District-level poverty estimation: a proposed method

Abstract

This paper develops a method of estimating micro-level poverty in cases where data are scarce. The method is applied to estimate district-level poverty using the household level Indian national sample survey data for two states, viz., West Bengal and Madhya Pradesh. The method involves estimation of state-level poverty indices from the data formed by pooling data of all the districts (each time excluding one district) and multiplying this poverty vector with a known weight matrix to obtain the unknown district-level poverty vector. The proposed method is expected to yield reliable estimates at the district level, because the district-level estimate is now based on a much larger sample size obtained by pooling data of several districts. This method can be an alternative to the “small area estimation technique” for estimating poverty at sub-state levels in developing countries.

Keywords:

• district-level poverty
• scarce data
• bootstrap
• extraneous information
• sub-sample estimate

JEL Classification :

• C13
• C42
• I32

Acknowledgements

The authors gratefully acknowledge the help offered by Mr Subhabrata Sarkar in arriving at a particular solution somewhere in the paper. The usual disclaimer applies.

Notes

See 15 35.

A subgroup decomposable poverty measure is the one for which the overall measure can be written as the population share- weighted sum of poverty measures of the individual subgroups (see 4 13).

See Appendix A.1 for proof of non-singularity of A.

The method is applicable to situations where there are a large number of districts in a state so that leaving out one district will not cause much change in the state level poverty estimate. The implicit assumption here is that the characteristics of the districts are not extremely divergent.

The method is different from the leave-one-out Jacknife method for testing robustness (see 9 18 19 30 32).

For surveys based on a complicated sample design, analytical derivation of the formula for sampling variance of the estimator of a parameter of interest is often difficult. The technique of IPNS eases the problem of estimation of standard errors of survey estimates in such cases. See 6 20 23 33 for a description of the IPNS technique.

See 10 for a description of bootstrap method. See 7 16 25 31 for application of bootstrap method in the analysis of poverty.

Since population is the only auxiliary variable that is required in this methodology, empirical comparison with other SAE methods have not been done, as the data requirement for these methods is much higher.

Source: http://planningcommission.nic.in/reports/articles/ncsxna/ar_pvrty.htm, Planning Commission, Government of India.

RSE is computed as the ratio of the standard error and the point estimate.