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Recoverability

Author

Listed:
  • Ryan Chahrour

    () (Boston College)

  • Kyle Jurado

    () (Duke University)

Abstract

When can structural shocks be recovered from observable data? We present a necessary and sufficient condition that gives the answer for any linear model. Invertibility, which requires that shocks be recoverable from current and past data only, is sufficient but not necessary. This means that semi-structural empirical methods like structural vector autoregression analysis can be applied even to models with non-invertible shocks. We illustrate these results in the context of a simple model of consumption determination with productivity shocks and non-productivity noise shocks. In an application to postwar U.S. data, we find that non-productivity shocks account for a large majority of fluctuations in aggregate consumption over business cycle frequencies.

Suggested Citation

  • Ryan Chahrour & Kyle Jurado, 2017. "Recoverability," Boston College Working Papers in Economics 935, Boston College Department of Economics.
    • Handle: RePEc:boc:bocoec:935
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    References listed on IDEAS

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    1. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez & Thomas J. Sargent & Mark W. Watson, 2007. "ABCs (and Ds) of Understanding VARs," American Economic Review, American Economic Association, vol. 97(3), pages 1021-1026, June.
    2. Mario Forni & Luca Gambetti & Marco Lippi & Luca Sala, 2017. "Noisy News in Business Cycles," American Economic Journal: Macroeconomics, American Economic Association, vol. 9(4), pages 122-152, October.
    3. Ryan Chahrour & Kyle Jurado, 2018. "News or Noise? The Missing Link," American Economic Review, American Economic Association, vol. 108(7), pages 1702-1736, July.
    4. Hansen, Lars Peter & Sargent, Thomas J., 1980. "Formulating and estimating dynamic linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 7-46, May.
    5. Sims, Christopher A. & Zha, Tao, 2006. "Does Monetary Policy Generate Recessions?," Macroeconomic Dynamics, Cambridge University Press, vol. 10(2), pages 231-272, April.
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    Cited by:

    1. Silvia Miranda Agrippino & Giovanni Ricco, 2018. "Identification with external instruments in structural VARs under partial invertibility," Sciences Po publications 24, Sciences Po.
    2. Miranda-Agrippino, Silvia & Ricco, Giovanni, 2019. "Identification with External Instruments in Structural VARs under Partial Invertibility," The Warwick Economics Research Paper Series (TWERPS) 1213, University of Warwick, Department of Economics.

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    More about this item

    Keywords

    structural vector autoregression; noise shocks;

    JEL classification:

    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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