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Measuring Health Inequality with Realization of Conditional Potential Life Years (RCPLY)


Health inequalities that are avoidable and unfair are considered more relevant for policy intervention. Recent work has improved on using life years (LY) to measure longevity inequality by developing a health indicator—the Realization of Potential Life Years (RePLY)—to adjust for unavoidable mortality risks. This approach, however, estimates unavoidable mortality risks by using the globally lowest mortality risks for each age–sex group of any country, and thus, benchmarking countries at different levels of development against the same unavoidable mortality risks without considering their heterogeneity. The current paper proposes to attempt to control for a country’s national resources in estimating their (conditional) avoidable mortality risks. This allows the construction of a new health indicator—Realization of Conditional Potential Life Years (RCPLY). This paper presents and contrasts the empirical results for LY, RePLY and RCPLY based on life tables for 136 countries from the year 2009.

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  1. 1.

    Health inequality due to risky behaviors such as smoking and drinking could be considered as avoidable but not necessarily unfair if people conduct those activities at free will and with the full knowledge of the consequences. See Fleurbaey and Schokkaert (2009) for a more detailed discussion.

  2. 2.

    For instance, Allison and Foster (2004) use self-reported health status data from the US National Health Interview Survey to examine health inequality in the US.

  3. 3.

    For discussions on the RePLY measure, see Castelli and Nizalova (2011), Norheim (2010) and Rodriguez and Lopez-Valcarcel (2011).

  4. 4.

    The actual population can be used to scale up the stationary population if one is interested in measuring average health or health inequality for a multi-country region or the world as a whole.

  5. 5.

    We do not use constant international dollars because of the lack of data.

  6. 6.

    This method is like the DEA method used in this paper, except that it does not involve any input and production function.

  7. 7.

    Here q is a conditional probability as it is conditional on the person having survived from birth till age x. However, we simply use the term “probability” rather than “conditional probability” throughout the paper so that we can preserve the word “conditional” for cases where the probabilities are measured after controlling for income.

  8. 8.

    In life tables, life expectancy at age x in country k, \(e_{xk}\), is defined as the number of further years a person is expected to live if the person has lived to age x.

  9. 9.

    The formulas for these indexes are provided as supplementary material to the paper.

  10. 10.

    Japan, however, does not have the highest survival probabilities for some age–sex groups.

  11. 11.

    In Petrie and Tang (2014), we achieve the same by developing an indicator that focuses on health-shortfall instead of health-attainment as in the current paper.

  12. 12.

    We would like to thank a reviewer for clarifying this.


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The authors would like to acknowledge helpful comments by Roberto Zelli on an earlier version of this paper. Kam Ki Tang would also like to acknowledge the support by a grant from Australian Research Council (DP0878752).

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Correspondence to Kam Ki Tang.

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Petrie, D., Tang, K.K. & Rao, D.S.P. Measuring Health Inequality with Realization of Conditional Potential Life Years (RCPLY). Soc Indic Res 122, 21–44 (2015).

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  • Mortality risk
  • Avoidable deaths
  • Longevity inequality
  • Data envelopment analysis