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Here, at a country-level, we employ the Theil measure developed by the University of Texas Inequality Project , while at a county-level we compute a between-sector Theil component for US counties. Notice however that, while we chose the Theil index for its decomposition characteristics, Cowell et al. To check for the eventuality that our results are driven by few spurious observations, in S1 Appendix we will replicate our exercise using the Gini index, a measure particularly stable to single outliers [ 61 ]. The trends found with the Gini index for evaluating wage inequality in the US counties are comparable to the one obtained with the Theil index which we then consider a satisfactory measure of between-sector inequality.
As already mentioned, one of the main goals of our paper is the identification of development by considering Fitness as complementary to a more classic measure of economic performances, GDP per capita. This section is organized as follows. In Subsection A global analysis: wage inequality among countries we will carry out a pooled cross-sectional study of development levels among countries. By using the CRRD defined by Eq 7 as a measure of development, we show that the relationship between development and wage inequality follows a curve that call to mind the one predicted by Kuznets.
Next, in Subsection Within one country: the case of the United States we will focus on the same relation within the United States with the purpose of checking if the movement of wage inequality with development at this scale shows different features. In Subsection Behind the curve we will look for the potential drivers of the relation between development and wage inequality at different scales. In conclusion, in Subsection Time evolution we will analyze the time evolution of this relationship both at a country-level and within the United States.
In this first exercise our purpose is to better tackle the relation to wage inequality and development when integrating the monetary information carried by GDP with that on country capabilities conveyed by Fitness. Thus, we expect to find a relation that might remember the Kuznets curve. We will first explore these relationships through a continuous non parametric description [ 62 ] and, in order to examine time and space dimensions simultaneously, we will pool all countries and years for a number of countries varying between and and over the period — Later we will move to a more traditional parametric description to provide a quantitative counterpart to the qualitative results found.
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Our starting point is the essentially declining relation between wage inequality and relative GDP per capita in Fig 3. Galbraith built the same plot, but used data from to , and found the same downward sloping relation [ 27 , 63 ]. However, by using only monetary information, it is easy to mistakenly asses the industrialization stage of a country.
China shows a diversified and increasingly complex economy, while Russia is characterized by a fundamentally extractive economy, almost only based on the export of raw materials.
This caused the divergent economic performances of the two countries in the last years [ 10 ]. When integrating the monetary information carried by GDP with that on country capabilities conveyed by Fitness we are able to grasp these crucial differences. And since here we are able to quantify development in a more detailed way, we can better tackle its relation to wage inequality. In panel a we show a wage inequality color-map obtained with a continuous non-parametric regression: from the diagonal variability of color we can see that both Fitness and GDP per capita play a role in the distribution of wages.
This yields naturally to panel b where we represent development as a monodimensional variable by synthesizing the combined effects of Fitness and per capita GDP in the CRRD. In both the tridimensional and the monodimensional representation in the first stages of development there is an increase in wage inequality, while as development advances the relation becomes negative. The diagonal variability of the color suggests that wage inequality between sectors, at this scale, is determined both by Relative GDP per capita and Fitness ranking and follows a pattern similar to the one predicted by Kuznets.
By employing the CRRD as an industrialization proxy, we recover the entire Kuznets curve not only its downward part. To provide a more formal analysis of the results shown in Fig 4 , we quantify the relation between industrialization and wage inequality with a parametric estimation.
To tackle some essential features of the clearly non-linear relationship between development and wage inequality we will use squares of the variables. We are in no way arguing that this relationship is parabolic; however, the estimation of the best fitting parabola is fruitful because, on the one hand, it is a widely used technique since it allows for comparability with other studies and, on the other hand, it allows a quantitative measure of non-linearity.
The results are presented in Tables 1 and 2 for different model specifications: Ordinary Least Squares and Fixed Effects Estimation respectively. OLS estimation, different model specifications. Fixed Effect estimation, different model specifications. The tables show how, while both the ranking of GDP per capita model 1 and the ranking of Fitness model 2 present significant negative quadratic terms, the CRRD model 4 outperforms both in terms of explained variance.
Since CRRD is a linear combination of the two rankings, this is a very strong result; it is even algebraically possible only because in model 3 we do not have the cross term Rank Fitness Rank GDPpc. Notice that we are not considering any controls. Indeed, theoretically the Fitness measure already discounts any further possible dependency. Empirically, adding some possible dimensions of analysis Education, Democracy, Freedom of Speech and Press, … would be useful if we were to analyze the causal role of our CRRD. However, this is not the point of the exercise: as we said, it could well be that development and wage inequality co-evolve without direct causality.
For this reason, by following Fig 4 , it is not possible to infer if a change in the Fitness or GDP of a country provokes an increase or decrease in wage inequality. We have completed the first part of our analysis: we were able to observe on a global scale a Kuznets-like curve connecting development, proxied by CRRD , and wage inequality. Although recovering the downward part of the inverted U-curve is already a solid result in the economic literature see for example [ 25 , 64 — 68 ] , we have retrieved the entire expected theoretical trajectory predicted by Kuznets.
Here, we conduct an analysis that mirrors the global one, but we look in detail at the comparative development of the constituents of a single country, the counties of the United States. As the United States is one of the highest GDP countries, over the two analyzed decades it is placed in the rightmost part of a Kuznets curve, among developed and prosperous societies, and its expected inequality trend should be negative. Hence, if the underlying forces influencing the relation between wage inequality and development were the same among countries and within the United States, we would expect to look at a simple zooming of the rightmost part of the curve in Fig 4 ; however, if the relation were not scale-invariant and ended up being shaped differently, this would hint at scale-specific explanations of the development-inequality relationship.
As explained in Subsection Sources of data , for this analysis we focus on employment and wages regarding the approximately counties of the United States over the period — From this data, for each county and each year, we compute a Theil index that measures inequality in the distribution of NAICS sectoral wages—the Theil component defined in Eq 9 —and, by implementing the method outlined in Subsection Variables of interest , we run the Fitness-Complexity algorithm as defined in Eq 5.
We then evaluate the Complex Relative Rank Development index by employing county average wage instead of GDP per capita as monetary variable. Counties constitute a variegated social context, in which the industrialization level, the predominant sectors, the dimension and ethnic composition of the population etc.
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Per contra, in the United States a relatively uniform culture dominates and most of the economic policies are made at the state or at the federal level. By analyzing data regarding sub-units of a single national entity, we are able to control most of those institutional, economic and cultural factors that differ among countries.
In fact, as shown by Moller et al. As in the previous section, we choose a continuous non parametric approach and pool all counties and sectors over — As shown in Fig 5 , we see immediately that among sectors and within counties the development-wage inequality relationship does not follow a Kuznets curve. The curve is in fact upward sloping: the more complex and diversified the productive system of a county, the higher the wage inequality among sectors in it. The same behavior is uncovered in the wage inequality color-map, as can be seen from the diagonal green band in Fig 5 panel a.
This picture differs radically from multi-country analysis performed in the previous section. This difference in the cross-sectional relationship between development and wage inequality is the footprint of a difference in its determinants at different scales. The next section will be focused on what we can learn from this empirical difference.
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From the diagonal green band it is clear that the highest Fitness counties are the most unequal. The relationship is positive-sloping: as industrial development increases so does wage inequality, which then shows a plateau for high F C values. The upturn in the relation of wage inequality to development that we found in the previous section puts into light a clear behavior change at different scales.
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Here we will sketch an analysis of the possible explanations of such lack of scale invariance. Notice that we are not defining the direction of causality: we are only looking at correlations. Any causal relations between development and inequality will likely go in both directions, and even through omitted variables. It could be inequality that drives institutional change and development or vice versa, or, even, institutions could be the drivers of both inequality and development.
We are looking for the potential drivers of the relation that are decisive when comparing countries but are missing when examining wage inequality among the constituents of a country; the most obvious candidate for this are institutional factors. Thus, we are now left with the determinants of the positive part of the relation of wage inequality to economic development observed for the United States. Kuznets followed a structural approach in explaining this inequality increase.
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Since within the United States institutions are not relevant, are then structural effects enough to determine the observed relation of wage inequality to economic development? How can changes in sectoral compositions along development lead to increased wage inequality? In our framework the most developed counties are often also the most diversified. By borrowing the terminology of biologists, industrial systems develop in a nested fashion [ 7 , 8 , 70 ]. This can be clearly noticed when observing the upper section of the county-sector matrix in Fig 4 in which almost all sectors are present in the highest Fitness counties matrix rows , from the least to the most complex.
A new sector is not introduced at random, but only when a productive system has developed the required basket of capabilities, and in this way gradually more and more complex sectors are introduced. For example, it would be unreasonable to believe that a region which has an economy that is strongly based on agriculture would abruptly start to produce electronic components for cars. This could only happen after a process of industrial, infrastructural, legislative and workforce skill adjustments. The nested structure of productive systems is strictly linked to wage inequality for three main reasons.
Firstly, higher industrial diversification increases the space of possible jobs independently from the order in which new sectors are introduced , and so intrinsically enlarges the inter-sectoral wage gap. Indeed, as can be seen in Fig 6 panel a , we observe that the more developed the counties, the more diversified and unequal they are.
In Fig 6 panel a we measure diversification with a Herfindahl-Hirschman Index HHI defined as such: 14 where, for each county, N is the number of sectors and s i is the workforce share of sector i. The Herfindahl Index is computed with the employment shares of 3-digit NAICS industries and, being a concentration measure, it shows that as industrial diversification increases so does wage inequality.
The Coefficient of Variation is here computed by considering the variability of wages at 6-digit aggregation level within every 3-digit NAICS sector at which the complexity on the abscissa refers. National sectoral wages increase as the complexity level of the sector grows. Thus, not only average retributions rise sharply for growing complexity, but within complex sectors wage variability is also higher.
Secondly, Fig 6 panel c displays that since the most complex sectors are more remunerated and by definition are present only in the most developed counties, inequality increases in the latter.