Abstract
The present paper is a selective overview, very considerably based on work in which the author himself has been involved, of the difficulties which can arise in the measurement of poverty and inequality when one compares populations of differing size. The paper begins with certain problems attending the measurement of poverty when the overall population size is fixed but the numbers of the poor are permitted to vary: one discovers a certain commonality of outcomes between Derek Parfit’s quest for a satisfactory theory of wellbeing and the economist’s quest for a satisfactory measure of poverty. Complications arising from both the poverty and inequality rankings of distributions when the aggregate size of the population is allowed to vary are also investigated. It is suggested in the paper that, from the perspectives of both logical consistency and ethical appeal, there are problems involved in variable population comparisons of poverty and inequality which deserve to be taken note of and enquired into.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Axioms for variable population poverty comparisons are less commonly present in the literature than axioms for fixed population comparisons. Here—following on the suggestion of one of the Editors of this special issue—are some simple numerical examples which should help to illustrate the import of these axioms. In everything that follows, we shall take it that the poverty line is given by z = 2. Suppose x = (1, 3) and y = (1, 1, 3, 3), then it is clear that y is just a 2-replication of x, and Replication Invariance requires that P(x; z) = P(y; z), whereas Replication Scaling requires that P(y; z) > P(x; z). If x = (1, 3) and y = (1, 1, 3), then Weak Poverty Growth requires that P(x; z) < P(y; z). If x = (1, 3) and y = (1, 3, 4), then Non-Poverty Growth requires that P(x; z) > P(y; z). If x = (1, 3) and y = (1, 3, 4), then Weak Population Focus requires that P(x; z) < P(y; z), while Population Focus requires that P(x; z) = P(y; z). If x = (1, 3) and y = (1, 5, 7), then Comprehensive Focus requires that P(x; z) = P(y; z). Finally, if x = (0, 0) and y = (0, 0, 3), then Maximality requires that P(x; z) > P(y; z).
- 2.
For readers who are relatively unfamiliar with axioms for variable population inequality comparisons, here, again, are a few simple arithmetical examples designed to illustrate the import of the axioms. Suppose x = (1, 3) and y = (1, 1, 3, 3), then since y is just a 2-replication of x, Replication Invariance will demand that I(x) = I(y). If x = (0, 0, 3) and y = (0, 0, 3, 3)—that is, y has been derived from x (an extremal distribution) by the addition of a person with the same income as that of the richest individual in x—then Upper Mole Monotonicity will require that I(y) < I(x). If x = (3, 3, 3, 3)—that is, x is a perfectly equal distribution of incomes—then Lower-Bound Normalization will require that I(x) = 0. Finally, if x = (0, 0, 3) and y = (0, 0, 0, 3)—that is, y has been derived from x (an extremal distribution) by the addition of a person with zero income—then Upper-Bound Normalization will require that I(y) = I (x).
- 3.
This, obviously, is also true for the well-known P α>0 family of poverty measures due to Foster et al. (1984). A distinguished member of this family is the P 2 index, given, for all x ∈ X and z ∈ S, as we have seen earlier (in Sect. 5.3), by: \( P_{2} ({\mathbf{x}};z) = {{H}}({\mathbf{x}};z)[{{I}}^{2} ({\mathbf{x}};z) + (1 - {{I}}({\mathbf{x}};z))^{2} {{C}}^{{P}} ({\mathbf{x}};z)] \). This is a measure of ‘how poor’ a society is. A corresponding measure of the ‘quantity of poverty’ in a society would be given by: P 2′(x;z) = A(x;z)[I 2(x;z) + (1 − I(x;z))2 C P(x;z)]: all one has to do to derive P 2′ from P 2 is to replace the headcount ratio by the aggregate headcount.
References
Anand, S. (1977). Aspects of poverty in Malaysia. Review of Income and Wealth, 23, 1–16.
Arriaga, E. E. (1970). A new approach to the measurement of urbanization. Economic Development and Cultural Change, 18, 206–218.
Bossert, W. (1990). Population replications and ethical poverty measurement. Mathematical Social Sciences, 20, 227–238.
Broome, J. (1996). The welfare economics of population. Oxford Economic Papers, 48, 177–193.
Chakravarty, S., Kanbur, S. R., & Mukherjee, D. (2006). Population growth and poverty measurement. Social Choice and Welfare, 26, 471–483.
Chateauneuf, A., & Moyes, P. (2006). A non-welfarist approach to inequality measurement, poverty and well-being. In M. McGillivray (Ed.), Inequality. Houndsmill (Basingstoke, Hampshire) and New York: Palgrave Macmillan.
Donaldson, D., & Weymark, J. A. (1986). Properties of fixed population poverty indices. International Economic Review, 27, 667–688.
Foster, J., Greer, J., & Thorbecke, E. (1984). A class of decomposable poverty measures. Econometrica, 52, 761–766.
Hassoun, N. (2010). Another mere addition paradox? A problem for some common poverty indexes in variable populations. WIDER Working Paper 2010/120. UNUI_WIDER, Helsinki. Available online: http://www.wider.unu.edu/publications/working-papers/2010/en_GB/wp2010-120/
Hassoun, N., & Subramanian, S. (2011). An aspect of variable population poverty comparisons, in press, corrected proof: Journal of Development Economics. Available online August 2011, http://dx.doi.org/10.1016/j.jdeveco.2011.07.004
Kanbur, S. R., & Mukherjee, D. (2007). Premature mortality and poverty measurement. Bulletin of Economic Research, 19, 339–359.
Kundu, A., & Smith, T. E. (1983). An impossibility theorem on poverty indices. International Economic Review, 24, 423–434.
Parfit, D. (1984). Reasons and persons. Oxford: Clarendon Press.
Pattanaik, P. K., & Sengupta, M. (1995). An alternative axiomatization of Sen’s poverty measure. Review of Income and Wealth, 41, 73–80.
Paxton, J. (2003). A poverty outreach index and its application to microfinance. Economics Bulletin, 9, 1–10.
Reddy, S. G., & Miniou, C. (2007). Has world poverty really fallen? Review of Income and Wealth, 53, 484–502.
Sen, A. K. (1976). Poverty: An ordinal approach to measurement. Econometrica, 33, 219–231.
Shorrocks, A. F. (2005). Inequality values and unequal shares. Helsinki: UNU-WIDER. Available online at: http://www.wider.unu.edu/conference/conference-2005-5/conference-2005.5.htm
Subramanian, S. (2000). Poverty measurement and the repugnant conclusion. S. Guhan memorial series discussion paper 3. Madras Institute of Development Studies, Chennai.
Subramanian, S. (2002a). An elementary interpretation of the Gini inequality index. Theory and Decision, 52, 375–379.
Subramanian, S. (2002b). Counting the poor: An elementary difficulty in the measurement of poverty. Economics and Philosophy, 18, 277–285.
Subramanian, S. (2005a). Fractions versus whole numbers: On headcount comparisons of poverty across variable populations. Economic and Political Weekly, 40, 4625–4628.
Subramanian, S. (2005b). Headcount Poverty Comparisons, International Poverty Centre One Pager No. 18, United Nations Development Programme: Brasilia, Brazil.
Subramanian, S. (2006). Poverty measurement and theories of beneficience. In: Rights deprivation, and disparity: Essays in concepts and measurement. Delhi: Oxford University Press.
Subramanian, S. (2010). Variable populations and inequality-sensitive ethical judgments. In B. Basu, B. K. Chakrabarti, S. R. Chakravarti, & K. Gangopadhyay (Eds.), Economics of games, social choices and quantitative techniques. Milan: Springer.
Subramanian, S. (2011a). On a Normalized and replication-invariant “threshold” inequality measure. Journal of Economic Theory and Social Development, 1.
Subramanian, S. (2011b). The focus axiom and poverty: On the co-existence of precise language and ambiguous meaning in economic measurement. Economics: The Open-Access, Open Assessment E-Journal, 6, 2012-8. Available online at: http://dx.doi.org/10.5018/economicsejournal.ja.2012-8
Sundaram, K., & Tendulkar, S. D. (2003). Poverty among social and economic groups in India in the 1990s. Economic and Political Weekly, 38, 5263–5276.
Acknowledgment
Over the years, I have benefited from helpful advice on the subject of this paper from several scholars, and without intending to implicate any of them, I would like to acknowledge my debt to Kaushik Basu, John Broome, Satya Chakravarty, Nicole Hassoun, Satish Jain, D. Jayaraj, Sripad Motiram, Manoj Panda, Prasanta Pattanaik, Sanjay Reddy, and John Weymark. Additionally, the paper has gained from suggestions made by the Guest Editors of this Special Issue. I am also grateful to UNU-WIDER, Helsinki, where an earlier version of this paper was written in the course of a Sabbatical Fellowship, and where it was published as UNU-WIDER Working Paper No. 2012/53.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer Science+Business Media Singapore
About this chapter
Cite this chapter
Subramanian, S. (2017). Variable Populations and the Measurement of Poverty and Inequality: A Selective Overview. In: Krishna, K., Pandit, V., Sundaram, K., Dua, P. (eds) Perspectives on Economic Development and Policy in India. India Studies in Business and Economics. Springer, Singapore. https://doi.org/10.1007/978-981-10-3150-2_5
Download citation
DOI: https://doi.org/10.1007/978-981-10-3150-2_5
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-3149-6
Online ISBN: 978-981-10-3150-2
eBook Packages: Economics and FinanceEconomics and Finance (R0)