Section 5
Who contributes more to overall low income? A decomposition analysis

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Different low income lines can also be assessed across groups of individuals, for example, by quantifying the contribution of each group of individuals to the aggregate index. In this regard, a decomposition analysis is useful. The decomposition analysis estimates the contribution to low income by each group of individuals. A low income line cannot be considered plausible if the analysis shows that individuals whose resources are severely constrained contribute little to the overall low income statistics. With this premise, we examined several groups of individuals who have been independently identified as being at high-risk of social exclusion. In the Canadian context, they include unattached individuals aged 45 to 59, lone parents and their children, individuals from families in which the major income earners are off-reserve aboriginals, new immigrants or those with work limitations.^1, 2

For simplicity, we chose to decompose the low income incidence only.³ To do that, we first classified individuals into mutually exclusive groups. If we classify N individuals of a population into k mutually exclusive groups, each group with n_j individuals, then the low income incidence index, P₀, can be decomposed additively as the following,

Description

where P_0j is the low income incidence of the j^th group of individuals. In this study, we classified the Canadian population into seven mutually exclusive groups: those who belong to one and only one of the five high-risk groups mentioned above, a multi-risk group that consists of individuals who are members of at least two of the five groups, and the rest of the population. Thus, for example, a lone mother who is not a recent immigrant, not an off-reserve aboriginal, does not have work limitation would belong to the lone parent group, while a lone mother who is also a recent immigrant would be classified as belong to the multi-risk group.⁴ The decomposition result under various low income lines is contained in Table 5.

Table 5 Decomposition of low income incidence under alternative lines

The table shows that, no matter which low income line is employed, individuals from groups at-risk of social exclusion contributed to low income a share  disproportionately large than their share in the population. Between 2000 and 2007, the at-risk groups of individuals accounted for 30% to 35% of the whole population, but they contributed much more to the overall low income incidence. Under Low Income Cut-Offs (LICO), they contributed 54% to 60%, under variable Low Income Measures (LIM), 53% to 58%, under fixed LIM, 53% to 60%, and under Market Basket Measure (MBM), they accounted for 50% to 55%.

Overall, the result shows that, no low income line had substantial or systematic advantage over the others in counting the contributions by individuals from the high-risk groups. Nevertheless, there were some noticeable differences between the lines. For individuals from families headed by persons with work limitations, the LICO and the two LIM lines were somewhat stronger than the MBM line. Under LICO and the two LIMs, this group of individuals contributed 16% to 20% to low income incidence, while under MBM, they contributed between 15% and 18%. But MBM and the two LIM lines were slightly stronger than LICO in capturing individuals from lone parent families. Under LICO, they contributed 8% to 11%, while under the other three lines, they contributed between 9% and 13% to the incidence.

Furthermore, individuals who were subject to multiple risks tended to contribute more under fixed LIM than under the other lines. Under fixed LIM, these individuals contributed between 14% and 19% to low income incidence, while under the other three lines, they contributed between 12% and 17%. But the two LIM lines appeared to be weaker than LICO and MBM in capturing individuals from families whose major income earners were recent immigrants. With the LIM lines, these individuals contributed as low as 4% to the incidence, while under LICO and MBM, the minimum contribution of these individuals was 6%.

The observation that individuals from families headed by new immigrants contributed more under LICO and MBM than under the two LIM lines is likely due to two facts. (1) The two LIM lines do not take the variations of costs of living between different localities into consideration, while MBM, and to a less extent, LICO do, and (2) new immigrants in Canada overwhelmingly chose to settle in large cities.⁵ The MBM and LICO thresholds were high in large cities while the LIM thresholds were independent of city size, and given that the income of new immigrants were usually low, it was not surprising that more new immigrants lived in large cities were captured by LICO and MBM than by the two LIM lines.⁶

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Notes

1. See, for example, Buirstein (2005).
2. New immigrants are defined as those who have lived in Canada between two and ten years. Those who lived in Canada for a year or less might not have complete income information and were thus excluded.
3. The other Foster, Greer and Thorbeck (FGT) Indexes can be similarly decomposed. See Foster et al. (1984).
4. Not all groups have interactions with others: an aboriginal cannot be a recent immigrant, although she can be a lone parent, and an unattached individual can be a recent immigrant, but cannot be a lone parent.
5. For example, more than 60% of immigrants who arrived in Canada between 1996 and 2001 settled in Toronto and Vancouver. See Citizenship and Immigration Canada (2005) or Bernard (2008).
6. This can be easily seen from Appendix tables A1 to A3 which show that the low income thresholds for large cities are higher than those for small cities or rural area. Indeed, the MBM thresholds for Toronto and Vancouver were the highest in the country.