World City Network: Data Matrix Construction and Analysis
Funded by HEFCE (dual support system) (1999)
Researchers: P.J. Taylor and D.R.F. Walker
Associated researchers: M. Hoyler and I. Taylor
Note: this is an exploratory project whose initial purpose is to test and evaluate a methodology and new data with a view to developing a more comprehensive project.
While providing the necessary substructure and groundwork for an exciting research agenda, Friedmann's and Sassen's early contributions complement each other in clearly illustrating the twin limitations of that agenda. On the one hand Friedmann attempts a comprehensive global treatment of world cities but with very little empirical evidence to back up his arguments (Taylor, 1997). In contrast, Sassen marshals lots of evidence for her interpretation of the global city triad but has little to say about all the other world cities and how they fit into the picture (Taylor, 1994). Hence the legacy of their foundation is to be either globally comprehensive and empirically challenged or empirically comprehensive and globally challenged. This dilemma is currently reflected in world city research by the plethora of studies of single city or comparisons of small numbers of cities (e.g. Todd (1995) on Toronto and Abu-Lughod (1995) on New York, Los Angeles and Chicago) in contrast to the few attempts to encompass world-wide patterns which invariably suffer from inadequate data (e.g. Michelson and Wheeler's (1994) use of Federal Express data, Rimmer's (1998) use of international airline data which describe general flows, including, for instance tourism, and omits important domestic links such as New York-Los Angeles). It is the purpose of this project to overcome this twin limitation by exploring the possibililities of producing an empirically rich and globally comprehensive study of world cities.
To fulfill this purpose requires two further objectives:
(i) to create a set of comprehensive data on world cities; and
(ii) to develop a methodology to analyse what will be a large data set in a theoretically-relevant manner.
A major reason why there has been a dearth of global-scale cross-city studies is because there are no easily accessible data available for analysis. Most published data are created by states for states one result of which is a very state-centric social science (Taylor, 1997). Even world city research has succumbed to this debilitating bias (Taylor, 1999). For sure there are census data and related materials collected by state agencies to describe cities: some limited cross-city comparisons are possible once allowance is made for differences in measurement. But there is no comprehensive collection of published data on world cities: to do global research on cities requires the creation of global-scale data.
In Project 2 on London, we collected comprehensive information on the offices of 74 advanced producer service firms in 263 cities. These offices are the outcomes of location decision making by firms operating under conditions of globalization. Their cross-city patterns thus represent the basic 'skeleton', as it were, of globalization. However because this information is largely obtained firm by firm there is no standardised composition of the data (Beaverstock et al., 2000). The kind of information we have on each firm's offices varies from simple presence in a city through to number of practitioners employed in each city. Turning this into a data set for use in our analysis involved three stages, first selecting cities, second selecting firms and third allocating values relating city to firm.
(i) Cities. The creation of a roster of world cities was a product of the previous project (Beaverstock, Smith and Taylor, 1999). The basic method used was to consider four service sectors (accountancy, advertising, banking/finance and law) separately and identify the leading cities in each sector. Cities were scored 3,2,1 depending on their importance in a given sector and combining these scores enabled us to produce an ordering of cities up to a maximum aggregate score of 12. From this list we derived our 'inventory of world cities' using the threshold score of four to qualify: out of 142 cities which appeared in the different sector lists, 55 were deemed to have world city status. These are cities studied in this project.
(ii) Firms. For this project we focus upon the major global firms in our data. The threshold we will use is that a firm must have offices in at least 15 separate cities. Setting up an office to provide advanced producer services is a very expensive undertaking for a firm since it is the nature of service provision that it takes time to build up clienteles. Furthermore, operating in this many cities inevitably means working in different legal frameworks and cultural settings. In short, to have 15 or more offices shows a firm to be committed to developing a significant cross-city provision for their particular producer service, we will call them global service firms. There are 46 firms in this category in our data and they are the firms studied in this project.
(iii) Variability. The variations in information we have on each office is dealt with by converting all the data into a simple ordinal scale (0, 1, 2, 3) as described elsewhere (Taylor et al. 2000) where the higher the score the larger the service provision by a firm in a city for a given sector. For instance, New York and London have more scores of three because most firms have decided they need to locate one of their largest offices in these two very important cities.
The end result of these operations is to create a data matrix of 46 global service firms across 55 world cities in which each cell records high (3), medium (2), low (or simple presence) (1), or absence (0) for a given firm in a given city. This will constitute the input to our analyses.
Faced with a matrix which contains 2,530 (55 x 46) pieces of information we need to reduce the detail into a relatively small number of common patterns for interpretation. Such parsimony is the basic purpose of the factor analytic family of statistical techniques of which the most straightforward (i. e. with least axiomatic baggage attached) is principal components analysis. This is the technique we will apply to our cities/firms matrix.
In principal components analysis, a data matrix consisting of x variables is treated as an x-dimensional space to which each variable contributes an axis. Each axis is one unit in length which represents the spread of values (variance) of a variable so that the total variance is x, the number of variables in the matrix. By analysing the co-variance (correlation) amongst the variables, an alternative set of axes of different lengths can be produced ranked by size. These are principal components, in which the first (largest) component describes the biggest cluster of co-variance amongst the original variables, the second component the next biggest of cluster of co-variance, and so on down to a very small final xth component. The idea is that most of the variation in the data is revealed in a relatively small number of large components so that many small components can be discarded as unimportant. The result, therefore, is to transform an original x-dimensional variable space into a much smaller y-dimensional component space defined by selection of only the large and important principal components. This is the parsimony, converting a large number of variables x into a relatively small number of relevant components y which, nevertheless, between them account for a large proportion of the original variance. For example, a very successful parsimonious analysis would transform, say, 80 variables into just 6 principal components which account for 75% of the original variation.
This is a standard statistical procedure, the skill is in the interpretation of the principal components. The chief way of interpreting components is to focus upon the location of these new component axes with respect to the original variable axes. These relations are measured as 'loadings' which are the correlations between each component and each variable. By looking at the high correlations, the cluster of variables which a component represents is revealed. In order to facilitate interpretation, the principal components are usually 'rotated' so as to maximise high loadings. The most common method is called varimax rotation which creates well-defined and orthogonal (independent) patterns of variability as new components. It is these rotated principal components which we use here for parsimonious analysis of the cities/firms data matrix. In effect, these rotated components are new 'super-variables' and as such they can be defined in terms of the original objects over which the input variables were measured. These 'component scores' are like the original variable measures and tell us about the differences between objects for a given component.
There is one crucial decision which has to be made in any principal components analysis: what is y, the number of relevant components to be selected from the x number of components which are actually created? There is no simple statistical answer to this question, ultimately it comes down to the researcher's judgement. In the analyses below, we use the maximum interpretable component method. This involves starting with a small number of components and then adding extra components one at a time and rotating them to see whether the last component is interpretable. To determine the latter we have arbitrarily set a threshold of a component having at least one loading above 0.6. Hence, when we come to a rotated solution where there is a component without a 0.6-or-above loading, we reject that analysis and return to the penultimate analysis as that containing the maximum interpretable components.
Finally there is the question of variables and objects. Since a matrix has two sides there are two ways of considering its variability, by columns (variable) or by rows (objects). Most principal component analyses use correlations between variables (called-R-mode analysis) as described above. In this project the variables are the 46 firms' distributions of offices across cities for which we carry out an R-mode analysis. However, it is just as statistically feasible to analyse from the perspective of the objects (called Q-mode analysis), which involves creating components out of the correlations between objects. In this project the objects are the 55 cities' distributions of offices across firms and for which we carry out a Q-mode analysis. In simplest terms, parsimony is achieved by the R-mode analysis seeking out patterns of similarity between firms, and the Q-mode analysis seeking out patterns of similarity between cities.
The main analysis above produces a basic typological insight into the data; if this is successful (i.e. plausible results are produced) then we will take the analysis further by experimenting with other techniques to reveal different aspects of the information contained in the data. This will include network analyses and multidimensional scaling to create networks and representations respectively.
Although this project is primarily exploratory in nature, if the quality of the results is sufficient the results will be written up and submitted to the relevant journals in the field. All papers prepared for publication will be posted as 'GaWC Research Bulletins'.
Abu-Lughod, J L (1995) Comparing Chicago, New York and Los Angeles: testing some world city hypotheses, in P L Knox and P J Taylor (eds) World Cities in a World-System. Cambridge, UK: Cambridge University Press
Beaverstock, Lorimer, H, J V, Smith, R G, Taylor, P J and Walker, D R F (2000) Globalization and world cities: some measurement methodologies, Applied Geography
Beaverstock, J V, Smith, R G and Taylor, P J (1999a) A roster of world cities, Cities 16, 445-58
Beaverstock, J V, Smith, R G and Taylor, P J (1999b) The long arm of the law: London's law firms in a globalising world-economy, Environment and Planning A 31, 1857-1876
Beaverstock, J V, Smith, R G and Taylor, P J (1999c) The global capacity of a world city: a relational study of London, GaWC Research Bulletin 7
Beaverstock, J V, Smith, R G and Taylor, P J (2000a) World city network: a new meta-geography?, Annals, Association of American Geographers (Special Millennium issue)
Beaverstock, J V, Smith, R G and Taylor, P J (2000b) Geographies of globalization: US law firms in world cities, Urban Geography
Friedmann, J (1986) The world city hypothesis, Development and Change 17, 69-83
Friedmann, J (1995) Where we stand: a decade of world city research, in P L Knox and P J Taylor (eds) World Cities in a World-System. Cambridge, UK: Cambridge University Press
Michelson, R L and Wheeler, J O (1994) The flow of information in a global economy: the role of the American urban system in 1990, Annals, Association of American Geographers 84, 87-107
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Sassen, S (1994) Cities in a World Economy. Thousand Oaks, CA: Pine Forge
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Taylor, P J (1997a) Hierarchical tendencies amongst world cities: a global research proposal, Cities 14, 323-332
Taylor, P J (1997b) Embedded statism and the social sciences: opening up to new spaces, Environment and Planning A 28, 1917-28
Taylor (1999) So-called "world cities": the evidential structure within a literature, Environment and Planning A31, 1901-1904
Taylor, P J (2000) World cities and territorial states under conditions of contemporary globalization, Political Geography 19
Taylor, P J, Beaverstock, J V and Walker, D R F (2000) Introducing GaWC: researching world city network formation, in S Sassen (ed) Cities and their Cross-Border Networks. Oxford: Blackwell Publishers
Todd, G. (1995) 'Going global' in the semi-periphery: world cities as political projects. The case of Toronto, in P L Knox and P J Taylor (eds) World Cities in a World-System. Cambridge, UK: Cambridge University Press