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

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.