Section 3
What happens to low-income statistics with all three modifications?

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3.1 Low-income rates: overall and across groups of individuals
3.2 Low-income gap and severity indexes under the existing and revised LIMs

We have examined the individual impacts of each of the modifications and the paper now turns to examine the combined effect of the three proposed modifications using the FGT (Foster, Greer and Thorbeck, 1984) family of low-income indexes over time and across several groups of individuals. Section 3.1 focuses on low-income incidences over time and across several groups of individuals, while Section 3.2 presents the low-income gap and severity indexes.

3.1 Low-income rates: overall and across groups of individuals

Our exercises in the previous section indicated that modifying the basic accounting unit from economic family to household and replacing the existing Low Income Measure (LIM) equivalence scale by the square root equivalence scale both tend to slightly reduce our estimated low-income rate. In the other direction, using individual rather than family weighting to estimate the low-income thresholds produces higher low-income thresholds when the sizes of families from the bottom of the income distribution were smaller than that of families from the top quartiles. Since the effects of the first two modifications were small while that of the last modification was large in recent years, we expected that the three modifications, jointly, would result in higher low-income rates for the recent years.

Figure 8 Effects of all three modifications on low-income rate

The overall low-income rates are illustrated in Figure 8. While the cyclical movements of low-income in the past 30 years were very similar, no matter which LIM methodology is employed, the levels differed. In the 1970s the revised LIM produced somewhat lower low-income rates than the existing LIM, while in the 1980s low-income rates under the revised LIM became somewhat higher than those under the existing LIM. The differences between the rates during those two periods were small. But since the late 1980s, the difference has been increasing with the revised LIM producing significantly higher low-income incidences than the existing LIM methodology, most likely due to the declining size of families at the bottom of the income distribution.

Similar patterns were observed for different groups of individuals according to their age, province and family types. The only exception was for unattached non-elderly (under 65 years old) men and women. For these individuals, two observations can be made: (1) the low-income rates were about 5 - 8 percentage points lower under the revised LIM than under the existing LIM in the past 30 years and (2) the differences were larger in the 1970s than in more recent years. Figure 9 illustrates these points through the low-income rates for unattached non-elderly men.1 The conditions for these to occur are that some of the non-elderly unattached low income individuals live with other individuals in the same household, such that their combined income, after adjusting for economies of scale, exceeds the new household's low-income threshold, and over time, the tendency for them to join other households have declined or their combined income increased more slowly than that of other households.

The main factor behind the first observation is that economic family is replaced by household as the basic accounting unit. By definition, unattached individuals consist of two groups: those who are household members but not members of economic families and those who live alone. Thus, under the existing LIM, each individual from the first group is counted as an economic family, and that the economies of scale he/she enjoyed by living together with other individuals or economic families are not taken into consideration. The proposed modification counts these individuals as household members and thus, any savings they experienced by living together with other individuals are now accounted for.

Figure 9 Low income rates for unattached non-elderly persons (men)

As an example, consider two unrelated young persons living in the same household. Each of them has an after-tax income of $15,000. Suppose that the low-income threshold under the existing LIM is $15,500 while under the revised LIM is higher, say, $16,000. Under the existing LIM, they are both identified as low-income individuals since they are counted as two economic families and each has an equivalence scale of 1, and hence their adjusted after-tax incomes are also $15,000, $500 below the existing threshold. But under the revised LIM, they are counted as one household, whose after-tax income is $30,000. Given the new equivalence scale of the square root of 2 = 1.4142 each of them enjoys an equivalent income of $21,213 (30,000/1.4142), which is well above the low-income threshold of $16,000, even though the threshold under the revised LIM is assumed higher than that under the existing LIM.

Figure 10 contains the proportions of unattached individuals living with unrelated persons/families (or not living alone) from 1976 to 2007. It is striking to observe that significant proportions of non-elderly men and women lived with other unrelated persons or families. In the mid 1970s, this was the situation for 39% of non-elderly women and 44% of non-elderly men. The proportions varied over time but the general trend was that they declined over time. Recall, however, that the proportion of individuals living in multiple economic family (EF) households was constant at about 5% over this period and thus, the decline was mostly due to the relative increase in the proportion of individuals living alone in their own household.

By 2007, the proportion had declined to 31% and 28%, respectively. On the other hand, their median incomes had been fairly stable between 1976 and 2007, while the median income of non-elderly family increased 18% during the same period (Figure 11). It appears that our observations of the gap in low income rates for unattached non-elderly individuals under the existing LIM and the revised LIM are consistent with the developments in their living arrangements and their income trends.

Figure 10 Percentage of unattached individuals living with others

But one question about the above argument is that, unattached elderly individuals may also choose to live with unrelated individuals or families, why then, the pattern on low income incidence for non-elderly unattached individuals does not hold for elderly unattached individuals? A plausible explanation is that few elderly unattached individuals would choose to live with unrelated people such that the savings from living with others were not sufficient to alter the overall low-income statistics under the new LIM methodology. The life-cycle theory predicts that elderly individuals would have accumulated a significant amount of assets which increase their demand for privacy, and hence one expects them to have a low probability of living with unrelated persons or families due to the saving motivation. Figure 10 suggests that this is indeed the case when comparing to non-elderly unattached individuals: the proportion of elderly unattached Canadians living with others was about 15% in the mid 1970s, and varied around 10% since the mid 1980s.

Figure 11 Median after-tax income of non-elderly families and unattached individuals (2007 constant dollars)

3.2 Low-income gap and severity indexes under the existing and revised LIMs

As Figure 12 indicates, the trends and levels of the low-income gap ratios under the existing and the revised LIMs are practically identical over the past thirty years. The revised LIM was slightly lower than the existing LIM in the late 1970's but by the early 2000's the situation reversed and the revised LIM was slightly higher.

The differences between the gap ratios under the existing and the revised LIMs behaved in a similar fashion to the difference between the incidences (Figure 8), suggesting that the existing LIM might contain some relative bias in the estimated gap ratio due to the structural changes in family and household formation.

Family and household sizes have been declining over time, regardless of income. But by the very nature of the two equivalence scale systems: that the smaller the family/household sizes, the closer are the resulting equivalence scales (see Table 3), it would not be surprising to see the gap ratio of the existing LIM decline relative to a revised LIM that is more sensitive to changes in family size.

Figure 12 Low-income gap ratios under existing and revised LIMs

Figure 13 indicates the same general pattern for low-income severity indexes as was seen for incidences and gap ratios. The trends and levels are practically identical over the past thirty years while the existing LIM declined relative to the proposed LIM.

Figure 13 Low-income severity indexes under existing and revised LIMs

The differences in levels in the severity indexes in the 1970s and early 1980s were large enough to be statistically significant for some years. It was unclear which line was biased; however, the difference has disappeared during the past 10 years.


  1. The result for unattached non-elderly women is the same.
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