com Contributions to Economics www.com Kesra Nermend Vector Calculus in Regional Development Analysis Comparative Regional Analysis Using the Example of Poland Physica‐Verlag A Springer Company www. Kesra Nermend Institute of Informatics in Management ul. Mickiewicza 64 71‐101 Szczecin Poland kesra@uoo.pl Book first published in Polish under the title Wydawnictwo Naukowe Uniwersytetu Szczecińskiego, Szczecin 2008 ‘‘Rachunek wektorowy w analizie rozwoju regionalnego’’ ISBN 978-3-7908-2178-9 e-ISBN 978-3-7908-2179-6 DOI: 10.1007/978-3-7908-2179-6 Contributions to Economics ISSN 1431-1933 Library of Congress Control Number: 2009921251 # Physica-Verlag Berlin Heidelberg 2009 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks.
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Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper Physica‐Verlag Berlin Heidelberg (www.com Contents List of Variables and Notation. 1 1 Regional Development Economic Perspective. Notion and Factors Determining Regional Development. Data Monitoring for Regional Development Assesment.
Regional Development Indicators. 24 2 Methodical Dilemma Over Regional Development Analysis. Organization of Analytical Processes in Regional Development Investigation. Review of Methods Used for Regional Development Analysis.
Reasons Behind Using Vector Calculus for Regional Development Analysis. 61 3 Methodology of Vector Calculus in Regional Development Analysis. Procedure for Applying Vector Calculus in Regional Development Analysis. Taxonomic Vector Measure of Regional Development.
Interpretation of Data in Space. Vector Component Along Another Vector. Comparison of Vectors in Unitary Space. Visualization of Local Development Measures in 3D Space.
90 4 Taxonomic Synthetic Vector Measure in the Assessment of Regional Development: Results of Empirical Research. Selection of Diagnostic Variables. Construction of the Standard Object .com vi Contents 4. Investigation of Spatial Relationships Between Groups of Variables.
119 5 Computer-Aided Regional Development Analysis. Computer System for Regional Development Analysis as a Decision Support System. Concept of Decision Support System in Regional Development Analysis. Data-Base Management System (DBMS).
Model-Base Management System (MBMS). Dialog Generation and Management System (DGMS). Functioning of Computer System for Regional Development Analysis. 159 List of Figures and Tables .com List of Variables and Notation X Matrix of objects describing variables xik Value of kth variable of ith object (first index – object number, second index – variable number) w Number of objects n Number of variables zik Standardized value of kth variable of ith object sk Standard deviation of kth variable xk Mean value of kth variable vk Variability level measure of kth variable Si Standard deviation of ith object’s variables I Stimulants set K Destimulant set L Nominants set Pi Point representing ith object Po Point representing the standard dij Similarity measure between ith and jth objects dðPi ; Pj Þ Similarity measure between ith and jth points mi Development measure of ith object m Mean measure of development of all objects sm Standard deviation of synthetic measure wgk Weight of kth variable rk Coefficient of object’s scale change along kth variable Dk Coefficient of object’s translation along kth variable ~A Designation of vector gij Metric tensor grij Border between classes odli jk Distance of ith object from the border between class jth and class kth odl wzgljk Percentage distance of ith object from the border between class jth i and class kth pas Coefficient controlling width of border belt szer klas Mean width of class pp i j Percentage reliability of ith object membership of jth class vii www.com viii List of Variables and Notation rozA~B~ ~ and B Similarity between two objects represented by two vectors A ~ calculated as length of their vectors difference ~ A ~ ~ jAj Unit vector along vector A ~ ~ c A~ B~ Projection of unit vector jAAj B ~ onto unit vector jBj ~ ~ jBj jAj ~ regk Value at point Pk of regular grid nregi Value at point Pi of irregular grid l klas Number of classes www.com Introduction Methods used for regional development analysis are employed mainly to make forecasts and comparisons.
Forecasting models of various types (e. econometric models) are usually used for forecasting. Recently, vector-autoregressive models (VAR) have become popular. These models were proposed by Sims in 1980.
On the contrary, taxonomic methods (that are in the center of attention as far as the present publication is concerned) are most often employed to make comparisons. Linear ordering methods, including standard methods, are the most popular among taxo- nomic methods. They are based on different distance and similarity measures, which leads to the fact that they do not always provide reliable information. When, for example, one construes the standard for a base year and then compares it with data for other years, it may turn out that the measure determined will have worse values than the standard for a real object (region, micro region) although this object is better from the standard.
Hence, one must look for new methods employed in regional development analysis or improve hitherto existing ones in such a way so that information obtained reflects the reality to a larger extent. The main aim of the present publication is to work out methodological basis for regional development analysis based on vector calculus together with assumptions about computer system supporting the implementation of the method suggested. In the context of the present discussion, the following three statements have been adopted as research hypotheses: 1. Methods hitherto used for regional development analysis do not meet require- ments of objective assessment of regions and micro regions both for the purpose of science and economic practice.
Author’s system of regional development assessment (made with the use of vector calculus) presented in the publication describes in detail the quality of socio-economic and environmental processes in the area examined and hence it could be useful in making economic and investment decisions. Adaptation of regular and irregular grids from the systems of spatial information for the purpose of spatial correlation analysis may make decision makers aware of the influence that particular groups of factors have on socio-economic development.com 2 Introduction In order to verify the first mentioned research hypothesis, the analysis of classical methods used for examining regional development has been carried out. This analysis will allow to indicate premises that these methods should meet, which will make it possible to achieve the aim of the present publication. In order to verify the second mentioned hypothesis, empirical research has been conducted with the use of both classical synthetic measures as well as taxonomic vector measure of regional development proposed by the author.
The empirical research relates to Polish counties as a case-study. The presented in the work measure can be used in wide variety of regional studies. At the same time, the application of standards construed not on the basis of maximal and minimal values of variables but on the basis of quartiles is a novelty here. Furthermore, in order to simplify the procedure for putting the approach suggested into practice, assumptions about computer system were made and the prototype of this system was developed.
The system discussed has been equipped with a module enabling to examine spatial relations among groups of variables, which was possible thanks to author’s adaptation of regular and irregular grids from systems of spatial information for the purpose of spatial correlation analysis. The layout of the present publication was determined by the research purpose and hypotheses. The publication consists of five chapters preceded by introduction and succeeded by conclusion. In the first chapter, the notion of ‘‘regional development’’ was analyzed together with factors determining this development.
Moreover, the importance of regional data monitoring in the procedure for regional development examination was high- lighted. Finally, indicators taken into account in the research were discussed. In the second chapter, issues relating to methodology of regional development analysis were raised paying special attention to classical methods. Furthermore, reasons behind looking for new methods or improving the existing ones (in order to make the research apparatus more precise) were presented.
While discussing the issues raised in the first and second chapters, the author employed elementary analysis method with the use of which the subject matter of research was divided into several parts and discussed individually. Causal analysis was used for determining the relationship between phenomena under examination, and deduction method – for discussing the questions important as far as the fulfillment of the main aim of the present publication was concerned. Discussion made in these chapters have deductive-logical and review character. The main method of justification is logical argumentation.
In the third chapter, methodical basis of regional development analysis (with the use of vector calculus methods) was presented. Particular stages of research proce- dure based on the method suggested were described. Moreover, the author also indicated features of the method thanks to which measures (obtained with the use of this method) were more accurate than classical measures. The possibility of pre- senting the results of analysis in 3D space was discussed as well.
The fourth chapter includes the description and results of research conducted by means of the method suggested. The research was carried out for NUTS IV level, i. for 314 Polish counties and at the same time, 42 diagnostic variables were taken www.com Introduction 3 into account. The research results were collated with analogical results received with the use of classical methods in order to present advantages of the method suggested.
In this sense, the fourth chapter formed a basis for verifying the research hypothesis formulated. Finally, in the fifth chapter, the author had presented assumptions about com- puter system supporting the regional development analysis that was supposed to provide computer environment for the implementation of the method suggested. This method is based on a complex mathematical apparatus and hence, can be difficult for persons who deal with shaping regional policy. In order to make it available to a wider circle of not only theoreticians, researchers and professionals dealing with regional analyses, but also practitioners, decision makers and politi- cians, one must create a computer system equipped with a friendly interface that could be used by persons who are not IT specialists.
Additional advantage of the system is the possibility of scaling it, i. using objects at different levels of spatial hierarchy, namely in communes, counties and voivodships, etc. for the analysis. Apart of the concept of the system discussed, its functioning had also been presented quoting the example of particular analyses.
In the last part, the author has presented the most important general conclusions from theoretical discussion and the research conducted. Furthermore, practical possibilities of using regional development analysis method devised as well as plausible directions of work on improving computer system created particularly for the purpose of this method have been presented.com Chapter 1 Regional Development: Economic Perspective 1.1 Notion and Factors Determining Regional Development Region is a notion used in many spheres of life. Its meaning is generally similar in economy, science, politics and every-day life. Analyzing the sense of ‘‘region’’, one should notice that this notion has different connotations in each of the aforemen- tioned spheres.
The word region derives from Latin regio, regionis that has two meanings in a direct translation. The first sense refers to a movement in a certain direction, whereas the other one refers to the direction outlining the space (in other words, surroundings, land, district).