- 1 - ECONOMIC GROWTH AND DOUBLE QUADRATIC INEQUALITY Ana Jesús López Menéndez, Mercedes Alvargonzález Rodríguez and Rigoberto Pérez Suárez Departamento de Economía Aplicada. Universidad de Oviedo Avda. del Cristo s/n 33.006 Oviedo. Spain Tel. 985 103757 mailto:malvarg@uniovi.es Abstract In this study we present an analytical approach to the growth-inequality relationship, adopting as a reference the Kuznets’inverted U. With this aim we consider not only the most common measures, but also new indicators based on the information theory: the quadratic and the double quadratic measures. The polynomic functions related to these measures provide more flexible expressions than those obtained from the common measures of inequality. As a consequence these new expressions allow the possibility of the existence of more than one point of return, suggesting a better capability of adaptation to different empirical realities. The work also includes the estimation of the growth-inequality relationship and the contrast of the Kuznets’hypothesis for an international database. Keywords: inequality, growth, Kuznets’hypothesis. 1. Introduction The existence of a relationship between inequality and growth was proposed by S. Kuznets (1955, 1963). From the empirical evidence of time series corresponding to England, Germany and the United States in the XIX and XX centuries, this author postulated his "inverted U" hypothesis, according to which inequality increases in the first levels of growth and then decreases after a certain "point of return". From these pioneering works a great amount of research has been developed, including both theoretical and empirical studies. These applications have lead to a wide variety of conclusions, due to the differences in the databases and the statistical techniques. In this paper we analyse the inequality-growth relationship, combining analytical and empirical approaches. In the following section we briefly review the properties of the Kuznets process and the relationships derived by S. Anand and S.M.R. Kanbur (1993) for inequality measures. This methodology is applied in the third section to the case of two new inequality measures which are broken down, deriving their connections with development indicators. An empirical application of these relationships appears in the fourth section, using an international sample of countries extracted from the Penn World Table and the Deininger and Squire database. 2. The Kuznets process The pioneering works of Kuznets (1955) based on information extracted from tax declarations describe how intersectoral changes from agriculture towards sectors with greater incomes would produce a pattern in which the inequality first increases and later decreases after a certain "point of return". Eight years later, Kuznets presented additional empirical evidence and postulated the U-inverted curve (also called Kuznets curve) initially showing an increasing pattern of inequality and later decreasing with regard to economic growth. The works of Kuznets assume a dual economy, denoting by x the proportion of population dedicated to the modern sector (considered as an indicator of the development level) while µ i