Defining and measuring the development of a country over time: a proposal of a new index

This paper introduces the concept of harmonic growth as an extended acceptation of the notion of development, and discusses its measurement via the Harmonic Growth Index (HGI). The growth is seen as harmonic when the behaviour of a benchmark time series, which here is a measure of wealth, such as per capita GDP, is followed by a similar pattern in socio-economic series. Unlike most widely used indicators in the literature, which take into account the measurement of development over a single time, HGI measures the degree to which a social indicator’s time series pattern matches with the GDP’s. The index is a function, ranging in [0, 1], of the coefficients of the uniform B-splines fitted to each time series, according to the functional data framework. A case study on Mediterranean welfare countries (Greece, Italy, Portugal, and Spain), in the period 1996–2007, shows critical differences in the selected indicators which can be ascribed to their dissimilar specific development models. HGI can be also considered as a general index to measure the similarity between time patterns, or as an alternative to correlation for (non-necessarily linear) time series. Copyright Springer Science+Business Media B.V. 2013