# Annex A. Spatial inequalities: across states or between rural and urban areas?

Income inequality can be decomposed along at least in three dimensions:

• Between states, as gaps in the average income among states;

• Urban/rural divide, as gaps in the average income between rural and urban households in the same state;

• Within component: as differences across households living in the same state and belonging to the same rural/urban group.

While the Gini or the Theil coefficients are the most frequently inequality measures used, they do not allow the decomposition of total inequality into more than two components. Hence other measures have to be used to break down inequality between the two spatial sub-groups of the population – here states; and urban and rural areas – and the “within” component (i.e. within states, within urban areas and within rural areas). The mean logarithmic deviation (MLD) and the squared coefficient of variation (SCV) have attractive properties. (For more discussion on the properties of the inequality indices, see Mookherjee and Shorrocks, 1982). Notably, these two indices allow decomposing inequality into more dimensions.

The mean logarithmic deviation can be used as follows:

While, for the squared coefficient of variation, we have:

Where:

• xi is the income of household i;

• is the average income of the state S to which household i belongs to;

• is the average urban or rural income, depending on whether the household lives in a rural or a urban area, in the state S to which household i belongs to;

• is India’s household average income.

Micro data for individual or household income are not available in India. Hence, the analysis is carried out with data on household consumption. This can introduce a downward bias in the measure of inequality as higher income households tend to consume a smaller part of their income. This can affect the overall inequality index as well as the three sub-components and in particular the urban/rural divide component as urban incomes are on average higher than rural ones. On the other hand, rural households may receive part of their pay in nature or self-produce part of the goods they consume. If this consumption is not captured by the survey, the urban/rural divide is overestimated.

Table A.1. Percentage of inequality explained by disparities across states and the urban/rural divide

Between states

Urban/rural divide

Within component

Mean logarithmic deviation (MLD)

2004

14.75

17.58

67.61

2012

18.85

16.46

64.79

Squared coefficient of variation (SCV)

2004

7.75

10.00

82.17

2012

9.01

9.30

81.76

Source: Authors’ calculation.

The main conclusions from this analysis are as follows:

• The most important source of income inequality is the “within component”. Using various indicators of income inequality, Subramanian and Jayaraj (2015) suggest that it has increased steadily within urban areas since the early 1980s while there is less of a clear cut trend in rural areas;

• The “urban/rural divide” contributed more to spatial inequality than the “between states” component in 2004. However, the contribution of the “between states” dimension to overall inequality has increased;

The two approaches differ as to the contribution of spatial inequality – either the “between states” or the “rural/urban divide” – to total inequality. This is mostly due to the sensitivity of the two indicators to different forms of inequalities, with the SCV being more influenced by the presence of extremely high or to extremely low values than the MLD.