1 Method and the Data
2.1.2 Decomposition of Education Gini Coefficient by Location (Urban and Rural Sectors)
Gini coefficient the most widely used measure of inequality (for e.g. gender inequality, income inequality, education inequality) and is derived from the Lorenz curve. Lorenz curve is a graph which vertical line represent labeled non-descending order cumulative income or expenditure share and horizontal line represent the labeled non-descending order cumulative population. The inequality results of Gini coefficient range from 0 to 1 and 0 represent perfect equality and 1 represent completely unequal. Gini coefficient satisfy many properties, mean independence, population size independence, and Pigou-Dalton Transfer sensitivity.
The decomposition analysis of Gini coefficient is used to analyze the educational attainment of household head differences in urban and rural sectors. The contribution can show within urban rural education inequality or between urban and rural education inequality is more important to overall education inequality. Although the generalized entropy class of measures, Theil T and Theil L can decompose additively into between-groups and within-groups contributions, there has some problem in decomposing the education inequality into between-group and within-group contributions by Gini coefficient. The problem is arising the residual term if the groups of education ranges overlap. However, we can still examine both of the education disparity of household head in urban and rural sectors and overlapping in the distribution of education attainment between urban and rural sector.
Given the population N, educational attainment of household head is measure by year of education that has been completed and urban and rural sectors are specified into 1 and 2. In order to measure the education inequality, the total Gini ratio defined by Gini is,
Where, || represent the mean of the absolute years of education differences, m is mean of the household head’s year of education, mean of the years of education and is the population in sector i.
In order to measure the decomposition of the Gini coefficient (Lambert and Aronson, 1993; Dagum, 1997), the decomposition of the Gini is defined as
Where, () is the within-group Gini index, () is the between-groups Gini index, and () is the residual term.
The Gini coefficient within urban and rural subpopulation () is defined as
and symbolizing by share of the population in urban and rural sectors, share of years of education in urban and rural sectors and Gini ratio of urban and rural sectors.
Moreover, || represent the mean of the absolute years of education differences in each urban and rural sectors and the Gini coefficient between urban and rural subpopulation () is defined as
Lastly, the equation represents the residual term and if the residual term is zero, we can assume there is no overlapping in the ranges of educational subgroup.
2.1.1 Blinder-Oaxaca Decomposition
Blinder Oaxaca Decomposition for linear regression models observe the group difference of any outcome variable between any two groups. In this study, Blinder-Oaxaca decomposition analysis (Blinder, 1973; Oaxaca, 1973) is used to examine the extent to which educational endowments describe the difference in mean per capita expenditure between households of urban and rural sectors in Myanmar. The linear regression model for how much of the difference in mean per capita expenditure of urban and rural sectors is,
Where, = the natural log of per capita expenditure,
= a vector of explanatory variables
= a vector of the least-squares estimates associated with
= error term
k = Urban and rural sectors.
The estimated urban-rural difference in mean per capita expenditure is given by:
Where, = a vector of coefficients obtained from the urban sector and rural sector
= a vector of nondiscriminatory coefficients obtained from the pooled
samples including both urban and rural sectors
= expected value for explantory variables.
The nondiscriminatory coefficient vector is used in the twofold decomposition suggested by Newmark (1988) to examine the contribution of the gaps in the predictors. It divides the equation (1) into explained part and unexplained part. The explained is the quantity effect of explanatory variables on expenditure differences in urban-rural sector, while the unexplained part is normally used as a measure of discrimination and it can also recognize as the effect of unobserved variables on expenditure differences in urban-rural sector.
In this Blinder-Oaxaca decomposition model, the natural log of per capita expenditure is used as the dependent variable and years of education, age, age squared, household size, and gender are used as the independent variables. The main explanatory variable year of education was predicted by using education level of household head, and regarded zero year for illiterate level, 1 year for literate level, 3 years for Monastic education level, 5 years for Primary Attainment, 9 years for Middle Attainment, 11 years for high school Attainment, 12 years for Vocational education and 14 years for graduate education level.
2.1.3 Hierarchical Decomposition of Expenditure Inequality by the Theil Index T
To analyze the effect of education on expenditure inequality in Myanmar, the hierarchical Theil decomposition method advanced by Akita and Miyata (2013) is used in this study. The hierarchical Theil decomposition method is based on generalized entropy class of measure Theil T and Theil L indices. Theil indices are additively decomposable into within-groups and between groups inequality and satisfy several desirable properties as a measure of regional income inequality and satisfied as other inequality measures Anonymity, Income Homogeneity, Population Homogeneity, Pigue-Dalton principle of Transfers.
Given the six educational groups that are classified into mutually exclusive and collectively exhaustive: No-Education, Pre-Primary, Primary Attainment, Middle Attainment, High School Attainment and Tertiary, all households in the sample are divided into urban group and rural group separately. The Theil index for overall per capita expenditure inequality is defined as
where, i represents the location of household urban and rural, j represents each educational groups and k represnets number of household in each sector. Furthermore, Y is the sum of the per capita expenditure for all household in urban and rural at every education level j.is the per capital expenditure of each household k located in sector i and whose household head is educated j level, , and is the number of households in each education level j located in each sector i.
The Theil index T can be decomposed hierarchically into the per capita expenditure inequality between urban and rural sectors (), the per capita expenditure inequality within urban and rural sectors between educational groups (), and the per capita expenditure inequality within urban and rural sectors within educational groups () , the hierarchical inequality decomposition for location and education by Thiel T index is as follows
Where, = inequality within urban sector and inequality within rural sector,
= inequality between education groups in urban sector and inequality
between education groups in rural sector,
= education inequality for each within education groups j in each urban
sector and rural sector.
The two-stage nested Theil decomposition method (Akita (2003)), is similar to hierarchical decomposition by Theil index, the only one difference is two-stage nested Theil decomposition used district level GDP data and hierarchical decomposition used household level data.