Research article Special Issues

Evidence of A Bimodal US GDP Growth Rate Distribution: A Wavelet Approach

  • Received: 06 March 2017 Accepted: 23 March 2017 Published: 10 April 2017
  • We present a quantitative characterisation of the fluctuations of the annualized growth rate of the real US GDP per capita at many scales, using a wavelet transform analysis of two data sets, quarterly data from 1947 to 2015 and annual data from 1800 to 2010. The chosen mother wavelet (first derivative of the Gaussian function) applied to the logarithm of the real US GDP per capita provides a robust estimation of the instantaneous growth rate at different scales. Our main finding is that business cycles appear at all scales and the distribution of GDP growth rates can be well approximated by a bimodal function associated to a series of switches between regimes of strong growth rate $\rho_\text{high}$ and regimes of low growth rate $\rho_\text{low}$. The succession of such two regimes compounds to produce a remarkably stable long term average real annualized growth rate of 1.6% from 1800 to 2010 and $\approx 2.0\%$ since 1950, which is the result of a subtle compensation between the high and low growth regimes that alternate continuously. Thus, the overall growth dynamics of the US economy is punctuated, with phases of strong growth that are intrinsically unsustainable, followed by corrections or consolidation until the next boom starts. We interpret these findings within the theory of "social bubbles" and argue as a consequence that estimations of the cost of the 2008 crisis may be misleading. We also interpret the absence of strong recovery since 2008 as a protracted low growth regime $\rho_\text{low}$ associated with the exceptional nature of the preceding large growth regime.

    Citation: Sandro Claudio Lera, Didier Sornette. Evidence of A Bimodal US GDP Growth Rate Distribution: A Wavelet Approach[J]. Quantitative Finance and Economics, 2017, 1(1): 26-43. doi: 10.3934/QFE.2017.1.26

    Related Papers:

  • We present a quantitative characterisation of the fluctuations of the annualized growth rate of the real US GDP per capita at many scales, using a wavelet transform analysis of two data sets, quarterly data from 1947 to 2015 and annual data from 1800 to 2010. The chosen mother wavelet (first derivative of the Gaussian function) applied to the logarithm of the real US GDP per capita provides a robust estimation of the instantaneous growth rate at different scales. Our main finding is that business cycles appear at all scales and the distribution of GDP growth rates can be well approximated by a bimodal function associated to a series of switches between regimes of strong growth rate $\rho_\text{high}$ and regimes of low growth rate $\rho_\text{low}$. The succession of such two regimes compounds to produce a remarkably stable long term average real annualized growth rate of 1.6% from 1800 to 2010 and $\approx 2.0\%$ since 1950, which is the result of a subtle compensation between the high and low growth regimes that alternate continuously. Thus, the overall growth dynamics of the US economy is punctuated, with phases of strong growth that are intrinsically unsustainable, followed by corrections or consolidation until the next boom starts. We interpret these findings within the theory of "social bubbles" and argue as a consequence that estimations of the cost of the 2008 crisis may be misleading. We also interpret the absence of strong recovery since 2008 as a protracted low growth regime $\rho_\text{low}$ associated with the exceptional nature of the preceding large growth regime.


    加载中
    [1] Aguiar-Conraria L, Joana-Soares M (2014) The continuous wavelet transform: Moving beyond uni- and bivariate analysis. J Econ Surv 28: 344-375. doi: 10.1111/joes.12012
    [2] Antonini M, Barlaud M, Mathieu P, et al. (1992) Image coding using wavelet transform. Image Process, IEEE Trans 1: 205-220. doi: 10.1109/83.136597
    [3] Ardila D, Sornette D (2016) Dating the financial cycle with uncertainty estimates: a wavelet proposition. Financ Res Lett 19: 298-304. doi: 10.1016/j.frl.2016.09.004
    [4] Argoul F, Arneodo A, Grasseau G, et al. (1989) Wavelet analysis of turbulence reveals the multifractal nature. Nat 338: 2.
    [5] Arneodo A, Argoul F, Muzy J, et al. (1993) Beyond classical multifractal analysis using wavelets: Uncovering a multiplicative process hidden in the geometrical complexity of diffusion limited aggregates. Fractals 1: 629-649. doi: 10.1142/S0218348X93000666
    [6] Atkinson T, Luttrell D, Rosenblum H (2013) How bad was it? the costs and consequences of the 2007-09 financial crisis. Staff Pap Fed Reserve Bank of Dallas 20: 1-22.
    [7] Baxter M, King RG (1999) Measuring business cycles: Approximate band-pass filters for economic time series. Rev Econ Stat 4: 575-593.
    [8] Burns AF, Mitchell WC (1946) Meas bus cycles.
    [9] Crowley PM (2007) A guide to wavelets for economists. J Econ Surv 21: 207-267. doi: 10.1111/j.1467-6419.2006.00502.x
    [10] Dabla-Norris E, Guo S, Haksar V, et al. (2015) The new normal: a sector-level perspective on productivity trends in advanced economies. IMF staff discuss note SDN/15/03.
    [11] Daubechies I (1992) Ten lectures on wavelets. SIAM.
    [12] Diebold FX, Rudebusch GD (1990) A nonparametric investigation of duration dependence in the american business cycle. J Political Econ 98: 596-616. doi: 10.1086/261696
    [13] Durland JM, McCurdy TM (1994) Duration-dependent transitions in a Markov model of U.S. GNP growth. J Bus Econ Stat 12: 279-288.
    [14] Erber G (2012) What is unorthodox monetary policy? SSRN Work Pap.
    [15] Fernald JG, Jones CI (2014) The future of US economic growth. Am Econ Rev: Pap Proc 104: 44-49. doi: 10.1257/aer.104.5.44
    [16] Filimonov V, Demos G, Sornette D (2017) Modified profile likelihood inference and interval forecast of the burst of financial bubbles. Quant Financ DOI: 10.1080/14697688.2016.1276298:120.
    [17] Geraskin P, Fantazzini D (2013) Everything you always wanted to know about log-periodic power laws for bubble modeling but were afraid to ask. Eur J Financ 19: 366-391. doi: 10.1111/j.1468-036X.2010.00604.x
    [18] Gisler M, Sornette D (2009) Exuberant innovations: the apollo program. Soc 46: 55-68. doi: 10.1007/s12115-008-9163-8
    [19] Gisler M, Sornette D (2010) Bubbles everywhere in human affairs. chapter in book entitled Modern RISC-Societies. Towards a New Paradigm for Societal Evolution, L. Kajfez-Bogataj, K. H. Muller, I. Svetlik, N. Tos (eds.), Wien, edition echoraum: 137-153, (http://ssrn.com/abstract=1590816).
    [20] Gisler M, Sornette D,Woodard R (2011) Innovation as a social bubble: The example of the human genome project. Res Policy 40: 1412-1425. doi: 10.1016/j.respol.2011.05.019
    [21] Hamilton JD (1989) A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57: 357-384. doi: 10.2307/1912559
    [22] Hodrick RJ, Prescott EC (1997) Postwar US business cycles: an empirical investigation. J Money, credit, and Bank: 1-16.
    [23] Johansen A, Sornette D (2001) Finite-time singularity in the dynamics of the world population and economic indices. Phys A 294: 465-502. doi: 10.1016/S0378-4371(01)00105-4
    [24] Louzoun Y, Solomon SG, Goldenberg J, et al. (2003) World-size global markets lead to economic instability. Artif life 9: 357-370. doi: 10.1162/106454603322694816
    [25] Moore GH, Zarnowitz V (1984) The development and role of the national bureau of economic researchs business cycle chronologie. NBER Work Pap 1394.
    [26] Morlet J, Arens G, Fourgeau E, et al. (1982) Wave propagation and sampling theory-part i: Complex signal and scattering in multilayered media. Geophys 47: 203-221. doi: 10.1190/1.1441328
    [27] Ramsey JB (1999) The contribution of wavelets to the analysis of economic and financial data. Philos Transac R Soc A 357: 2593-2606. doi: 10.1098/rsta.1999.0450
    [28] Silverman BW (1981) Using kernel density estimates to investigate multimodality. J R Stat Soc 43: 97-99.
    [29] Slezak E, Bijaoui A, Mars G (1990) Identification of structures from galaxy counts-use of the wavelet transform. Astron Astrophys 227: 301-316.
    [30] Sornette D (2008) Nurturing breakthroughs: lessons from complexity theory. J Econ Interac Coord 3: 165-181. doi: 10.1007/s11403-008-0040-8
    [31] Sornette D, Cauwels P (2014) 1980-2008: The illusion of the perpetual money machine and what it bodes for the future. Risks 2: 103-131. doi: 10.3390/risks2020103
    [32] Sornette D, Cauwels P (2015) Financial bubbles: mechanisms and diagnostics. Rev Behav Econ 2: 279-305. doi: 10.1561/105.00000035
    [33] Yiou P, Sornette D, Ghil M (2000) Data-adaptive wavelets and multi-scale singular-spectrum analysis. Phys D 142: 254-290. doi: 10.1016/S0167-2789(00)00045-2
    [34] Yogo M (2008) Measuring business cycles: A wavelet analysis of economic time series. Econ Lett 100: 208-212. doi: 10.1016/j.econlet.2008.01.008
    [35] Yukalov V, Yukalova E, Sornette D (2015) Dynamical system theory of periodically collapsing bubbles. Eur Phys J B 88: 1-14.
  • Reader Comments
  • © 2017 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(5315) PDF downloads(1244) Cited by(7)

Article outline

Figures and Tables

Figures(8)  /  Tables(2)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog