Infant Mortality and Income per Capita of World Countries for 1998–2016: Analysis of Data and Modeling by Increasing Returns

Abstract

Annual cross-country data from the World Bank database during the years 1998 and 2016 demonstrate wide variation in infant mortality rates (IMR) and gross domestic product per capita (GDPpc). The row data, a descriptive analysis of the data and a K-means clustering of the countries into groups depending on the GDPpc and IMR measurements draw attention to the underlying structure of the data. We find that IMR follows a convex descent trend, where there is a range of high infant mortality rates at low GDPpc levels and there is a range of high GDPpc levels with low infant mortality rates. Thus, we assume that GDPpc is subject to increasing returns. This is equivalent to assuming that IMR comes from an unknown underlying convex relationship on the IMR observations at the GDPpc observations. Hence we consider the application of a method that makes least the sum of the squares of the errors to each dataset subject to the constraints from the assumption of non-decreasing returns. Our numerical results show that the estimated IMR values reach a point at which they obtain the lowest value and then increase again while GDPpc is at the highest levels. Thus they suggest that our assumption not only adequately describes reality, but also the ensuing model is able to capture imperceptible features of the underlying process.