Variations in output volatility: Evidence from international historical data

Economics Letters 178 (2019) 102–105

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Variations in output volatility: Evidence from international historical data Bruno Ćorić University of Split, Faculty of Economics, Cvite Fiskovića 5, 21000 Split, Croatia

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The The The The

study focuses on the variations in output volatility. research is based on the historical output data for 38 counties. results suggest declining of output volatility over the last two centuries. results point to different patterns of output volatility across countries.

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Article history: Received 17 January 2019 Received in revised form 25 February 2019 Accepted 7 March 2019 Available online 8 March 2019 JEL classification: N10 E3

a b s t r a c t The paper investigates variations in output volatility in 38 OECD and non OECD countries over the last two centuries. Our tests reveal significant structural changes in output volatility in all countries. A more than 70% of detected structural changes indicates a reduction in volatility suggesting that output volatility has been declining over the last two centuries in general. The results, however, reveal different patterns of output volatility across countries. © 2019 Elsevier B.V. All rights reserved.

Keywords: Output volatility Structural changes Historical analysis

1. Introduction The current insight on the time series characteristics of output volatility derives mainly from the literature on the Great Moderation and the early studies of historical data. The Great moderation literature is based upon the results of the tests for discrete changes in output volatility of the US economy and other economies across the world (McConell and Perez-Quiros, 2000; Mills and Wang, 2003; Stock and Watson, 2002; Ćorić, 2012). This literature, however, has only considered the data for the post World War Two (WWII) period. The studies of historical data are focused on the relatively small group of developed economies (see Bacus and Kehoe, 1992; Bergman et al., 1998; Basu and Taylor, 1999). Moreover, these early studies do not employ formal tests for changes in output volatility. They provide simple comparisons of output volatility between historical landmarks and/or important economic events (the end of the gold standard, WWII, etc.) taking these events as a common turning points for all countries. E-mail address: [email protected]. https://doi.org/10.1016/j.econlet.2019.03.008 0165-1765/© 2019 Elsevier B.V. All rights reserved.

To improve our understanding of output volatility we use Barro and Ursua’s (2008, 2012) historical data. The data set includes annual real GDP p.c. data for 42 countries up to 2009. Country starting dates vary, ranging from 1790 to 1913. We employ data for 20 OECD and 18 non OECD countries for which it is possible to get continuous output series. For each country separately we test for a structural breaks in the output growth volatility. 2. Methodology Following McConell and Perez-Quiros (2000), Stock and Watson (2002) we modelled output growth as a AR process and tested for breaks in the mean of the absolute values of the AR model residuals. More precisely, for each country we constructed the AR model for output growth. The lag length (p) in each AR model is determined using the Bayesian Information Criterion and the Ljung– Box test. Since possible breaks in the mean output growth may result in the spurious conclusion that volatility of output growth has changed we allow for five breaks in the mean output growth

B. Ćorić / Economics Letters 178 (2019) 102–105

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Table 1 Structural breaks in output volatility. Country

Argentina Australia Austria Belgium Brazil Canada Chile China Colombia Denmark Egypt Finland France Germany Iceland India Indonesia Italy Japan Korea Mexico Netherlands New Zealand Norway Peru Portugal Russia S. Africa Spain Sri Lanka Sweden Switzerland Taiwan Turkey United Kingdom Uruguay United States Venezuela

Breaks in output volatility SD

Year

SD

9.995 9.187 2.280 1.738 5.621 6.549 6.215 7.180 1.138 2.826 5.380 5.405 5.129 2.211 3.421 6.734 2.651 1.863 7.444 4.958 5.712 12.712 7.619 4.170 2.867 2.290 10.056 8.649 5.067 5.234 4.751 5.588 12.435 13.977 3.227 9.925 3.100 10.304

1905D*** 1898D*** 1913I* 1893D*** 1931D*** 1946D*** 1982D*** 1976D*** 1925I*** 1877D** 1977D*** 1948D** 1913I* 1913I** 1915I** 1921D** 1925I* 1913I* 1949D** 1934I** 1934D*** 1817D** 1882D*** 1865D*** 1924I** 1914I* 1945D*** 1937D* 1963D*** 1950D*** 1942D*** 1949D*** 1948D* 1888D** 1946D*** 1934D*** 1892I*** 1950D**

5.362 4.348 15.474 0.684 3.744 2.299 3.165 2.552 3.078 1.524 1.850 3.174 11.506 21.240 6.661 3.220 7.982 8.520 3.211 13.419 3.194 2.972 3.709 1.870 8.493 6.427 3.552 2.541 2.519 2.737 2.233 2.341 3.062 3.629 1.980 5.503 7.115 5.427

Year

SD

Year

SD

1947D** 1952D* 1913I***

2.046 2.532 14.365

1999D** 1981D* 1951D***

0.751 1.621 2.044

1951D*** 1914I**

2.123 6.708

1946D**

2.434

1948D*** 1947D** 1971D**

1.560 4.111 3.336

1979D*** 1976D**

1.134 1.347

1976D* 1946D* 1974D** 1953D**

4.346 2.815 2.140 3.658

1916I** 1929I** 1916I*** 1935D** 1947D* 1989I**

12.028 6.472 6.648 2.833 3.439 8.175

1958D** 1953D*** 1948D*** 1977I**

1.952 2.322 1.721 6.333

1914I** 1991D*

11.705 1.031

1954D**

2.822

2.845

1984D***

1.280

1946D***

Year

SD

1986I**

5.173

The years denote break points. D indicates that volatility after the break decreased. The opposite is the case for I. SD denotes the standard deviation of the output growth. *indicate 10% of significance. **indicate 5% of significance. ***indicate 1% of significance.

(that is, the constant of AR model). So, we consider the linear AR model with m breaks (m+1 regimes) for each country,

1yt = αj + β1 1yt −1 + · · · + βp 1yt −p + εt

(1)

for j = 1, . . . , m + 1 and p = 1, . . . , n, where 1yt denotes the output growth rate at time t. αj (j = 1, . . . , m + 1) is the constant of the AR model in the jth regime. β1,...,p are the autoregressive parameters of the AR model and εt is the regression error at time t. The break points are treated as unknown and are estimated by Bai and Perron’s (1998) testing procedure. After the parameters in Eq. (1) are estimated, we employed the models residuals to test for structural breaks in the output growth volatility. Particularly, we tested for breaks in the mean of the absolute values of the AR model residuals εˆ t .

⏐ ⏐ ⏐εˆ t ⏐ = γj + ut

(2)

Where γj (j = 1, . . . , m + 1) is the constant in the jth regime and ut is the regression error at time t. Bai and Perron (1998) proposed several tests for multiple structural breaks with unknown break points. Following Bai and Perron (2003) we first employed the test for l versus l+1 breaks and sequentially tested the hypothesis of l versus l+1 breaks using supF (l+1| l) statistics. In the presence of multiple breaks there may be cases when configurations of changes are such that it is

very difficult to reject the null hypothesis of 0 versus 1 break in the model, but is not difficult to reject the hypothesis of 0 versus a higher number of breaks. The sequential procedure breaks down in such cases. Hence, in all cases when the used sequential procedure indicated no breaks we considered the results of UDmax and WDmax tests, as well. If these tests indicated the presence of at least one break, the results of the supF (1| 0) test are ignored and the number of breaks is selected upon the results of the supF (l+1| l) and supF(l+1| 0) tests. 3. Results The results of tests for structural breaks are reported in Table 1.1 To provide a better insight the results are also presented graphically in Figs. 1 and 2.2 1 Due to the space limit, we do not report the results of all the employed tests, but just the years of detected breaks. As in Stock and Watson (2002), since we are regressing the absolute value of residuals from an autoregression of real GDP growth on a constant and allowing a break in the constant from the auxiliary regression, the break estimator has a non-normal and heavytailed distribution, and the computed confidence intervals are so wide as to be uninformative. The results of all tests, as well as, the confidence intervals are available on request. 2 Countries are classified across the groups of OECD and non OECD countries based on the original Barro and Ursua, Barro and Ursua’s (2008, 2012) classification.

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B. Ćorić / Economics Letters 178 (2019) 102–105

Fig. 1. Output volatility in OECD countries. (Vertical lines indicate break points reported in Table 1.)

Fig. 2. Output volatility in non OECD countries. (Vertical lines indicate break points reported in Table 1.)

Taken together, we detected 72 breaks in output volatility at

out of 38 countries under investigation two or more breaks in

standard levels of statistical significance. A majority (52 out of

output volatility are detected. A single break in output volatility

72) of these breaks points toward a reduction in volatility. In 21

is detected in 17 countries.

B. Ćorić / Economics Letters 178 (2019) 102–105

Since more than 70% of the detected breaks indicates a reduction in output volatility, our results suggest that output volatility has been declining over the last two centuries in general. However, our results reveal different patterns of output volatility across countries. These patterns cannot be easily generalized as continuous decline in output volatility or some more complex common process shaped by global turning point(s) in volatility. Consistently with the literature, our results indicate a reduction in output volatility at the end of the 20th century in 12 countries and a reduction in output volatility after the WWII in 24 economies. Yet, in 9 countries breaks in volatility that correspond to these periods are not identified. In 7 countries both breaks are detected, while in 22 countries only one of these two breaks is identified. The identified breaks in output volatility appear to be dispersed across years and decades suggesting that the WWII and/or the 1984 (the starting year of the Great Moderation in the US) cannot be considered as the universal global turning point(s) in output volatility. The breaks in output volatility before the WWII show a similar kind of dispersion implying that global turning points cannot be identified in this period neither. Conversely, comparison of the detected breaks in volatility after the WWII to the results reported in Ćorić (2012) reveal that, in some countries, the date or number of breaks has been different. These differences could be caused by a few reasons. Given the limitation of available historical data we employ real GDP p.c. to investigate variations in output volatility, while Ćorić (2012) uses real GDP. Due to the differences in the length of the time series the minimal number of observations between two breaks imposed by Bai and Perron (1998) testing procedure is not identical for corresponding countries in these two studies. The results of Monte Carlo simulations in Jones and Olken (2008) suggest that the Bai and Perron’s (1998) method is conservative in detecting breaks, capturing only major changes. Accordingly, the smaller number of breaks in this study indicates that some breaks detected in Ćorić (2012) appear to be relatively small when considered in historical perspective. Our results also show that the post WWII period and the last decades of the 20th century were not the only periods with the low output volatility. The episodes of the lower output volatility are identified in 16 countries before the WWII. The detected breaks in output volatility reveal that some of these countries have been passing through the consecutive phases of higher and lower volatility during their history. The analysis of the historical data used in this study reveal another interesting point. The analyses of the post WWII data

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regularly suggest that developing economies are more volatile as compared to the developed economies. We also detect significant difference in output volatility after the WWII between non OECD and OECD countries in our sample (standard deviations are 4.32% and 2.83%, respectively; p = 0.00). However, at the same time our data show that when the entire historical data sets are compared the output volatility in OECD countries does not appear to be significantly smaller as compared to output volatility in non OECD countries (standard deviations are 5.35% and 6.08%, respectively; p = 0.221). The standard deviations of output growth in the period before WWII in non OECD and OECD countries are 7.18% and 6.33%, respectively (p = 0.28). So, the significantly lower output volatility in the OECD countries, as compared to the non OECD countries, appears to be related only to the post WWII period. Acknowledgement This work has been supported in part by Croatian Science Foundation under the project (IP-2016-06-4682). References Bacus, D., Kehoe, P., 1992. International evidence on the historical properties of business cycles. Amer. Econ. Rev. 82, 864–888. Bai, J., Perron, P., 1998. Estimating and testing linear model with multiple structural changes. Econometrica 66, 47–78. Bai, J., Perron, P., 2003. Computation and analysis of multiple structural change models. J. Appl. Econometrics 18, 1–22. Barro, R., Ursua, J., 2008. Macroeconomic crises since 1870. Brook. Pap. Econ. Act. 1, 255–335. Barro, R., Ursua, J., 2012. Rare macroeconomic disasters. Ann. Rev. Econ. 4, 83–109. Basu, S., Taylor, A., 1999. Business cycles in international historical perspective. J. Econ. Perspect. 13, 45–68. Bergman, M., Bordo, M., Jonung, L., 1998. Historical evidence on business cycles: The international experience. In: Fuhrer, J., Schuh, S. (Eds.), Beyond Shocks: What Causes Business Cycles? Federal Reserve Bank of Boston, Boston, pp. 65–113. Ćorić, B., 2012. The global extent of the great moderation. Oxf. Bull. Econ. Stat. 74, 493–509. Jones, B.F., Olken, B.A., 2008. The anatomy of start-stop growth. Rev. Econ. Stat. 90, 582–587. McConell, M., Perez-Quiros, G., 2000. Output fluctuations in the United States: What has changed since the early 1980’s? Amer. Econ. Rev. 90, 1464–1476. Mills, T., Wang, P., 2003. Have output growth rates stabilized? Evidence from the G-7 economies. Scott. J. Political Econ. 50, 232–246. Stock, J., Watson, M., 2002. Has the business cycle changed and why? NBER Macroecon. Annu. 17, 159–218.