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Measurement Error with Accounting Constraints: Point and Interval Estimation for Latent Data with an Application to U.K. Gross Domestic Product


  • Richard J. Smith
  • Martin R. Weale
  • Steven E. Satchell


An econometric methodology is proposed for reconciling inaccurate measures of latent data which are subject to accounting constraints. The method deals with the case in which the measurement errors are serially correlated, generalizing previous contributions. A class of efficient estimators are derived for the latent data. Consistent estimators for the weight matrices applied to the observed information based on a linear regression procedure are obtained together with confidence interval estimators for these weight matrices. Approximate confidence intervals are suggested for the latent data themselves together with specification tests for the assumptions underlying the procedure. An application of the proposed method is made to U.K. Gross Domestic Product in constant prices for 1958Q1–1989Q4.

Suggested Citation

  • Richard J. Smith & Martin R. Weale & Steven E. Satchell, 1998. "Measurement Error with Accounting Constraints: Point and Interval Estimation for Latent Data with an Application to U.K. Gross Domestic Product," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(1), pages 109-134.
  • Handle: RePEc:oup:restud:v:65:y:1998:i:1:p:109-134.

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    Cited by:

    1. Martín Almuzara & Gabriele Fiorentini & Enrique Sentana, 2023. "Aggregate Output Measurements: A Common Trend Approach," Advances in Econometrics, in: Essays in Honor of Joon Y. Park: Econometric Methodology in Empirical Applications, volume 45, pages 3-33, Emerald Group Publishing Limited.
    2. Mazzi Gian Luigi & Mitchell James & Carausu Florabela, 2021. "Measuring and Communicating the Uncertainty in Official Economic Statistics," Journal of Official Statistics, Sciendo, vol. 37(2), pages 289-316, June.
    3. Aruoba, S. Borağan & Diebold, Francis X. & Nalewaik, Jeremy & Schorfheide, Frank & Song, Dongho, 2016. "Improving GDP measurement: A measurement-error perspective," Journal of Econometrics, Elsevier, vol. 191(2), pages 384-397.
    4. Martín Almuzara & Dante Amengual & Gabriele Fiorentini & Enrique Sentana, 2022. "GDP Solera. The Ideal Vintage Mix," Working Papers wp2022_2204, CEMFI.
    5. Tincho Almuzara & Dante Amengual & Enrique Sentana, 2017. "Normality Tests for Latent Variables," Working Papers wp2018_1708, CEMFI.
    6. Martín Almuzara & Dante Amengual & Enrique Sentana, 2019. "Normality tests for latent variables," Quantitative Economics, Econometric Society, vol. 10(3), pages 981-1017, July.
    7. Gary Koop & Stuart McIntyre & James Mitchell, 2018. "UK regional nowcasting using a mixed frequency vector autoregressive model," Working Papers 1805, University of Strathclyde Business School, Department of Economics.
    8. Dennis J. Fixler & Jeremy J. Nalewaik, 2007. "News, noise, and estimates of the \"true\" unobserved state of the economy," Finance and Economics Discussion Series 2007-34, Board of Governors of the Federal Reserve System (U.S.).
    9. Ammi, Mehdi & Arpin, Emmanuelle & Allin, Sara, 2021. "Interpreting forty-three-year trends of expenditures on public health in Canada: Long-run trends, temporal periods, and data differences," Health Policy, Elsevier, vol. 125(12), pages 1557-1564.
    10. Gary Koop & Stuart McIntyre & James Mitchell, 2020. "UK regional nowcasting using a mixed frequency vector auto‐regressive model with entropic tilting," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 91-119, January.

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