Socio-Environmental Development Index
for the State of Bahía
Leonardo Araújo, Elaine Fernandes and Patrícia Rosado
Building the Environmental Conditions Index
for the Municipalities of Bahía

The Environmental Conditions Index (eci ) is used to measure the proportion of environmental quality in an area of a specified municipality. It was constructed in two stages. In the first, the Partial Index of Environmental Conditions (piec) was developed by means of a Multivariate Factor Analysis. In the second, based on the ipca, the weighting attributed to each of the variables that made up eci ’s composition was estimated, using regression analysis, applying the restricted least square method (rls). The factors estimated by the technique should explain a significant part of the variation of the group of original variables, taking into account that the first factor has the largest explanation percentage of the total variation, the second factor has the second largest percentage, and so forth successively (Corrar et al., 2007).

The orthoganality property of the estimated factors point was used to construct the partial index. Meanwhile, it should be noted that the orthoganality associated with the matrix of factors, does not necessarily imply orthoganality of the factor point, the factor points being evaluated to establish if they are orthogonal by means of the variation and covariance matrix between these points. (Corrar et al., 2007)

The piec may be estimated through the following equation:


in which pieci is the Partial Index of Environmental Conditions associated with the i th Bahía municipality, and Fij are the estimated factor points according to the principal components procedure. The factorial analysis was carried out with the indicators presented in the data source, with the exception of the following variables: income per capita, life expectancy at birth, and school attendance, which were used to construct the Index of Socio-economic Environmental Development (idsa). To this end, the following indicators were used: (X1) persons who live in homes with refuse collection; (X2) persons who live in homes with running water; (X3) persons who live in homes with a general sewage or rainwater drainage network; (X5) persons who live in homes without automobiles; and (X9) contribution of industry to municipal gdp . These variables make up the infrastructure of the State and are used in the current analysis as a proxy of environmental quality, and therefore, quality of life. The last variable analyzed (X10 = vegetation cover) directly represents environmental quality and was defined as the value of woodland and forest areas in the municipalities divided by the value of the total municipal area.

The Partial Index only reflects a ranking of municipalities in terms of environmental conditions. It cannot therefore be used to estimate environmental quality as a percentage for each of the municipalities. For this the eci is used. This index was constructed by taking into account the weighting of each of the variables used in the previously mentioned Partial Index (Equation 1). These weightings were obtained through regression analysis using the restricted least square method (rls) in which the piec is the dependent variable and the indicators (X1), (X2), (X3), (X4), (X5) and (X8) are the explanatory variables. Equations (2) and (3) show how the eci is made up.



in which Pj are the parameters estimated for Equation (3) which together are equal to 1; and Xi are the variables used to construct the piec.