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The Effect of Information and Communication Technologies on Urban Structure [with Discussion] Author(s): Yannis M. Loannides, Henry G. Overman, Esteban Rossi-Hansberg, Kurt Schmidheiny and Omer Moav Source: Economic Policy, Vol. 23, No. 54 (Apr., 2008), pp. 201-242 Published by: Wiley on behalf of the Centre for Economic Policy Research, Center for Economic Studies, and the Maison des Sciences de l'Homme Stable URL: http://www.jstor.org/stable/40071845 . Accessed: 16/01/2014 01:43

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\\Jy SUMMARY

This paper examines the effects of information and communication technobgies (ICT) on urban structure. Improvements in ICT may lead to changes in urban

structure, for example, because they reduce the costs of communicating ideas from a distance. Hence, they may weaken local agglomeration forces and thus provide incentives for economic activity to relocate to smaller urban centres. We use inter- national data on city size distributions in different countries and on country-level characteristics to test the effect of ICT. We find robust evidence that increases in the number of telephone lines per capita encourage the spatial dispersion of popu- lation in that they lead to a more concentrated distribution of city sizes. So far the evidence on internet usage is more speculative, although it goes in the same direction. We argue that the internet is likely to have similar, or even larger, effects on urban structures once its use has spread more thoroughly through different economies.

- Tannis M. Ioannides, Henry G. Overman, Esteban Rossi-Hansberg and Kurt Schmidheiny

Economic Policy April 2008 Printed in Great Britain © CEPR, CES, MSH, 2008.

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The effect of information and communication technologies on urban structure

Yannis M. loannides, Henry G. Overman, Esteban Rossi-Hansberg and Kurt Schmidheiny Tufts University; London School of Economics; Princeton University; Universitat Pompeu Fabra

1. INTRODUCTION

The geographic concentration of economic activity occurs because transport costs for

goods, people and ideas give individuals and organizations incentives to locate close to each other. If such costs did not exist economic activity would tend to spread evenly over space. Historically all of these transport costs have been falling. For example, the steam engine, railways, the combustion engine and the use of containers for transportation

«HHHi

This paper was presented at the 46th Panel Meeting of Economic Policy in Lisbon, October 2007. Thanks go to Kwok Song Too for data, and to Filipe Lage de Sousa, Kay Shan and Stefanie Sieber for research assistance. Comments by Marcus Berliant, Antonio Ciccone, Anna Hardman, Vernon Henderson, Soks Kim, Jed Kolko, Diego Puga, Will Strange, Ping Wang and Zhu

Wang, and other participants at presentations at Athens University of Economics and Business, University of Helsinki, Univer-

sity College London, Washington University in Saint Louis, Universitat Pompeu Fabra, Kansas City Federal Reserve Bank, and the International Workshop on Agglomeration and Growth in Knowledge-based Societies' in Kiel are gratefully acknowledged. Last but not least, Philippe Martin, the editor in charge and three referees made unusually generous and very perceptive comments on all aspects of the paper. We thank them as well as the Panel members and other participants at the Lisbon

meeting. Kurt Schmidheiny thanks the Swiss National Science Foundation (grant PA00 1-1 05026) and the Spanish Ministry of Education and Science (Ramon y Cajal Fellowship and grant SEJ2007-64340/ECON) for their support. The Managing Editor in charge of this paper was Philippe Martin.

Economic Policy April 2008 pp. 201-242 Printed in Great Britain © CEPR, CES, MSH, 2008.

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204 YANNIS M. IOANNIDES ETAL.

have all worked to reduce the cost of shipping goods, while the automobile, com- muter railways and the airplane have performed a similar role for the cost of moving people. More recently, new information and communication technologies (ICT) have also significantly reduced the cost of transmitting and communicating information over both long and short distances. Such changes could lead us to predict the death of distance. That is, to suggest that location will no longer matter and that economic

activity will, in the near future, be evenly distributed across space. This paper is concerned with one particular aspect of this prediction: the impact that less costly communication and transmission of information might have on the urban structure and the spatial distribution of economic activity.

Two innovations in the twentieth century have changed dramatically the cost of

communicating and transmitting information. The first is the widespread adoption of telephony (first fixed line, then mobile), which made possible oral communication over long distances. The second main innovation is the internet and e-mail, which has

played a similar role for written documents, voice and images. Both these technologies may require substantial upfront fixed investments, but once made they essentially eliminate the link between the cost of communication and the distance between locations.

What are the implications of these changes in ICT for urban structure and the distribution of economic activity in space? This paper provides a partial answer to this question. We begin with a brief description of the adoption path for a number of recent ICT innovations before turning to consider in more detail the ways in which ICT might affect urban structure. We next present the main theoretical argument and identification strategy. Our model suggests that improvements in ICT will increase the dispersion of economic activity across cities. That is, it will make city sizes more uniform. In the empirical section, we test this prediction using cross-country data and find empirical support for this conclusion. A concluding section spells out a number

of policy implications.

2. ICT AND URBAN STRUCTURE

Changes in ICT are very clear in the data, especially if we focus on technology adoption.

Figure 1 presents the number of cars, phone lines, mobile phones, and personal com-

puters during the last five decades, using Comin and Hobijin's 'Historical Cross-Country

Technological Adoption Dataset' (2004). The adoption of the telephone was well

under way by the 1950s. By the end of the 1990s, the number of telephone lines

exceeded 150 million in both Europe and the United States. In contrast, changes in

personal computers are all concentrated in the 1980s and 1990s. The United States

went from less than 5 million computers in the early 1980s to more than 140 million

computers in the late 1990s. This is a remarkable change that is likely to have very

important effects. The data show a similar pattern for the EU that went from less

than 5 million personal computers to 100 million in the late 1990s. The EU and the

United States have also experienced similar dramatic changes in the use of mobile

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Figure 1. Private cars, mobile phones and personal computers Source: Comin and Hobijin (2004).

phones, but with the growth occurring even later than for personal computers. Mobile

telephone technology was practically unused in 1985, but more than 150 million people . owned a mobile phone in the 1990s in the EU, and more than 85 million in the

United States. Of course, these numbers alone do not reflect the costs associated with

implementation of these technologies but they do show the dramatic growth in adoption. Particularly significant is therefore to contrast the linear growth in number of cars

or phones with the exponential growth in new forms of ICT. If part of the role of cities is to save on communication costs, and given that the dramatic growth in ICT

adoption has clearly lowered these costs, it seems intuitive that these changes could have some significant implications for urban structure. It is to these implications that we now turn.

Economists use the phrase 'agglomeration economies' to describe the advantages that occur when economic activity is densely concentrated. The first source of

agglomeration economies is known as human capital or knowledge spillovers. In areas of dense economic activity, workers casually exchange knowledge about technology and

production conditions at their places of employment. Such transfers happen fortui-

tously but also are sometimes sought out deliberately by firms, as anecdotal evidence about life in California's Silicon Valley testifies. A second force for agglomeration is labour market pooling. At any point in time, firms are subject to idiosyncratic shocks (e.g. as a result of changing demand for their particular product) that makes them want to hire or fire workers. Because these shocks are idiosyncratic, when one firm is firing, another firm may well be hiring. If firms locate in close proximity to one another, it is easy for workers to move from firms experiencing bad times to those experiencing

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206 YANNIS M. IOANNIDES ETAL.

good times. As the saying in Silicon Valley goes, 'people change jobs but not parking lots'. Agglomeration is thus attractive to workers because it helps insure them against idiosyncratic shocks. It is also attractive for firms because it weakens the impact on

wages of their own idiosyncratic shock and thus mitigates in part the effect of un-

certainty in the economic environment. This actually makes employment in bad times more costly than it would otherwise have been, but this is more than compensated for by the ease of expansion in good times. A third force for agglomeration comes from the greater variety of intermediate products and richer mix of labour skills and expertise that are available in larger urban areas. Greater variety of goods and services lowers prices and wages and also enhances firms' options in choosing tech-

nologies for production and distribution of their products. The associated effects on firms are known as pecuniary externalities (as distinct from real externalities, the latter term being reserved for non-market interactions among economic agents' decisions). Finally, local amenities due to weather, physical attractiveness, culture or tradition are important factors in enhancing the appeal of particular urban

agglomerations. These mechanisms, whose articulation essentially goes back to Alfred Marshall's Principles of Economics, explain at least some of the spatial concentration that we observe throughout the world.

Of course, if these agglomeration economies were the only forces driving the location of economic activity then we would expect to observe extreme spatial concentration. In reality, we do not, because these agglomeration economies are offset by costs (disper- sion or congestion forces) as activity becomes increasingly concentrated. These costs take many forms but all arise from the fact that competition for local resources, broadly defined, increases with spatial concentration. For example, congestion occurs as a result of increased competition for space, firms pay higher rents and wages as a result of increased competition for land and workers, while they receive lower prices for their output as a result of increased competition in goods markets. The balance between these agglomeration and dispersion forces determines the spatial structure of the economy (see Henderson, 1974).

The strength and importance of these agglomeration and dispersion forces depend on many things, including notably the cost of communicating information across

space. Knowledge spillovers, for example, depend on the role that distance plays in inhibiting efficient communication of ideas. The importance of face-to-face com- munication shows just how dramatic these distance effects can be. But the telephone, e-mail and video conferencing, for example, are all reducing these costs of com-

municating ideas from a distance.

Changing communication costs may also affect the benefits from labour market

pooling. Recall, these benefits require workers to move from firm to firm. ICT may increase the efficiency of this process as news about vacancies in one firm are more

easily communicated to workers who may be looking for work. A similar story could be told about the benefits of pecuniary externalities. For example, falling information costs allow firms to more easily identify potential suppliers of intermediate goods

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or workers with particular skills. Turning to dispersions forces, ICT may facilitate

e-working, allowing individuals to avoid the high costs of commuting in congested cities. Alternatively, it may increase the competition faced by firms as consumers find it easier to identify alternative sources of supply.

Thus, new ways to transport ideas and to communicate information are, in general, likely to affect all of the agglomeration and dispersion forces that urban and regional economists have identified as key determinants of the concentration of economic

activity in space. Independently of the sources of agglomeration forces, ICT will likely have an impact on spatial concentration. In what follows, we illustrate the potential impact of ICT by focusing on production externalities as the main source of agglom- eration. This gives us a specific prediction about the impact of ICT that we then confirm using real world data. These effects may also be consistent with other models where ICT has a similar effect on different agglomeration economies. So, our exer- cise does not allow us to discriminate between different models which predict that ICT will disperse economic activity across cities. It does, however, suggest that models that predict changes to city structure in the opposite direction (i.e. increasing concen-

tration) are not consistent with the data. ICT can, in principle, have many distinct effects on the distribution of economic

activity in space. On the one hand, it can increase the spatial scope of knowledge spillovers - it is easier for any professional to acquire context that helps her assess information she casually receives from counterparts in other firms. Therefore, fewer

person-to-person interactions may suffice to obtain a better understanding of what other firms are up to. To the extent that knowledge spillovers, whether deliberate (as among employees of the same firm) or fortuitous, are productive, we would expect that ICT would strengthen them among individuals who are located further apart. Local increasing returns are thus less localized when a wider set of people across an entire country or across countries can interact with each other by using new techno-

logies and while economizing on commuting costs. In this sense, improvements in ICT reduce the importance of the quantities of productive factors employed in a city on that city's productivity. This is the stand we take on the theory we present in the next section and in more detail in Appendix A.

This implies that local urban agglomeration effects become less important and lead to less concentration of people and jobs in a few successful (and larger cities) or urban

agglomerations. Agents and firms obtain smaller benefits from locating close to each other and so they locate more evenly in space in order to economize on land rents (and other congestion costs). ICT, in particular, can help businesses create opportunities by improving their communications with other firms, suppliers and clients worldwide. For example, real estate, tourism and hotel operators may market their products directly, without relying on city-based intermediaries. This is important, as most of the recent urban growth worldwide has been fuelled by growth in service sectors, while

manufacturing has been relocating to smaller urban centres with good transportation links (Henderson, 1997) and often are outsourced to lower cost countries.

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208 YANNIS M. IOANNIDES ETAL.

These arguments associate ICT with greater spatial dispersion in economic activ-

ity. This would, in turn, imply larger concentration of the city size distribution. That

is, it would be associated with a reduction in the variance of city sizes. Arguably, this

potential advantage may not be fully realized if the interurban transportation system does not develop sufficiently to serve a greater network of urban centres. However, at

any given level of development, improvements in ICT increase the incentives for economic activity to relocate to smaller urban centres.

On the other hand, ICT may also make certain local public goods more important as a share of consumption or as a share of inputs. For example, the internet has increased the intensity of use and broader usefulness of public libraries, at least in the United States (see Bertot et al.y 2006). Also, changes in the industrial composition of cities, which have been favouring services, may on balance foster concentration of certain services due to increasing returns at the plant level. London, New York or Paris are attractive in part because there are certain products and services that can only be found there. Similarly, urban living affords better consumption prospects. As individuals spend more on amenities, such as theatres and other artistic activities, certain large cities would become relatively more attractive and therefore likely to

grow relative to smaller or medium size cities. On top of increasing the share of some of these goods and services in consumption, better ICT may make these goods and services more readily available and cheaper to consume. Clearly, to the extent that

public goods (and other forces of urban concentration) become effective and far-

reaching with ICT, we should observe a more dispersed size distribution of cities and a more concentrated spatial distribution of economic activity.

From this verbal discussion - and other ones in the literature, like Glaeser (1998) which is more extensive but still qualitative - it should be clear that there are two key

paths through which ICT may affect the urban structure. But it is still not clear which

effect is likely to dominate. Thus our next step is to develop a theoretical model which

will make all these connections clear. In particular, it will connect changes in ICT

with changes in the size distribution of cities. As we will show, the effect on urban

structure generated by the model will depend on the particular assumption made on

how ICT affects agglomeration forces. This relationship is monotonic and so it helps us design an empirical exercise that is informative on which of these different effects

dominates in reality.

3. A MODEL OF ICT AND URBAN EVOLUTION

As discussed above, any reasonable model of urban structure or of the role of space in economic activity, more generally, would predict that improvements in ICT should

alter the distribution of economic activity in space. However, no model of urban

systems seems to have explicitly incorporated the effects of ICT. We use the theory in Rossi-Hansberg and Wright (2007), from now on RHW, to illustrate how ICT may lead to more urban dispersion.

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To reiterate, the trade-off between agglomeration effects - the benefits that firms and individuals obtain from being close to each other - and congestion costs deter- mines the size of cities. Most of these agglomeration effects are related to interactions of different types of individuals. These interactions will be affected by the communi- cation and information technology used by these agents. But how will ICT affect

agglomeration forces? And how will these changes in agglomeration forces change the distribution of economic activity in space?

The model in RHW views the connection between agglomeration effects and

productivity as mediated by industry-specific physical and human capital. Agglomera- tion effects are the result of an externality generated by the amount of human capital and labour employed in the city. To illustrate this mechanism, suppose that an industry receives a positive and persistent productivity shock. Naturally, firms in the cities that

produce in those industries will want to produce more. This implies that the demand and price of these industry specific factors increases and this will create incentives to accumulate more of these factors. So next period the industry will have more industry specific factors. Because of the agglomeration effects (and this is the key) having more of these factors will imply more workers being hired and more local productivity spillovers, which in turn will elicit further accumulation of factors and induce larger cities, even if next period's productivity shock is lower. That is, the effect of the original productivity shock on city size will be persistent through its effect on the accumula- tion of industry specific factors. The stocks of these factors are determined by the accumulated history of the industry's productivity shocks and, therefore, the size distribution of cities is determined by the history of these shocks. It is the long-run distribution of these factors across industries which then determines the long-run size distribution of cities.

The mechanism described above relies crucially on the impact that the level of human and physical capital has on the level of productivity in a city - that is, on the

strength of the agglomeration effects, which will be affected by ICT. If agglomeration forces are very small and the productivity of an industry producing in a given city is essentially independent of the level of human capital and employment in the city (and therefore the level of physical capital), today's productivity shock will have only a temporary effect on city size and no effect on the long-term stock of these factors.

Hence, cities will not grow and may even decline substantially depending on the

history of shocks to an industry. This implies that all cities will have similar sizes and so the distribution of city sizes will be extremely concentrated. If all cities are of similar sizes, the distribution of economic activity in space will exhibit a lot of

dispersion. Note that the more concentrated the size distribution of cities the more

dispersed the distribution of economic activity in space. In contrast, if agglomeration effects depend heavily on the amount of factors

employed in a city, the effect of past shocks on the stock of industry specific factors will be very important. Cities specialized in industries that received a history of good shocks will be very large, and cities that received a history of bad shocks will be small.

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210 YANNIS M. IOANNIDES ETAL.

Hence, the size distribution of cities will be very dispersed and the distribution of economic activity in space wall be very concentrated.

In Appendix A we present the details of the model in RHW that yields the result discussed above. The model allows for accumulation of physical and human capital and city creation and yields a realistic size distribution of cities. However, the main economic mechanism can be illustrated in a much simplified model, albeit a static and partial equilibrium one, which we sketch here. Consider a city with an aggregate production function that implies output per person in the form

T=A(N)T(JV)

where A(N) = AN*, JV is total employment in the city, A is a productivity shock and

7{JV) = TN~X the time agents have left for work after commuting. The latter specifi- cation is a shorthand in order to express the combined effect of declining marginal productivity of labour and congestion. We assume that the respective elasticities

satisfy T > £ so that in effect city production is subject to diminishing returns. The parameter £ plays a key role in our analysis. It captures the extent to which

the size of the city affects its productivity through knowledge spillovers. More specifi- cally, £ denotes the elasticity of productivity with respect to city size. We model this

elasticity as a result of knowledge spillovers, but in fact it can be the result of any other agglomeration mechanism. Note that the level of £ will also affect the average size of spillovers. So an increase in £ will tend to induce concentration in large cities.

With free labour mobility across cities and identical productivity shock process in all cities it has to be the case that income per person is the same across cities. Call this equilibrium income level w. Then, by using the above specifications we have:

AtNe-T=w

which, given w, determines the equilibrium value of population in a particular city JV as

So the elasticity of JV with respect to A is equal to 1 /(T - £). Now let the quality of

ICT determine the value of £. If £ decreases with better ICT, agglomeration forces

become less important with ICT and, in the long run (under some technical condi-

tions), the variance of the size distribution of cities falls. The reverse is true when £

increases with better ICT. So the actual effect of ICT on £ is, ultimately, an empirical

question that we try to settle in this paper. A similar analysis may be cast in terms of

a possible role of telecommuting in affecting the elasticity of time left for work with

respect to total city employment, but will not be discussed here for reasons of brevity.

Again, the model presented in Appendix A allows for much greater generality and

detail.

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Of course, changes in ICT will in general change the level of technology too. Local interactions may become less important with ICT, but global ones will then become more important. The latter change would be reflected in an increase in the mean of A.

Ideally one would model explicitly the decision of agents in a city to adopt ICT. This has not been done in the literature in a way that may be readily adopted for our purposes. Here we only study the effect on urban structure given exogenous technology adoption decisions. We refrain from developing such a theory because it is unlikely that in view of our data we would be able to distinguish between alterna- tive theories of the precise role of ICT in affecting the elasticities of the spillover effects.

4. EMPIRICAL METHODOLOGY

Our theoretical model, as developed in Appendix A, predicts that ICT should make the distribution of city sizes in the long run more concentrated if it weakens agglom- eration effects. We study this prediction empirically by looking at the effect of ICT on the distribution of city sizes across different countries.

Unfortunately, as will be clear when we discuss our data in Section 5 below, the available data only tend to cover the larger cities in each country. This is a problem for our empirical implementation because such truncated data (i.e. data that do not cover the smaller cities) do not allow us to calculate the mean and variance of the entire city size distribution directly. To get around this problem, we proceed as follows.

First, we assume that the city size distribution is Pareto (alternatively referred to as

following a power law). Given this assumption we can express the log of the propor- tion of cities that are larger than 5, that is, the log of the counter-cumulative of the size distribution of cities, as a linear function of log city size:

In />(*>£) = -£ In S0+£lnS, (2)

where So denotes the minimum city size, which defines the lower bound of the city size distribution, and £ the elasticity of the proportion of cities larger than S with

respect to S. The latter is a negative number that is commonly referred to as the Zipf coefficient. See Box 1 for details. Given a set of cities and their sizes, an estimate of the Zipf coefficient is provided by running a regression of log rank on log city size. When the distribution is Pareto the Zipf coefficient can be consistently estimated by running the regression only on the sample of the larger cities, that is, the upper tail of the distribution.

We have underscored the model's prediction that improvements in ICT will decrease the variance of the cross-sectional distribution of cities. In Appendix A we show that this leads to a higher absolute value of the Zipf coefficient, | C,(S) | . Hence, the absolute value of the Zipf coefficient increases with improvements in ICT, at least when attention is restricted to the upper tail of city sizes. In other words, improvements in the quality of ICT decrease the variance of the size distribution

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212 YANNIS M. IOANNIDES ETAL.

Box 1. Zipf's law and the Pareto distribution

Zipf's law for cities (Zipf, 1949) is an empirical regularity that has attracted considerable interest by researchers. In its strict version, which is also known as the rank-size rule, the law is a deterministic rule that states that the second

largest city is half the size of the largest, the third largest city is a third of the size of the largest city, etc. To illustrate, let us take a country (for instance the United States), and order its cities by population: New York as the largest has rank 1, Los Angeles as the second largest has rank 2, etc. We then draw a

graph, known as a Zipf plot (see Figure Bl): on the j-axis, we place the log of the rank (New York has log rank In 1, Los Angeles log rank In 2); on the x- axis, the log of the population of the corresponding city (which will be called the size of the city). If the rank-size rule holds, this produces a downwards sloping line with slope equal to -1.

Generally, and to a remarkable extent, statistical analyses for many different

countries, as Gabaix (1999) emphasizes and Gabaix and Ioannides (2004) dis- cuss in detail, obtain estimated coefficients that are concentrated often around one. This indicates that the size distribution of cities is well approximated by Zipf's law with coefficient one. Nevertheless, there is substantial variation in

Zipf coefficients across time and across countries, a fact that ought to cause some doubts as to the full validity of the law.

Consider the three Zipf plots in Figure Bl. They look quite similar to one

another, yet the slopes of ordinary least squares lines fitted to them are not

Figure Bl. Zipf plots for three countries

Source: Authors' own calculations.

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equal to -1. Note that the plot for France is steeper than that for the United

Kingdom which in turn is steeper than that of the United States; the respective estimates are -1.55, -1.46, and -1.37, are all estimated with very high preci- sion and using 96, 232 and 552 observations, respectively. Note also that the

plot for the United States is furthest to the right because its cities are larger than those of the United Kingdom with the same rank, whose plot in turn is further out than that of France, for the same reason. The techniques employed in the main part of the paper are aimed at backing out from such differences the effect of ICT across countries and over time.

Can we obtain Zipf 's law by means of theoretical arguments? The simplest direct theoretical argument one could make would be by invoking Gibrat's law. If different cities grow randomly with the same expected growth rate and the same variance (Gibrat's law for means and variances of growth rate), then the limit distribution of city sizes converges to Zipf 's law. See Gabaix and Ioannides (2004) for an extensive discussion of this issue. Empirically, on the other hand, Zipf 's law for cities is an instance of a power law (see further below for details). Power laws are attractive in various sciences, especially in physics, because they are 'scale

free', in that they do not depend on the definitions of units of measurement.

Naturally, this is an important concern in physics. Rossi-Hansberg and Wright (2007) provide a rigorous justification for a power law that is directly rooted in economic theory. It follows as a special case of the model outlined in Appendix A.

A power law of cities states that the proportion of cities that are greater than a particular city of size 5, the counter-cumulative of the size distribution of

cities, is of the form:

P(* >£) = (£), (Bl)

where £ denotes a negative parameter, and So the lower boundary of the

distribution, also a parameter and itself a function of the various determinants of city sizes as discussed in the main body of the paper and Appendix A. The mean city size and the variance associated with the law given by Equation (Bl), which is also known as a Pareto probability distribution, are given by:

The mean is finite, if | £| > 1; the variance is finite, if | £| > 2. Zipf's law is the case of a Pareto law with £= - 1. These properties also help underscore that the rank-size rule cannot correspond to a reasonable probability distribu-

tion, strictly speaking, as such a distribution would have neither a finite mean nor a finite variance.

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With these caveats, it is still interesting to note that with our data, reasonable

good statistical fits are obtained when we regress the log rank against log city size and a constant, which is the so-called Zipf regression. Interestingly, for all

country-year pairs we strongly reject the null hypothesis that the Zipf coeffi- cient is equal to minus one. In other words, we strongly reject Zipf 's law,

strictly construed.

'Every cloud has a silver lining', however. Starting from an empirical law, like Zipf 's law, one may motivate a more general and far reaching inquiry into urban structure and growth and therefore on the determinants of city size distributions. This is what we have sought to do in this paper!

Our use of the Zipf coefficient as a measure of dispersion in this paper is both original and may be easily defended on the basis of the properties of a

power law for cities (B2). Specifically, the coefficient of variation, defined as standard deviation divided by the mean, is given by (£/(l + Qjf'5, and is there- fore a monotone increasing function of the Zipf coefficient only. Similarly, the Gini coefficient is given by - 0.5£+ 1.

We think that rigorous research along the lines of our paper helps caution

economists, sociologists, urban scientists and econophysicists against undue

predictions. For example, as groups of countries integrate, like the EU, eco- nomic forces are unleashed which reshape their urban systems. What is likely to happen to the sizes of their larger cities and their ranks? Zipf 's law offers a

straightforward prediction. But is it reliable? We think not, and have instead

proposed a way to make predictions that rely on underlying determinants of

city sizes in a dynamic world.

while they increase the absolute value of the Zipf coefficient. Since the Zipf coeffi-

cient is negative, they decrease its algebraic value. This result holds independently of

whether or not the city size distribution is Pareto. Of course, if it is not Pareto, the

Zipf coefficient will not be a constant, but the model predicts that its value will

change in the same direction for all, large enough, city sizes. It is important to note

that even though our basic theory implies a Pareto distribution of city sizes only for

particular cases (see RHW for details), we approach the data using Zipf coefficients

that are specified as independent of city size. That is, we assume that the size distri-

bution is always Pareto. So our assumption of a particular distribution for city sizes gives us a specification

that can be estimated given the data that we have at our disposal and that allows us

to directly test our theory on the impact of ICT on the city size distribution. The

crucial question is then, of course, whether this is an appropriate assumption. It turns

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CITIES 215

out that empirical evidence gives us good reason to think that the Pareto distribution is a reasonable fit for real world city size distributions across a large number of countries and at many different points in time. Even if the distribution is not Pareto, it is likely that reductions in variance will be associated with change for the Zipf coefficient (as discussed above) in the same direction. In the discussion of our empir- ical results, Section 6 below, we also address this concern by presenting robustness checks using other measures of dispersion in the upper tail.

Once we have the estimated Zipf coefficient, we may use it as a summary of the

city size distribution for different countries and examine how variations in the city size distribution may be attributed to the observed changes in ICT. Clearly a large number of other factors will determine the city size distribution and we will need to control for these if we want to isolate the effect of ICT. We discuss and motivate these additional controls in the results section below.

To capture the effects of ICT we use data on the number of telephone lines and on access to the internet. Our main focus is on the number of telephone lines for several reasons. First, because we have more data. Second, because the impact on the urban structure will take time and, as Figure 1 shows, the rapid adoption of internet

technology has only occurred relatively recently. Third, because for telephone lines we have a way to deal with the endogeneity problem for ICT. That is, we have a way to control for the fact that the number of telephone lines may be driven by the urban

structure, rather than the other way round. As no such instrumental variable is available for the internet, our results when we use access to the internet as an addi- tional explanatory variable are necessarily more speculative (although both sets of results point in the same direction). We discuss this issue further below after we

provide details of our empirical strategy. The Zipf coefficient for a country c in year t is obtained from the following

regression:

RKt = Xct + CA + 4* (3)

where Rkt = ln(rank^ is the log of the rank of city i in country c in year t, Pkt is the

log population of that city, Xct is a country-year specific intercept, and £rt is a country- year specific Zipf coefficient.

We follow Rosen and Resnick (1980) and subsequently Soo (2005) in seeking to understand the determinants of the Zipf coefficient £rf in (3) in terms of country characteristics:

£ct=ec + 8t + Xctr] + ect, (4)

where 6C is a constant which may be country specific, S is a linear time trend and 7] is a vector of unknown coefficients. The parameter 0ci sometimes known as a country fixed effect, controls for the fact that the Zipf coefficient may be higher or lower for some particular country in all years for reasons that are unobservable to us as researchers. The linear time trend controls for the fact that the Zipf coefficient

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216 YANNIS M. IOANNIDES ETAL.

may be increasing or decreasing over time for all countries for reasons that, again, are unobservable to us as researchers. Finally, the coefficients in 7J capture the effect of changes in explanatory variables (including ICT) on the Zipf coefficient. The coefficients in Equation (4) can be estimated by means of a regression of Zipf coeffi-

cients, £„ that are estimated for each country and year according to (3), on a collection of explanatory variables Xct that are thought to determine the city size distribution.

We make three modifications to this standard approach. The first deals with a

potential bias in the estimation of the Zipf coefficient. In a recent paper, Gabaix and Ibragimov (2006) return to a known bias of the estimate of the Zipf coefficient from Equation (3). This bias arises from the fact that ranks and sizes are obviously correlated. The bias is strong in small samples and their proposed correction1 is to use /?•* = ln(rank^-0.5) in place of the log rank in the left-hand side of Equation (3).

The second modification exploits the fact that we have panel data (i.e. data on cities and country characteristics for several years) to control for unobserved country specific determinants of differences in the city size distribution. This is captured by the country specific intercept, or fixed effect, 0c in Equation (4). Of course, as usual, if Xct contains time invariant observed characteristics then their coefficients cannot be

separately identified via econometric procedures because the country specific inter-

cept captures all time invariant differences across countries whatever their source. The third modification deals with the likely endogeneity of telephone lines with

respect to the urban structure. We want to be able to interpret the coefficient on

telephone lines from Equation (4) as capturing the impact on the Zipf coefficient of

changing the number of telephone lines per capita. That is, we want to be able to talk about the causal effect of ICT on urban structure. But what if changes to the urban

structure come from some other source (say the increasing use of the automobile, which incidentally we do control for, in part via the road density variable) and coun-

tries respond to this by changing the number of telephone lines per capita? Then, the

number of telephone lines per capita would be driven by a different underlying factor.

They would be a function of urban structure, and thus endogenous. In such a case, our regression will capture an association between ICT and urban structure which

includes both the direct causal effect (from ICT to urban structure) and any indirect

feedback effects (from urban structure to ICT). In the worst case scenario, there may

actually be no causal effect of ICT on urban structure, but we may reach the erro-

neous conclusion that there is an effect, because our regressions pick up the reverse

feedback effect from urban structure to ICT. To control for this we adopt an instrumental variables approach. That is, we look

for some variables (i.e. country characteristics) that (a) do not change if the urban

1 According to Gabaix and Ibragimov (2006), Theorem 1, the correction of the bias in the OLS estimate is optimal in the sense

that the proposed transformation of the dependent variable reduces the bias to leading order only.

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CITIES 217

structure changes for some exogenous reason (e.g. the increase in the availability of the automobile), that (b) do not themselves independently affect the urban structure, but that (c) are correlated with the number of telephone lines. We can then use these instrumental variables to capture the causal effect of the number of telephone lines on urban structure. To do this, we first predict the number of telephone lines in a

given country and year on the basis of the values of the instrumental variables. We then include these predicted values in place of the actual values of telephone lines in

Equation (4). If we find that these predicted values of telephone lines still have an effect on urban structure, then we can reason as follows. We know that the predicted values are not capturing any direct effect of the instrumental variables on urban structure (because we assumed - condition (b) - that these variables do not independ- ently affect the urban structure). We also know that the predicted values cannot be

capturing any feedback effect from urban structure to ICT because we are predicting phone lines per capita as a function of the instrumental variables (and we assumed -

condition (a) - that these variables were independent of exogenous changes to urban

structure). Thus, the predicted values must be capturing the causal impact of ICT on urban structure. Of course, for this strategy to work our instrumental variables must be correlated with ICT - condition (c) - so that the predicted values bear some relation to the actual values.

Our idea is to construct instrumental variables based on the market structure in the telecommunications sector. Clearly market structure in the telecommunications sector should affect the number of phone lines thus satisfying condition (c) for a valid instrument. Results that we report below show that this is indeed the case. Telecom- munications market structure is also unlikely to have a direct effect on the urban structure (independent of its effect on ICT), thus satisfying condition (b) for a valid instrument. What about condition (a) that telecommunication market structure is not affected if urban structure changes for some exogenous reason? We find it hard to come up with a convincing story where market structure is directly affected by changes to the urban structure. But it is possible to come up with stories where both market structure and urban structure are being driven by some common factor that we have omitted from our estimation. For example, the general trend towards liber- alization of the economy during the 1980s affected many sectors in addition to the telecommunications sector. Perhaps it was the reform of one of these sectors (e.g. transport) that changed urban structure. In that case, our instrument will fail to satisfy the first condition because it is actually changes in attitudes to liberalization (exoge- nous to our model) that are changing both urban structure and market structure. By including other measures of liberalization, we are able to provide some indirect evidence that this is not the case and that our instruments are likely to be valid. But, formally, conditions (a) and (b) are 'maintained assumptions' that cannot be easily tested and the instrumental approach relies on their holding. We find these assump- tions reasonable, but some readers may not do, in which case our assertion of a causal effect of ICT on urban structure will need to be interpreted with caution.

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218 YANNIS M. IOANNIDES ETAL.

We can identify three broad market structures for the countries in our sample during the years that we study: competitive, public or private monopoly. Two of the instruments that we use are dummies for whether the country has a public monopoly or a private monopoly with a competitive structure as the excluded category. The other two instruments measure the time that has passed since the end of the private and public monopolies for countries that have liberalized their telecommunications sector. As no such instrumental variables are available for the internet, our results when we use access to the internet as an additional explanatory variable are neces-

sarily more speculative (although both sets of results do point in the same direction). Finally, in addition, we report in Appendix B a fourth modification which increases

the efficiency of the estimators by implementing a one-step procedure that estimates

Equations (3) and (4) simultaneously. Before turning to the implementation of our approach, we reiterate that, although

we rely on the Pareto law to motivate our econometric approach, our estimations should capture more generally the impact upon the entire distribution of city sizes that emanate from changes in underlying determinants of interest.

5. DATA

We use the same city data as that used in Soo (2005), which were taken from Thomas Brinkhoff 's City Population project (http://www.citypopulation.de). Soo's paper pro- vides a fairly extensive discussion of the nature of the data, particularly with regard to the issue of the definition of cities.2 Data on population, GDP per capita in 2000

Purchasing Power Parity (PPP), trade and government expenditure as a percentage of GDP, non-agricultural economic activity and land area come from the World Bank

World Development Indicators. Data on kilometres of roads come from the Inter-

national Road Federation World Road Statistics.3 GDP growth is calculated as log difference of GDP in 2000 PPP; its volatility is measured as the empirical standard deviation over the observed time period.

We use two different measures to evaluate the role of ICT in determining the city size distribution: telephones and the internet. As already discussed, our main focus is

on telephones, because we have data for a longer time period and can construct a set

of potential instruments. Data on the number of telephone land lines and internet

users per 1000 also come from the World Bank World Development Indicators. We

multiply these numbers by 1000 and use per capita measure of phone lines and

internet users in the estimations. The information on the market structure of the telecommunications sector (private

or public monopoly versus competitive provision) that we use to instrument the number

2 We use data on cities as opposed to urban agglomerations because they are more consistently available internationally. 3 Further details on all these variables are provided in Soo (2005). A large number of the explanatory variables were also kindly

provided by Kwok Tong Soo and supplemented by the authors.

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CITIES 219

of telephone lines comes from the OECD International Regulation Database.4 This same source provides the data that we use to capture the general degree of competi- tion in the economy when considering the validity of our instruments.

We start with city-level data for 73 countries covering 7,530 different cities recorded at various time periods between 1972 and 2001. There are 197 country-year pairs meaning that, on average, we observe each country 2.7 times. Detailed inspection of the data reveals that the relevant explanatory variables are missing for many coun- tries. Fortunately, the variables are available for three blocks of countries - North

America, Europe and some of the former countries of the Soviet Union.5 Deleting countries with missing data leaves us with 24 countries covering 2,955 cities recorded at various time periods between 1980 and 2000. There are now 63 country-year pairs meaning that, on average, we observe each country 2.6 times. For the internet re-

gressions we have to drop Mexico and restrict the time period to 1990 to 2000. This

gives us 23 countries and 41 country-year pairs covering 2,792 cities. Table 1 presents

Table 1. Descriptive statistics

Mean Std. Dev. Min Max Obs

City specific variables City size 132 282 339 529 10 054 8 405 000 6975 Normalized city size 0.0042 0.0105 0.0002 0.2024 6975 log(norm. city size) -6.31 1.25 -8.64 -1.6 6975

Country specific variables Phone lines per capita 0.402 0.178 0.065 0.722 63 log(Phone lines per capita) -1.043 0.574 -2.736 -0.326 63 Internet users per capita 0.091 0.135 0.000 0.441 41 log(Internet users per capita) -4.060 2.223 -8.265 -0.820 41 Inverse road density 0.033 0.067 0.002 0.329 63 Country population 35 200 000 57 400 000 4 209 000 282 000 000 63 log(country population) 16.632 1.108 15.253 19.458 63 GDP per capita, PPP 18 287 7,838 4369 33 970 63 log(GDP per capita), PPP 9.692 0.544 8.382 10.433 63 Trade, % GDP 0.735 0.317 0.205 1.680 63 Non-agric. sectors, % GDP 0.936 0.054 0.732 0.988 63 Gov. expend., % GDP 0.377 0.082 0.161 0.491 63 Std. dev. of GDP growth 0.029 0.019 0.013 0.083 63 Land area, km2 1612 057 3 853 566 30 230 16 900 000 63 log(land area) 12.390 1.748 10.317 16.642 63 Number of cities/ 1000a 0.111 0.114 0.022 0.555 63

Notes: Descriptive statistics for the sample used in Tables 2, 3 and Al. For variable definitions, see text and Web Appendix. a

Average over time.

4 See the Indicators of Product Market Regulation Homepage at: http://www.oecd.org/eco/pmr and described in Conway and Nicoletti (2006). Missing data points for Eastern European countries were filled by the authors based on media coverage. 5

Specifically, we use data on Austria, Belarus, Belgium, Bulgaria, Canada, Denmark, Finland, France, Greece, Hungary, Italy, Mexico, the Netherlands, Norway, Poland, Portugal, Romania, the Russian Federation, the Slovak Republic, Spain, Sweden, Switzerland, the United Kingdom and the United States. We have to drop Germany because of the reunification of 1990 and the ensuing adoption of Federal Republic of Germany institutions in former German Democratic Republic territory which cause definitional problems.

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220 YANNIS M. IOANNIDES ET AL.

the descriptive statistics of the variables used in our empirical analysis below. Addi- tional details on our data variable definitions may be found in the online Data Appendix.

6. RESULTS

We start by estimating Equation (3) for each country-year pair to get some idea of the distribution of Zipf coefficients for the countries in question. The mean Zipf coefficient across our 63 country-year pairs is -1.370. The maximum value is -0.928 for Belarus in 1998, the minimum is -1.714 for Belgium in 2000. Interestingly, for all country-year pairs we strongly reject the null hypothesis that the Zipf coefficient is equal to minus one.6 That is, we strongly reject Zipf 's law, strictly construed as an estimated Zipf coefficient (£ - the elasticity of the proportion of cities larger than S with respect to S) being equal to -1. See Box 1 for more details.

We now turn to consider the effect that ICT has on the city size distribution as summarized by the Zipf coefficient. As discussed in the data section, our main focus is on the impact of phone lines. Figure 2 plots our estimates of Zipf coefficients for different countries at different times against the number of telephone lines. Two

things stand out from the plot. The first is that, overall, the relationship between Zipf coefficients and the number of telephone lines is as predicted. Second, looking at

Figure 2. Estimated Zipf coefficients against telephone mainlines, per 1000 inhabitants, different countries and years Source: Authors' own calculations.

6 Our results are broadly in line with those reported in Soo's Table 1 (2005), which are for the last year for each country-pair and which do not implement the Gabaix-Ibragimov correction.

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CITIES 221

individual countries, we can see the same effect replicated within the country in terms of changes over time. This is, perhaps, easiest to see for Belgium (BEL) and Austria

(AUT), but careful inspection will convince the reader that a similar pattern is observed for many countries. The rest of this section formalizes the findings that

emerge from this scatter plot, showing that they are robust to the introduction of additional explanatory variables and to controlling for the endogeneity of telephone lines.

We begin by estimating the simplest possible specification where we treat phone lines and a time trend as the only variable that explains differences in the Zipf coefficient across countries and time. That is, we estimate Equation (4) with phone lines and time as the only explanatory variable (JQ. The results are shown in column 1 of Table 2. The positive time trend picks up the fact that, on average, across all

countries, variance in the city size is increasing over time. Our focus, however, is on

phone lines and we find that these have a significant negative impact on the Zipf coefficient. That is, the more phone lines a country has, the more concentrated is its

city size distribution. This is consistent with our theoretical result that improvements in ICT (or, in the data, an increase in the number of phone lines) lead to smaller local external effects and therefore a more concentrated city size distribution.

Clearly, there are many omitted characteristics of countries that could be corre- lated with both phone lines and the degree to which population is spread out across the city size distribution. Column 2 begins to address this problem by including several additional explanatory variables. Before turning to discussing the empirical results, we briefly motivate each of the additional control variables.

We include the inverse of road density as a proxy for transport costs within the

country. Countries with a low road density are likely to have high transport costs

encouraging population to concentrate in just a few cities. Thus, we expect the coefficient on inverse road density to be positive (fewer roads imply higher inverse road density, higher transport costs and urban population that is more concentrated in fewer cities).

We include three variables to control for the economic and geographic size of the

country: population, income and land area. More densely populated countries are

likely to have more equal city size distribution, so we expect the coefficient on popu- lation to be negative while that on land area should be positive. Although we do not constrain the coefficients to be equal, these two variables could pick up other effects, thus introducing some ambiguity about the expected signs on their coefficients. Given our focus on more developed countries we have no strong prior on the sign of the coefficient on GDP. Models in the New Economic Geography tradition predict that our measure of trade openness (trade as a percentage of GDP) would have a negative effect on spatial concentration and hence on the Zipf coefficient if international trade weakens agglomeration forces, as predicted by Fujita et al. (1999, Chapter 18). More recent research (e.g. Rossi-Hansberg, 2005), however, allows for a greater number of

parameters (such as rate at which agglomeration effects attenuate with distance, total

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222 YANNIS M. IOANNIDES ETAL.

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CITIES 223

factor productivity, transport costs and, of course, particular country geography) and therefore greater variety of possibilities. We would expect higher agricultural produc- tion to lead to less concentration and a flatter city size distribution. That is, we expect the coefficient on non-agricultural sectors as a percentage of GDP to be positive. A measure of the size of government (government expenditure as a share of GDP) allows for the possibility that larger governments may imply higher population con- centration. That would indeed be the case if (as Ades and Glaeser, 1995 emphasize) rent seeking behaviour encourages citizens to locate close to policy-makers in the

capital city. Conversely, large governments have more means to work against agglom- eration forces and support peripheral regions through regional policies. Thus we have no strong priors on the sign of the coefficient on government expenditure.

Finally, we include the standard deviation of the rate of growth of real GDP since the theory underlying our approach (discussed in Appendix A) indicates that a higher volatility of total factor productivity shocks should lead to a larger variance of the size distribution and therefore larger Zipf coefficients. We also include the number of cities as a convenient way of allowing for non-linearities in the Zipf regression.7

Results reported in column 2 are in line with our expectations for all variables

except the inverse of road density and the volatility of GDP (which are insignificant). Introducing country fixed effects and instrumenting for phone lines per capita alters these findings so we consider the issue no further for now. Instead, we draw attention to the fact that introducing all of these controls does not change our conclusion on the role of phone lines. The coefficient is still negative and significant, albeit slightly smaller in absolute value. Thus, introducing a large number of additional controls does not change our conclusion that telephone lines are associated with more con- centrated city size distributions.

Columns 3 and 4 of Table 2 report results after introducing a country-specific fixed effect. Column 3 reports results when phone lines and a time trend are the only explanatory variable in Xct. Column 4 reports results when we include the additional control variables. Note that the coefficients for four time invariant variables cannot be identified in the fixed effect specification and therefore these variables are omitted in the regression reported here. These variables are time invariant either because of data availability (government expenditure as a percentage of GDP, standard deviation of GDP growth) or because they show very little time series variation (land area and number of cities). Moving from column 2 to column 3 we see that introducing unobservable country-specific effects decreases the absolute value of the coefficient on phone lines, although the coefficient remains negative and significant. Introducing additional controls in column 4 now strengthens the effect of telephone lines per

7 Several studies, including notably Black and Henderson (2003) and RHW, have emphasized that the log rank - log population relationship is roughly concave. The relationship therefore exhibits a steep (negative) slope for the highest ranked cities and a flatter (still negative) slope for lower rank cities. RHW offer a theoretical justification for this property. Increasing the number of cities may therefore have a positive impact on the coefficient.

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224 YANNIS M. IOANNIDES ETAL.

capita. Note that, as alluded to above, the introduction of fixed effects now gives us a positive sign on inverse road density that is consistent with our theory (although the coefficient is insignificant). Thus, our finding that telephone lines are associated with less dispersed city size distributions is robust to controlling for other country charac- teristics both observed and unobserved.

Of course, one may still worry that the relationship is being driven by time varying unobserved characteristics of countries and that it is changes in these unobserved characteristics that drive changes in urban structure which, in turn drive changes in our explanatory variables. For example, increasing car ownership may lead to the

dispersion of population and telephone lines then respond to that dispersion (rather than vice versa). To control for this, we adopt the standard solution of looking for instrumental variables as discussed, in depth, at the end of Section 4.

One might have similar concerns about inverse road density as a proxy for trans-

port costs. That is, more dispersed population leads to more roads and lower trans-

port costs rather than transport costs driving population dispersion. We have

experimented with lagged road density as an instrument but this resulted in consid- erable reductions in sample size and little change in the coefficient on road density. As our main interest is in the ICT variables, which we are able to instrument, we do not worry about this further other than to note that the coefficients on inverse road

density should be interpreted with caution.8 We assume that all other right hand side variables are exogenous.

Table 3 reports first stage regression results from the regression of phone lines per capita on the exogenous and instrumental variables (corresponding to columns 5-8 of Table 2). In the cross section (column 5), both public and private sector monopolies significantly decrease the number of telephone lines. Adding additional control vari- ables (column 6) substantially weakens the effect of the instruments. However, once

we have included a fixed effect (columns 7 and 8) we see that public monopolies are

significantly positively associated with the number of phone lines. The F-test on the

joint significance of the instruments for our preferred specification (column 8) show

that the model is fairly well instrumented (i.e. our instruments are fairly highly partially correlated with ICT).

Some of the time series variation in these variables comes from liberalization

that moved countries from private monopolies to competition. Most of the variation,

however, comes from privatization coupled with liberalization which moved countries

from public monopolies to competition.9 Our results in the most relevant specification

8 In our preliminary investigations we also tried to instrument for trade as a percentage of GDP using two dummies indicating when a country joined EU or NAFTA. These two variables turned out to be very weak instruments for trade, but reasonable additional instruments for ICT. For this reason, we no longer instrument trade, but continue to use these two additional instruments. We note that instrumenting trade using these regional trade agreement dummies does not change our main finding on ICT. Using only the market structure instruments for ICT also does not change our results. 9

During the time period we consider there were no privatizations that replace a public monopoly with a private monopoly, although this had certainly happened in earlier periods (e.g. in the United Kingdom).

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CITIES 225

Table 3. First stage regressions for Table 2

Dep. variable: WLS

log(phone lines per capita) [5] [6] [7] [8]

Public monopoly -0.687*** -0.035 0.245*** 0.305*** (0.185) (0.147) (0.074) (0.055)

Private monopoly -0.393* 0.07 0.01 0.181 (0.227) (0.177) (0.177) (0.153)

Time since end public monopoly 0.01 -0.001 -0.021 0.004 (0.027) (0.020) (0.014) (0.014)

Time since end private monopoly 0.029 -0.009 0.004 -0.009 (0.029) (0.021) (0.026) (0.024)

EU 0.077 0.113 -0.126 -0.297*** (0.091) (0.141) (0.106) (0.081)

NAFTA 0.211 -0.052 -0.111 -0.222* (0.326) (0.246) (0.148) (0.109)

Inverse road density - 1 .054 0.1 02 (1.166) (0.514)

log(country population) -0.265** -1.334 (0.103) (0.935)

log(GDP per capita), PPP 1 .0 1 7*** -0.211 (0.256) (0.315)

Trade, % GDP 0.011 0.472*** (0.200) (0.150)

Non-agric. sectors, % GDP 2.467 3.804*** (1.650) (0.877)

Gov. expend., % GDP 1.806** (0.775)

Std. dev. of GDP growth 15.633* (8.430)

log(land area) 0.181*** (0.063)

Number of cities/ 1 000 0.559 (0.849)

Time -0.039 0.017 0.047* 0.060** (0.027) (0.020) (0.027) (0.026)

Constant -0.506** -12.352*** country fixed efFects (0.223) (3.843)

F-test instruments3 13.77 1.03 6.48 9.04 R2 0.660 0.899 0.943 0.978 Obs country-year 63 63 63 63 Obs countries 24 24 24 24

Notes: Standard errors in brackets. ***, **, and * indicate significance at the 1%, 5% and 10% level, respectively. Within Z?2 is reported for fixed effects models. Weighted least squares (WLS) is weighted by the inverse standard error of the estimated Zipf coefficient.

"Jointly tests public and private telephony monopoly, EU/EEC-, NAFTA-membership.

in column 8, Table 3, suggest that, at least in terms of the number of phone lines, the

efficiency effects of liberalization were outweighed by changes to public service agree- ments and the tendency for newly privatized firms to reduce the cross-subsidization of residential lines by business users. Note that in all cases the predicted phone lines from the first stage regressions are increasing over time. The general increase of

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226 YANNIS M. IOANNIDES ETAL.

telephone mainlines is explained by the time trends as well as increases in population, road density, and GDP.

Columns 5-8 in Table 2 show what happens when we use these variables to instrument for the number of phone lines. Column 5 ignores country fixed effects and includes instrumented phone lines as the only explanatory variable. Comparing to column 1 we see that our results change very little. The effect of phone lines turns

insignificant as we introduce more explanatory variables (compare column 6 to col- umn 2) but it is again significant if we introduce fixed effects with phone lines on their own (column 7 versus column 3) and if we introduce fixed effects and time-varying explanatory variables (column 8 versus column 4).

In sum, we find a robust negative significant effect of the number of phone lines

per capita on the Zipf coefficient. Over our study period, increasing phone lines per capita have tended to cause the dispersion of population across the urban structure

resulting in a more concentrated city size distribution. Columns 1 and 2 of Table 4 show that we reach a similar conclusion for the impact

of the internet on the city size distribution. Column 1 presents results from a regres- sion of Zipf coefficients on the number of internet users per capita and a time trend. That is, from estimating Equation (4) with internet users per capita and a time trend as the only explanatory variable (JSQ. We see a negative significant effect on the Zipf coefficient, although the effect is smaller than that of phone lines. Column 2 shows what happens when we introduce the same additional controls as we did for phone lines. Introducing additional controls more than halves the absolute value of the coeffi- cient on internet users per capita and turns it insignificant. Columns 3 and 4 show that the negative effect of the internet vanishes once we also consider telephone mainlines.

Results, not reported here, show that instrumenting by means of the same set of instru- mental variables gives very similar coefficients, but at a slightly lower level of significance (5% instead of 1% in column 1). Only 16 countries have more than one year of data for internet usage so, not surprisingly, implementing the fixed effects specification gives insignificant results. Finally, introducing fixed effects and instrumenting leads to

coefficients that are essentially zero.10 This is hardly surprising given the limited

number of observations and the fact that market structure in the telecommunications

sector does not provide good instruments for the number of internet connections.

Our results about the effect of internet connections on urban structure are

encouraging for another reason, too. As Figure 1 documents, the incidence of mobile

telephony adoption is similar to that of the internet. While direct measures of

mobile telephony are available for some countries, the pattern of availability as of

now would reduce sample size substantially. We think it is difficult to find good instruments, especially since the development of mobile telephony markets have

been influenced by the different standards adopted by providers. Therefore, we take

10 These results are available on request and documented in the Web Appendix.

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CITIES 227

Table 4. Internet users, phone lines and the city size distribution

Dep. variable: WLS

Estimated Zipf coefficient [1] [2] [3] [4]

log(internet users per capita) -0.035*** -0.013 0.006 -0.015 (0.012) (0.018) (0.016) (0.017)

log(phone lines per capita) -0.185*** -0.312** (0.056) (0.127)

Inverse road density -0.886 -0.998 (0.635) (0.587)

log(country population) -0.006 -0.053 (0.046) (0.046)

log(GDP per capita), PPP -0.217 0.06 1 (0.135) (0.168)

Trade, % GDP -0.12 -0.067 (0.105) (0.099)

Non-agric. sectors, % GDP 0.067 -0.389 (0.800) (0.761)

Gov. expend., % GDP -1.058** -0.874** (0.399) (0.376)

Std. dev. of GDP growth -1 .48 1 -0.432 (4.632) (4.294)

log(land area) 0.01 1 0.046 (0.027) (0.029)

Number of cities/ 1000 -0.357 -0.27 (0.410) (0.379)

Time 0.013** 0.007 -0.002 0.01 (0.006) (0.009) (0.007) (0.008)

Constant -1.694*** 1.07 -1.450*** -1.311 (0.122) (1.963) (0.131) (2.052)

/? 0.199 0.686 0.381 0.742 Obs country-year 41 41 41 41 Obs countries 23 23 23 23

Notes: Standard errors in brackets. ***, **, and * indicate significance at the 1%, 5% and 10% level, respectively. Weighted least squares (WLS) is weighted by the inverse standard error of the estimated Zipf coefficient.

the results of the internet connections, where in fact telephone use is also controlled

for, as suggestive of the impact of mobile telephony, a technology that is conceptually akin to a combination of telephony and the internet.11

6.1. Additional robustness checks

A question concerning the nature of our instrumental variables strategy arises from

considering the literature on the political economy of urbanization. This literature

suggests that urban concentration may be driven by the general degree of competition

1 ' Modern mobile, that is cellular, telephony was not invented in the same countries where it was first commercialized, such as

Japan, but did indeed spread fast in sparsely populated countries, such as the Nordic European countries, with whom it is indeed

nowadays closely associated. Still, adoption per capita is greatest is densely populated but small countries, like Hong Kong and

Luxemburg.

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228 YANNIS M. IOANNIDES ETAL.

in the economic and political spheres. This raises the possibility that some measure of the degree of competition in the economy should be included directly in the regres- sion, violating the second requirement for the validity of an instrument (that it should have no direct effect on urban structure). Using this line of reasoning, one could

argue, for example, that the industrial organization of the telecommunications sector is actually just proxying for an overly centralized public sector which favours larger cities. To summarize, if industrial organization of the telecommunications sector is

capturing other factors that have a direct effect on urban concentration, then it is

inappropriate as an instrument. We explore this possibility by controlling for the general degree of competition in the economy using the OECD 'RegRef

' indicators of regula- tory conditions in the airlines, telecommunications, electricity, gas, post, rail, and road

freight industries of member countries (Conway and Nicoletti, 2006). The OECD claims that the RegRef indicators are a good proxy for the overall degree of compe- tition in the economy. The RegRef indicators are, unfortunately, only available for a subset of the countries in our data set. Specifically, data are not available for Belarus,

Bulgaria, Hungary, Mexico, Poland, Romania, Russian Federation, and Slovak Repub- lic leaving 45 country-year pairs instead of the 63 pairs originally. Re-estimation of the original model (column 8 in Table 2) with the reduced set of countries produces a stronger effect for phone lines, -0.308, which is significant at 1%. Including the

average of all RegRef indicators as an additional explanatory variable only slightly reduces the effect of phone lines to -0.280 and its significance to 2%. The coefficient on this new explanatory variable is virtually zero and highly insignificant.12 Taken

together these results suggest that concerns about the validity of our instrument as a

result of political economy stories are theoretically interesting, but empirically invalid.

Another question concerns what happens with other measures of urban con-

centration. We have experimented with the Gini index, the normalized Herfindahl con-

centration index and the coefficient of variation as alternative dependent variables.

These measures reflect different aspects of dispersion and are defined at the country level. The coefficient of variation, a standard measure of dispersion, averages the

squared deviations from the mean and then divides by the mean. The normalized

Herfindahl concentration index reflects squared normalized city sizes. The Gini

coefficient is the mean absolute deviation among all pairs of cities, relative to the mean

city size. Table 5 reports results for the coefficient on telephone lines for the same

eight specifications that appear in Table 2.

Remarkably for such different measures of dispersion, the results for the coeffi-

cients of telephone line per capita with the Gini and Herfindahl indices as dependent variables are - up to a scale factor - very similar to the two-step using Zipf (although

just statistically insignificant in column 8). The coefficient estimates with the coeffi-

cient of variation as a dependent variable are also negative and thus consistent with

our findings using the Zipf coefficient. It is worth recalling, however, that our choice

12 These results are available on request and documented in the Web Appendix.

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CITIES 229

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230 YANNIS M. IOANNIDES ETAL.

of Zipf coefficient as a measure for urban concentration is not arbitrary, being driven instead by a desire to link our empirical results firmly with our theoretical model of urban structure. In contrast, while all three of these alternative measures of urban concentration appear intuitive, when estimated on the truncated sample of larger cities

they are not consistent estimators of the population variables and cannot be linked to our theoretical prediction of decreasing variance for all cities. For this reason, the

Zipf coefficient results represent our preferred specification and we take these robust- ness checks as broadly consistent with our overall findings.

7. POLICY DISCUSSION AND CONCLUSION

We find robust evidence that increases in the number of telephone lines per capita lead to a more concentrated distribution of city sizes and so correspondingly to more

dispersion in the distribution of economic activity in space. The basic model that underlies our approach rationalizes this empirical result. As access to telephones improves, the ensuing changes in city size distributions imply that local production externalities decrease. That results in an urban structure that is less dependent on

past shocks and hence a size distribution of cities with smaller variance. This smaller variance is reflected in Zipf coefficients that are larger in absolute value.

Figure 3 illustrates the magnitude of our empirical results (using column 8 in Table 2). It assumes that the size distribution of city sizes is Pareto, that the smallest

city has 100 000 inhabitants. It plots the distribution for the average Zipf coefficient in our data (labelled 'actual' in the figure) and the distribution we would expect if the

Figure 3. Effect of phone lines per capita on the size distribution of cities

Source: Authors' own calculations.

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CITIES 231

log of phone lines per capita were to increase by one standard deviation (all other effects being set to zero). The figure also compares these two distributions with the one associated with Zipf 's law, that is, a Pareto distribution with coefficient minus

one, according to Equation (2). The increase in phone lines per capita concentrates the distribution, by making the Zipf relationship steeper. If ICT improves, cities are not as large. For example, the share of cities with more than a million inhabitants is reduced by 0.6 percentage points. Since the share of cities with populations larger than a million is about 4.3%, this implies about a 14% decrease in the number of these large cities. This is a significant change in urban structure!

We argue that the internet is likely to have similar, or even larger, effects on urban structures once its use has spread more thoroughly through the different economies. So far the evidence on internet usage is more speculative, although it goes in the same direction. The data suggest that as the number of internet users increases we should see effects that are about one-tenth of the size of the ones we observe for phone lines. As we argue in the introduction, massive internet adoption is a fairly recent phenom- enon, and at least in so far as our measurement of the extent of its adoption is

concerned, urban structure may take some time to adjust. This may explain the small coefficients we find in the data.

We find that public and private monopolies on average increase the number of

phone lines per capita. An average country with a public monopoly will therefore have a more concentrated size distribution of cities. These effects are also economi-

cally substantial. If the average country with a public telephone monopoly transitions to a competitive telecommunications sector, our results indicate that the change in the distribution of city sizes should be about a tenth of the change in Figure 3, but in the opposite direction. That is, the Zipf curve will become flatter as the number of larger cities increases. According to our calculations above, this change would lead to an increase of around 9% in the number of cities with more than a million residents.

Even though the analysis in this paper allows us to derive conclusions about the effect of ICT on the urban structure, as it stands it is not designed to derive implica- tions on welfare. So far we can conclude that according to the theory above, ICT causes a decrease in the strength of intra-urban spillovers. That is, ICT reduces the

importance of local factors of production on the city's productivity and has led to the evolution of a more uniform distribution of cities. So far, it looks like ICT trades off

spatial concentration of economic activity for total factor productivity, and thus bears a conceptual similarity to infrastructure and other regional policies, that are discussed

by Martin (1999) and Baldwin et al (2003, Ch. 17), and typically generate trade-offs.

However, increases in the scope (from urban to possibly regional, national or inter-

national) of spillovers or factor complementarities are likely to be associated with ICT as well. As the scope of externalities increases, we should also expect increases in the

growth rate of total factor productivity everywhere. ICT implies not only smaller local spillovers but also larger national or international spillovers. In this sense, ICT would behave more like the 'win-win' policies discussed in Baldwin et al. (2003, p. 444).

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232 YANNIS M. IOANNIDES ETAL.

In fact, if only the scope but not the average size of externalities changes, by con- struction ICT will lead to a welfare gain.

This paper studies the first effect of ICT that leads to changes in the size distribu- tion of cities. This effect by itself is likely to have a negative impact on welfare as it reduces the local externality. However, ICT will also have the second effect, on

spillovers at a larger spatial scope, which will not affect the distribution of economic

activity in space, but is likely to have important implications for the growth of aggre- gate total factor productivity over time. This effect will have positive effects on wel- fare. In order to understand the ultimate welfare effects of ICT, one needs to account for both the local and national or international effects. As a first step, we have studied the local implications of ICT only.

The theory presented above implies that we can expect to see agents reallocating across cities as a result of improvements in ICT. Moreover, our empirical results imply both that the reallocation that we have observed, and that will likely observe in the

future, are substantial. Moving costs are also important and we have not commented on them so far in this paper. Some of these costs are due to regulation and lack of

flexibility in labour markets. Others reflect frictions in the adjustment of urban public infrastructure. Yet other costs are due to the cost of selling and buying homes, and the actual transport and organizational costs involved in moving across cities. Our results highlight the importance of government policy in reducing this type of costs. If moving costs are artificially high, because of government regulation and various

types of interference, economies will not be able to take advantage of the gains associated with the ICT improvements, since agents will not respond by redistributing themselves accordingly in space.

It is imperative to allow for the natural reallocation that will result from further

improvements in ICT. After all, this reallocation across space is the adjustment by the individuals and by firms to an economic environment where physical location is

becoming less important.

Discussion

Omer Moav Royal Holloway, University of London, Hebrew University, Shalem Center, and CEPR

Ioannides et al. study the effect of the development in information and communication

technologies (ICT) on the distribution of city size, thereby estimating the interaction

between ICT and the returns to agglomeration in the production process. The authors develop a simple model that generates a straightforward prediction

regarding the effect of development of ICT on the distribution of city size. The model

implies a one-to-one relationship between the sign of the cross derivative of income

per worker in a city with respect to city size (agglomeration) and ICT, and the

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CITIES 233

variance in the distribution of city size. In particular, if and only if city size and ICT are substitutes in the production process, the development of ICT would reduce the variance in the distribution of city size, and if (and only if) the two are complements, the development of ICT would increase the variance in the distribution of city size.

Hence, the authors propose a clever way to indirectly estimate the interaction between agglomeration and ICT, by utilizing data on ICT adoption and the distri- bution of city size. Their model, however, uses specific functional forms and hence one might worry regarding the generality of the 'one-to-one' prediction regarding city size distribution and the interaction between agglomeration and ICT.

In this comment I show that the 'one-to-one' relationship generated by the specific functional forms doesn't hold in a more general framework. However, the prediction that a negative effect of ICT on city size variance implies that ICT and agglomera- tion are substitutes is maintained. Hence, since the empirical findings show that the

implementation of ICT has a negative effect on the variance of the distribution of

city size, the model developed here supports the authors' conclusion that ICT is a substitute for agglomeration.13

Suppose income per worker in city i is

y = AiF{tf,ICT) (5)

where A is the city specific productivity parameter and N is the size of the working force in i. The level of ICT is identical across all cities. The function F is increasing in both JV* and ICT

' (FN > 0, FICT > 0), it is strictly concave in N{ {Fm < 0), and the

marginal return to size approaches zero at very large cities (limy^ i^= 0). The sign of the cross derivative, FNICT, could be positive or negative, allowing for agglomera- tion and ICT to be complements or substitutes in the production process.

Under the assumption of free mobility, income across cities, net of congestion costs, C(jV), is equal:

AjFytf, ICT) - C{N) = w (6)

where C > 0, C" > 0, C(0) = 0, and lim^0C'{JV) = 0. Under the properties of Fand C, AF(JST, ICT) - C(Nl) has an inverse U shape with

respect to jV. It follows from (6) that in equilibrium the size of the working force in

city i is a function of the city's productivity, the development of ICT, and the equi- librium income net of congestion costs, w,

JV*{ = JV{A\ ICT, w). (7)

Stability considerations imply that in equilibrium the slope of AF(Jf, ICT) - C(JVi) with respect to N{ is negative: AFN(N*\ ICT) - C(JV*{) < 0. That is, the equilibrium size of each city is on the downward slope of the inverse U function for that city.

13 The specific model developed by Ioannides et al. has an additional undesirable implication that is resolved by the following model. It implies that if ICT and agglomeration are substitutes, then the marginal effect of city size on income (net of congestion cost) is always negative, and hence the optimal city size is approaching zero.

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234 YANNIS M. IOANNIDES ETAL.

It follows from implicit differentiation of (6) that the derivative of city size with respect to the productivity parameter is

_ F(N\ICT) Na~ _ a%-c (8)

where at the equilibrium (N = jfi]A% - C" < 0, and therefore NAi >0. As follows from (7), cities vary in size only if there is a variance across cities in the

productivity parameter, A\ Moreover, for a given distribution of A\ the larger is NA, the larger is the variance in the distribution of city size. Hence, we are interested in

the effect of ICT on NA>, which is captured by the sign of the cross derivative of JV

(in Equation 7) with respect to A1 and ICT: NA,JCT. If the data reveal a positive effect of ICT on the variance of city size we conclude that NA,ICT > 0, whereas a negative effect implies the opposite.

Taking the derivative of (8) with respect to ICT, implies that

^-FIcr(A%-C') + A%JCTF

A'JCT (A%-C'f

Noting that at the equilibrium A{FN - C < 0, and that FICT > 0, it follows that if agglomeration and ICT are complements (if FNICT > 0), then NAitICT > 0.

If, however, agglomeration and ICT are substitutes {FMICT<0), then the sign of NA> ICT is ambiguous.

Therefore, if, as suggested by the data, development of ICT reduces the variance in the city size distribution, and hence NA,ICT < 0, the conclusion that agglomeration and ICT are substitutes in the production process follows, as consistent with the

conclusion of the authors, based on the specific functional forms of their model.

Finding the opposite, NA> ICT > 0, does not imply, however, that agglomeration and

ICT are complements.

Panel discussion

Commenting on the predictions of the theoretical model, Allan Drazen noticed that

in the paper a steeper slope implies more dispersion within a given set of cities, but

wondered what can be said about the other cities. For instance, it could be the case

that the top 50 cities become more or less important because of ICT.

There were several comments on the welfare implications of the results. Hans-Werner

Sinn pointed out that, following Moav's discussion, welfare effects of telephones must be

positive. The new technology can indeed reduce congestion externalities and this

entails important policy implications. Philippe Martin stressed that given the many externalities that are present in cities, it is not obvious whether, in laissez faire, cities

are too small or too large.

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CITIES 235

Provided that telephone lines were introduced in stages, initially at the local level, then at the interstate level, possibly entailing different implications, Marcello Estevao wondered whether the authors can introduce telephone growth in history, both within and across cities. As regards the evolution of ICT technologies, mobile phones have become more important as substitute telephones, and, as Christian Schultz

pointed out, maybe telephone lines are not a good measure any more. Several panellists addressed the topic of distance. Richard Portes remarked that

there is a substantial literature on the economic effects of distance, such as gravity equations in trade, where the role of the latter does not appear to have changed over

time, and wondered how the approach of the paper relates to these studies. Luigi Guiso added that in the banking sector there is evidence that distance (between borrowers and lenders) has become less important, possibly due to better ICT

monitoring possibilities. He also stressed that it is important to distinguish between

personal interactions and communication. ICT for communication should be more relevant in cities where activities are less specialized and people interact more, with

respect to cities where activities are more specialized, as for instance in bureaucracy, as Washington is. Perhaps, looking at information about the sector-specialization of cities at the time the technology was introduced could help to sort out causality.

Finally, Jose Tavares stressed the importance of knowing what a 'city' meant to the authors. The choice to use city or urban limits is important, because people can move towards suburbs within large cities and, thus, the same kind of effect detected in the

paper can be found in cities with large urban areas around them.

APPENDIX A: A MODEL OF ICT, URBAN EVOLUTION AND CITY SIZE DISTRIBUTIONS

We illustrate how to study the role of ICT on the urban hierarchy by considering the basic theoretical model in RHW. Total factor productivity, that is the level of tech-

nology, in industry j at time / is given by

where Ntj and Htj denote the city's total industry j employment and specific human

capital, and In Atj is an independent and identically distributed (i.i.d.) productivity shock with mean zero and variance V across all industries j and time period t. Thus

parameters y and Ej determine the importance of knowledge spillovers from total

employment in industry 7 and industry j-specific human capital in the economy, which are external to individual firms in the industry but internal to the urban economy due to the presence of city developers. If both parameters )* and £j are equal to zero there are no external effects and economic activity has no incentive to agglomerate in cities. The larger both of these parameters the more important are a city's total human capital and employment in determining Atj> the city-specific total factor pro- ductivity of industry j.

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236 YANNIS M. IOANNIDES ETAL.

A very simple way to introduce the effect of ICT is therefore to let these two

parameters vary with I., the quality of information technology. Namely, let )*(l,) be such that dyj(l)/dlt < 0 and, similarly, let £-(l,) be such that de^l)/dlt < 0. Essentially, this assumption amounts to ICT decreasing the importance of agglomeration effects since people located far away can now interact at a smaller cost and so the number of people living in the city are less important in determining the city's productivity level. Conversely, we could assume that both )*(i,) and £j(l) depend positively on the

quality of ICT, which would be consistent with arguments that emphasize the greater importance of public goods as a result of changes in ICT. Which effect dominates is,

ultimately, an empirical question that we try to settle in this paper. In order for city sizes to be well defined, it will be clarified shortly below that we need

to guarantee that the knowledge spillover parameters y- and £j satisfy yj(i) + Sj(l) < 1/2 for all I. Otherwise, cities would, in a sense, be too productive and therefore would grow unboundedly since agglomeration effects would dominate congestion costs at all popu- lation levels. As long as this condition is satisfied, as a city grows eventually congestion costs become more important than agglomeration costs and so city sizes are finite.

Cities consist of a central business centre, where all agents work and all production is located, and residential areas surrounding it. Each agent consumes the services of one unit of land per period. For spatial equilibrium within each city agents should be indifferent about where to live in the city. Therefore, equilibrium rents at a distance

Z from the centre should obey R(z) = t(z - z), where z denotes a city's radius, where rent is equal to 0. Hence, total rents in a city of radius z are given by

TR = \l2KZR(z)dz

= ff

= ^1

since everyone in the city lives in one unit of land, a city of population N and

b = 2K2 T/3 . Total commuting costs are given by P -

TCC= 2nzTzdz = bN\ Jo

Assuming the presence of city developers or governments that internalize city-wide externalities, RHW show that in this framework the unique equilibrium allocation

may be obtained as a solution to the following planning problem14: Choose state

contingent sequences {Cp Xp N^ fy, Kp H^lj=l to maximize

(\-S)Ee j^S% f lnQ/^J (Al)

14 RHW describe how to solve for an equilibrium in which some of the externalities are not internalized by city planners or

developers and, therefore, cities are inefficient. Independently of the ability to internalize all potential urban externalities or not, this problem can be solved using a pseudo-planner problem and in all cases yields results we underscore in this paper. The main role that city developers or city governments play is to coordinate agents to work in the equilibrium number of cities. Land

developers and city governments traditionally have played this coordination role by offering guarantees and incentives to locate in a particular area.

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CITIES 237

subject to, for all t and j,

JV, = 5X (A3)

jti+0. = *;>*;.-> (A4)

#„„• = #,•[*? + o -«*)*]•] (A5) where: JV^, Kp X^ and //& denote total employment, total physical capital, physical capital investment, and total human capital in industry j in the economy, B®, BjOCj and Pj are positive parameters satisfying 0 < G£ + /^ < 1 ; C& denotes total consumption of representative household i9 and jU& the number of cities producing goods in industry j; Uj denotes the fraction of time agent i devotes to work. Thus, the maximization

problem above amounts to maximizing the sum of households' lifetime utilities (Al), subject to: a resource constraint, Equation (A2), which expresses that the use of resources for consumption, investment, and commuting costs may not exceed current

output (and presupposes that rents are redistributed back to the city residents); a labour market equilibrium condition, Equation (A3), according to which the total labour force is allocated to all industries and all cities (free labour mobility); and the two factor accumulation equations, for physical and human capital. That is, respec- tively, Equation (A4), according to which current investment and the existing capital stock produce capital stock in the next period (with (Oj being a parameter satisfying 0 < (Oj < 1), and Equation (A5), where human capital is augmented at a rate that

depends on the portion of each individual's endowment of leisure not allocated for work.

The problem of maximizing with respect to the number of cities ty is a static

problem with first order condition

r ~i2

So the size of a city, s§9 with core industry j is then given by

H "

[^]^V>?^-\* (A6)

where the auxiliary variables Ap dp pp and 0^ are defined as: i

a - ji-2(r,+f,) ^ _ aj +

Yj *

- *

'«;-i-2(r.+£.)' ^ _

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238 YANNIS M. IOANNIDES ET AL.

Hj 1-2(7, +£,)'

J l-2(7, + £,)

/<• = (1 - 2(Yj + Sj)) [2(7j + £,)/*f >+ W'>.

Given this log-linear specification, RHW show that capital investments and

consumption in each industry are constant fractions of output net of commuting costs, and the fraction of time devoted to work u§ is constant across time. Taking natural logarithms of both sides of Equation (A.6) that defines city size, we get

In r. • = 2 yfg + In %rJ

+ ty + In A ^ + A J In K, (A7) r. • = 2

(^ yfg +

1-2(7, + e,) In

* +

1-2(7, + *,) In A ^ + J In K,

')

where the auxiliary variable y/^ includes all non-stochastic variables that enter the

planning problem, including N$ and Hp If In A$ and K§ are the sole stochastic variables in Equation (A7), then the mean

and variance of city sizes are easily obtained and given, respectively, by

^ h = {v, +

,_2^ + £j) * ̂ P1 + 4£dn ^)] (A8)

V^^ = {i-2(yj + £j))

V + Mjf ̂ n *t

It is now clear why condition )j(i) + £j(i) < 1/2 must hold. They are to ensure that the mean and variance of the city size distribution are mathematically well defined. RHW show that as t - > «> the variance of the log of physical capital in industry J is:

so that the variance of the long run log-city size distribution may be obtained from

(A8) and given by

F0[ln 5,.] »J = 4V I I +f & - \ . (A9) 5,.] »J =

\{l-2(yJ

+ ej) {l-2(yj

+ eJ) + Pj

- \

Note that the variance of the city size distribution is then increasing in )*(l,) + £,(*/)• Therefore, any assumption that we make about the dependence of these elasticities

on ICT is reflected in changes on the invariant distribution of city sizes.

In the example of Section 3 in the main text, roughly speaking, the parameter £

corresponds to y-(i) + Ej(lt) here. The parameter T corresponds to b here.

We would also like to connect the variance of the distribution of city sizes to the

Zipf coefficient, in order to be able to connect our theoretical results with the data

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CITIES 239

through this coefficient. The local Zipf coefficient is given by the elasticity of the counter-cumulative of the city size distribution, P(s > S), with respect to city size,

SV ; P{s>S) dS

Given the mean of the distribution of city sizes, as we increase the variance we are

shifting mass to the tails of the distribution. This implies that for S high enough (large enough city sizes) the term | £(S) | will be smaller the larger the variance. As the variance goes to infinity, £(£) > -2, ]ims_^coQS) converges to the Pareto coefficient.

APPENDIX B: ONE-STEP ESTIMATION

It is possible to obtain one-step estimation results for the relationship between tele-

phone mainlines per capita and the Zipf coefficient. This appendix reports such results for the purpose of comparison. While the one-step procedure is more efficient, it is less intuitive and requires slightly stronger assumptions on the error term.

In the one-step procedure we substitute ga from Equation (4) into Equation (3) and estimate directly:

/g = K + *A + SP* + [*Ato +<2, (Aio) where e*t = ekt + £ctPkt is now composed of an i.i.d. error plus the interaction between rank and error from the first step, while all other coefficients and variables are as defined before. The interacted variable XctPkt is instrumented by using the predicted values from a regression of XctPkt on Za^kt and the other exogenous explanatory variables (see Wooldridge, 2002, p. 235 for why this is the correct approach).

Results for telephones and internet usage per capita are reported in Tables Al and A2 respectively. Focusing only on our key variables of interest, we see that this one-

step procedure gives the same substantive effect of telephones and internet usage on urban structure although the more efficient estimation procedure increases the signi- ficance of the coefficients. As the one-step estimation procedure requires stronger assumptions on the error term, and as these particular empirical results do not correct for the resulting complicated error structure in (A10), we view these results as

placing an upper bound on the significance of the two core explanatory variables of the urban structure, telephone lines and internet users per capita. It is encouraging that the point estimates obtained by the one-step estimation are close, as in fact they should be, to those obtained by the two-step estimation and reported in Tables 2 and 3 above.

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240 YANNIS M. IOANNIDES ETAL.

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CITIES 241

Table A2. Internet users and the city size distribution (one-step estimation)

Dep. variable log(rank-0.5) OLS

[i] ra [3] m_

log(city size) x log(internet users per capita) -0.045*** -0.025*** -0.002 -0.028***

(0.002) (0.004) (0.004) (0.004) x log(phone lines per capita) -0.190*** -0.400***

(0.013) (0.025) x Inverse road density -0.757*** -0.851***

(0.120) (0.117) X log(country population) -0.040*** -0.096***

(0.010) (0.010) x log(GDP per capita), PPP -0.255*** 0.055

(0.030) (0.035) x Trade, % GDP -0.047** 0.038*

(0.022) (0.022) x Non-agric. sectors, % GDP 0.491*** 0.237

(0.158) (0.155) x Gov. expend., % GDP -0.934*** -0.868***

(0.079) (0.077) x Std. dev. of GDP growth -2.959*** -2.791***

(0.921) (0.898) X log(land area) 0.023*** 0.061***

(0.005) (0.005) x Number of cities/ 1 000 -0. 1 1 0.007

(0.078) (0.077) xTime 0.023*** 0.015*** 0.002 0.018***

(0.001) (0.002) (0.002) (0.002) x Constant -1.678*** -1.399*** -1.146*** -1.179***

(0.019) (0.042) (0.040) (0.043) Constant country-year specific country-year specific Obs cities 4906 4906 4906 4906 Obs country-year 41 41 41 41 Obs countries 23 23 23 23

Motes: Standard errors in brackets. ***, **, and * indicate significance at the 1%, 5% and 10% level, respectively. Interacted variables are mean-shifted.

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