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Phillips' averaging procedure as a 'crude' version of the Haar wavelet filter

Author

Listed:
  • Marco Gallegati

    (Dipartimento di Scienze Economiche e Sociali - Universita' Politecnica delle Marche)

  • James B. Ramsey

    (Department of Economics, New York University)

Abstract

The aim of this study is to investigate the exact nature of Phillips' (1958) findings. We show that the application of the simplest type of wavelet basis function developed by Haar in 1910 allows to replicate the output of Phillips' data transformation procedure, i.e. the six mean coordinates. Specifically, the resemblance between the coarsest scale level coefficients from the Haar wavelet filter and the six crosses suggests the long-term nature of Phillips' (wage-unemployment) relationship. The application of the Haar wavelet filter allows us to examine the effects of two main features of Phillips' 'unorthodox' averaging procedure: the arbitrarily choice of variable-width intervals and the choice of sorting observations in ascending order of unemployment rate values. Our results show that the arbitrary selection of intervals affects only the smoothness (regularity) of the nonlinear pattern of the wage-unemployment relationship, but not its shape which is determined by sorting and grouping unemployment rate values in ascending order. Indeed, when observations are ordered according to a chronological sequence a simple linear relationship is evident. These findings are robust to different samples, 1861-1913 and 1861-1958.

Suggested Citation

  • Marco Gallegati & James B. Ramsey, 2019. "Phillips' averaging procedure as a 'crude' version of the Haar wavelet filter," Working Papers 437, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    • Handle: RePEc:anc:wpaper:437
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    References listed on IDEAS

    as
    1. Marco Gallegati & Mauro Gallegati & James Bernard Ramsey & Willi Semmler, 2011. "The US Wage Phillips Curve across Frequencies and over Time," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 73(4), pages 489-508, August.
    2. Wulwick, Nancy J, 1989. "Phillips' Approximate Regression," Oxford Economic Papers, Oxford University Press, vol. 41(1), pages 170-188, January.
    3. A. W. Phillips, 1958. "The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861–1957," Economica, London School of Economics and Political Science, vol. 25(100), pages 283-299, November.
    4. repec:bla:econom:v:43:y:1976:i:169:p:51-57 is not listed on IDEAS
    5. repec:bla:econom:v:42:y:1975:i:165:p:1-19 is not listed on IDEAS
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    More about this item

    Keywords

    Phillips curve; Haar wavelet transform; Moving average filter;
    All these keywords.

    JEL classification:

    • B22 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Macroeconomics
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E24 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Employment; Unemployment; Wages; Intergenerational Income Distribution; Aggregate Human Capital; Aggregate Labor Productivity

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