Comparing regional low income in Canada

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Table 5 reports the estimates of headcount ratios (and asymptotic standard errors) for the 10 provinces and for selected low-income lines, varying from $4,000 to $20,000 of equivalent income. Provinces are ranked from left to right—most low income to least low income— according to their headcount rates.¹⁷ It reveals that the rankings of low income are sensitive to where the low-income line is drawn. In fact, provinces in Western Canada experience higher headcount rates for low-income lines below $8,000. When the lines are set to $10,000 or above, low-income orderings change dramatically: headcount rate now becomes significantly higher in Quebec and Newfoundland and Labrador (N.L.), while Saskatchewan, Alberta and Ontario all experience a drop in headcount rankings.

The results for dominance relations by the 10 provinces (a total of 45 pairs) are presented in Tables 6 to 11: t statistics are calculated at each value of x observed in the sample, and the minimum t-ratio approach is used to test for the null of non-dominance. A value '1' in the cell indicates that column first-order dominates the row, and the two parentheses below indicate the lower/upper thresholds in which the column province dominates the row province in low income within the boundary at the 5% significance level. Similarly, a '2' represents a second-order dominance, and a '3' illustrates third-order dominance. When a dominance relation cannot be found up to the third-order condition, a 'Z' is marked to indicate that low income between the two provinces cannot be ranked.¹⁸ The overall low-income rankings are obtained from the simple method of pair-wise comparisons and the rankings are displayed in ascending order (1, 2, 3...) representing the highest to lowest levels of low income. That is, for any given two provinces, the one with more total cases of dominance is considered to have less low income. If head-to-head comparisons between two provinces cannot be determined, and both provinces have the same total cases of dominance over other provinces, then both are tied in the low-income rankings.

In Table 6, t statistics are calculated over the full spectrum of the lower-part income distribution (i.e., low-income lines from $0+ to $20,000). For reference, the commonly used low-income cutoff (LICO)-headcount ratios are also reported in the table. Overall, Table 6 shows that rank order can be determined and the lower/upper limits for dominance can be obtained in 41 out of the 45 comparisons, up to third-order condition. In 2000, British Columbia (B.C.) had the highest level of low income, as B.C. was first-order stochastically dominated by all other provinces for a wide range of low-income lines.¹⁹ The ordering is then followed by Manitoba and Quebec, Saskatchewan/Alberta, Ontario and the Atlantic Provinces, with New Brunswick (N.B.) and Prince Edward Island (P.E.I.) dominating all other provinces at the first-order condition. Interestingly, such rankings are not necessarily in accordance with the LICO-headcount rates. For instance, N.L. has a significantly higher LICO-headcount rate than Ontario, Alberta and Saskatchewan, indeed N.L. dominates these provinces in low income at a higher order. It is because N.L. has a relatively smaller proportion of 'very poor' people among the low-income population compared with other provinces.

This use of information over the distribution of income helps rank the two provinces that appeared to be statistically indistinguishable in a LICO comparison. For instance, one cannot rank low income between Ontario and Saskatchewan, based on the LICO-headcount rates, because the difference at this particular point is statistically insignificant. However, more marked regional differences may be discovered when we look at a wide range of low-income lines. Using the stochastic dominance approach, we can conclude that Ontario's first order dominates Saskatchewan stochastically over a restricted domain ($17,651, $20,000+).

Although first-order dominance is commonly seen in most cells in Table 6, there are six comparisons where dominance relations must be determined at a higher order condition, and there are also four cases where no clear conclusion can be obtained up to the third-order condition. This may occur because the two curves are not differentiable, or because the two curves crossed over the range of interest. In the latter case, it is possible that the dominance relation may change if a restricted domain—which now excludes the crossing point—is focused. Indeed, literature has suggested focusing on restricted dominance, instead of unrestricted dominance, because there may be a sampling issue at the tails of the distributions. In addition, from a social welfare perspective, it might be sensible to impose a minimum income that is needed for an individual to perform normally in a given society to meet certain ethical principles (see Davidson and Duclos 2006 for more discussion).

For this reason, we introduce a reasonable lower limit ($5,000) and t statistics are computed over the restricted domain ($5,000, $20,000) in Table 7. We refer this table to 'the base-case' model. Surprisingly, rank-order changed only slightly compared with Table 6. The only exceptions are Quebec and Manitoba, where rank order is reversed. Manitoba was third-order dominated by Quebec in Table 6, but it now dominates Quebec at first order over domain ($13,167, $14,629). The reversal occurred because in Manitoba there are relatively more deprived people living below $5,000 and these people were ignored when focusing on restricted domain. It is reasonable to believe that low-income ranking may be in a complete different order as domain of interest becomes more restricted.

In Table 8, we further limit t statistics to be calculated over an even more restricted range from $10,000 to $20,000. Now N.L. shows more low income, as its rankings move from seventh place in the base-case model to fourth place. Rank reversals are observed between N.L. and three other provinces—Saskatchewan, Alberta and Ontario. It is not surprising, because N.L. overall has relatively more people in the lower part of the income distribution—but very few at the bottom— compared with the three aforementioned provinces. Testing based on a more restricted domain, therefore, reduces comparative advantage for N.L. and results in a higher ranking in low income. Furthermore, two comparisons that failed to reject the null of non-dominance in the base-case model—Nova Scotia (N.S.)/N.L. and Ontario/N.S.—now show dominance relations at first-order condition. The overall low-income rankings, therefore, can be ordered more precisely.

It should be emphasized that the interpretation of low-income rankings needs to be supplemented with the range of dominance that is estimated in the tables. In some cases, such as the comparison with B.C., dominance relation is very robust for a wide range of low-income lines. In other cases, such as the N.B./Ontario comparison, it only concludes that N.B.'s first order dominates that of Ontario for a very restricted domain ($14,606, $15,904). The two provinces are virtually not distinguishable when comparing low-income lines outside the limit.

Sensitivity analyses

It is emphasized that the long standing debate on poverty often involves discussions on choosing different scaling factors to define equivalent income and also on issues about choosing absolute or relative low-income lines. The remaining subsection, therefore, examines the robustness of low-income rankings to the choice of some underlying assumptions—namely, equivalence scales, cost-of-living factors and relative low-income lines.

Table 9 shows tests of dominance for which equivalent income is calculated using 'square-root family size' instead of a LICO-equivalence scale. In order to attribute rank change to the choice of equivalence scale, income is still price adjusted, using the LICO cost-of-living index. In comparing with the base-case results, Table 9 shows that low-income rankings are virtually insensitive to the choice of equivalence scale. Rank order remained exactly the same for 44 out of 45 comparisons with minor changes over domain of dominance. The only difference is N.S./N.L., where dominance relation cannot be determined in the base-case model but it is clear now that N.S.'s first order dominates that of N.L. for low-income lines ($13,864, $18,871). Nevertheless, it is important that no rank reversal occurred to the choice of equivalence scales.²⁰

Next, we examine how the choice of spatial price factor affects geographical distribution of low income. This is relevant, especially when no satisfactory spatial cost-of-living index is available for Canada. It is well documented that using different indices for spatial-price differences could reverse rankings for poverty measures (see, for examples, Ravallion and Bidani 1994, Jolliffe 2004). This is also the case in Canada. Compared with the base-case results, Table 10 reveals that dominance relations change considerably when the market basket measure (MBM)-based price index is used.

Except for B.C., where low income remained the highest among the nation for a wide range of low-income lines, rank order for other provinces reshuffled. Overall, low income becomes more serious in the Atlantic provinces and less so in the Prairie provinces and Ontario. It is striking that Quebec, which was ranked second place in low income from the base-case model, has now become the province with the least low income. On the other hand, the use of the MBM-price index significantly increases low income for P.E.I.—from the least low income to the third highest among provinces. Indeed, a complete reversal of low-income ranking is observed in 21 out of 45 cells, particularly for relating comparisons to Quebec, P.E.I. and Manitoba. For instance, eight out of nine Quebec-involved comparisons turned to the opposite result.

Despite the reshuffling, the overall low-income rankings become more obvious because now we only reject the null of non-dominance for two cells, compared with four in the base-case model. The four comparisons (e.g., N.S./N.L.), in which rank-order could not be determined in Table 7, now show clear dominance relations at the first order for some range of low-income lines. Nevertheless, the use of the MBM-price index also changed relations for two cells (i.e., N.S./P.E.I. and Saskatchewan/N.L.) from dominance to non-comparability, up to the third-order condition.

Comparing Table 7 with Table 10, dominance relations remained the same for only 18 out of 45 comparisons (with one cell changed order condition). The tests of dominance are robust for B.C., regardless of the choice of cost-of-living index. However, it is striking that as many as 21 cells reached a complete reversal of ranking. It is also interesting that such reversals are not observed equally across provinces. Rather, they mainly concentrate among comparisons relating to Quebec, P.E.I., Manitoba and Alberta, as 19 out of the 21 reversals involve these provinces. The results reflect significant inter-provincial differences in the costs of necessities, information that is masked in the LICO cost-of-living index; and, such costs of MBMs are considerably lower in certain provinces, such as Quebec and Manitoba. This, of course, raises issues about how the MBM thresholds were calculated and how to keep them updated over time. Also, it is debatable whether there is a need to differentiate a regional basket at such a detailed level, given that people can move freely. The answer to these questions, however, is beyond the scope of this paper.

Finally, in Table 11, we examine low-income dominance using relative low-income lines. In the cases of cross-country/region comparison, it is often more desirable to view low income as a relative term. People may feel deprived or excluded, simply because they have fewer resources relative to the average standard of the society in which they reside, not necessary because their income/consumption level is below an absolute subsistence of living. When adopting a relative low-income concept, low-income lines are allowed to vary by different income distributions across provinces, with low-income lines set to a proportion of the provincial median income.

In order to compare with the base-case model, tests statistics are calculated at each normalized value of x for a range from 15% to 70% of provincial median income.²¹ Overall, Table 11 shows that B.C. still ranks first in low income, even with relative lines. The ordering then follows with Ontario, the Prairie provinces, Quebec and the Atlantic provinces. The overall rankings show some resemblance to the base-case model as the rankings of B.C. and the Atlantic provinces all stay in the same places as in Table 7. In fact, about 33 out of 35 comparisons relating to these provinces keep the same dominance results. Switching from an absolute to a relative low-income concept, however, has greater impact on low-income comparisons between Ontario, Quebec and the Prairie provinces. It is striking that a reverse outcome is observed in 8 out of 10 comparisons among these provinces. Ontario now ranks second highest in low income—compared with second place in the base-case model—while low income becomes relatively lower for Quebec and Manitoba, as their rankings dropped a couple of places compared with Table 7.

It is reasonable to infer that rank reversal is more likely to happen when comparing provinces in which median income differs markedly. A typical case is Ontario, where median-equivalent income is much higher than that of other provinces. The use of relative low-income lines, therefore, places more people into low income in Ontario in the sense of relative deprivation. This also propels Ontario's rankings in low income toward the top among all provinces. On the other hand, relative deprivation is of less concern in provinces like Quebec, where median income is considerably lower. It is also noteworthy that two cells—N.S./Ontario and P.E.I./N.B.—that failed to reject the null of non-dominance before, now display first-order dominance over a reasonable range of relative low-income lines. For Saskatchewan/Alberta and N.S./N.L., their low-income rankings are still undetermined up to third-order condition when relative low-income lines are used.