Endnotes

View the most recent version.

1. See also, for example, Lee 2000 and National Council of Welfare 2004; comparisons based on measures other than headcount or poverty gap can also be seen, for example, in Osberg and Xu 1999, who compare inter-provincial poverty in Canada using the modified Sen index of poverty intensity.
2. See, for example, Atkinson 1987, Foster and Shorrocks 1988, Jenkins and Lambert 1997 and Zheng 2000. Statistical issues on stochastic dominance can be found, for example, in Bishop, Formby and Smith 1991, Bishop, Formby and Thistle 1992, Kaur, Prakasa Rao and Singh 1994 and Anderson 1996 for discussing test of the ordinates of the curves, and in Davidson and Duclos 2000 for deriving the limiting distribution of estimated ordinates. Empirical studies using the technique of stochastic dominance can be seen, for example, in Madden and Smith 2000, Sahn 2001 and Anderson 2003. Canadian studies that apply a similar method to make a robust regional comparison include Xu and Osberg 1998, who developed a testing procedure for deprivation dominance with application to four regions in Canada.
3. That is, the low-income measure is a fixed percentage (50%) of median needs-adjusted income. The market-basket measures, on the other hand, are estimated costs of a specific basket of goods and services related to food, clothing and footwear, shelter and transportation; and the costs are calculated for 29 community sizes in the 10 provinces and another 19 specific urban centres. See Human Resources Development Canada (2003) for details.
4. That is, the FGT measures satisfy Sen's 1976 Monotonicity Axiom for a >0, and the Transfer Axiom for a >1.
5. See Davidson and Duclos 2000, 2006 for a more in-depth discussion about different hypothesis testing.
6. This is opposed to a union-intersection test (Bishop, Formby and Smith 1991, for example), where dominance of B over A can be declared if there exists at least one x where DA(x)-DB(x) is rejected.
7. That is, we have both positive and negative t statistics at significance level.
8. That is, the equivalence scale for the calculation of the low-income cutoff (LICO) is 1 for people living alone; 1.217 for families of 2; 1.516 for families of 3; 1.891 for families of 4; 2.153 for families of 5; 2.388 for families of 6; and 2.623 for families of >=7. The scaling factor used in the low-income cutoff to adjust prices to its large-city equivalent (population 500,000 and above) is 1.529 for those in rural areas; 1.336 in urban areas of population <30000; 1.197 in urban areas of 30,000 to 99,999; and 1.182 in urban areas of 100,000 to 499,000.
9. The OECD-modified scale assigns a value of 1 to the first household member, 0.5 to each additional adult member and 0.3 to each child.
10. The other potential price indices across regions is the consumer price index (CPI), which measures price changes by comparing, through time, the cost of a fixed basket of commodities. The CPI is calculated for the 10 provinces and for an additional 16 urban centres.
11. See Human Resources Development Canada 2003 for more details.
12. The use of relative poverty lines may further complicate the testing procedure, as the calculation of sampling variances for estimates of relative poverty measures now includes a stochastic component of the poverty line, which needs to be estimated from samples at the same time (see Preston 1995, Zheng 2001) for detailed discussion about inference for poverty measures with relative poverty line). In this paper, for simplicity, the sampling variations of estimated poverty lines are ignored.
13. Generally, for un-weighted data, one can use a reference by Kakwani 1993 to calculate the asymptotic standard errors for the FGT poverty measures. However, the Survey of Labour and Income Dynamics has a complicated design; this paper, therefore, follows a reference (Duclos and Araar 2006, chap. 16) to take into account the sampling design of the survey.
14. Bootstrap estimates of standard errors (not shown) for the lower/upper thresholds are computed based on 50 replications from the original sample with replacement.
15. That is, we first arbitrarily select a base region (i.e., Toronto in this example), and then the cost-of-living scaling factors for other regions can be obtained by the ratio of costs of basket for Toronto and costs of basket for the region in comparison. As a result, equivalent incomes are adjusted to a Toronto-equivalent basis.
16. Income is still spatial price-adjusted using the low-income cutoff cost-of-living index.
17. Rankings for the estimates of poverty-gap ratio and squared poverty-gap ratio are offered in Appendix Tables A1 and A2, respectively.
18. There are two cases when a Z is marked. First we fail to reject the null of non-dominance everywhere in the domain of interest (i.e., the two distributions coincide together). Second there are at least two closed intervals in the domain of interest and the minimum t statistic is significant in both intervals, but with a different sign (i.e., the two distributions crossed). In theory, dominance results may be obtained at higher orders (>3) condition. For practical reasons, we limit tests up to the third-order condition.
19. Note that Quebec only dominates British Columbia over a relatively limited range ($0+, $8,641) at the first order. However, the range of dominance extends to ($0+, $17,884) at the second-order condition.
20. The results are robust, even when the other equivalence scale (i.e., the modified OECD scale) is used (not shown). Tests of poverty dominance based on the OECD scale show great resemblance to those obtained from the 'square root family size' equivalence scale.
21. The values of 15% and 70% of the provincial median income are roughly close to the restricted domain ($5,000, $20,000) defined in the base-case model.