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An EM Algorithm for Modelling Variably-Aggregated Demand

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Listed:
  • Grose, S.
  • McLaren, K.

Abstract

This paper develops an EM algorithm for the estimation of a consumer demand system involving variably aggregated data. The methodology is based on the observation that more highly aggregated data does in fact contain information on the finer subcategories. It is therefore possible, under certain simplifying assumptions, to derive the distribution of the unobserved fine-level expenditures conditional on the observed but more highly aggregated data. The expectation of the log-likelihood is then taken with respect to this conditional distribution. Under the assumption of multivariate normality both these steps can be performed analytically, resulting in an EM criterion that can be maximised iteratively at comparatively little cost. The technique is applied to an ABS dataset containing historical information relating to private final consumption expenditures on up to 18 commodities.

Suggested Citation

  • Grose, S. & McLaren, K., 2000. "An EM Algorithm for Modelling Variably-Aggregated Demand," Monash Econometrics and Business Statistics Working Papers 2/00, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2000-2
    as

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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2000/wp2-00.pdf
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    References listed on IDEAS

    as
    1. de Boer, P. M. C. & Harkema, R., 1986. "Maximum likelihood estimation of sum-constrained linear models with insufficient observations," Economics Letters, Elsevier, vol. 20(4), pages 325-329.
    2. Fry, Jane M. & Fry, Tim R. L. & McLaren, Keith R., 1996. "The stochastic specification of demand share equations: Restricting budget shares to the unit simplex," Journal of Econometrics, Elsevier, vol. 73(2), pages 377-385, August.
    3. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
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    More about this item

    Keywords

    EM Algorithm; Singular demand systems; Linear expenditure system; Missing data.;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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