Education as a dimension of human development: A Provincial-level Education Index for Ecuador

variation, CV2. This choice is due to the simplicity of this measure in terms of calculation and interpretation and because it offers the desired properties of a measure of inequality (for a review of measures of inequality and their properties, see e.g. [96]), one of which is the possi- bility of its additive decomposability by factors [97]. As is well known, the square of the coefficient of variation of PEI, CV2 PEI, is equal to s2 PEI=m2 PEI where s2 PEI and m2 PEI are, respectively, the variance and the square of the mean of the PEI. The closer the value of CV2 PEI is to zero, the lower the educational development inequality. Conversely, since this coefficient is not upper bounded, the larger its value, the greater the inequality. Considering that PEI = (MYS + EYS) / 2 and following Shorroks’s methodology [97], the “natural” decomposition of the square of the coefficient of variation is CV2 PEI ¼ 1 4 � m2 PEI s2 MYS þ sMYS;EYS � þ 1 4 � m2 PEI ðs2 EYS þ sMYS;EYSÞ where s2 MYS, s2 EYS, and sMYS;EYS are the variances of MYS and EYS, and the covariate between these education indices, respectively. This decomposition implies that the interaction term, 2 � sMYS;EYS, is allocated in the same way for both indices. Thus, ðs2 MYS þ sMYS;EYSÞ=4 � s2 PEI and ðs2 EYS þ sMYS;EYSÞ=4 � s2 PEI are the proportions of overall educational inequality contributed by MYS and EYS, respectively. Finally, given that the numerator of CV2 PEI is the variance of PEI, simple calculations leaded us to see that the contribution of province i to overall inequality is equal to PEIi mPEI ð Þ2=n � s2

PEI, where n is the number of provinces. Empirical results Fig 1 shows the spatial distribution of the PEI in Ecuador for 2006 and 2014 (education indica- tors data, and PEI and its components data available in S5 and S6 Tables). The Ecuadorian map illustrates the PEI distribution in 2014 taking the classification by quartiles as reference. It can be seen how provinces with a large urban population, such as Pichincha (whose capital is Quito, an eminently metropolitan area), Loja or Guayas, evidenced the highest levels of educa- tion, whereas the lowest levels corresponded to provinces with a greater concentration of rural population, such as Chimborazo, Cotopaxi, Los Rı´os, and Orellana. Pastaza is an interesting case, as it was the only province in the Amazonia that was among the group of Ecuadorian provinces which displayed the highest level of educational development. Although no regional pattern is evident–since the provinces exhibiting the highest and lowest PEI values were spread around the three regions considered in the study–, what did emerge is that provinces located in the southwest part of the country, such as Guayas, El Oro, and Loja, displayed greater devel- opment in education. Meanwhile, Sucumbı´os and Orellana–located to the north-east–were two of the provinces lagging furthest behind in the education dimension of well-being. Table 1 complements the information provided in Fig 1. This table shows the Ecuadorian provinces classified according to their level of educational development in 2014. To conduct

this classification, firstly, we considered the values of the education index calculated by UNDP for all countries with available information in 2014 [29]. Secondly, following the aforemen- tioned UNDP methodology for its HDI, we calculated the values 0.500, 0.664 and 0.784, corre- sponding to the first, second and third quartiles, respectively, of the HDI education index. These quartiles were the thresholds that determined the level of educational development of each province: low, if its PEI was less than 0.500; medium, if its PEI was greater than or equal to 0.500 and less than 0.664; high, if the PEI was greater than or equal to 0.664 and less than PLOS ONE Education as a dimension of Human development PLOS ONE | https://doi.org/10.1371/journal.pone.0270932 July 8, 2022 10 / 27