Asymmetry indices of international position of countries: Geometric approach

Abstract

The article is devoted to the substantiation and testing of a new method for assessing the international position of countries. On the one hand, one of common methods of international comparative research is to construct a convex hull of the states of countries on the plane of certain indicators. Data Envelopment Analysis is the most well-known example of this approach. In particular, this method is used to build a world technology frontier. On the other hand, one of universal methods of initial indicators conversion is to normalise them. The method proposed in the article combines the construction of a convex hull on the plane of initial indicators with their min-max normalisation. The purpose of the study was to measure relative distances of countries to opposite sides of a certain hull of data. The problem is that at extremum points absolute distances to opposite sides of the original hull are equal to zero, and therefore relative distances cannot be determined. The authors solve this problem by constructing two secondary hulls of data, each of which allows determining of the asymmetry index by a certain coordinate. Opposite sides of the secondary hull are the midlines between the levels of opposite extrema and corresponding sides of the primary hull. A value that is reciprocal to the number of countries on the side of the primary hull, on which this extremum is located, is used as a weighting factor of the extremum. According to the proposed method, each country is characterised by a unique pair of asymmetry indices. This distinguishes it from the Data Envelopment Analysis method, according to which all countries on the boundary of efficiency are characterised by a unit distance. The proposed method has been tested on data for the countries of the European Union, Iceland and Switzerland for 2005, 2010, 2015 and 2020. The net international investment position (as a percentage of gross domestic product) and the difference between the stocks of immigrants and emigrants (as a percentage of the country’s population excluding migrants) have been chosen as initial indicators. During the testing, the existence of a positive correlation between certain distances of countries on the plane of indices has been confirmed. It has been found that the global financial crisis of 2008 led to a radical shift in the hull of countries’ states on this plane. Mapping of the international state of mean indices on the plane of initial indicators can be used in econometric models