Mathematical Models in Regional Economics - Peter Nijkamp, Jacques Poot

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Mathematical Models in Regional Economics - Peter Nijkamp, Jacques Poot MATHEMATICAL MODELS IN ECONOMICS –- Vol. II – Mathematical Models in Regional Economics - Peter Nijkamp, Jacques Poot MATHEMATICAL MODELS IN REGIONAL ECONOMICS Peter Nijkamp Free University Amsterdam, The Netherlands Jacques Poot University of Waikato, New Zealand Keywords: structural simultaneous equations model, input–output model, computable general equilibrium model, spatial econometrics, spatial interaction, new economic geography, endogenous growth, spatial decision support system, neural network Contents 1. The modeling revolution in economics 2. The evolution of models in regional economic research 3. From theory to empirics 4. Trans-disciplinary advances in regional modeling 5. The future of regional-economic models Glossary Bibliography Biographical Sketches Summary This chapter reviews the evolution of mathematical and statistical models that have been used for the development of theory and policy analysis in regional economics. The benefits of mathematical approaches are outlined. Theories and estimation techniques have developed in tandem with developments in the availability of geo-referenced data, new technologies and particularly computing power. Regional modeling was initially strongly influenced by macro-econometric and input-output models developed for national economies, but evolved into models that integrated these approaches into multi-regional settings that are often of a highly nonlinear nature and explicitly account for various forms of spatial interaction. New theoretical developments such as the new economic geographyUNESCO and endogenous growth – theo EOLSSry have had a major impact on recent modeling trends and on the increasing popularity of spatial econometrics. Regional economic modeling has a long tradition of integrating approaches from different disciplines and in this paper we provide several examples of trans-disciplinary advances, notablySAMPLE entropy-interpretations of CHAPTERSspatial interaction, computational neural networks and complexity theory. We conclude with outlining a range of areas of regional modeling in which promising developments are likely. 1. The Modeling Revolution in Economics We cannot imagine modern economics without the use of mathematical and statistical tools. The past fifty years of economic science can indeed be characterized by the development of a plethora of quantitative methods for describing, analyzing and ©Encyclopedia of Life Support Systems (EOLSS) MATHEMATICAL MODELS IN ECONOMICS –- Vol. II – Mathematical Models in Regional Economics - Peter Nijkamp, Jacques Poot predicting economic phenomena. There are very good reasons why such quantitative approaches have become almost universally adopted in economic research throughout the world: models offer a concise and compact – and hence efficient – representation of a multi-faceted economic reality; the use of models presupposes a clear and unambiguous definition of variables and symbols, so that a transparent discussion of economic phenomena can take place; models reduce a complex reality to a more simple but still insightful image that should encapsulate the most prominent economic forces and drivers, as well as their consequences; a formal quantitative approach is able to derive testable hypotheses, so that a consistent validation of economic theory can be ensured; a quantitative approach is not only able to test empirical statements about the economy in a statistically justified way, but is also able to infer statements on the same phenomenon in a different research domain (referred to as transferability); and, finally, models are an important communication tool, not only among economists, but also between scientists from other disciplines. The quantitative revolution in economics has had far reaching impacts on the practice of economic research and has penetrated in almost all research domains of economics: macro-economics, industrial organization, finance, consumer behavior, international trade, labor market analysis, environmental policy, and so forth. This trend has also manifested itself in regional and urban economics, where often similar tools and techniques are deployed. However, the nature of spatial processes is such that new techniques for data analysis and modeling have been warranted, and in recent decades realized with advances in computing and information availability, such as Geographical Information Systems (GIS), spatial interaction modeling, and spatial econometrics. In addition, regional and urban economics has a strong policy orientation and is therefore often at the interface of related disciplines, such as geography, planning, political science, environmental science, etc. The cross-fertilization with these disciplines hasUNESCO also had its own impact on modeling– EOLSS developments in regional and urban economics. A multi- and trans-disciplinary approach has been the genesis of regional science as a unifying framework for all social science phenomena with a spatial dimension. Commencing with Walter Isard’s 1956 book Location and Space-Economy, regional scienceSAMPLE emerged as the common gr oundCHAPTERS for urban and regional policy analysis in the word’s developed economies and in recent years is increasingly spreading to less developed parts of the world. The 2004 special issue of Papers in Regional Science provides an excellent overview of influential developments and challenges for the future. The focus of this EOLSS chapter is specifically on the use of models in regional economics. Models for urban, resource, environmental and transportation issues are addressed in separate chapters of the EOLSS. Against this background, we start in the next section with a brief history and typology of regional models that evolved in regional economic theory since the middle of the ©Encyclopedia of Life Support Systems (EOLSS) MATHEMATICAL MODELS IN ECONOMICS –- Vol. II – Mathematical Models in Regional Economics - Peter Nijkamp, Jacques Poot 20th century. Then we will address some issues of empirical regional modeling with an explicit spatial dimension. Next, we will take a cross-border view on modeling developments in relation to complementary disciplines. We will highlight – by way of interesting examples – a few areas where regional theoretical and empirical modeling has made a particularly important contribution. And finally, we will conclude with some speculative comments on the future of regional modeling. 2. The Evolution of Models in Regional Economic Research Regional-economic models started in the tradition of macro-economic models as developed in particular in the 1950s by Nobel-Prize winner Jan Tinbergen. The main aim was to depict the interwoven spatial-economic mechanisms in quantitative terms so as to arrive at reliable predictions or adequate policy decisions. In the 1960s, mainly two classes of regional-economic models were developed, viz. (i) traditional Keynesian- type models for macro-economic policy (including private and public consumption and expenditures) estimated at a regional scale and (ii) regional input-output models in the spirit of the path-breaking work of W.W. Leontief. The use of matrix algebra greatly condenses mathematical modeling into compact expressions. A very simple regional macro-economic model is of the form Ax+= By c (1) which is a system of N linear equations in which y refers to a vector of N endogenous variables that are determined by the regional economy, c is a N ×1 vector of constants and x refers to a vector of K exogenous variables. The latter are either determined outside the region or instruments of economic policy with values that can be changed by regional or national economic policy makers. The matrices A ()NK× and B ()NN× represent coefficients of behavioral equations and identities. Some of the y variables will have desired values that could be considered goals of economic policy. Hence, the effect of changes in policy instruments on regional economic outcomes can be calculated as Δ=y BAx-1 ΔUNESCO – EOLSS(2) in which Δ refers to a change in one or more elements of a vector. Potential trade-offs between goals can be identified by considering various alternative changes to x . Where specific goals areSAMPLE aimed for, the number of inCHAPTERSstruments would in general have to be at least equal to the number of desired goals. In the case of the regional input-output model, the fundamental principle is that inputs of regional sectors may be outputs of other regional sectors, or imports from outside the region. Sales of regional sectors, which can be represented by a vector q, are either to other regional sectors or are final demand by households or the public sector in the region, gross fixed capital formation, or exports to elsewhere. Final demand can be aggregated into the vector f . Assuming proportionality between a sector’s sales and its ©Encyclopedia of Life Support Systems (EOLSS) MATHEMATICAL MODELS IN ECONOMICS –- Vol. II – Mathematical Models in Regional Economics - Peter Nijkamp, Jacques Poot various input requirements (including imports) yields for each sector a vector of input requirements per unit of output, that can be combined in a matrix A of technical production coefficients. Because total production in the regional economy is in equilibrium the sum of inter-industry sales and total final demand, the following equation describes the regional equilibrium: xAxf=+ (3) This equation can be used to assess how changes in regional final demand and/or exports would affect the production of each sector by solving
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