Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-19T13:27:04.375Z Has data issue: false hasContentIssue false
  • English
  • Français

DATA REDUCTION BY THE HAAR FUNCTION: A CASE STUDY OF THE PHILLIPS CURVE

Published online by Cambridge University Press:  24 May 2021

Marco Gallegati ,
Meghnad Desai  and
James B. Ramsey
Marco Gallegati*
Affiliation:
Polytechnic University of Marche
Meghnad Desai
Affiliation:
House of Lords
James B. Ramsey
Affiliation:
New York University
*
Address correspondence to: Marco Gallegati, DISES, Faculty of Economics “G. Fuà”, Polytechnic University of Marche, Piazzale Martelli 8, Ancona, Italy. e-mail: marco.gallegati@univpm.it. Phone: +390712207114.
Get access Rights & Permissions [Opens in a new window]

Abstract

The unorthodox estimation procedure, which Phillips (1958) adopted in his original paper, is examined using the Haar wavelet filter. The application of the Haar wavelet transform to Phillips’ original data shows that Phillips’ six pairs of mean coordinates display a striking similarity with the Haar scaling coefficients that represent averages with a period greater than 16 years. This is consistent with Desai’s (1975) intuition on the interpretation of the Phillips Curve. We show that the choice of sorting observations by ascending values of the unemployment rate is crucial for reaching the goal of estimating the eye-catching nonlinear hyperbolic shape of the wage–unemployment relationship that would be otherwise linear. Interestingly, the Haar filter can account not only for the facts characterizing the Phillips’ relationship up to the early 1960s but also for two important facts mostly debated among policymakers: the downward shift of the Phillips Curve and its flattening over time.

Keywords

Data Reduction MethodsPhillips’ Averaging ProcedureHaar Wavelet Filter
Type
Articles
Information
Macroeconomic Dynamics , Volume 26 , Issue 8 , December 2022 , pp. 2086 - 2103
Copyright
© Cambridge University Press 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

A preliminary version of the paper has been presented at 2019 History of Economics Society Conference at Columbia University, New York, 20–23 June. The authors are grateful to Antonella Rancan and Jim Thomas for valuable inputs and comments on previous versions of this paper.

References

Aguiar-Conraria, L. and Soares, M. J. (2014) The continuous wavelet transform: Moving beyond uni- and bivariate analysis. Journal of Economic Surveys 28, 344–375.CrossRefGoogle Scholar
Brown, A.J., ‘Phillips’ curve’, and economic networks in the 1950s. Journal of the History of Economic Thought 40, 243–64.CrossRefGoogle Scholar
Brown, A. J. (1955) The Great Inflation, 1939–1951. Oxford: Oxford University Press.Google Scholar
Carney, M. (2017) [De]Globalisation and Inflation, IMF Michel Camdessus Central Banking Lecture.Google Scholar
Charpe, M., Brdiji, S. and Mcadam, P. (2020) Labor share and growth in the long run. Macroeconomic Dynamics 24, 1720–1757.10.1017/S1365100518001025CrossRefGoogle Scholar
Corry, B. (2001) Some myths about Phillips’ Curve. In: Arestis, P., Desai, M. and Dow, S. (eds.), Money, Macroeconomics and Keynes: Essays in Honour of Victoria Chick, Vol. 1, London: Routledge.Google Scholar
Cunliffe, J. (2017) The Phillips curve: Lower, flatter or in hiding? Bank of England speech at Oxford Economic Society.Google Scholar
Desai, M. (1975) The phillips curve: A revisionist interpretation. Economica 42, 1–19.CrossRefGoogle Scholar
Dowd, K., Cotter, J. and Loh, L. (2011) U.S. core inflation: A wavelet analysis. Macroeconomic Dynamics 15, 513–536.CrossRefGoogle Scholar
Forder, J. (2014) Macroeconomics and the Phillips Curve Myth. Oxford: Oxford University Press.CrossRefGoogle Scholar
Gallegati, M., Gallegati, M., Ramsey, J. B. and Semmler, W. (2011) The US wage Phillips curve across frequencies and over time. Oxford Bullettin of Economic and Statistics 73, 489–508.CrossRefGoogle Scholar
Gencay, R., Selcuk, F. and Whitcher, B. (2003) Systemic risk and timescales. Quantitative Finance 3, 108–116.CrossRefGoogle Scholar
Gilbert, C. L. (1976) The original phillips curve estimates. Economica 43, 51–57.CrossRefGoogle Scholar
Haar, A. (1910) Zur Theorie der orthogonalen Funktionensysteme. Mathematische Annalen 69, 331–371.CrossRefGoogle Scholar
Hayek, F. A. (1952) The Sensory Order: An Inquiry Into the Foundations of Theoretical Psychology. Chicago: University of Chicago Press.Google Scholar
Hendry, D. F. and Mizon, G. E. (2000) The influence of A.W. Phillips on econometrics. In: Leeson, R. (ed.), A.W.H. Phillips: Collected Works in Contemporary Perspective, pp. 353–364. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Hoover, K. D. (2014) The Genesis of Samuelson and Solow’s Price-Inflation Phillips Curve, CHOPE Working Paper: No. 2014-10.Google Scholar
Hudgins, L., Friehe, C. A. and Mayer, M. E. (1993) Wavelet transforms and atmospheric turnulence. Phisycal Review Letters 71, 3279–3282.CrossRefGoogle Scholar
Klein, L. R. (2000) The phillips curve in macroeconomics and econometrics. In: Leeson, R. (ed.), A.W.H. Phillips: Collected Works in Contemporary Perspective, pp. 288–295. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Leeson, R. (2000) A.W.H. Phillips: Collected Works in Contemporary Perspective. Cambridge: Cambridge University Press CrossRefGoogle Scholar
Lipsey, R. G. (1960) The relation between unemployment and the rate of change of money wage rates in the United Kingdom, 1862–1957: A further analysis. Economica, New Series 27, 1–31.CrossRefGoogle Scholar
Lipsey, R. G. (2000) The famous Phillips Curve article. In: Leeson, R. (ed.), A.W.H. Phillips: Collected Works in Contemporary Perspective, pp. 232–242. Cambridge: Cambridge University Press.Google Scholar
Mallat, S. (1989) A theory for multiresolution signal decomposition: The wavelet representation. IEEE Transaction Pattern Analysis 11, 674–693.CrossRefGoogle Scholar
Percival, D. B. and Walden, A. T. (2000) Wavelet Methods for Time Series Analysis. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Phillips, A. W. H. (1958) The relation between unemployment and the rate of change of money wage rates in the United Kingdom. 1861–1957. Economica 25, 283–299.Google Scholar
Phillips, A. W. H. and Quenouille, M. H. (1960) Estimation, regulation and prediction in interdependent dynamic systems. Bulletin de l’Institute de Statistique 37, 335–343.Google Scholar
Ramsey, J. B. and Lampart, C. (1998) Decomposition of economic relationships by timescale using wavelets: Money and income. Macroeconomic Dynamics 2, 49–71.CrossRefGoogle Scholar
Ramsey, J. B. and Zhang, Z. (1995) The analysis of foreign exchange data using waveform dictionaries. Journal of Empirical Finance 4, 341–372.CrossRefGoogle Scholar
Samuelson, P. A. and Solow, R. M. (1960) Analytical aspects of anti-inflation policy. American Economic Review 50, 177–194.Google Scholar
Shadman-Mehta, F. (2000) Does modern econometrics replicate the phillips curve? In: Leeson, R. (ed.), A.W.H. Phillips: Collected Works in Contemporary Perspective, pp. 315–334. Cambridge: Cambridge University Press.Google Scholar
Sleeman, A. G. (2011) The phillips curve: A rushed job? Journal of Economic Perspectives 25, 223–238.Google Scholar
Staiger, D., Stock, J. H. and Watson, M. W. (2002) Prices, wages and the U.S. NAIRU in the 1990s. In: Krueger, A. and Solow, R. (ed.), The Roaring Nineties: Can Full Employment be Sustained?. New York: Russell Sage Foundation.Google Scholar
Stein, C. M. (1981) Estimation of the mean of a multivariate normal distribution. The Annals of Statistics 9, 1135–1151.10.1214/aos/1176345632CrossRefGoogle Scholar
Thomas, R. and Dimsdale, N. (2016) Three Centuries of Data - Version 2.3. Bank of England, http://www.bankofengland.co.uk/research/Pages/onebank/threecenturies.aspxGoogle Scholar
Torrence, C. and Webster, P. J. (1998) The annual cycle of persistence in the El Nino-Southern oscillation. Quarterly Journal of the Royal Meteorological Society 124, 1985–2004.Google Scholar
Wulwick, N. J. (1987) The Phillips curve: Which? Whose? To do what? How? Southern Economic Journal 54, 834–857.CrossRefGoogle Scholar
Wulwick, N. J. (1989) Phillips’ approximate regression. Oxford Economic Papers, New Series, 41, 1, History and Methodology of Econometrics, 170–188.CrossRefGoogle Scholar
Wulwick, N. J. and Mack, Y.-P. (1990) A Kernel Regression of Phillips’ Data. Working Paper No. 40, New York, Jerone Levy Economics Institute, Bard College.Google Scholar