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Estimating Latent Total Consumption in a Household

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  • Erling Røed Larsen

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    (Statistics Norway)

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    Abstract

    This article presents a new way of estimating latent total consumption in a household that may improve the accuracy of studies into permanent income and consumption inequality. While the frequently used total purchase expenditure in a household is an unbiased estimator of latent total household consumption, it is inoptimal since total purchase expenditure is an un-weighted sum of expenditures that contain measurement errors. We derive a competing estimator, unbiased and variance minimizing, based on a latent variable model. From estimates of error term variance among consumption indicators, we give accurate indicators more weight, and align weights to minimize variance. An advantage of the suggested estimator is that it allows both expenditure and non-expenditure indicators of latent total consumption. We demonstrate empirically how the minimum-variance estimator reduces variance, and find that on Norwegian expenditure data from 1993 the reduction is 44 per cent.

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    Bibliographic Info

    Paper provided by Research Department of Statistics Norway in its series Discussion Papers with number 324.

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    Date of creation: Aug 2002
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    Handle: RePEc:ssb:dispap:324

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    1. Henri Theil & Charles B. Moss, 1999. "Note The measurement of inequality by components of total expenditure," Empirical Economics, Springer, vol. 24(3), pages 559-561.
    2. Attanasio, Orazio P & Browning, Martin, 1995. "Consumption over the Life Cycle and over the Business Cycle," American Economic Review, American Economic Association, vol. 85(5), pages 1118-37, December.
    3. Baxter, Marianne, 1996. "Are Consumer Durables Important for Business Cycles?," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 147-55, February.
    4. Blundell, Richard & Pashardes, Panos & Weber, Guglielmo, 1993. "What Do We Learn About Consumer Demand Patterns from Micro Data?," American Economic Review, American Economic Association, vol. 83(3), pages 570-97, June.
    5. Karl Jöreskog, 1978. "Structural analysis of covariance and correlation matrices," Psychometrika, Springer, vol. 43(4), pages 443-477, December.
    6. Goldberger, Arthur S, 1972. "Structural Equation Methods in the Social Sciences," Econometrica, Econometric Society, vol. 40(6), pages 979-1001, November.
    7. Marianne Baxter & Urban J. Jermann, 1999. "Household Production and the Excess Sensitivity of Consumption to Current Income," NBER Working Papers 7046, National Bureau of Economic Research, Inc.
    8. Kay, J. A. & Keen, M. J. & Morris, C. N., 1984. "Estimating consumption from expenditure data," Journal of Public Economics, Elsevier, vol. 23(1-2), pages 169-181.
    9. Goldberger, Arthur S, 1972. "Maximum-Likelihood Estimation of Regressions Containing Unobservable Independent Variables," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(1), pages 1-15, February.
    10. Caballero, R.J., 1988. "Consumption Puzzles And Precautionary Savings," Discussion Papers 1988_05, Columbia University, Department of Economics.
    11. Saunders, Christopher, 1980. "Measures of Total Household Consumption," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 26(4), pages 351-66, December.
    12. John Sabelhaus & Jeffrey A. Groen, 2000. "Can Permanent-Income Theory Explain Cross-Sectional Consumption Patterns?," The Review of Economics and Statistics, MIT Press, vol. 82(3), pages 431-438, August.
    13. Jørgen Aasness & Erling Røed Larsen, 2002. "Distributional and Environmental Effects of Taxes on Transportation," Discussion Papers 321, Research Department of Statistics Norway.
    14. Lewbel, Arthur, 1996. "Demand Estimation with Expenditure Measurement Errors on the Left and Right Hand Side," The Review of Economics and Statistics, MIT Press, vol. 78(4), pages 718-25, November.
    15. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
    16. Campbell, John Y. & Mankiw, N. Gregory, 1991. "The response of consumption to income : A cross-country investigation," European Economic Review, Elsevier, vol. 35(4), pages 723-756, May.
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    Cited by:
    1. Erling Røed Larsen, 2005. "Distributional Effects of Environmental Taxes on Transportation. Evidence from Engel Curves in the United States," Discussion Papers 428, Research Department of Statistics Norway.
    2. Erling Røed Larsen, 2002. "Consumption Inequality in Norway in the 80s and 90s," Discussion Papers 325, Research Department of Statistics Norway.

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