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Econometric history of the growth–volatility relationship in the USA: 1919–2017

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Abstract

In this paper, we investigate the relationship between output volatility and growth using the standard GARCH-M framework and the US monthly industrial production index (IPI) for the period January 1919–December 2017, by taking into account the presence of shocks and variance changes. The results show that the IPI growth is strongly affected by large shocks which are associated with strikes in some industries, recessions, World War II and natural disasters. We also identify several subperiods with different level of volatility where the volatility declines along the subperiods, with the pre-WWII period (1919–1946) the highest volatile period and the aftermath period of the GFC (2010–2017) the lowest volatile period. We find no evidence of relationship between output volatility and its growth during the full sample 1919–2017 and also for all the subperiods. From a macroeconomic point of view, this implies that economic performances, as measured by IPI growth, do not depend on the uncertainty as measured by IPI volatility.

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Notes

  1. See Fang and Miller (2008) for a discussion of the growth–volatility relationship.

  2. The critical values are defined by \(g_{T,\lambda }=-\log \left( -\log (1-\lambda )\right) b_T+c_T\), with \(b_T=1/\sqrt{2\log T}\), and \(c_T=(2\log T)^{1/2}-[\log \pi + \log (\log T)]/[2(2\log T)^{1/2}]\). Laurent et al. (2016) suggest setting \(\lambda =0.5\).

  3. Fang and Miller (2014) also detect and correct the outliers in the growth rate of real GNP using another approach. They first detect the outliers if \(|y_t-{\overline{y}}|>k\times \sigma _y\), where k measures the stringency imposed on outlier detection, and then apply the method of Ané et al. (2008) to correct the outliers identified. However, this approach is very sensitive to the value of k since when \(k=2\), 3 and 4 it identifies 36, 7 and 1 outliers, respectively. The choice of \(k=3\) by Fang and Miller (2014) is only based on the number of outliers found in previous studies.

  4. Note that Inclán and Tiao (1994) advised that ‘it is advisable to complement the search for variance changes with a procedure for outlier detection.’

  5. The IPI data had been seasonally adjusted by FRED prior to the analysis and are available at https://fred.stlouisfed.org/series/INDPRO.

  6. Most of explanations associated to the detected shocks are found in the Federal Reserve Bulletin of the Board of Governors of the Federal Reserve System for the 1920–1997 period (https://fraser.stlouisfed.org) and in the Industrial Production and Capacity Utilization - G.17 of the Board of Governors of the Federal Reserve System for the 1997–2017 period (https://www.federalreserve.gov/releases/g17/).

  7. Note that the studies on the US quarterly GNP/GNP growth exhibit only one structural break during the post-WWII period, around 1984Q2 (see, e.g., Stock and Watson 2005; Summers 2005; Cecchetti et al. 2006; Fang and Miller 2014; Charles and Darné 2018).

  8. Among the potential factors of this Great Moderation period, the literature put forward (1) ‘good practices,’ i.e.: improved inventory management (e.g., McConnell and Perez-Quiros 2000; 2) ‘good policies,’ i.e.: good monetary policy (e.g., Clarida et al. 2000; Bernanke 2004; Boivin and Giannoni 2006; Galí and Gambetti 2009); and (3) ‘good luck,’ i.e.: a decline in the volatility of exogenous shocks (e.g., Stock and Watson 2003, 2005; Ahmed et al. 2004).

  9. We wish to thank the referee for pointing out that the GFC should not be considered as a part of the Great Moderation and thus should be excluded from the last subperiod. The results show the impact of the GFC on the summary statistics.

  10. Under the assumption of a normal distribution \(k=3\), so the condition becomes \(3\alpha ^2+2\alpha \beta +\beta ^2<1\).

  11. Under a normal distribution \(\delta =\frac{1}{2}\).

  12. Trypsteen (2017) also use a GJR-GARCH model to capture the asymmetric effect, whereas Fang and Miller (2014) apply an EGARCH model.

  13. As in Fang and Miller (2008) and Fang et al. (2008), we have also introduced lagged output growth into the conditional variance equation in the GARCH-in-Mean model to avoid potential endogeneity bias, but the results are not significant.

  14. This problem can be explained by the very low number of observations to estimate an ARCH-M model (less than 100 observations).

  15. Empirical evidence of the growth–volatility relationship is mixed: negative (Henry and Olekalns 2002), positive (Fountas and Karanasos 2006; Fang and Miller 2014) or no statistically significant relationship (Grier and Perry 2000; Fang et al. 2008). The disagreements can be explained by the differences in terms of the time period examined, the frequency of the data and the methodology employed.

  16. To have a better fit for the GARCH models we focus on macroeconomic data with a high frequency. The correlation between industrial production and CFNAI is of 0.86 on the period 1967–2017.

  17. The economic indicators are drawn from four broad categories of data: (1) production and income; (2) employment, unemployment and hours; (3) personal consumption and housing; and (4) sales, orders and inventories. The derived index provides a single, summary measure of a factor common to these economic data.

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Acknowledgements

We are grateful for useful comments on a previous version of this paper by anonymous referees.

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  1. Audencia Business School, 8 Route de la Jonelière, 44312, Nantes Cedex 3, France

    Amélie Charles

  2. LEMNA, University of Nantes, Chemin de la Censive du Tertre, BP 52231, 44322, Nantes, France

    Olivier Darné

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Charles, A., Darné, O. Econometric history of the growth–volatility relationship in the USA: 1919–2017. Cliometrica 15, 419–442 (2021). https://doi.org/10.1007/s11698-020-00209-y

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