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On the Estimation of Lower and Upper Bounds of Poverty Line: An Illustration with Indian Data

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Abstract

This paper introduces an iterative methodology for the estimation of lower and upper bounds of poverty line. A poverty index based on the concept of fuzzy poverty line has also been introduced. Empirical illustrations are provided with Indian data for 2004–2005 and 2009–2010. It has been observed that for most of the states of India the government estimates of the poverty lines lie in between these two bounds. Poverty rates have been found to decline regardless whether lower or upper bounds of poverty lines is considered. Fuzzy poverty index has also declined.

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Notes

  1. Readers interested in the literature of Indian poverty estimation are referred to Dandekar and Rath (1971a), Dandekar and Rath (1971b), Government of India (1979), Government of India (1993), Dev and Ravi (2007), Deaton and Drèze (2009), Patnaik (2010), Manna (2007), Manna et al. (2009), Pal and Bharati (2009), Government of India (2011), Pal and Bharati (2013), Manna (2012), Vaidyanathan (2013) etc.

  2. For further details of the Tendulkar committee methodology, see Swaminathan (2010) and Pathak and Mishra (2015).

  3. Bangladesh household survey on consumer and expenditure is conducted by the Bangladesh Bureau of Statistics (BBS). For application of this method on Pakistan one can use the Household Integrated Economic Survey (HIES) data set.

  4. Following recommendations of task force (1) heavy workers include persons engaged in cultivation, agricultural labor, mining and quarrying and construction; (2) moderate workers include persons engaged in livestock, forestry, hunting, plantations, orchards and allied activities, manufacturing, servicing and repairing; (3) sedentary workers include persons engaged in trade and commerce, transport, storage, communication and other allied services. Unemployed individuals are also assumed to be sedentary workers. Note that, calorie requirement also differs with the height and weight of an individual. Incorporating, such additional informations will give better estimates of the norm. However, NSSO does not collect such data.

  5. Creating a subgroup of population automatically incorporates a bias in the sample estimates of the parameters. However, this bias is negligible and we may ignore it (Maiti and Pal 1988).

  6. In order to compute \(f_i\) we use individual level informations of NSSO data. For each individual’s this survey contains informations on age and sex. In order to determine the activity status (heavy/moderate/sedentary) we use the National Classification of Occupation (NCO) collected by the Directorate General of Employment and Training in Ministry of Labour. For further details on computations of calorie norms interested readers are referred to Manna (2007).

  7. Originally this method was suggested by Ravallion and Bidani (1994). However, the variable household size and its square was not present. This has been mainly included to consider the scale effects for households of different sizes. In the empirical analysis we find that even if we ignore this factor our result remains more or less same.

  8. In the classical set theory an element may either fully belong in a set or is completely absent in that set. However, in the context of fuzzy set theory some elements in a set may belong partially. Or in other words there might exist some elements whose association to the set might be fuzzy. The degree of association of an object is captured using a fuzzy membership function. For further details see Zadeh (1965).

  9. This is done simply by multiplying expenditure for the 365 days scheduled items, by the factor 30/365.

  10. In the 66th round consumer expenditure survey, two types of schedules of enquiry namely Schedule 1.0 Type 1 and Schedule 1.0 Type 2; were used to collect data. The schedules differs only in terms of specification of the recall periods for reporting consumption. Type 1 schedule is exactly same as the NSSO 61st round. In the Schedule Type 2 the very frequently used items (Edible oil; egg, fish and meat; vegetables, fruits, spices, beverages and processed foods; pan, tobacco and intoxicants) are collected on the basis of a recall period of seven days. In order to maintain the comparability of the 61st and 66th round, we consider schedule type 1 data.

  11. Note that in the first step we consider a parametric approach for the estimation of FEI lines. However, from the second step onwards in each iteration we rely on the CBN2 approach. We repeat the process 10 times and obtain a precision level of \({{ FPL}}_i-{{ FPL}}_{i-1}< 10^{-3}\); where \({{ FPL}}_i\) is the FPL obtained at i th (i being a strictly positive integer and \(i>1\)) iteration.

  12. Note that FEI is estimated on the basis of a parametric approach. In order to remain focused, we have dropped the regression results.

  13. The commodity bundle specified in Table 3, has been normalized by the calorie norm specified in Table 2.

  14. In Assam, Bihar and Haryana considering \(z_l\) as the poverty line, the decline of poverty cannot be statistically validated for any of the FGT measures. In Madhya Pradesh, this validation has not been observed only for the squared poverty gap.

  15. We are thankful to an anonymous referee for pointing our attention in this direction.

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Acknowledgements

We sincerely acknowledge two anonymous referees for comments on an earlier version of this paper. This paper is a part of PhD thesis of Sandip Sarkar awarded by the Indian Statistical Institute in 2015. The usual disclaimer applies.

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  1. Centre for Training and Research in Public Finance and Policy, Centre for Studies in Social Science, Kolkata, India

    Sandip Sarkar

  2. Economic Research Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata, 700108, India

    Manoranjan Pal

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Correspondence to Sandip Sarkar.

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Sarkar, S., Pal, M. On the Estimation of Lower and Upper Bounds of Poverty Line: An Illustration with Indian Data. Soc Indic Res 138, 901–924 (2018). https://doi.org/10.1007/s11205-017-1687-0

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