Poverty comparisons with common relative poverty lines

ABSTRACT

Relative poverty lines are increasingly being used in poverty comparison studies. Existing methods assume that the distributions being compared are distinct with independent relative poverty lines. However, this practice may be problematic when comparing two subgroups of a population. We follow up on a recent proposal for the usage of common relative poverty lines in such cases, and develop a test for comparing poverty between subgroups of a single population, using inequality restrictions. Monte Carlo experiments are conducted in order to examine the size and power of our proposed test. We illustrate our procedure using some U.S. household income data.

KEYWORDS:

• Bootstrap inference
• Income distribution
• Relative poverty

MATHEMATICS SUBJECT CLASSIFICATION:

• 91B82
• 62F03

Notes

1 For example, the Organisation for Economic Co-operation and Development (OECD) often reports poverty rates for its member countries by setting poverty lines to 40%, 50%, and 60% of the national median income level.

2 Such poverty measure estimates themselves require an estimate of the underlying poverty line and therefore the sampling variance of the poverty line must be taken into consideration.

3 The restrictions on the individual deprivation function follow from the “focus axiom” (see Foster, 1984).

4 If one is interested in a common mean-based poverty line, then z = cμ where . In this case, the asymptotic expression (1(1) ) would need to be changed accordingly.

5 The consistency of such estimators has been rigorously established in the literature (see, e.g., Li and Racine, 2007).

6 Zheng (2001) suggested using the approach for testing a similar type of hypothesis (but under the assumption of distinct relative poverty lines). Stengos and Thompson (2012) also use it in testing for bivariate stochastic dominance.

7 As discussed earlier, quantile-based poverty lines require density estimation in calculating the covariance structure. We use kernel estimation with a Gaussian kernel and a “rule-of-thumb” bandwidth (see, e.g., Li and Racine, 2007, Ch. 1).

8 More details can be found on the Institute for Research on Poverty website: http://www.irp.wisc.edu