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

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

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

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

  8. See below.

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

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

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

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

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

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

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

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

  20. Industrial sponsoring.

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

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

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

  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. 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. Housing and domestic services value series.

  32. Professions and civil servants volume series.

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

  34. Idem.

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

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


  • Asselain J-C (2007) Le projet français d’ “ histoire économique quantitative”: Ambitions et resultats”, Economies et Sociétés Série “Histoire économique quantitative. Ser AF 4(36):567–609

    Google Scholar 

  • Baker M, Collins M (1999) Financial crises and structural change in english commercial bank assets, 1860–1913. Explor Econ Hist 36(4):428–444

    Article  Google Scholar 

  • Baubeau P (2004) Les cathédrales de papier, Naissance et subversion du système de l’escompte en France, fin 18e-premier 20e siècle. PhD dissertation, Université Paris X Nanterre, pp. 236–237

  • Billoret J-L (1969) Système bancaire et dynamique économique dans un pays à monnaie stable, France 1816–1914. Thèse en vue de l’obtention du doctorat ès-sciences économiques, Université de Nancy, Nancy, p 63

  • Bourguignon F, Lévy-Leboyer M (1985) L’économie française au XIXe siècle: Analyse macroéconomique. Economica, Paris

    Google Scholar 

  • Caron F, Bouvier J (1993) Les indices majeurs. In: Labrousse E, Braudel F. Histoire économique et sociale de la France, vol. 4, années 1880–1950, La croissance industrielle, Le temps des Guerres mondiales et la Grande crise Paris, PUF (1st edn 1979)

  • Cazelles B, Chavez M, Constantin de Magny G, Guégan J-F, Hales S (2007) Time dependent spectral analysis of epidemiological time series with wavelets. J R Soc Interface 4:625–636. doi:10.1098/rsif.2007.0212

    Article  Google Scholar 

  • Coquelin C (1852) Crises économiques. Dictionnaire d’économie politique, vol 1. Guillaumin, Paris

    Google Scholar 

  • Crafts N (2004) Productivity growth in the industrial revolution: a new growth accounting perspective. J Econ Hist 64:521–535

    Article  Google Scholar 

  • Crafts N, Harley K (1992) Output growth and the industrial revolution: a restatement of the Crafts-Harley view. Economic History Review, 45

  • Diebolt C (2005) Long cycles revisited, an essay in econometric history. AFC Working Paper, no. 5

  • Diebolt C, Doliger C (2005) Kuznets versus Kitchin, Juglar & Kondratieff: Renewed spectral analysis of comparative growth of per capita GDP series in the OECD countries in the nineteenth and twentieth centuries. AFC Working Papers, no. 2

  • Efron B, Tibshirani RJ (1993) An introduction to the bootstrap. Chapman and Hall, London

    Google Scholar 

  • Iacobucci A (2003) Spectral analysis for economic time series. OFCE Working Paper, November 2003, no. 07

  • Juglar C (1862) Des crises commerciales et de leur retour périodique. Guillemin, Paris

    Google Scholar 

  • Kuznets S, Epstein L, Jenks E (1941) National income and its composition: 1919–1938. C.U.P, New York

    Google Scholar 

  • Labrousse E (1993) A livre ouvert sur les élans et les vicissitudes des croissances. In: Labrousse E, Braudel F (eds) Histoire économique et sociale de la France, vol 3, 1789- années 1880, L’avènement de l’ère industrielle, Paris, PUF (1st edn 1976)

  • Lau WK-M, Weng H (1995) Climatic signal detection using wavelet transform: how to make a time series sing. Bull Am Meteorol Soc 76:2391–2402

    Article  Google Scholar 

  • Maddison A (2003) L’économie mondiale: statistiques historiques. OCDE, Paris

    Google Scholar 

  • Mallat S (1998) A wavelet tour of signal processing. Academic Press, San Diego

    Google Scholar 

  • Mitchell BR (2003) International historical statistics, vol 3. Palgrave, Basingstoke

    Google Scholar 

  • Nishimura S (1971) The decline of inland bills of exchange in the London money market, 1855–1913. Cambridge University Press, Cambridge

    Google Scholar 

  • Ramon G (1929) Histoire de la banque de france d’après les sources originales. Grasset, Paris

    Google Scholar 

  • Ritschl A, Uebele M (2005) Stock markets and business cycle comovement in germany before World War I: evidence from spectral analysis. SFB 649 Discussion Paper 2005–056, Humboldt-Universität zu, Berlin

  • Roulleau G (1914) Les règlements par effets de commerce en France et à l’étranger. Paris, Imp. Dubreuil, Frèrebeau et Cie

  • Schleicher C (2002) An introduction to wavelets for economists. Bank of Canada Banque du Canada, Working Paper 2002–3/Document de travail 2002–3

  • Shumway RH, Stoffer DS (2000) Time series analysis and its applications. Springer

  • Temin P (1996) Two views of the British industrial revolution. NBER Working Paper Series on Historical Factors in Long Run Growth, NBER, 81, 1996 (published in 1997 in The Journal of Economic History)

  • Temin P (2000) A response to Harley and Crafts. J Econ Hist 60(3):842–846

    Article  Google Scholar 

  • Torrence C, Compo GP (1998) A practical guide to wavelet analysis. Bull Am Meteorol Soc 79:61–78

    Article  Google Scholar 

  • Toutain J-C (1996) Comparaison entre les différentes évaluations du produit intérieur brut de la France de 1815 à 1938 ou L’histoire économique quantitative a-t-elle un sens ? Revue économique 47(4):893–919.

  • Toutain J-C (1997) Le produit intérieur brut de la France, 1789–1990. Economies et Sociétés, Histoire économique quantitative Série HEQ no 1, no 11, pp 5–136

  • Verley P (1995) L’industrialisation, 1830–1914. In: Gueslin A (ed) Nouvelle histoire économique de la France contemporaine. vol. 2, Paris, La Découverte (1st edn 1989) pp 12–13

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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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