Appendix
The first component is the population-share weighted average of withingroup inequalities, and the second term is the between-group inequality. Now, suppose we are interested in the dynamic decomposition of the second Theil measure between periods t0 and t1. The decomposition of changes in inequality between these two periods is ΔIT 2 (x) = IT 2 (x; t1) − IT 2 (x; t 0 ) K
K
K
k =1
k =1
k =1
= ∑ v k (t 0 )ΔIT 2 (x k ) + ∑ IT 2 (x k ; t1)Δv k + ∑ ln
K 1 1 k Δ v + v k (t 0 )Δ ln k , ∑ k m (t1) m k =1
(A.3) where Δ represents the change in the variables from time t0 to t1. The four components can be interpreted as (a) the intertemporal change in withingroup inequality, (b) the change in the population shares of the groups in the within-group component, (c) the change in population shares of the groups in the between-group component, and (d) the change in the relative incomes of the subgroups. Table A.7 provides a dynamic decomposition of the overall Georgian income inequality using the second Theil measure. Results in the table correspond to changes across years 2003 and 2006. The variable for our analysis is consumption expenditure in lari per month. Row 1 reports the change in overall inequality. Rows 2 through 5 decompose this change into four factors, as explained in the previous paragraph. Row 2 reports the change in overall within-group inequality. Rows 3 and 4 report the effect of changes in population shares on the within-group inequality and the between-group inequality, respectively. Row 5 reports the change in relative subgroup incomes. Table A.7: Dynamic Decomposition of Inequality Using the Second Theil Measure GE(0) A 1
Change in aggregate inequality
−0.011
2
Within-group inequality
−0.015
3
Population shares of within-group inequality
0.000
4
Population shares of between-group inequality
0.000
5
Mean group incomes
0.004
Source: Based on ADePT Poverty and Inequality modules using Integrated Household Survey of Georgia 2003 and 2006. Note: GE = generalized entropy.
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