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On the Estimation of Nonlinearly Aggregated Mixed Models

Author

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  • Tommaso Proietti

    (Dipartimento di Scienze Statistiche, Udine)

Abstract

The article proposes an iterative algorithm for the estimation of fixed and random effects of a nonlinearly aggregated mixed model. The latter arises when an additive Gaussian model is formulated at the disaggregate level on a nonlinear transformation of the responses, but information is available in aggregate form. The nonlinear transformation breaks the linearity of the aggregate model, yielding a nonlinear tight observational constraint. The algorithm rests upon the sequential linearization of the nonlinear aggregation constraint around proposals that are iteratively updated until convergence. Likelihood inferences on the hyperparameters are also discussed. As a by product we provide a solution to the problem of disaggregating over the units of analysis the aggregate responses, enforcing the nonlinear observational constraints. Illustrations are provided with reference to the temporal disaggregation problem, concerning the distribution of annual time series flows to the quarters making up the year.

Suggested Citation

  • Tommaso Proietti, 2004. "On the Estimation of Nonlinearly Aggregated Mixed Models," Econometrics 0411012, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpem:0411012
    Note: Type of Document - pdf; pages: 19
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/em/papers/0411/0411012.pdf
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    References listed on IDEAS

    as
    1. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
    2. Litterman, Robert B, 1983. "A Random Walk, Markov Model for the Distribution of Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(2), pages 169-173, April.
    3. Litterman, Robert B, 1983. "A Random Walk, Markov Model for the Distribution of Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(2), pages 169-173, April.
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    Citations

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    Cited by:

    1. Cecilia Frale, Serena Teobaldo, Marco Cacciotti, Alessandra Caretta, 2013. "A Quarterly Measure Of Potential Output In The New European Fiscal Framework," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - Italian Review of Economics, Demography and Statistics, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 67(2), pages 181-197, April-Jun.
    2. Moauro, Filippo, 2010. "A monthly indicator of employment in the euro area: real time analysis of indirect estimates," MPRA Paper 27797, University Library of Munich, Germany, revised 30 Dec 2010.
    3. Proietti, Tommaso, 2008. "Structural Time Series Models for Business Cycle Analysis," MPRA Paper 6854, University Library of Munich, Germany.
    4. SILVESTRINI, Andrea & VEREDAS, David, 2005. "Temporal aggregation of univariate linear time series models," CORE Discussion Papers 2005059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Sieds, 2013. "Complete Volume LXVII n.2 2013," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - Italian Review of Economics, Demography and Statistics, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 67(2), pages 1-197, April-Jun.
    6. Marco Cacciotti & Cecilia Frale & Serena Teobaldo, 2013. "A new methodology for a quarterly measure of the output gap," Working Papers 6, Department of the Treasury, Ministry of the Economy and of Finance.
    7. Tommaso Proietti, 2006. "Temporal disaggregation by state space methods: Dynamic regression methods revisited," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 357-372, November.
    8. Cecilia Frale & Massimiliano Marcellino & Gian Luigi Mazzi & Tommaso Proietti, 2008. "A Monthly Indicator of the Euro Area GDP," Economics Working Papers ECO2008/32, European University Institute.
    9. Proietti, Tommaso, 2008. "Estimation of Common Factors under Cross-Sectional and Temporal Aggregation Constraints: Nowcasting Monthly GDP and its Main Components," MPRA Paper 6860, University Library of Munich, Germany.
    10. Cecilia Frale, "undated". "Do Surveys Help in Macroeconomic Variables Disaggregation and Estimation?," Working Papers wp2008-2, Department of the Treasury, Ministry of the Economy and of Finance.

    More about this item

    Keywords

    Temporal and spatial disaggregation; Best linear unbiased prediction; Box-Cox transformation; Constrained nonlinear optimization.;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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