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Instrumental variables and wavelet decompositions

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  • Ramsey, James B.
  • Gallegati, Marco
  • Gallegati, Mauro
  • Semmler, Willi

Abstract

The application of wavelet analysis provides an orthogonal decomposition of a time series by time scale, thereby facilitating the decomposition of a data series into the sum of a structural component and a random error component. The structural components revealed by the wavelet analysis yield nearly ideal instrumental variables for variables observed with error and for co-endogenous variables in simultaneous equation models. Wavelets also provide an efficient way to explore the path of the structural component of the series to be analyzed and can be used to detect some specification errors. The methodology described in this paper is applied to the errors in variables problem and simultaneous equations case using some simulation exercises and to the analysis of a version of the Phillips curve with interesting results.

Suggested Citation

  • Ramsey, James B. & Gallegati, Marco & Gallegati, Mauro & Semmler, Willi, 2010. "Instrumental variables and wavelet decompositions," Economic Modelling, Elsevier, vol. 27(6), pages 1498-1513, November.
    • Handle: RePEc:eee:ecmode:v:27:y:2010:i:6:p:1498-1513
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    References listed on IDEAS

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    1. James Ramsey, 1999. "Regression over Timescale Decompositions: A Sampling Analysis of Distributional Properties," Economic Systems Research, Taylor & Francis Journals, vol. 11(2), pages 163-184.
    2. Mark Gertler & Jordi Gali & Richard Clarida, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1661-1707, December.
    3. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-529, October.
    4. Ramsay, James O. & Ramsey, James B., 2002. "Functional data analysis of the dynamics of the monthly index of nondurable goods production," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 327-344, March.
    5. Gali, Jordi & Gertler, Mark, 1999. "Inflation dynamics: A structural econometric analysis," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 195-222, October.
    6. Mark Gertler & Jordi Gali & Richard Clarida, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1661-1707, December.
    7. Jinyong Hahn & Jerry Hausman, 2003. "Weak Instruments: Diagnosis and Cures in Empirical Econometrics," American Economic Review, American Economic Association, vol. 93(2), pages 118-125, May.
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    Citations

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    Cited by:

    1. Fratianni, Michele & Gallegati, Marco & Giri, Federico, 2022. "The medium-run Phillips curve: A time–frequency investigation for the UK," Journal of Macroeconomics, Elsevier, vol. 73(C).
    2. Marco Gallegati, 2018. "A systematic wavelet-based exploratory analysis of climatic variables," Climatic Change, Springer, vol. 148(1), pages 325-338, May.
    3. Gallegati, Marco & Ramsey, James B., 2014. "The forward looking information content of equity and bond markets for aggregate investments," Journal of Economics and Business, Elsevier, vol. 75(C), pages 1-24.
    4. Gallegati, Marco & Ramsey, James B., 2013. "Bond vs stock market's Q: Testing for stability across frequencies and over time," Journal of Empirical Finance, Elsevier, vol. 24(C), pages 138-150.
    5. Fan He & Xuansen He, 2019. "A Continuous Differentiable Wavelet Shrinkage Function for Economic Data Denoising," Computational Economics, Springer;Society for Computational Economics, vol. 54(2), pages 729-761, August.
    6. Antonis A. Michis, 2021. "Wavelet Multidimensional Scaling Analysis of European Economic Sentiment Indicators," Journal of Classification, Springer;The Classification Society, vol. 38(3), pages 443-480, October.
    7. Gallegati, Marco & Ramsey, James B., 2013. "Structural change and phase variation: A re-examination of the q-model using wavelet exploratory analysis," Structural Change and Economic Dynamics, Elsevier, vol. 25(C), pages 60-73.
    8. Rizvi, Syed Aun R. & Arshad, Shaista & Alam, Nafis, 2015. "Crises and contagion in Asia Pacific — Islamic v/s conventional markets," Pacific-Basin Finance Journal, Elsevier, vol. 34(C), pages 315-326.
    9. Charpe, Matthieu & Bridji, Slim & Mcadam, Peter, 2020. "Labor Share And Growth In The Long Run," Macroeconomic Dynamics, Cambridge University Press, vol. 24(7), pages 1720-1757, October.
    10. Taheri Bazkhaneh , Saleh & Ehsani , Mohammad Ali & Gilak Hakimabadi , Mohammad Taqi & Farzinvash , Asodollah, 2018. "Analysis of the Relationship between the Business Cycle and Inflation Gap in Time-Frequency Domain," Journal of Money and Economy, Monetary and Banking Research Institute, Central Bank of the Islamic Republic of Iran, vol. 13(3), pages 401-422, July.
    11. Rua, António, 2017. "A wavelet-based multivariate multiscale approach for forecasting," International Journal of Forecasting, Elsevier, vol. 33(3), pages 581-590.
    12. Gallegati, Marco & Ramsey, James B. & Semmler, Willi, 2014. "Interest rate spreads and output: A time scale decomposition analysis using wavelets," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 283-290.

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