Scale-dependent stratification: a skyline–shoreline scatter plot

Abstract

Most performance exercises help identify size-dependent and size-independent indicators which separately represent quantity and quality proxies. A good example is the evaluation of a country’s scientific performance relative to its economic standing. Scientific performance is usually evaluated in terms of publications and citations and economic performance is measured in terms of gross domestic product (GDP). In this paper we use exergy, which is a scalar second-order product of publications and citations as a measure of output, with GDP as input. X and GDP are scale-dependent terms. We shall take the ratio X/GDP as the scale-dependent measure of performance relative to economic strength. A scatter plot of X/GDP to GDP serves as a quality–quantity map and from this it is possible to identify what are called the skyline and shoreline boundaries showing the scale-dependent upper and lower bounds of performance. One lesson that emerges is that quality does not necessarily grow with size; there is a noticeable scale-dependent stratification. It is also possible to identify a few economies that stand out noticeably from the rest.