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Regional income disparities have long been a phenomenon in Canada. Examining the extent in magnitude of differences among regional income distributions, particularly low-income outcomes, has had important policy implications. In Canada, a low-income profile across policy regimes is not officially conducted, but it can often be obtained by constructing some cardinal measures—such as the headcount ratio or poverty gap—based on Statistics Canada's low-income cutoffs (LICOs). However, questions have always been raised concerning the robustness of the results, particularly when measurements of the welfare function and low income itself are controversial. The use of such cutoffs entails arbitrary choices, with respect to the proportion of spending on necessities and what constitutes necessities. It can be argued that any revision of these standards would lead to a completely different geographic distribution of low income.

This paper provides a robust way to compare a regional profile of low income in Canada without arbitrarily specifying a low-income line. The empirical analysis is based on the theory of stochastic dominance, which can be used in examining the rankings of income distributions with multiple criteria for a wide range of low-income lines. That is, by comparing the cumulative distribution functions of income between two regions, one may judge whether the choice of a low-income line affects the conclusion about ranking. This avoids using one single line to make a comparison.

Furthermore, this paper also discusses robustness of the results with respect to underlying assumptions made to defining equivalent income: namely, spatial price deflators and equivalence scales. Such scaling factors are required in comparable analysis of income distributions to account for differences in cost-of-living across regions and differences in household composition. That is, in addition to LICO-based price deflators and equivalence scales, we also use an alternative cost-of-living index derived from the market basket measure (MBM) and two other equivalence scales—square root of family size and Organisation for Economic Co­operation and Development (OECD) scales—in the analysis. Finally, since people often compare their relative individual fortune with that of others in similar circumstances, the extent to which the findings are sensitive to the choice of an absolute or a relative concept of low income is also examined.

The main findings are summarized as follows. First, in most cases dominance relations between any two provinces can be determined, and regional low income can be ordered for a wide range of low-income lines. Second, it reveals that rankings of low income based on commonly used LICOs are not robust. An illustration for Newfoundland and Labrador and Ontario shows that the opposite outcomes can be concluded when different lines are chosen. Also, the LICOs only compare the headcount at one low-income line, while ignoring the depth and intensity of low income. The methodology used in this paper offers a more informative and revealing understanding of the distribution of low income. For instance, it is found that Newfoundland and Labrador's low income dominates Alberta at second order, despite the former having a significantly higher LICO-headcount rate than the latter. Third, in 2000, British Columbia ranked the highest in low income, as British Columbia was first-order dominated by all other provinces. Quebec and Manitoba were in the second and third places in the rankings, with Saskatchewan and Alberta fourth, Ontario sixth, and Newfoundland and Labrador and Nova Scotia seventh. New Brunswick and Prince Edward Island were the two provinces with the least low income in Canada.

This paper also demonstrates that dominance results are sensitive to assumptions made to defining equivalent income and the concept of low income. Generally, dominance results are robust to the choice of equivalence scales, while rank reversal occurs when alternative cost-of-living deflators are used. Switching from an absolute to a relative concept of low income has virtually no effect on low-income rankings for British Columbia and the Atlantic provinces, but not in the case for other provinces. The findings urge closer scrutiny on underlying assumptions. Finally, the answer to the question "Where is low income greatest in Canada?" can be confidently referred to British Columbia for the year of 2000. The result is robust for all scales regardless of the choices of low-income lines, cost-of-living factors, equivalence scales and an absolute or a relative concept of low income.