Estimates of Spatial Prices in India and Their Sensitivity to Alternative Estimation Methods and Choice of Commodities


This paper provides Indian evidence on sub-national PPPs that point to considerable spatial price heterogeneity within the country, based on Indian National Sample Survey (NSS) data. The prices of various commodities have been generated from the household specific unit values obtained from the information on expenditures and quantities from the NSS unit records. This paper shows that the CPD model, proposed in the cross country context, can be adapted to the household context to estimate spatial prices in the intra country context. The proposed CPD based model is shown to be formally equivalent to certain well known fixed weight price indices under certain parametric configurations. The empirical contribution includes a systematic comparison between the spatial price indices from alternative models, namely the CPD and utility based models, and the result that the utility based methods point to a much greater extent of spatial price heterogeneity than is suggested by the CPD type models. The results also record the sensitivity of the spatial price indices to the choice of commodities in the utility based approach. The pairwise comparison of estimates suggests that commodity selection may be more important than model selection in its impact on the spatial price estimates, though the latter is important as well. The study provides estimates of rural–urban differentials in spatial price indices that suggest some interesting differences between the constituent states. The results make a strong case for further research on the topic of sub-national PPPs in the context of large heterogeneous countries.

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Fig. 1


  1. 1.

    See, for example, the results of latest ICP exercise contained in World Bank (2015).

  2. 2.

    See, for example, the evidence summarised in Hill and Syed (2014).

  3. 3.

    See Clements et al. (2006) for a review of ‘stochastic index numbers’ and an extension of Diewert’s work within the context of the CPD framework.

  4. 4.

    Note that in the second stage estimation the dependent variable \( \hat{\phi }_{jrt} \) will have standard errors (se) from step 1. One possibility could have been to incorporate (1/se) as weighting factors in the second step. We have, however, not done it here.

  5. 5.

    As pointed out by Professor Ken Clements, this condition rules out inclusion of items that have unit quality elasticities (with respect to income) in the numeriare region, as \( \lambda_{jt} = 1 \) implies zero weight for such items.

  6. 6.

    We have, however, not done the calculations for other rounds.

  7. 7.

    See World Bank (2015).

  8. 8.

    See Majumder et al. (2012) for a description of the methodology for generating the prices of the various commodities from the household specific unit values obtained from the information on expenditures and quantities from the NSS unit records.

  9. 9.

    To save space, we have reported in Table 4 only the results for NSS round 66.


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This paper draws on joint work with Manisha Chakrabarty of the Indian Institute of Management, Calcutta and Kompal Sinha of Monash University, Melbourne. The authors are grateful to Dr. Sattwik Santra for his help with the STATA programs. They also thank Professor Kenneth W. Clements for insightful remarks on the HRPD model introduced in this paper. Helpful comments from two anonymous referees are gratefully acknowledged. The disclaimer applies.

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Correspondence to Ranjan Ray.


Appendix 1

See Tables 6 and 7.

Table 6 List of commodities used in different methods
Table 7 Abbreviation of names of states and census population

Appendix 2

See Fig. 1.

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Majumder, A., Ray, R. Estimates of Spatial Prices in India and Their Sensitivity to Alternative Estimation Methods and Choice of Commodities. Soc Indic Res 131, 145–167 (2017).

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  • Household Regional Product Dummy Model
  • Spatial price index
  • Sub-national PPP

JEL Classification

  • C12
  • C18
  • D12
  • E30
  • E31