating specialized workers than by the size of the market. The city can be thought of as an organization that reduces the costs of coordination by reducing the costs of collecting and disseminating information.

II. Theory

We were led to consider the importance of human capital by recent developments in growth theory, especially Lucks (1988), who argued that cities were "mainly and convincingly concerned with the external effects of human capital" (p. 37). Lucas formulated a model in which the total level of human capital in a society increased the productivity of each person, given their individual level of human capital. The acquisition of knowledge of one person, then, generates external economies for everyone else in the city.

We adopt the notion of city-specific human capital, introduced by Glaeser et. al. (1992) to help explain the relative growth of cities. The ability to contact people at low cost is important because much economic activity requires face-to-face contact. It may well be that the communications revolution may someday eliminate the need for face-to-face contact, but it certainly has not done so yet. In our theory, we associate the stock of city-specific human capital with an information service sector, that is, a sector in which people's main task is the gathering or dissemination of information. It is reasonable to suppose that much of the information gathered and provided by people within a city becomes a public good linked associated with those people and to that city.

The ties between firms and the patterns of commerce that become routine are a manifestation of what might be thought of as a city's information infrastructure. The acquisition of information capital is costly and irreversible; once acquired, much information can be exploited at virtually zero marginal cost within the city. To exploit such information between cities is more costly. Empirically, we associate the city's information sector with people who have high levels of human capital. The link between information and human capital is straightforward; the external economies that arise from activities that do not routinely involve the acquisition of or transmission of knowledge – examples include barbering, retailing, and tailoring – appear to be small.

III. The Model

In our work on relative city growth in America, we adapted Rivera-Batiz's (1988) model of equilibrium city size, which applies Roamer (1987) model of intermediate product differentiation to the city. We augmented the model to include the concept of city-specific knowledge, introduced by Glaeser et. al (1992). We assume that each city produces a manufacturing good (according to a Cobb-Douglas production function) using labor, land, and knowledge:

(1) Mt = f(LMt, T, It),

where LMt is the quantity of labor, T is the quantity of land (which we assume is fixed), and It is the quantity of information services, all at time t. There are nt types of information services, where nt is determined endogenously. The output of each of the nt components of the service sector is Sit, and each Sit is produced subject to increasing returns to scale using only labor. In Rivera-Batiz (1988), It is a function of St = ∑iSit and the variety of services, nt. In our version of the model, we make It a function also of the current stock of city-specific knowledge, Kt. We therefore have:

(2) It = g(Kt, St, nt).

The relationship between It and the Sit depends on the degree of substitutability between the Sit. The less the degree of substitutability, the greater the impact of variety on It.

The first order conditions for employment in manufactures equates marginal revenue product to the wage at each time t. We can solve Lmt, St, and nt in terms of total city population, Lt = Lmt + Lst, where Lst is the quantity of labor employed in the information service sector. It is then possible to show that the movement of wages over time is given by:

(3) ln(Wt+1 / Wt) = aln(Lt+1 / Lt) + b ln(Kt+1 / Kt),

where a and b depend on the parameters in the production functions (1) and (2). Whether a is positive or negative depends on the degree of diminishing marginal returns to labor, the share of information services in output, and the degree of substitutability between information services. The term b is positive, indicating that other things the same, a higher rate of growth of city-specific knowledge leads to higher wage growth in the city.

The key question in our theory is what determines the rate of growth of city-specific knowledge over time. Jovanovic and Rob (1989) modeled the growth and diffusion of knowledge, emphasizing the importance of being able to exchange ideas at low cost. In particular, they argued that it is important for many people with different ideas to mingle, for people could then synthesize new, better ideas. We build this notion into our model by assuming that the rate of growth of city-specific knowledge is positively related to the number of people employed in the information sector, Lst , and the variety of information services, nt:

(4) (Kt+1 / Kt) = h(Lst, nt).

As the city grows (and wages rise) over time, residents bid up the price of land, causing utility to fall, other things the same. Rivera-Batiz (1988) assumed that city residents maximize a Cobb-Douglas utility function. In our version of his model, there are two goods: an internationally traded consumption good and housing. We assume that there is a fixed amount of residential land in the city. The rate of growth of utility of a resident in the city is then given by:

(5) ln(Ut+1 / Ut) = 1 ln(Wt+1 / Wt) - 2 ln(Lt+1 / Lt),

where 1 and 2 are the (positive) exponents on goods and housing in a Cobb-Douglas utility function. Long run equilibrium requires that utility be equal across cities at each time t, implying that utility grows at the same rate across cities. Replacing equation (3) into equation (5), the growth of utility over time is equal to:

(6) ln(Ut+1 / Ut) = 1b ln(Kt+1 / Kt) + (1a - 2) ln(Lt+1 / Lt).

If cities were identical, they would grow at the same rate. One way to generate differences in growth rates is to assume that initial conditions differ. We assume that initially, some cities had a higher concentration of human capital, which in our model translates into a larger number of people in the information sector (Lst) and a wider variety of services (nt). According to our hypothesis in equation (4), this will cause a higher rate of growth in the level of city specific knowledge, and, by equation (6), such cities will grow faster, other things the same.

IV. Growth Regressions

Our theory states that cities with greater initial proportion of highly skilled providers of information will grow faster, other things the same. We collected data on population and on certain occupations for the 79 leading cities in England and Wales for the year 1861, our base year. The census divided eighteen general occupational categories into numerous sub-categories. We experimented with several different measures of professional employment, but settled on a rather narrow one: business professionals, which includes bankers, brokers, agents, accountants, bookkeepers, insurance agents, merchants (not retailers), among others.

We entered professional employment as a share of total employment. Our city growth regressions are of the form:

(7) ln(Final City Size/1861 City Size) = Constant + b 1 1861 City Size + b 2 1861 Professional Share + error.

Final City Size is city population in either 1911 or 1961.

The empirical results are contained in column 1 in Parts A (1911 final year) and B (1961 final year) of table 1. The estimated coefficient on professional employment share is positive and significant, indicating that cities with a higher share of professional employment indeed grew faster over both the 50 and 100-year periods following 1861.

We tried adding lawyers and engineering and scientific persons to business professionals, but doing so only weakened the relationship between growth and professional share. On the one hand, this surprised us because the opposite was true of the results we obtained for U.S. cities. On the other hand, the base years in our growth regressions for U.S. cities were 1880 and 1900; perhaps the later time period is the reason for the different results. We also experimented with a very broad category of professionals, which included doctors, druggists, dentists, actors, artists, teachers, musicians, and writers, but this category did not help us to predict growth. In sum, although we find higher growth in cities with greater employment shares of professionals, the composition of professionals that help us predict growth is different for English and Welsh cities than for American cities.

A. Transport Cost and Manufacturing Base Theories of Growth

There are, of course, other theories of city growth. Some theories emphasize the role of the city as a break in transport, that is, as a crossroads, terminus, and cross-shipment point. We therefore tried augmenting equation (7) with various definitions of transport employment share. Other theories emphasize the importance of manufacturing. During and after the industrial revolution the leading English cities exported a high proportion of their output. Cotton had much to do with Manchester's growth, shipping with Liverpool's, and steel with Sheffield's. North (1955) used an export base model of regional growth to explain differences in population growth across regions. Some versions of the manufacturing base model imply that cities that start with proportionately larger manufacturing sectors should grow faster, other things the same.

We ran regressions similar to those in equation (1) above, but with transportation and manufacturing employment shares entered along with professional employment share as explanatory variables. We found that employment on river and sea were the only good predictors of city growth in the transport sector. Our measure of manufacturing employment is restricted to employment in the factory industries: textiles, mining, iron and steel, metal-working, glass and pottery, industries that get chapters to themselves in histories of the industrial revolution and the ones that would head most people's top ten list in "manufacturing base" theories.

These regressions are contained in column 2 of table 1. As can be seen, manufacturing and water employment shares help to predict city growth over the 50-year period, but not over the 100-year period following 1861. This did not surprise us. The initial advantages of access to water must have been less important in the age of road, rail, and air. As for manufacturing, city growth due to a successful export need not be self-sustaining; when the particular industry's growth levels off, the city's growth may also level off. The coefficient on professional share, however, remained positive and significant.

We tried one last measure of information services: the employment share in telegraphs. These regressions are reported in column 3. The coefficients on professional share fall and the coefficients on telegraph employment share are positive, but insignificant. The coefficient on professionals for the final year 1961 is insignificant, but this is because of a single outlier. Coventry's growth rate (adjusted for variables other than professional share) was the highest of the 79 cities in our sample, a result that we attribute as probably due to the buildup of industry there during the Second World War.

V. Conclusion

We used information from the occupational census of leading cities in 1861 to predict city size 50 and 100 years into the future. The providers of information services were not a large proportion of city population, yet their presence may have made the difference between fast growth, slow growth, and stagnation. An early, and probably inadvertent, investment in information services and the professionals that provide them gave a city a continuing advantage over its rivals.

The results were remarkably similar to those we obtained in our study of American cities, which is all the more surprising in that American was still becoming an urban nation at the beginning of the period studied. As in America, transportation explained some part of city growth over the late nineteenth century period, In America's case, however, it was rail, and not sea, and we found that the effects of rail lasted longer in America than the effects of water in England. Cities with higher manufacturing employment shares grew faster in the nineteenth century in both England and in America; the effects in America, however, lasted considerably longer than we found in England.

The results of our exercise corroborate those theories of cities that focus on the exchange of information. The city is the place where knowledge is absorbed and acted on most quickly. As Hayek put it, "the economic problem of society is mainly one of rapid adaptation to changes in the particular circumstances of time and place." Although Hayek goes on to argue that only the "`man on the spot'" can know the particular circumstances of time and place, he cannot decide on the basis of his limited knowledge. "There still remains the problem of communicating to him such further information as he needs to fit his decisions into the whole pattern of changes in the economic system." Cities are the institutional innovation that still, even as the communications evolution proceeds, that allows the dissemination of information at lowest cost.

Table 1. City Growth, 1861-1911 and 1861-1961
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Dependent Variable: Log(City Size in Final Year / City Size in 1861):

A. 1911  Final Year 

                                (1)               (2)              (3)              
 1861 City Size	-1.9 x 10 -7	-1.5 x 10-7	-1.0 x 10-7	
		(1.3)	(1.0)	(0.7)

 1861 Proportion  	39.790	34.019	28.797
  Professionals	(2.8)	(2.3)	(1.9)

 1861 Proportion	...	0.667	0.768
  Manufacturing   		(1.5)	(1.8)

 1861 Proportion	...	3.898	3.937
 Water Transport		(2.0)	(2.1)

 1861 Proportion	...	...	363.968
 Telegraph			(1.4)

 Constant	0.368	0.276	0.218

 R-Square	0.0941	0.1543	0.1766


B. 1961 Final Year 

 1861 City Size	-1.3 x 10-7	-9.6 x 10-8	-2.0 x 10-8
		(0.7)	(0.5)	(0.1)

 1861 Proportion   	40.608	32.532	25.308
  Professionals	(2.3)	(1.7)	(1.3)

 1861 Proportion	...	-0.331	-0.192
  Manufacturing  		(0.6)	(0.3)

 1861 Proportion	...	2.326	2.381
  Water Transport		(0.9)	(1.0)	

 1861 Proportion	...	...	503.522
  Telegraph			(1.5)

 Constant	0.603	0.651	0.570


 R-Square	0.0645	0.4757	0.1123
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