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Linear regression using both temporally aggregated and temporally disaggregated data: Revisited

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  • Qian, Hang

Abstract

This paper discusses regression models with aggregated covariate data. Reparameterized likelihood function is found to be separable when one endogenous variable corresponds to one instrument. In that case, the full-information maximum likelihood estimator has an analytic form, and thus outperforms the conventional imputed value two-step estimator in terms of both efficiency and computability. We also propose a competing Bayesian approach implemented by the Gibbs sampler, which is advantageous in more flexible settings where the likelihood does not have the separability property.

Suggested Citation

  • Qian, Hang, 2010. "Linear regression using both temporally aggregated and temporally disaggregated data: Revisited," MPRA Paper 32686, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:32686
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    File URL: https://mpra.ub.uni-muenchen.de/32686/1/MPRA_paper_32686.pdf
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    References listed on IDEAS

    as
    1. Koop,Gary & Poirier,Dale J. & Tobias,Justin L., 2007. "Bayesian Econometric Methods," Cambridge Books, Cambridge University Press, number 9780521671736, March.
    2. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2006. "Predicting volatility: getting the most out of return data sampled at different frequencies," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 59-95.
    3. Christian Gourieroux & Alain Monfort, 1981. "On the Problem of Missing Data in Linear Models," Review of Economic Studies, Oxford University Press, vol. 48(4), pages 579-586.
    4. Palm, F. C. & Nijman, T. E., 1982. "Linear regression using both temporally aggregated and temporally disaggregated data," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 333-343, August.
    5. Geweke, John F, 1978. "Temporal Aggregation in the Multiple Regression Model," Econometrica, Econometric Society, vol. 46(3), pages 643-661, May.
    6. Andreou, Elena & Ghysels, Eric & Kourtellos, Andros, 2010. "Regression models with mixed sampling frequencies," Journal of Econometrics, Elsevier, vol. 158(2), pages 246-261, October.
    7. John F. Geweke, 1995. "Bayesian inference for linear models subject to linear inequality constraints," Working Papers 552, Federal Reserve Bank of Minneapolis.
    8. Hsiao, Cheng, 1979. "Linear regression using both temporally aggregated and temporally disaggregated data," Journal of Econometrics, Elsevier, vol. 10(2), pages 243-252, June.
    9. Dagenais, Marcel G., 1973. "The use of incomplete observations in multiple regression analysis : A generalized least squares approach," Journal of Econometrics, Elsevier, vol. 1(4), pages 317-328, December.
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    More about this item

    Keywords

    Aggregated covariate; Maximum likelihood; Bayesian inference;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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