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Urban Agglomeration, City Size and Productivity: Are Bigger, More Dense Cities Necessarily More Productive?

by Ron Martin

Economists and Cities

Over the past three to four decades, economists’ interest in cities has undergone an unprecedented expansion. The renaissance of urban economics (hence the moniker ‘new urban economics’) and the rise of the ‘so-called ‘new economic geography’ (inspired especially by Paul Krugman), have together directed considerable theoretical and empirical attention to cities, how they function as economies and their importance as sources of economic growth and prosperity. This heightened focus on cities no doubt reflects the fact that, globally, the majority of people now live in cities, and that it is in cities that the bulk of economic activity is located, jobs are concentrated, and wealth is produced. And as the urbanist Jane Jacobs emphasised nearly forty years ago, cities are the main nodes in national and global trade networks.[1] Such is now the economic significance and success of cities that the leading urban economist Ed Glaeser has been moved to declare the ‘triumph of the city’, as the ‘invention that makes us richer, smarter, greener, healthier and happier’.[2]

Whilst geographers have long studied cities, not just as economic entities but also as arenas of social and cultural life, it has been the work of these urban and spatial economists that has attracted the attention of policymakers, in large part, one suspects, because of the seeming formal rigour of the models that many of these economists have used to guide and underpin their analyses of cities, and their deployment of those models to derive policy implications. The equilibrist nature of many of these models – whereby the concentration of economic activity into cities is an equilibrium outcome of market-driven economic processes – also probably appeals to policy-makers, since policies can then be justified if they work to assist the operation of those market processes and help to overcome any ‘market failures’.

The Mantra of Agglomeration

If there is one aspect of this body of economists’ work on cities that has become a dominant theme, it is that of agglomeration. Indeed, the notion has assumed almost hegemonic status in the new urban economics, the new economic geography and other related branches of spatial economics, in that the agglomeration of firms and skilled workers in cities is assumed to be the driver of various positive externalities and increasing returns effects (such as knowledge spillovers, local supply chains, specialised intermediaries, and pools of skilled labour) that in turn are claimed to be instrumental in fostering innovation, productivity, creativity, and enterprise.  Further, according to this chain of reasoning, other things being equal, the larger a city is, or the greater is the density of activity and population in a city, the more powerful and pervasive are the associated agglomeration externalities: bigger is better, and denser is better.

Policymakers have eagerly seized on this sort of argument. Almost every policy statement and strategy for boosting local and regional economic performance – whether emanating from central UK Government policymakers, from the local and city policy community or from the policy reports prepared by ‘think tanks’ and consultancies – sooner or later singles out boosting ‘agglomeration’ as a key imperative. It has almost reached the point where the agglomeration argument has become unassailable, a conventional wisdom that is all but taken for granted, and unquestioned.  Voices of dissent are either ignored or dismissed (typically for not being based on the sort of formal models used by the exponents of the agglomeration thesis).  In many respects, agglomeration theory has become protected by ‘confirmation bias’, where empirical support (often selective) is exaggerated and evidence that runs counter to or which fails to confirm the theory is discounted.[3]

City Size and Productivity

One of the issues that illustrates this state of affairs is the claim that city size (and hence greater agglomeration) promotes higher productivity.[4] This is a particularly pertinent claim with respect to economic debates in the UK because of the current policy concern over the stagnation of national productivity, in general, and the low productivity of many of the country’s northern cities, more specifically.

A number of studies of the advanced economies – the UK included – have been conducted to estimate how productivity increases with city size, typically involving cross-section models that regress the former on the latter (with or without controlling variables). The size of the effect of city size on city productivity from these studies is, however, modest to say the least. Typically, a doubling of city size is estimated to be associated with an increase in the level of productivity of between 2-5 percent (see, for example, Ahrend et al, 2014; OECD, 2020[5]). To put these sorts of estimates into the UK context, compare, for example, London and Manchester. In 2016, London’s nominal labour productivity (as measured by GVA per employed worker) of £57,000 was 50 percent higher than Manchester’s £38,000. So, if we assume an elasticity of 5 percent, a doubling of Manchester’s population (or employment) – even if that was achievable and desirable – would only raise Manchester’s productivity to around £40,000. This hardly represents a major ‘levelling up’ towards the level of London, the aim of current Government policy. 

In fact, the evidence for the UK suggests that the city size argument should be viewed with caution. Using the estimates of labour productivity for some 85 British cities defined in terms of travel to work areas, the (logged regression) relationship between labour productivity (GVA per employed worker) and city size is small (a doubling of city size is associated with a mere 4 percent higher productivity (Figure1).[6] London, as the largest and most dense city, has the highest labour productivity.  However, the next largest cities – Manchester, Birmingham, Glasgow, Sheffield, Newcastle, Edinburgh, Bristol and Nottingham – all have much lower productivity, in fact below the national average. Some of the highest productivity cities after London – such as Reading, Milton Keynes, Swindon and Oxford – are all much smaller in size or less dense as urban centres.  If we measure agglomeration in terms of the density of employment, as many economists would argue, the association is even smaller ( a doubling of density yields only a 2.5 percent increase in city productivity – Figure 2). Clearly, other factors than size or agglomeration alone are at work in influencing a city’s labour productivity.[7]

What Makes London So Different?

Nevertheless, the agglomeration argument has proved tenacious. Both academic economists and many policymakers have argued that the productivity gap between London and major northern UK cities is not that London is exceptional but that major northern cities are too small.  Advocates of this view have invoked Zipf’s law of city sizes, sometimes known as the rank-size rule. This rule states that the population of a city is inversely proportional to its rank. If the rule held exactly, then the second largest city in a country would have half the population of the biggest city; the third largest city would have one third the population, and so on. Put another way, according to Zifp’s law, if we plot the ranks of a country’s cities against their sizes on a graph, using logarithmic scales, then the line relating rank to population is downward sloping, with a slope of -1. Appealing to this law, Overman and Rice (2008), for example, argue that while medium sized cities in England are, roughly speaking, about the size that Zipf’s law would predict given the size of London, the largest city, the major second-tier cities in the north of the country all lie below the Zipf line and hence are smaller than would be predicted.[8] This is assumed to mean that they lack the agglomeration effects that London enjoys.

The empirical evidence for Zipf’s Law is, however, highly varied internationally (see Brakman, Garretsen and van Marrewijk, 2019).[9] Further, there is no generally accepted theoretical economic explanation of Zipf’s law, nor does the ‘law’ tell us how far a city can fall below the rank-size rule line before it is deemed to be ‘too small’, or how this will affect its economic performance. Perhaps more seriously, it is indeed the case that Zipf’s law does not in fact hold for a national urban political economic system of the sort that characterises the UK.

As Paul Krugman (1996) argues, while the Zipf relationship holds fairly closely for the cities of the United States, and has done so over a long period of time, indicating a pattern of equal proportionate growth across the urban system, this is not necessarily the case elsewhere:

Zipf’s law is not quite as neat in other countries as it is in the United States, but it still seems to hold in most places, if you make one modification: many countries, for example, France and the United Kingdom, have a single ‘primate city’ that is much larger than a line drawn through the distribution of other cities would lead you to expect. These primate cities are typically political capitals: it is easy to imagine that they are essentially different creatures from the rest of the urban system. (Krugman, p. 41, emphases added).[10]

London is indeed a ‘different creature’ from the rest of the UK’s urban system.  Not only is it the national capital, but a major global centre, and its development is likely to reflect the benefits of that role, and be less linked to (even significantly decoupled from) the rest of its national urban system.[11] These observations suggest that in such cases, it makes little real economic sense to argue that second tier cities below the primate capital city are ‘too small’ relative to what the rank-size rule would predict, since the size of the capital itself has to do with national political and administrative roles and factors in addition to the purely economic.

As the nation’s capital, London has long benefited from being the political centre (one the most centralised of the advanced economies), containing the nation’s main financial institutions an markets (that historically were much more regionally distributed), the main organs of Government policy-making (the UK is one of the most centralised on the OECD countries), a large number of headquarters of major corporations, the largest concentration of top universities, and a high degree of policy autonomy relative to other UK cities. This has meant that it attracts much of the talent and skilled of the country’s workforce.[12] In recent years, it has also benefited from a disproportionate share of major infrastructural investment. Under these circumstances, it is hardly surprising that it has a high productivity. Yet the high productivity of several much smaller cities suggests that size and agglomeration are not everything.

Beyond the Agglomeration Credo

This is not to say that agglomeration is irrelevant – clearly all cities of whatever size benefit to a greater or lesser extent from the local concentration and proximity of workers, firms and infrastructures. But aiming to improve the productivity of Britain’s northern cities by substantially expanding their size or density may be neither necessary nor sufficient as a strategy. The relevant question to pose is why are smaller, and less dense, cities more productive, and what policy lessons might be learned from their experience?   What a city does is obviously important, not just in sectoral terms, but also in terms of functions and tasks (and hence roles in domestic and international supply networks and chains). So, relatedly, is its export base. Further, and crucially, its innovative capacity; its ability to produce and retain, highly educated and skilled workers; its levels of entrepreneurship; the quality and efficiency of its infrastructures; and the extent of its decentralised powers of economic governance; these are all of key importance.  Cities outside London have for decades scored poorly on such factors. But these drivers of productivity cannot simply or solely be reduced to ‘insufficient agglomeration’. The ‘Northern Powerhouse’ cities traditionally once formed polycentric regional systems of innovative and competitive, export-orientated manufacturing. They have lost that role through sustained deindustrialisation, in part because of globalisation and technological lock-in, in part because of spatial biases in national economic policy and management that favoured London and ignored manufacturing. Finding a new role for Britain’s northern cities will be key to their economic renaissance.  Cities do not have to be big or more dense to succeed, but adaptive, dynamic and with appropriate powers of self-determination.[13] Theorising and understanding economic adaptability might yield greater policy dividends than yet more theorising and promotion of agglomeration.

[1] Jane Jacobs (1985) Cities and the Wealth of Nations: Principles of Economic Life, New York: Vintage Books.

[2] Ed Glaeser (2011) The Triumph of the City: How or Greatest Invention Makes us Richer, Smarter, Greener, Healthier and Happier, London: Macmillan.

[3] The negative effects of increasing size and density – such the diseconomies of increased congestion, pollution, travel time, and land and housing costs, are infrequently given the due empirical attention they deserve. It is also significant that in surveys of quality of life satisfaction, large cities often score less well than smaller cities and towns.  London reports some of the lowest average life satisfaction in the UK (see, for example).

[4] See, for example, Glaeser, E. (2010) Agglomeration Economics, Chicago: University of Chicago Press; Glaeser, E. (2011) The Wealth of Cities: Agglomeration Economies and Spatial Equilibrium in the United States, NBER Working Paper 14806; Combes, P., Duranton, G., Gobillon, L., Puga, D., & Roux, S. (2012). The Productivity Advantages of Large Cities: Distinguishing From Firm Selection, Econometrica, 80, pp. 2543-2594. Ahrend et al (2017)  The Role of Urban Agglomerations for Economic and Productivity Growth, International Productivity Monitor,  32, pp. 161-179.

[5] Ahrend, R., et al. (2014) What Makes Cities More Productive? Evidence on the Role of Urban Governance from Five OECD Countries, OECD Regional Development Working Papers, No. 2014/05, OECD Publishing, Paris. OECD (2020) The Spatial Dimension of Productivity: Connecting the Dots across Industries, Firms and Places,  OECD Regional Development Working Papers 2020/1, Paris: OECD.

[6] For a comprehensive study of the productivity performance of British cities over the past half century, see Martin, R., Gardiner, B., Evenhuis, E., Sunley,P. and Tyler, P. (2018) The City Dimension of the Productivity Puzzle, Journal of Economic Geography, 18,  pp. 539-570.

[7] Nor does the spatial agglomeration or clustering of individual firms in the same or related industries necessarily increase their productivity, another conventional wisdom in the business and economics literatures (see  Harris, R. Sunley, P., Evenhuis, E., Martin,, R. and Pike, A.(2019)Does Spatial Proximity Raise Firm Productivity? Evidence from British Manufacturing, Cambridge Journal of Regions, Economy and Society, 12, pp. 467-487

[8] Overman, H., and P. Rice. 2008. Resurgent cities and regional economic performance. SERC Policy Paper 1, London School of Economics.

[9] Brakman, S., Garretsen, H. and Marrewijk, C. (2019) An Introduction to Geographical and Urban and Economics: A Spiky World, Cambridge: CUP.

[10] P. Krugman (2006) The Self-organising Economy, Cambridge Mass: MIT Press.

[11] For an interesting analysis of how decoupled London has become from the rest of the UK economy, see Deutsche Bank (2013) London and the UK economy: In for a penny, in for a pound? Special Report, Deutsche Bank Markets Research, London.

[12] As Vince Cable, when Secretary of State for Business in the Coalition Government of 2010, put it: “One of the big problems that we have at the moment… is that London is becoming a kind of giant suction machine, draining the life out of the rest of the country.” (Cable, V. 2013, London draining life out of rest of country). Cable was in fact merely echoing a similar view expressed 75 years earlier by the famous Barlow Commission report on rebalancing Britain’s economy: “The contribution in one area of such a large proportion of the national population as is contained in Greater London, and the attraction to the Metropolis of the best industrial, financial, commercial and general ability, represents a serious drain on the rest of the country” (Barlow Commission, 1940, Royal Commission on the Distribution of the Industrial Population. London: H.M. Stationery Office.

[13] Martin, R. L. and Gardiner, B. (2017) Reviving the ‘Northern Powerhouse’ and Spatially Rebalancing the British Economy: The Scale of the Challenge, in Berry, C. and Giovannini, A. (Eds) Developing England’s North: The Political Economy of the Northern Powerhouse, London: Palgrave Macmillan, pp. 23-58.

Ron Martin is Professor of Economic Geography at the University of Cambridge.

Other posts from the blogged conference:

The Institutionalization of Regional Science  In the Shadow of Economics by Anthony Rebours

Cities and Space: Towards a History of ‘Urban Economics’, by Beatrice Cherrier & Anthony Rebours

Economists in the City: Reconsidering the History of Urban Policy Expertise: An Introduction, by Mike Kenny & Cléo Chassonnery-Zaïgouche

The Institutionalization of Regional Science

In the Shadow of Economics

by Anthony Rebours

The history of regional science offers an interesting case study, as well as a one of the few examples, of the institutionalization of an entirely new scientific field in the years after 1945.  Its foundation by Walter Isard and a group of social scientists in the 1950s represents the most institutionalized attempt to stimulate the relationship  between economics and geography. The original project of Isard, who was trained as an economist at Harvard, was to promote the study of location and regional problems.

And at the outset, regional science was, in various ways, a success. It attracted many scholars from different disciplines, mostly economics, geography and urban/regional planning, and it quickly became institutionalized formally through the foundation of the Regional Science Association (RSA) in 1954 and establishment of a Regional Science Department at the University of Pennsylvania in 1958. At the same time, the creation of the Papers and Proceedings of The Regional Science Association in 1955 and of the Journal of Regional Science in 1958, offered new publication venues for scholars interested in location analysis, in particular quantitative geographers who found it difficult to publish in traditional geography journals. Within economics, regional science influenced analytical works in urban economics, as, for instance, William Alonso’s thesis, widely recognized as one of the foundational works of urban economics, was written at Penn under the supervision of Isard in 1960.

However, the prevailing processes of knowledge production and evaluation which shaped the emergence of this new field were deeply influenced by economics. Geographers became dissatisfied with Isard’s vision of the hierarchical division between geographers and economists, and the primacy given to economic theorizing and modelling as the core of the new regional science. Thus, the social organization of the field of regional science and its interactions with other disciplines mirrored the particularity of economics, a hierarchical discipline organized around a strong theoretical core and an insularity from the rest of social sciences. In this short article, I discuss the findings of an analysis I have conducted of the contents of the main journal for the field – Journal of Regional Science –and associated archival materials, in order to shed light on the ways in which this field was institutionalized.

The emergence of regional science as a field of study

Regional science emerged in a particularly favourable context. In the US, the impetus for studies about regional development which began during the 1930s, supported by the success of the Tennessee Valley Authority program, persisted after the war. The Second World War and the ensuing Cold War provided new opportunities for the development of scientific research with an unprecedented increase in funding, student enrolment and collaboration between academics and external bodies, such as military institutions. This period confirmed economists’ aspirations to be treated as scientists, and resulted in the increasing prevalence of statistical methods and mathematical modelling, and the accompanying theory of rational and maximizing agents.

In 1942, Walter Isard obtained his doctoral degree under the supervision of Alvin Hansen, who was attached to the National Resources Planning Board, and Abbott Usher, who taught him about the  German tradition of location analysis, at the Economics Department of Harvard. There, and during a graduate fellowship at Chicago, he encountered other leading economists, such as Edward Chamberlin, Joseph Schumpeter, Jacob Viner, Frank Knight and Oscar Lange. At the end of the war, Isard produced a series of research articles in which he offered conventional economic analysis of production costs about the regional implications of the development of the airline industry, the atomic energy industry, and the future location of the iron and steel industry. At the time, these industries were considered as particularly important for national security and economic development.

In the late 1940s, Isard became increasingly concerned about the lack of interest among economists in the location of economic activities. His perception of the subject was not really different to his colleagues, but he wanted to improve the theory they used, which, following the British tradition of the late 19^th century, suffered from a lack of spatial dimension. He did not seek to challenge the general equilibrium economic theory that was becoming dominant, but sought instead to integrate a spatial aspect within it.  

In the late 1940s, he started to be more active in the promotion of location analysis but failed to convince the American Economic Association (AEA) to organize sessions on regional topics at the annual conventions. In 1949 Isard was recruited to Harvard by Wassily Leontief to develop an input-output approach to regional development. During the war, input-output analysis received much attention because it enabled the American Air Force to identify the best targets for bombing. As a consequence, Leontief had received large research funds to develop his input-output framework. Drawing on Leontief’s financial resources, Isard was able to organize a series of multi-disciplinary sessions on regional research at meetings of various social science associations between 1950 and 1954. An informal newsletter was also created to disseminate the discussions and papers presented at the meetings.  

In 1949, at Harvard, Leontief also persuaded the faculty to create a new course on location theory at the Economics Department in which Isard would teach. During the course, he promoted the same kind of research he was doing at the Leontief project and that he would continue to conduct and support after having established formerly regional science. In a context where there was a large influx of war veterans returning to Harvard to complete their graduate studies, Isard managed to gather around him a core of young scholars to contribute to this work.  

The institutionalization of regional science

In 1954, after four years of informal meetings and discussions, the Regional Science Association was officially created during a meeting held conjointly with the American Economic Association and the American Social Sciences Association this time. Sixty participants from different disciplines—economics, geography and planning being the largest — as well as organisations like the RAND Corporation and Resources For the Future, were present. The papers presented were published in the first issue of The Papers and Proceedings of the Regional Science Association which was established at the same time. In 1956, Isard opened the first PhD program in regional science at the Penn’s Wharton School, and, in 1958, the first Department of Regional Science. The same year, the Journal of Regional Science, the future leading journal of the field, was founded.

These events were key to the institutionalization of the field, and reflected the thinking of Isard and his colleagues about the main focus and boundaries of regional science. This reflected an amalgam of diverse approaches to the study of regional and spatial issues, drawing on different disciplines, in particular economics and geography, with a strong emphasis on the same kind of analytical and statistical methods he learned at Harvard and from his work with Leontief.

In what follows, I look more closely at the constituent parts of the new discipline.

The centrality of economics for regional science is clearly visible in Figure 1, which maps the network of co-citations for articles published in the Journal of Regional Science (JRS) between 1958 and 1967. The co-citation technique allows us to measure the conceptual proximity of different journals cited in different papers of JRS. This technique is complemented by the use of a community detection algorithm in order to identify coherent sub-groups that have stronger links with each other than with the rest of the journals. The most striking feature of this mapping is the distance and the net distinction between economics journals and geography journals. While some leading journals such as the Geographical Review and the Annals of the Association of American Geographers, were among the most cited in the network (respectively the fourth and fifth most cited), geography journals occupied a peripheral position, along with journals of other disciplines like sociology (green). More surprising is the relative prominence of psychology journals (blue) which were more strongly associated with economics journals (purple) and represented the second most cited discipline of the period. However, in the next decade the situation completely changed, and psychology journals received less than 1% of the total citations in 1968–1977 (Table 1). For the whole period, 1958 to 1977, the geography is the second most cited discipline but with only 13,4% of the total citations of the period, far behind economics with 55,2% of the citations.

This first result is consistent with the idea, expressed by Isard in Location and Space-Economy (1956), of a hierarchical division between economists, who provided the analytical foundations of regional science, and the geographers, who provided the empirical facts and testing. Another way to confirm this asymmetrical relationship between economics and geography is to compare the most cited disciplines (Table 1) with the disciplines that cited the most JRS (Table 2). While geography journals were by far the ones cited most in the JRS, with 44,1% of the total citations, they only received 10,7% of the citations within it. At the same time, economics journals, which represented only 12,6% of the total citations to the JRS, were the most cited,  41,5%. Regional science, thus, was more important for geographers than economists, while the reverse was not true as economics was more important for regional scientists than geography. This result is also consistent with the idea that the quantitative turn in geography and the emergence of regional science were closely associated.

These trends persisted in the next period (1968–1977). The size of the network in Figure 2 is representative of the increase of publications of the JRS during the period, with an increase in issues per years after 1969. The separation between the cluster of economics journals and geography journals persisted. Moreover, and despite an increase of the proportion of citations to geography journals, economics became even more important in the network and accentuated the difference of size with geography (Table 1). On the other hand, regional science became even more important for geography as the discipline represented 50% of the citations to JRS in the period, while it also received more citations from economics journals in this period than in the preceding one (Table 2). More generally, the data show that economics and geography were the two most important disciplines for the authors who published in the JRS between 1958 and 1977, a trend that has continued after 1967.

The fact that the JRS was much less quoted by economics journals doesn’t mean that it was completely ignored by economists as, in fact, the JRS was among the most cited economic journals in 1970. However, it shows that regional science was more discussed by scholars publishing in geography journals than economics. As already indicated, this situation is certainly related to the dynamics of both disciplines at the time. While, the identity of economics was legitimated and reinforced by its success during the war, in geography, there was an increasing dissatisfaction with the regional geography approach that dominated the field in the1950s. The Cold War context facilitated the promotion of a new generation of quantitative geographers looking for more scientific methods. Most of them were early members of the Regional Science Association, and as Brian Berry, were interested in the potential of regional science to transform geography. On the other hand, the stronger identity of economists meant that when they associated with other scholars, they were inclined to retain their own frameworks and methods, as Walter Isard did for regional science. However, by the mid-1970s, regional science experienced a progressive decline when geographers started to distance themselves from the analytical methods that were promoted by Isard. But even after the Regional Science Department at Penn closed its doors in 1993, regional science journals remained a going concern and continued to promote studies of spatial issues notably from urban economics and, after 1991, New Economic Geography.

Anthony Rebours is currently a graduate student at University Paris 8 and a young fellow of the Center for the History of Political Economy (CHOPE) at Duke University. His dissertation deals with the relationships between economics and neighbouring disciplines such as geography and regional science. It combines archival work and sociological methods for quantitative history.

Other posts from the blogged conference:

Cities and Space: Towards a History of ‘Urban Economics’, by Beatrice Cherrier & Anthony Rebours

Economists in the City: Reconsidering the History of Urban Policy Expertise: An Introduction, by Mike Kenny & Cléo Chassonnery-Zaïgouche