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Distance-Based Methods: An improvement of Ripley’s K function vs. the K density function


  • José M. Albert

    () (Department of Economics, Universitat Jaume I, Castellón, Spain)

  • Marta R. Casanova

    () (Department of Applied Economics, University of Valencia, Spain)

  • Jorge Mateu

    () (Department of Mathematics, Universitat Jaume I, Castellón, Spain)

  • Vicente Orts

    () (IEI & Department of Economics, Universitat Jaume I, Castellón, Spain)


In this paper, we propose a non-cumulative function for evaluating the spatial concentration of economic activity. This function, which we have called the M marginal function, comes from the tradition of spatial statistics but, at the same time, incorporates some key features from the economic geography approach to measure the tendency of economic activity to cluster. Our technique is a straightforward extension of the ‘modified Ripley’s K function’, converted into a non-cumulative function and more similar in spirit to Duranton and Overman’s K density function. Furthermore, it fulfils all the requirements that have already been recognised by the literature on economic geography as the ones that must be met by any measure of localisation. This M marginal function is enough to provide a global view of the spatial structure of economic activity, to test for localisation and to obtain far more detailed information about cluster structures at fairly short distances. Finally, the two distance-based methods are implemented on a comprehensive set of micro-geographic data from Spanish manufacturing sectors to observe how they behave.

Suggested Citation

  • José M. Albert & Marta R. Casanova & Jorge Mateu & Vicente Orts, 2013. "Distance-Based Methods: An improvement of Ripley’s K function vs. the K density function," Working Papers 2013/07, Economics Department, Universitat Jaume I, Castellón (Spain).
  • Handle: RePEc:jau:wpaper:2013/07

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    References listed on IDEAS

    1. Krugman, Paul, 1980. "Scale Economies, Product Differentiation, and the Pattern of Trade," American Economic Review, American Economic Association, vol. 70(5), pages 950-959, December.
    2. Audretsch, David B. & Feldman, Maryann P., 2004. "Knowledge spillovers and the geography of innovation," Handbook of Regional and Urban Economics,in: J. V. Henderson & J. F. Thisse (ed.), Handbook of Regional and Urban Economics, edition 1, volume 4, chapter 61, pages 2713-2739 Elsevier.
    3. José M. Albert & Marta R. Casanova & Vicente Orts, 2012. "Spatial location patterns of Spanish manufacturing firms," Papers in Regional Science, Wiley Blackwell, vol. 91(1), pages 107-136, March.
    4. Giuseppe Arbia & Giuseppe Espa & Danny Quah, 2008. "A class of spatial econometric methods in the empirical analysis of clusters of firms in the space," Empirical Economics, Springer, vol. 34(1), pages 81-103, February.
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    More about this item


    distance-based method; non-cumulative function; micro-geographic data; Ripley’s K function; K-density function; spatial location patterns;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

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