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Conditionally Efficient Estimation of Long-run Relationships Using Mixed-frequency Time Series

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Abstract

I analyze efficient estimation of a cointegrating vector when the regressand is observed at a lower frequency than the regressors. Previous authors have examined the effects of specific temporal aggregation or sampling schemes, finding conventionally efficient techniques to be efficient only when both the regressand and the regressors are average sampled. Using an alternative method for analyzing aggregation under more general weighting schemes, I derive an efficiency bound that is conditional on the type of aggregation used on the regressand and differs from the unconditional bound defined by the infeasible full-information high-frequency data-generating process. I modify a conventional estimator, canonical cointegrating regression (CCR), to accommodate cases in which the aggregation weights are either unknown or known. In the unknown case, the correlation structure of the error term generally confounds identification of the conditionally efficient weights. In the known case, the correlation structure may be utilized to offset the potential information loss from aggregation, resulting in a conditionally efficient estimator. Efficiency is illustrated using a simulation study and an application to estimating a gasoline demand equation.

Suggested Citation

  • J. Isaac Miller, 2011. "Conditionally Efficient Estimation of Long-run Relationships Using Mixed-frequency Time Series," Working Papers 1103, Department of Economics, University of Missouri, revised 30 May 2012.
  • Handle: RePEc:umc:wpaper:1103
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    File URL: https://economics.missouri.edu/working-papers/2011/wp1103_miller.pdf
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    1. Mark Armstrong & John Vickers & Jidong Zhou, 2008. "Prominence and Consumer Search," Economics Series Working Papers 379, University of Oxford, Department of Economics.
    2. Mark Armstrong & John Vickers & Jidong Zhou, 2009. "Prominence and consumer search," RAND Journal of Economics, RAND Corporation, pages 209-233.
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    Cited by:

    1. Iwan Bos & Joseph E. Harrington, 2015. "Competition Policy And Cartel Size," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56, pages 133-153, February.
    2. Jan Feld & Nicolás Salamanca & Daniel S. Hamermesh, 2016. "Endophilia or Exophobia: Beyond Discrimination," Economic Journal, Royal Economic Society, vol. 126(594), pages 1503-1527, August.
    3. Thomas B. Götz & Alain Hecq & Jean‐Pierre Urbain, 2014. "Forecasting Mixed‐Frequency Time Series with ECM‐MIDAS Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(3), pages 198-213, April.
    4. J. Isaac Miller, 2012. "Mixed-frequency Cointegrating Regressions with Parsimonious Distributed Lag Structures," Working Papers 1211, Department of Economics, University of Missouri.
    5. Eric Ghysels & J. Isaac Miller, 2014. "On the Size Distortion from Linearly Interpolating Low-frequency Series for Cointegration Tests," Working Papers 1403, Department of Economics, University of Missouri.
    6. Götz Thomas B. & Hecq Alain & Urbain Jean-Pierre, 2012. "Real-Time Forecast Density Combinations (Forecasting US GDP Growth Using Mixed-Frequency Data)," Research Memorandum 021, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    7. Shawn Ni & Michael Podgursky, 2016. "How Teachers Respond to Pension System Incentives: New Estimates and Policy Applications," Journal of Labor Economics, University of Chicago Press, vol. 34(4), pages 1075-1104.
    8. Eric Ghysels & J. Isaac Miller, 2015. "Testing for Cointegration with Temporally Aggregated and Mixed-Frequency Time Series," Journal of Time Series Analysis, Wiley Blackwell, pages 797-816.
    9. Götz, Thomas B. & Hecq, Alain & Smeekes, Stephan, 2016. "Testing for Granger causality in large mixed-frequency VARs," Journal of Econometrics, Elsevier, pages 418-432.
    10. J. Isaac Miller, 2014. "Mixed-frequency Cointegrating Regressions with Parsimonious Distributed Lag Structures," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 12(3), pages 584-614.
    11. Arne J. Nagengast & Robert Stehrer, 2016. "The Great Collapse in Value Added Trade," Review of International Economics, Wiley Blackwell, pages 392-421.
    12. Götz, T.B. & Hecq, A.W. & Smeekes, S., 2015. "Testing for Granger Causality in Large Mixed-Frequency VARs," Research Memorandum 036, Maastricht University, Graduate School of Business and Economics (GSBE).

    More about this item

    Keywords

    cointegration; canonical cointegrating regression; temporal aggregation; mixed-frequency series; mixed data sampling; price elasticity of gasoline demand;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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