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

where uj is the number of individuals of age j enrolled out of a total of vj individuals. Finally, we applied the expansion factor to each individual enrolled in each age group. We estimated the PEI for the provinces of the regions: Sierra (Azuay, Bolı´var, Cañar, Carchi, Cotopaxi, Chimborazo, Imbabura, Loja, Pichincha, and Tungurahua); Costa (El Oro, Esmeraldas, Guayas, Los Rı´os and Manabı´), and Amazonia (Morona Santiago, Napo, Pastaza, Zamora Chinchipe, Sucumbı´os and Orellana). We did not take into consideration the single- province region of Galapagos due to a lack of representativeness in both LSMS [78, 82]. Although the fifth round of the LSMS is only representative at the regional level for Amazonia, we estimated the PEI for its provinces for this round as well. Sometimes it is not possible to find representative samples of the population, which raises the dilemma between the desire to obtain more accurate results–whose reliability could be statistically evaluable–, and the prac- tice of calculating less accurate results [87]–which allow us to approach the reality to be ana- lyzed–. In this study, we critically evaluated this particular context [88] and opted for the second option. Therefore, we were cautious in interpreting the results for these Amazonian provinces when they referred to the fifth round of the survey. Processing the information at a provincial level involved identifying the codes of the coun- try’s territorial divisions. This was by no means a trouble-free procedure, as in 2007 the prov-

ince of Santo Domingo de los Tsachilas (hereafter Santo Domingo) and in 2008 the province of Santa Elena were created, which did not exist in the fifth round of the LSMS, and whose populations belonged to Pichincha and Guayas, respectively [89]. The creation of new politi- cal-administrative units affects the construction of chronological series of socioeconomic indi- cators for the various spatial levels. These new units, which tend to be established based on a grouping of smaller units, as is the case here, change the previously existing boundaries and make spatial standardization of the time series even more difficult. Consequently, with a view to drawing comparisons between the PEI values for 2006 and 2014, it was necessary to calcu- late a “combined” value of the estimations for each of the education indicators. These estima- tions were made using the micro-databases from the sixth round for Pichincha and Santo Domingo, on the one hand, and for Guayas and Santa Elena, on the other. In order to obtain these values, we used the means estimation procedure in the stratified sampling, taking the ini- tial estimations of the values of indicators in the four provinces and using, for this case, the weightings determined by the corresponding population ratios obtained from the 2014 popu- lation forecasts [90]. To validate our results, we compared our provincial estimations of the mean years of schooling indicator, in 2014, to the information offered by the Secretaría Nacional de Planifica-

ción y Desarrollo (National Department of Planning and Development, or SNPD) [91] on this variable at a provincial level for said year, which was also obtained from the microdata of the sixth round of the LSMS. This is the only information from official statistics for Ecuador that may be deemed “homogeneous” vis-à-vis drawing comparisons. In any case, the mean years of schooling provided by the SNPD was estimated on the population aged 24 and over, which does not allow comparisons with UNDP data, unlike the methodology proposed in this paper. Given that the estimations were conducted on different population groups, we used the Spear- man´s rank correlation coefficient to compare the classifications determined on the provinces both by our estimations and by those from the SNPD in order to assess the validity of our results. Moreover, and bearing in mind that the SNPD statistics offer data for Santo Domingo and Santa Elena, we included the estimations of the indicator for these provinces in said analy- sis. The estimated value of the coefficient equal to 0.99 and statistically significant at the 1% level is indicative of near perfect concordance between the classifications given by the two indi- cators and therefore evidences the consistency of our estimations. Furthermore, there are no official statistics for the expected years of schooling indicator at a provincial level in Ecuador. PLOS ONE Education as a dimension of Human development PLOS ONE | https://doi.org/10.1371/journal.pone.0270932 July 8, 2022 8 / 27