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French economic cycles: a wavelet analysis of French retrospective GNP series


Although 50 years of scientific work has been invested in building retrospective economic time series, their reliability is still debated, a good example being the two competing nineteenth century French GNP series. Instead of trying to bring up some new details to gauge their respective accuracy, we propose a different route, i.e. testing the intrinsic features of these two series, in absolute terms first, then by benchmarking them to a non-retrospective time series. In order to do that, we rely on new mathematical tools—wavelet spectrum analysis—developed in signal processing. This leads to a new approach, which separates the accuracy of a series between amplitude and time variations, and brings nuanced conclusions as to which of the two series tested is the best: indeed, since a trade-off is almost inescapable between the two criterions of accuracy, the statistical quality of one retrospective time series tends to linger either on one side (amplitude level) or the other (time variations). Our study also shows that variance distribution along the time axis is a good proxy for complex retrospective series accuracy.

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  1. 1.

    Maddison picked up what he estimated to be the most relevant sub-series to built its own estimate of the French nineteenth century GNP.

  2. 2.

    Schleicher (2002) An introduction to wavelets for economists. Bank of Canada Banque du Canada, Working Paper 2002-3/Document de travail 2002-3. This paper is one of the best introductions to wavelets for the beginner.

  3. 3.

    Version 6.5 and 7.x, The MathWorks, Natick, Massachusetts, United States.

  4. 4.

    B. Cazelles and al, 2007, op. cit.

  5. 5.

    In Bourguignon and Lévy-Leboyer (1985), based upon a collaboration between a historian (Lévy-Leboyer) and an economist (Bourguignon), only the former collected the data and built the series.

  6. 6.

    J.-C. Asselain (2006) op. cit. It may be interesting to add that in the speech he delivered in Novembre 2006 (“Le projet français d’ “histoire économique quantitative”: Ambitions et resultats”, communication à la journée de l’A.F.H.E. du 24 novembre 2006, mimeo, 37 p., downloadable on, Asselain expressed even more doubts than he dared to write.

  7. 7.

    These series are published in the annexes of Bourguignon and Lévy-Leboyer (1985).

  8. 8.

    See below.

  9. 9.

    SGF—Statistique générale de la France—and INSEE—Institut national de la statistique et des études économiques—are the successive two main producers of statistical data in France (state-controlled but scientifically independent), responsible for official statistics (prices index, national product and growth, etc.).

  10. 10.

    Founded 1800, the Banque de France was during all the 19th century a privately-owned joint-stock company incorporated into a sui generis legal charter that protected its independence as long as the State was not strongly willing to intervene into its missions. As Napoleon put it: “I want the Bank to be quite in the hands of the Government, and not too much.” (“Je veux que la Banque soit assez dans les mains du Gouvernement, et n’y soit pas trop.”), 27 March 1806, quoted in Ramon (1929).

  11. 11.

    Banque de France, Rapport annuel à l’assemblée générale des actionnaires, exercice 1836, Banque de France archives [BFA], Paris.

  12. 12.

    “L’histoire des crises reste à faire”, Id., p. 15.

  13. 13.

    Rapports annuels à l’assemblée générale des actionnaires, 1801–1914, BFA, Paris.

  14. 14.

    Slight differences led us to prefer to use the original Banque de France’s figures.

  15. 15.

    Starting 1848, some new types of bills were discounted: warehouse warrants (1848), agricultural warrants (1898), hotel warrants (1913). But these new bills never accounted for a significant proportion of the total amount of bills discounted before 1914.

  16. 16.

    That is, branches operations, which also include Paris area (town and suburb) branches.

  17. 17.

    “Crédits de campagne”, first designed for beef feeders (crédits d’embouche), then extended but modestly, to finance infra-annual industrial production cycles.

  18. 18.

    Crédits d’embouche (cf. note 46 supra) were limited to traditional rural feeding areas.

  19. 19.

    From the name of the founder of Crédit lyonnais, at the time the French biggest commercial bank.

  20. 20.

    Industrial sponsoring.

  21. 21.

    There is not such a model at hand. The only global econometric model addressing nineteenth century France is the one built by F. Bourguignon to test M. Lévy-Leboyer’s figures (Bourguignon and Lévy-Leboyer 1985). But the authors clearly put aside monetary factors to concentrate on “real” factors.

  22. 22.

    The same detrending method is used for wavelets and correlation analysis—see above.

  23. 23.

    See P. Baubeau 2004, op. cit., pp. 237 sq.

  24. 24.

    J.-C. Toutain, 1997, op. cit., tab. 4 p. 18 and M. Lévy-Leboyer, 1985, op. cit., tab. A-1, pp. 318 sq.

  25. 25.

    G. Roulleau was a statistician at the Banque de France from the end of the nineteenth century to the Interwar period. His work, while known in France, may have been overlooked abroad. He devised a more satisfactory statistical way to build a series of bills emitted from 1841 (the year of the Stamp tax law) to 1911 than his English counterparts, who first tried to build such series, W. Leatham in 1840 and W. Newmarch in 1851 (Nishimura 1971). It would be very interesting to cross his results with Nishimura (1971)

  26. 26.

    His memoir, presented to the Société de Statistique de Paris in 1912, got in 1913 the Emile Mercet prize of the Société and was praised to be “actually superior to the others”, G. Roulleau, op. cit., foreword by Fernand Faure, excerpt from the report for the prize Emile Mercet, p. III.

  27. 27.

    Art. XI of the Statutes of the Banque de France, adopted in the Décret en Conseil d’Etat du 16 janvier 1808, by Napoléon Bonaparte Empereur des Français, in Banque de France, 1809, Lois, décrets impériaux et règlements relatifs à la Banque de France et à son régime intérieur, Paris, Imprimerie de la Banque de France.

  28. 28.

    Billoret (1969) for the 1830 crisis and RamonG, op. cit., p. 218 for the 1848 crisis.

  29. 29.

    Proclaimed 4 September 1870, French 3rd Republic (1870–1940) was not actually founded before the 1875 constitutional laws, and it is only after 1879 that republican politicians retained most constitutional powers.

  30. 30.

    Toutain, 1997, op. cit., p. 29 sq and 111 sq (Annexe E), gives the detail of the data categories used to build his services series: housing (“logement”), professions (“professions liberales”), domestic service (“domestiques”), civil servants (“services publics”), transportation (“transports”) and retail trade (“commerce”).

  31. 31.

    Housing and domestic services value series.

  32. 32.

    Professions and civil servants volume series.

  33. 33.

    J.-C. Toutain (1997), op. cit., p. 122.

  34. 34.


  35. 35.

    “L’incidence de ce postulat est faible.” Idem.

  36. 36.

    Cl. Juglar, op. cit., p. 8.


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Correspondence to Patrice Baubeau.

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Many thanks to Professor Kenneth Mouré, University of California, Santa Barbara, for his incredible help in finalizing this text. We are also deeply indebted to the three anonymous referees who patiently guided us to a more focused approach.



To stress the interest of variance rescaling using wavelet decomposition, we have performed “high-pass” filtering on the Banque de France total discounts series. The graph A0 displays the comparison of the wavelet power spectrum computed either without (the top panel) or with (the low panel) rescaling of the variance. This rescaling is done simply by selecting the periodic components with periods less than some threshold and it is classically named “high-pass” filtering (Shumway and Stoffer 2000). The analysis of the raw series clearly shows that the main variance of the series (the oscillations around the mean) is for periodic components between 24 and 48 years but mainly after 1890 (the top panel). Nevertheless, these components appear non-significant (right box). After rescaling (the low panel), we focus only on the oscillating components with periods less than 33 years, some of which appear highly significant (right box). This allows us to highlight the evolution of these periodic components that were present (see the top panel) but masked by the components with higher periodicity.

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Baubeau, P., Cazelles, B. French economic cycles: a wavelet analysis of French retrospective GNP series. Cliometrica 3, 275–300 (2009).

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  • Wavelets
  • Data estimation methodology
  • Macroeconomics

JEL Classification

  • C49
  • E01
  • E32
  • E51
  • E58
  • N13
  • N24
  • N01