CROSS‐COUNTRY EVIDENCE ON OUTPUT GROWTH VOLATILITY: NONSTATIONARY VARIANCE AND GARCH MODELS
| Author | Stephen M. Miller,ChunShen Lee,WenShwo Fang |
| Published date | 01 September 2008 |
| Date | 01 September 2008 |
| DOI | http://doi.org/10.1111/j.1467-9485.2008.00464.x |
CROSS-COUNTRY EVIDENCE ON
OUTPUT GROWTH VOLATILITY:
NONSTATIONARY VARIANCE AND
GARCH MODELS
WenShwo Fang
n
, Stephen M. Miller
nn
and ChunShen Lee
n
Abstract
This paper revisits the issue of conditional volatility in real gross domestic product
(GDP) growth rates for Canada, Germany, Italy, Japan, the United Kingdom, and
the United States. Previous studies find high persistence in the volatility. This
paper shows that this finding largely reflects a nonstationary variance. Output
growth in the six countries became noticeably less volatile over the past few
decades. In this paper, we employ the modified iterated cumulative sum of squares
(ICSS) algorithm to detect structural change in the variance of output growth.
One structural break exists in each of the six countries after identifying outliers
and mean shifts in the growth rates. We then use generalized autoregressive
conditional heteroskedasticity (GARCH) specifications, modeling output growth
and its volatility with and without the break in volatility. The evidence shows that
the time-varying variance falls sharply in Canada and Japan, and disappears
entirely in Germany, Italy, the United Kingdom and the United States, once we
incorporate the break in the variance equation of output for the six countries. That
is, the integrated GARCH (IGARCH) effect proves spurious and the GARCH
model demonstrates misspecification, if researchers neglect a nonstationary
variance. Moreover, we also consider the possible effects of our more correct
measure of output volatility on output growth as well as the reverse effect of output
growth on its volatility. The conditional standard deviation possesses no statistical
significance in all countries, except a significant negative effect in Japan. The
lagged growth rate of output produces significant negative and positive effects on
the conditional variances in Germany and Japan, respectively. No significant
effects exist in Canada, Italy, the United Kingdom, and the United States.
I Intro ductio n
The Great Moderation captured the attention of macroeconomists, especially
because the decline in volatility of real gross domestic product (GDP) growth
n
Department of Economics, Feng Chia University
nn
College of Business, University of Nevada
Scottish Journal of Political Economy, Vol. 55, No. 4, September 2008
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Journal compilation r2008 Scottish Economic Society. Published by Blackwell Publishing Ltd,
9600 Garsington Road, Oxford, OX4 2DQ, UK and 350 Main St, Malden, MA, 02148, USA
509
occurs in numerous developed countries. Kim and Nelson (1999), McConnell
and Perez-Quiros (2000), and Blanchard and Simon (2001), among others,
document a structural change in the volatility of US GDP growth, finding a
rather dramatic reduction in GDP volatility since the early 1980s. Mills and
Wang (2003), Summers (2005), and Stock and Watson (2005) discover a
structural break in the volatility of the output growth rate for the G7 countries
and Australia, although the break occurs at different times. Kent et al. (2005)
show a considerable decline in the volatility of real output around the developed
world. That is, on average, across 20 selected OECD countries, the standard
deviation of the annual growth rate of GDP fell by more than one percentage
point since the 1970s. Cecchetti et al. (2005) examine shifts in the volatility of
growth in 25 developed and less-developed countries. They find at least one
break in all but nine countries and at most two breaks in six of the 25 countries.
Among the 22 breaks, only one takes place in the 1970s, 12 are in the 1980s, and
another nine are in the 1990s.
Several important issues emanate from this phenomenon. First, what caused
the decline in volatility? Analysts offer several hypotheses, including better
macroeconomic policies, structural change, or good luck.
1
Second, how does
one model the decline in volatility? Researchers frequently employ some form of
a generalized autoregressive conditional heteroskedasticity (GARCH) modeling
strategy to capture the movement in volatility under the assumption of a stable
variance process. Third, does the reduction in output growth volatility affect the
real GDP growth rate and/or does the output growth rate affect its volatility?
The existing empirical evidence on this third question provides mixed evidence.
Our paper focuses on the latter two questions, putting aside the issue of what
precipitated the decline in macroeconomic volatility. First, we argue that the
extant methods of modeling the time-series properties of the volatility of the real
GDP growth rate contain misspecifications associated with structural shifts. We
address such misspecifications by introducing structural shifts in the volatility
process. Second, given our improved specification of output growth volatility,
we reconsider the effect of the real GDP growth rate volatility on the real GDP
growth rate and the effect of the output growth rate on its volatility. In
addressing both questions, we examine six countries – Canada, Germany, Italy,
Japan, the United Kingdom, and the United States.
2
1
Bernanke (2004) organizes his thinking by using the most efficient inflation and output
volatilities frontier, the so-called Taylor curve (trade-off) (Taylor, 1979, 1994; Cecchetti, 1998).
Fuhrer (1997) and Lee (1999, 2002) estimate the Taylor trade-off for the United States.
Inefficient monetary policy leaves the economy above the frontier, whereas changes in the
volatility of random shocks will shift the lower-bound frontier. Stock and Watson (2003, 2005)
attribute the Great Moderation to good luck, implying that the frontier shifted toward the
origin. Bernanke (2004) argues that a substantial portion of the Great Moderation reflects
better monetary policy, implying a movement toward the frontier. The distinction proves
important. Good luck can turn into bad luck and the frontier can shift back to a more
unfavorable trade-off, or maintaining good policy can continue the benefits of the Great
Moderation.
2
We exclude France, another G7 country. When the Lagrange multiplier (LM) test of Engle
(1982) checks for conditional heteroskedasticity, insignificant LM statistics suggest no need of
W. FANG, S.M. MILLER AND C. LEE510
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Most research on the various aspects of output volatility, such as asymmetry
or its effect on the growth rate, assumes a stable GARCH process governing
conditional growth volatility. The neglect of structural breaks in the variance of
output leads to higher persistence in the conditional volatility. For example, in
Hamori (2000), the GARCH persistence of volatility equals 0.972 for Japan,
0.857 for the United Kingdom, and 0.987 for the United States. Caporale and
McKiernan (1996) and Speight (1999) conclude near unitary persistence of 1.09
and 0.9889, respectively, for the United Kingdom, and Fountas et al. (2004) find
volatility persistence of 0.982 for Japan. In Ho and Tsui (2003), the exponential
GARCH (EGARCH) persistence of volatility equals 0.848 for Canada, 0.834 for
the United Kingdom, and 0.916 for the United States. In sum, all the persistence
measures fall close to one.
Economic growth involves long-run phenomena. For longer sample periods,
structural changes in volatility will occur with a higher probability. Hamilton
and Susmel (1994) and Kim et al. (1998) suggest that the long-run variance
dynamics may include regime shifts, but within a regime it may follow a
GARCH process. Kim and Nelson (1999), Mills and Wang (2003), Bhar and
Hamori (2003), and Summers (2005) apply this approach of Markov switching
heteroskedasticity with two states to examine the volatility in the growth rate of
real GDP. The GARCH modeling approach provides an alternative to deal with
this issue, but relaxing the implicit assumption of a constant variance process.
Diebold (1986) raises the concern that structural changes may confound
persistence estimation in GARCH models. He notes that Engle and Bollerslev’s
(1986) integrated GARCH (IGARCH) may result from instability of the
constant term of the conditional variance, that is, nonstationarity of the
unconditional variance. Neglecting such changes can generate spuriously
measured persistence with the sum of the estimated autoregressive parameters
of the conditional variance heavily biased towards one. Lamoureux and
Lastrapes (1990) explore Diebold’s conjecture and provide confirming evidence
that not accounting for discrete shifts in unconditional variance, the
misspecification of the GARCH model, can bias upward GARCH estimates of
persistence in variance. Including dummy variables to account for such shifts
diminishes the degree of GARCH persistence. Mikosch and Sta
˘rica
˘(2004) argue
theoretically that the IGARCH model makes sense when non-stationary data
reflect changes in the unconditional variance. Hillebrand (2005) shows that in
the presence of neglected parameter change-points, even a single deterministic
change-point, GARCH inappropriately measures volatility persistence. More
recently, Kramer and Azamo (2007) argue that the changes in the variance could
arise from changes in the mean. They demonstrate that the estimated persistence
parameter in the GARCH(1,1) model contains upward bias when researchers
ignore structural changes in the mean.
The evidence of declining output volatility combined with finding an
IGARCH in conditional volatility motivates us to revisit conditional volatility
GARCH modeling for France. Cecchetti et al. (2005) report that France experiences no breaks
in persistence and volatility of GDP growth.
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