  By borrowing methods from complex system analysis, in this paper we analyze
the features of the complex relationship that links the development and the
industrialization of a country to economic inequality. In order to do this, we
identify industrialization as a combination of a monetary index, the GDP per
capita, and a recently introduced measure of the complexity of an economy, the
Fitness. At first we explore these relations on a global scale over the time
period 1990--2008 focusing on two different dimensions of inequality: the
capital share of income and a Theil measure of wage inequality. In both cases,
the movement of inequality follows a pattern similar to the one theorized by
Kuznets in the fifties. We then narrow down the object of study ad we
concentrate on wage inequality within the United States. By employing data on
wages and employment on the approximately 3100 US counties for the time
interval 1990--2014, we generalize the Fitness-Complexity algorithm for
counties and NAICS sectors, and we investigate wage inequality between
industrial sectors within counties. At this scale, in the early nineties we
recover a behavior similar to the global one. While, in more recent years, we
uncover a trend reversal: wage inequality monotonically increases as
industrialization levels grow. Hence at a county level, at net of the social
and institutional factors that differ among countries, we not only observe an
upturn in inequality but also a change in the structure of the relation between
wage inequality and development.
