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Deriving Weights for Additivity of Chained Volume Measures in the National Accounts

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  • Dumagan, Jesus C.

Abstract

In current practice in all countries, subaggregate chained volume measures (CVMs) are not weighted and, thus, not additive. However, weights are necessary because without them, nonadditivity permits the nonsensical result that a subaggregate CVM could exceed the aggregate CVM. This paper derives weights to make the sum of weighted subaggregates equal the aggregate (i.e., additivity) and avoid this nonsensical result. The weights are ratios of subaggregate to aggregate chained price deflators that exceed, equal, or fall below 1 depending on relative prices. CVMs in current practice are additive only in the special case of constant relative prices when all weights equal 1. Without weights, they are not additive when relative prices change and, in this case, empirical results show that nonadditivity could significantly distort the sectoral composition of GDP.

Suggested Citation

  • Dumagan, Jesus C., 2011. "Deriving Weights for Additivity of Chained Volume Measures in the National Accounts," Discussion Papers DP 2011-08, Philippine Institute for Development Studies.
    • Handle: RePEc:phd:dpaper:dp_2011-08
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    File URL: https://www.pids.gov.ph/publication/discussion-papers/deriving-weights-for-additivity-of-chained-volume-measures-in-the-national-accounts
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    References listed on IDEAS

    as
    1. Dumagan, Jesus C., 2010. "Computing Additive Chained Volume Measures of GDP Subaggregates," Discussion Papers DP 2010-16, Philippine Institute for Development Studies.
    2. Diewert, W Erwin, 1978. "Superlative Index Numbers and Consistency in Aggregation," Econometrica, Econometric Society, vol. 46(4), pages 883-900, July.
    3. Dumagan, Jesus C., 2011. "Implementing Weights for Additivity of Chained Volume Measures in the National Accounts," Discussion Papers DP 2011-09, Philippine Institute for Development Studies.
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    Cited by:

    1. Patieene Alves Passoni, 2022. "Prezzi relativi e deflazione delle tabelle input-output: implicazioni per l'analisi strutturale (Relative prices and deflation of relative prices and deflation of input-output tables: Implications for," Moneta e Credito, Economia civile, vol. 75(299), pages 307-325.
    2. Dumagan, Jesus C., 2012. "Consistent GDP Aggregation and Purchasing Power Parity," Discussion Papers DP 2012-02, Philippine Institute for Development Studies.
    3. Dumagan, Jesus C., 2011. "Implementing Weights for Additivity of Chained Volume Measures in the National Accounts," Discussion Papers DP 2011-09, Philippine Institute for Development Studies.

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