The growth-volatility relationship redux: what does volatility decomposition tell?
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Debdulal Mallick
Abstract
This paper revisits the empirical relationship between volatility and long-run growth, but the key contribution lies in decomposing growth volatility into its business-cycle and trend components. This volatility decomposition also accounts for enormous heterogeneity among countries in terms of their long-run growth trajectories. We identify a negative effect of trend volatility, which we refer to as long-run volatility, on growth, but no effect of business-cycle volatility. However, if long-run volatility is omitted, there would be a spurious (negative) effect of business-cycle volatility. Our results draw attention to a crucial question about different volatility measures and their implications in macroeconomic analyses.
Appendix
A Examples of heterogeneous growth trajectories
Costa Rica and Trinidad and Tobago: These two developing countries had the same average growth rate (approximately 0.021) and BC volatility (0.026), but LR volatility in Trinidad and Tobago (0.043) was more than twice as large as that in Costa Rica (0.017).
Ireland and Egypt: These countries had nearly the same average growth rate (0.031) and BC volatility (0.0189), but LR volatility in Ireland (0.026) was much larger than that in Egypt (0.015).
Austria and Japan: These two countries are similar in terms of average growth rate (approximately 0.020) and BC volatility (approximately 0.016) but differ with respect to LR volatility (0.007 and 0.015, respectively).
Fiji and Sweden: These two countries are similar in terms of average growth rate (approximately 0.016) and LR volatility (approximately 0.012) but differ with respect to BC volatility (0.039 and 0.018, respectively).
Nepal vs. Pakistan: These two countries are similar in terms of average growth rate (approximately 0.020) and LR volatility (approximately 0.009) but differ with respect to BC volatility (0.024 and 0.013, respectively).
Guatemala and Switzerland: Although both countries had the same average growth rate (0.010), BC volatility was larger in Switzerland (0.018) than in Guatemala (0.013), whereas LR volatility in Guatemala (0.017) was nearly twice as large as that in Switzerland (0.009).
There are examples in which countries with very different average growth rates experienced similar fluctuations. For example, the growth rate in Vietnam (0.040) was much higher than that in Bangladesh (0.019), but both countries had the same BC volatility (0.021) and LR volatility (0.016). Similarly, China and Greece had the same BC volatility (0.025) and similar LR volatility (0.022), but China’s economy grew at an average rate of 0.054, whereas the Greek economy grew at the slower rate of 0.012.
The above examples illustrate an enormous heterogeneity among countries’ respective growth trajectories. More specifically, very dissimilar growth trajectories can lead to the same average growth, and apparently similar growth trajectories can lead to different average growths. This heterogeneity can also be visualized in Figure 1A–H below, which display the long-run growth trajectories of the country pairs discussed above.
Comparison of long-run growth trajectories (Low-pass filtered annual growth rate).
B Comparison of spectral densities for 5-, 7-, 8-, and 10-year averaging
The spectral density for averaging over T years is given by: (1/T)2 (1 – cosTω)/(1 – cosω), where ω is the frequency ranging between 0 and π (for derivation, see Sargent 1987, 275). The spectral densities for T = 5, 7, 8, and 10 are displayed in Figure A.1 below. The spectral densities are normalized, using appropriate scalars, so that the area under all curves are equal. A vertical line is drawn at 0.786 to mark the critical frequency that separates the long-run from the cyclical frequencies. Note that the periodicity (p) and frequency are inversely related by the formula: p = 2π/ω. For a critical periodicity of 8 years, the corresponding critical frequency is 0.786. It can be seen from the graph that 5-year averaging does not reweight the variances of the raw series adequately across low frequencies, thus, the transformed data are more likely to be contaminated by high frequencies. For 5-year averaging, the area to the right of the vertical line is 14% of the total area under the curve. This area substantially reduces to 9.3% for 7-year averaging, remains the same for 8-year averaging, and reduces only to 8.8% for 10-year averaging.
Spectral densities for 5-, 7-, 8-, and 10-year averaging.
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Articles in the same Issue
- Advances
- What does a relative price of investment wedge reveal about the role of investment-specific technology?
- Envelope wages, hidden production and labor productivity
- Should individuals migrate before acquiring education or after? A new model of Brain Waste vs. Brain Drain
- Investment, technological progress and energy efficiency
- Bounded rationality and the ineffectiveness of big push policies
- Contributions
- Dissecting the act of god: an exploration of the effect of religiosity on economic activity
- Cross-industry growth differences with asymmetric industries and endogenous market structure
- Persistent Inequality, Corruption, and Factor Productivity
- The Finnish Great Depression of the 1990s: reconciling theory and evidence
- The growth-volatility relationship redux: what does volatility decomposition tell?
- Fiscal stimulus and unemployment dynamics
Articles in the same Issue
- Advances
- What does a relative price of investment wedge reveal about the role of investment-specific technology?
- Envelope wages, hidden production and labor productivity
- Should individuals migrate before acquiring education or after? A new model of Brain Waste vs. Brain Drain
- Investment, technological progress and energy efficiency
- Bounded rationality and the ineffectiveness of big push policies
- Contributions
- Dissecting the act of god: an exploration of the effect of religiosity on economic activity
- Cross-industry growth differences with asymmetric industries and endogenous market structure
- Persistent Inequality, Corruption, and Factor Productivity
- The Finnish Great Depression of the 1990s: reconciling theory and evidence
- The growth-volatility relationship redux: what does volatility decomposition tell?
- Fiscal stimulus and unemployment dynamics
