QUANTITATIVE METHODS IN THE SOCIAL SCIENCES: ACHIEVEMENTS AND CHALLENGES

1. QUANTITATIVE METHODS IN THE SOCIAL SCIENCES:ACHIEVEMENTS AND CHALLENGES Alan Wilson University of Leeds

2. 1. Perspectives: setting the agenda • QM in the social sciences – what for? • avoiding the philosophical traps: QM does not imply logical positivism! Does anyone still believe this? • need 1: handling data sets, from small to giant; learning from data sets; traditionally, this is statistics • need 2: handling complexity; modelling complex systems; developing ‘What if’ forecasting/flight simulator capabilities. [Some philosophical traps here again – ‘model’, ‘system’; connect to ‘theory’]

3. breadth = range of skills, concepts and perspectives • depth = making the highest levels of skill available • the agenda: • social science systems • examples • demography • impacts of migration • input-output • doing cluster policies properly? • grounding regional development policies • the UK in Europe; in the global economy

4. work • future of work issues • residence • the future of housing and associated land use • services • land use • public service delivery issues

5. system definitions: entitation, classification, geography and scale – many alternatives; hierarchies • theories • methods • huge field – can only work by example in this introduction

6. 2. What do we need to know? 2.1. The basics • statistics – the assumptions’ issue • algebra – subscripts and superscripts: system representation, matrices and multi-dimensional arrays • It can be argued [1] that a comprehensive framework to build a picture of an urban and regional system can be constructed through the arrays • {Xmgi(m)}, {Ymngi(m)j(n)} and {Zngj(n)} [1] Wilson (2003); and see Wilson (2000), Chapter 7

7. m and n are sectors and g is a good or service produced in sector m and used in sector n. i and j are zones and it is assumed that each sector can have a different zone system – a powerful new idea? [2] • So the X-elements are total products (sometimes known for obvious reasons as the make matrix [3] ), the Z-elements are totals used (the absorption matrix) and the Y-elements are the interaction terms. The m, n and g superscripts can all be lists [4] if more detail is required. [2] If {i(m)} is a set of points, then this almost integrates discrete zone systems with continuous ones. [3] Macgill (1977). [4] e.g. m becomes m1m2m3…..

8. It can be shown that any of the usual models can be represented in this framework – spatial demographic and economic models, spatial interaction models and so on – by appropriate definitions of ‘sectors’. If this system can be specified, and appropriate data associated with it, then this is a starting systems description (and becomes a way of organising a GIS).

9. The main elements of a general model can be represented as

10. The ways of constructing the submodels that form the elements of such a general model are well known. This can be done in as simplified a way as possible – as with the original Lowry model [5] – or maximum detail can be added [6]. [5] Lowry (1964) [6] Wilson (1974), Bertuglia et al (1987)

11. to build the models, basic mathematical and computing skills are required: • matrix algebra • calculus – through to nonlinear dynamics • mathematical programming • algorithms • standard software and its dangers • simulation methods

12. 2.2. Higher levels – applying the basics • account-based models • interaction and location models • transport • underpinnings of transport policy • retail – GMAP-type skills – simulators again for major systems • public services • health • education • police

13. economic and econometric models • dynamical systems • urban and regional development • optimisation; mathematical programming • simulation methods • usually syntheses of earlier elements • but, NB, microsimulation • understanding how any of these models can be constructed from the general framework

14. 2.3. Advanced • linking perspectives • algebra and coordinate geometry – an easy example • economic underpinnings and alternative representations • positive returns to scale • graphical models, cellular automata,…... • interpretations; mutual generosity from different standpoints • stocktake of problems

15. 3. Achievements and challenges Achievements • high levels of skill in statistics, demographic modelling, economic modelling, urban and regional modelling, simulation,……. • much of this is basic social science • much of it, given the nature of the social sciences, capable of application • but typically not applied systematically

16. Challenges • ubiquitous delivery of the highest levels of skill • an ability to understand and to link different perspectives that can be applied to the same problem, e.g.: • entropy-maximising, utility maximisation in imperfect markets • continuous vs. discrete representations of time and space

17. The research agenda • urban development • regional economic development • finding advanced mathematical techniques that will solve outstanding social science problems – e.g. Cauchy’s theorem and solutions to the urban structure problem:

18. Ten challenges • linking disciplinary paradigms • alternative mathematical representations • mathematics and algorithms • representations and scales • configurations • learning • nonlinearities and path dependence • developing theory of planning: what can be planned? • perfect ‘data’: models to fill gaps • achieving best practice: building the general model

19. Applications • in the public arena: all forms of planning – city and regional, economic, health, education • commercial: retail, in the broadest sense

20. References Bertuglia, C. S., Leonardi, G., Ocelli,l S., Rabino, G. A., Tadei, R. and Wilson, A. G. (eds.) (1987) Urban systems: contemporary approaches to modelling, Croom Helm, London. Lowry, I. S. (1964) A model of metropolis, RM-4035 -RC, Rand Corporation, Santa Monica. Macgill, S. M. (1977) Rectangular input-output tables - multiplier analysis and entropy-maximising principles: a new methodology, Regional Science and Urban Economics, 8, 355-70.. Wilson, A. G. (1974) Urban and regional models in geography and planning, John Wiley, Chichester

21. Wilson, A. G. (2000) Complex spatial systems, Prentice Hall, London Wilson, A. G. (2003) A generalised representation for a comprehensive urban and regional model, forthcoming. Wilson, A. G., Coelho, J. D., Macgill, S. M. and Williams, H. C. W. L. (1981) Optimisation in locational and transport analysis, John Wiley, Chichester.