Qual Quant (2013) 47:2473–2494
DOI 10.1007/s11135-012-9665-8
Defining and measuring the development of a country
over time: a proposal of a new index
Daria Mendola · Raffaele Scuderi · Valerio Lacagnina
Published online: 19 January 2012
© Springer Science+Business Media B.V. 2012
Abstract This paper introduces the concept of harmonic growth as an extended accepta-
tion 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 differ-
ences 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.
Keywords Social and economic development · Well-being index ·
Multidimensional growth · Time series · Spline interpolation
D. Mendola
Dipartimento di Scienze Economiche, Aziendali e Finanziarie,
University of Palermo, Viale delle Scienze ed. 13, 90128 Palermo, Italy
e-mail: daria.mendola@unipa.it
R. Scuderi
School of Economics and Management, Free University of Bozen/Bolzano,
Universitätsplatz 1 - Piazza Università 1, 39100 Bozen/Bolzano, Italy
e-mail: raffaele.scuderi@unibz.it
V. Lacagnina (
B
)
Dipartimento di Scienze Statistiche e Matematiche ‘Silvio Vianelli’,
University of Palermo, Viale delle Scienze ed. 13, 90128 Palermo, Italy
e-mail: valerio.lacagnina@unipa.it
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