- Email: [email protected]
Capital controls and stock market volatility in frequency domain
Economics Letters 91 (2006) 222 – 228 www.elsevier.com/locate/econbase
Capital controls and stock market volatility in frequency domain Alexei G. Orlov * Department of Economics, Radford University, Radford, VA 24142, United States Received 20 December 2003; received in revised form 2 May 2005; accepted 7 September 2005 Available online 20 March 2006
Abstract The link between capital controls and stock market volatility is examined using frequency domain techniques. Conventional analyses of the second moments can produce spurious results if the high-frequency volatility is reduced (increased) while the overall volatility is increased (reduced). D 2006 Elsevier B.V. All rights reserved. Keywords: Capital controls; Stock market volatility; Spectral analysis JEL classification: F36; G15; C14
1. Capital controls and financial stability Researchers and policymakers debate whether restrictions on capital mobility can help to ensure financial stability (e.g., Fischer, 1998; Edwards, 1999; Errunza, 2001). Among the focal points of this debate is the ability of capital control policies to alleviate excessive stock market volatility (e.g., Levine and Zervos, 1998; Huang and Yang, 2000; Edison and Reinhart, 2001; Kumhof, 2001). On the one hand, a country’s integration with the world markets can lead to a higher efficiency of the domestic stock markets due to greater transparency and improved disclosure rules (Kim and Singal, 2000), so capital controls may increase stock market volatility. On the other hand, capital account liberalization can trigger an inflow of speculative hot money, which, in turn, can lead to a sharp increase in the volatility of returns (Henry, 2003); thus, capital controls may be associated with lower stock market volatility. This * Tel.: +1 540 831 5889; fax: +1 540 831 6209. E-mail address: [email protected]. 0165-1765/$ - see front matter D 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2005.09.014
A.G. Orlov / Economics Letters 91 (2006) 222–228
223
paper re-examines the issue in a frequency-domain framework, thereby taking a new step toward resolving this debate empirically. Spectral density estimation offers a valuable perspective on the potency of capital controls — a perspective which helps to refine results of the conventional time-domain analyses. In the extant literature, the study of volatility does not go beyond the analyses of the second moments. For instance, Edison and Reinhart (2001) test for the equality of first and second moments of the data between capital controls and free capital mobility periods. To see why this conventional time-domain approach can be misleading, suppose that the stock market volatility is higher for the period with capital controls than without. In this case the researcher would be tempted to conclude that capital controls are impotent at reducing stock market volatility. However, this conclusion should be deemed spurious if, with capital controls in place, most of the variability can be accounted for by the longer-period components.
2. Methodology This paper uses spectral analysis to determine relative importance of cycles of different frequencies in accounting for stock market volatility during two periods — with and without capital restrictions. Each time series is decomposed into a number of orthogonal components associated with various frequencies, and the power spectrum estimates the contribution of the components in a given frequency band to the total variance (Granger, 1966). Since stock market quotes arenonstationary processes, we first transform our data by defining stock market returns as r ¼ 100ln ppt1t , where p t is stock market closing quote at date t, and p t1 is date t 1 quote.1 To perform the spectral analysis, we use finite Fourier decomposition to describe the value of the time series as a weighed sum of periodic functions. We then form a periodogram, which gives us the contribution of the kth harmonic x k to the total sum of squares. Finally, since the periodogram is a volatile and inconsistent estimator of the spectrum, we produce spectral density estimates by smoothing the periodogram ordinates. Because such kernel estimate is an average over a number of frequencies, and because estimates of the power spectrum at x k and x l are independent for k p l (Hamilton, 1994), kernel estimates are less volatile and more consistent estimates of the spectrum than periodogram.
3. Empirical results The issue of stock market volatility has received very close attention in the wake of financial crises in Asia, Latin America and Russia. This section uses the methodology outlined above to study the effects of capital controls on stock market volatility in seven countries listed in Table 1. Our choice of countries was motivated by two main considerations. First, our sample is representative in that (i) it includes countries that regulated (Malaysia and Russia) and those that deregulated their capital accounts during the late 1990s (Brazil, Chile, China, India and Indonesia), and (ii) some countries placed an emphasis on restricting the inflows of capital, while others targeted capital outflows. Second, and more importantly, our sample includes only countries with no significant changes within 1
Applying the first difference filter to the stock market quotes produces results that are nearly identical to those for the returns.
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Table 1 Changes in capital control policies and data summary Country Brazil Chile China India Indonesia Malaysia Russia a
Date of policy changea April 24, 1997 September 16, 1998 July 15, 1999 November 20, 1999 July 2, 1998 September 1, 1998 August 17, 1998
Liberalization or repression Lib. Lib. Lib. Lib. Lib. Rep. Rep.
Stock market index Bovesa Sao Paulo Santiago Stock Exchange Shanghai Composite BSE 30 Jakarta Composite KLSE Composite Moscow Times
Stock returns Mean
SD
0.61% 0.15% 0.26% 0.09% 0.26% 0.09% 0.50%
5.77 5.77 3.02 4.27 6.36 4.16 11.20
Based on the IMF’s Exchange Arrangements and Exchange Restrictions Annual Reports.
two and a half years prior to and two and a half years after the bmajorQ policy change reported in the second column of Table 1. Fig. 1 plots spectral densities of weekly returns on the stock market indices listed in the fourth column of Table 1 for the period from 1995 to 2001.2 Ultimately, we would like to know if capital controls are able to reduce the high-frequency volatility and magnify the low-frequency fluctuations. The shaded areas in Fig. 1 highlight the frequencies of 0 : 24 or lower (corresponding to the periodicity of 26 weeks or more) and frequencies higher than or equal to 1 : 57 (corresponding to the wavelength of 4 weeks or less). Fig. 1a reveals that after Brazil liberalized its capital account in 1997, the volatility of returns increased along all frequencies without exception. Chilean capital controls were able to reduce the volatility of stock market returns at high frequencies and magnify the low-frequency fluctuations (Fig. 1b). The spectral densities of Chinese stock market returns in Fig. 1c show that the removal of capital controls in 1999 shifted the weight away from low-frequency and toward higher-frequency components.3 The opposite is true for Indonesia (Fig. 1e): after the capital controls were lifted in 1998, we observe less volatility at the irregular components and more volatility near the trend. To produce accurate conclusions in the cases of India (Fig. 1d), Malaysia (Fig. 1f) and Russia (Fig. 1g) — and to quantify the results for the entire sample — we compute the exact percentage change in stock market volatility due to frequencies higher and lower than certain cut-off levels. The portion of the variance of stockR returns that is attributed to cycles with frequencies greater than or equal to x 1 can be k calculated as 2 x1 sˆ ðxÞdx, where sˆ (x) is the sample periodogram, or the sample analog of the population spectrum s(x) at frequency x. RSimilarly, the portion of the variance that is associated with x frequencies less than or equal to x 2 is 2 0 2 sˆ ðxÞdx. Thus, to calculate the contribution of various frequencies, we multiply the spectral density sˆ (x k ) from Fig. 1 by 4k n , where n is the number of observations in a time series, and sum over the relevant frequencies. We compare the contributions of x z 1.57 and x V 0.24 before and after imposing (lifting) capital controls.4 2 Weekly sampling frequency copes well with noise and spurious serial correlation caused by market microstructure and other effects (Poon and Granger, 2003). 3 One should, therefore, conclude that Chinese restrictions on capital mobility were successful, which (as we confirm below) cannot be inferred from the comparison of the second moments alone. 4 The results are largely invariant to choosing alternative cut-off frequencies.
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Table 2 reports the main findings and draws conclusions that emerge from the comparison of timeseries and frequency-domain analyses. In this table, columns two through four perform the comparison of second moments for two subperiods — with and without capital controls. A negative percent change indicates that variance is lower when capital controls are in place. The next six columns report the frequency-domain results. Columns five through seven show the volatility of returns due to frequencies x z 1.57 for the two subperiods, as well as the percent change relative to the no-controls subperiod. A positive (negative) sign in column seven indicates that the high-frequency volatility is higher (lower) for the period with capital controls. Columns eight through ten perform the analysis for the frequencies x V 0.24. The last column provides a comparison between the spectral and time-domain analyses. The timeseries results are deemed baccurateQ if the variance changes in the same direction as both the highfrequency and low-frequency volatility. If the variance changes in the opposite direction of the highfrequency volatility change, the time-series results are bspurious.Q We conclude that the time-domain results are bunderstatedQ (bexaggeratedQ) if the changes in the variance and high-frequency volatility are negative (positive), while the low-frequency change is positive (negative). We notice that for Brazil and India the time-series and spectral results paint an identical picture. For these two countries, capital controls are able to reduce both high- and low-frequency volatility, which drives the negative percent change in variance. At the other extreme is China as an example of a gross inconsistency between the time-domain conclusions and the true potency of capital controls. For this country, we observe a 17% increase in variance relative to the no-controls subperiod, which prompts one to believe that Chinese capital controls are incapable of reducing stock market volatility. However, such conclusion is erroneous, as high-frequency fluctuations are 15% lower with capital controls as compared to the no-controls subperiod. The fact that Chinese capital restrictions lead to a 57% increase in the lowfrequency volatility should be viewed in a positive light. However, the standard time-series analysis fails to recognize this and, worse, a variance-based study interprets this positive impact of capital controls as a failure! While the time-series results for Chile, Indonesia, Malaysia and Russia are broadly consistent with the spectral analysis (in that high-frequency volatility changes in the same direction as the overall volatility), frequency-domain results are much more informative, as for these countries low-frequency volatility changes in the opposite direction relative to the variance. Thus, in these instances timedomain results overstate or understate the true effectiveness of capital controls. Chile and Malaysia provide examples of how capital controls can be more effective than what can be judged from the second moments. Chilean stock market overall volatility is only 21% lower when capital controls are in place relative to the no-controls subperiod. However, the high-frequency volatility is 48% lower with capital controls. So although the time-series analysis correctly predicts that Chilean capital controls were effective, it severely underestimates the true effectiveness of Chilean policies. The explanation lies in the fact that lifting capital controls led to a whooping 131% decrease in lowfrequency volatility. The imposition of capital controls in Russia and Indonesia in 1998 led to an increase in variance and high-frequency volatility, and a reduction in the low-frequency (bgoodQ) volatility. As it turns out, our sample is representative in one additional way: it includes countries for which the time-series results are quite accurate (Brazil and India), a country for which timedomain conclusions should be deemed spurious (China), countries for which the second-moment analysis understates the true potency of capital controls (Chile and Malaysia), and countries for
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(a) Brazil
(b) Chile
12
6
spectral density
spectral density
no cc 8
4
cc
0 0.4
2.4
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1.2
1.6
2.0
2.4
2.8
4 3
no cc
2
3.2
0.0
0.4
0.8
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1.6
2.0
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frequency
(c) China
(d) India 4.0
cc
spectral density
spectral density
cc
1 0.0
2.0 1.6
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2.4
2.8
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2.8
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cc
2.4 2.0
0.8 0.0
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1.6
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1.6
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frequency
(e) Indonesia
(f) Malaysia
16
6
cc
12
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spectral density
5
8
no cc 4 0
cc
5
no cc 4 3 2 1
0.0
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1.6
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2.4
2.8
3.2
frequency
0.0
0.4
0.8
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1.6
2.0
2.4
frequency
(g) Russia
spectral density
28
cc
24
The shaded areas indicate (i) periodicity of 26 weeks or more, and (ii) wavelength of 4 weeks or less
20 16
no cc 12 8 0.0
0.4
0.8
1.2
1.6
2.0
frequency
2.4
2.8
3.2
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Table 2 Capital controls and volatility of stock market returns: a comparison of time- and frequency-domain results Country
Brazil Chile China India Indonesia Malaysia Russia a b
Volatility due to x z 1.57a
Volatility due to x V 0.24b
Without CC
With CC
Percent change
Without CC
With CC
Percent change
Without CC
With CC
Percent change
Assesment of time-domain results
50.71 18.16 8.45 19.63 30.82 19.31 106.56
15.99 14.31 9.87 17.09 61.02 14.24 125.75
68.46% 21.24% +16.86% 12.92% +97.99% 26.24% +18.01%
22.82 10.05 4.82 9.73 14.77 10.12 54.28
9.33 5.22 4.10 8.83 40.29 6.50 65.63
59.12% 48.04% 15.06% 9.25% + 172.80% 35.77% +20.90%
6.06 1.14 0.69 1.63 5.41 2.15 10.86
1.30 2.63 1.08 1.45 5.39 2.50 9.20
78.60% + 130.60% + 57.18% 10.93% 0.25% + 16.59% 15.27%
Accurate Understated Spurious Accurate Exaggerated Understated Exaggerated
Variance
Frequencies xz 2k 4 c1:57 corresponds to the periodicity of 4 weeks or less. Frequencies xV 2k 26 c0:24 corresponds to the periodicity of 26 weeks or more.
which the time-series studies exaggerate the true effectiveness of capital restrictions (Indonesia and Russia).
4. Conclusions This paper contributes to the body of research that explores the link between capital restrictions and financial stability. The conventional time-domain approach can lead to spurious results if the highfrequency volatility of the financial data is reduced (increased) at the same time as the overall volatility is increased (reduced). The results reported for China exemplify this possibility. Capital controls should be viewed in a positive light if they shift the weight away from irregular components and toward the trend component of volatility — even if the overall volatility is intact. Needless to say, in this scenario a second-moment study would conclude that the volatility of financial markets is immune to changes in capital control policies. These potentially misleading results, as well as ensuing policy implications, of the time-domain analyses necessitate a detailed examination of all frequency components. This logic — and our examples — prompts re-examination of results reported in Levine and Zervos (1998); Huang and Yang (2000); Kim and Singal (2000); Edison and Reinhart (2001); Kumhof (2001) and elsewhere. Even if the frequency-domain conclusions are generally consistent with the timedomain results, spectral analysis offers a deeper understanding of the effects of capital controls on stock market volatility. We show that time-domain techniques can exaggerate or understate the true potency of capital controls. For instance, if capital restrictions are able to dampen the high-frequency volatility while boosting the low-frequency components (as was the case in Chile and Malaysia), the true potency of capital controls will exceed the estimation based on the simple examination of the second moments.
Fig. 1. Spectral densities of stock market returns with (solid lines) and without (dashed lines) capital controls. The shaded areas indicate (i) periodicity of 26 weeks or more, and (ii) wavelength of 4 weeks or less.
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Acknowledgement I would like to thank, without implicating, an anonymous referee for helpful comments on an earlier draft.
References Edison, H.J., Reinhart, C.M., 2001. Stopping hot money. Journal of Development Economics 66 (2), 533 – 553. Edwards, S., 1999. How effective are capital controls? Journal of Economic Perspectives 13 (4), 65 – 84. Errunza, V., 2001. Foreign portfolio equity investments, financial liberalization, and economic development. Review of International Economics 9 (4), 703 – 726. Fischer, S., 1998. Capital account liberalization and the role of the IMF. Princeton Essays in International Finance 207, 1 – 10. Granger, C.W.J., 1966. The typical spectral shape of an economic variable. Econo-metrica 34 (1), 150 – 161. Hamilton, J.D., 1994. Time Series Analysis. Princeton University Press, Princeton. Henry, B.H., 2003. Capital account liberalization, the cost of capital, and economic growth. American Economic Review 93 (2), 91 – 96. Huang, B.-N., Yang, C.-W., 2000. The impact of financial liberalization on stock price volatility in emerging markets. Journal of Comparative Economics 28 (2), 321 – 339. Kim, E.H., Singal, V., 2000. Stock market openings: experience of emerging economies. Journal of Business 73 (1), 25 – 66. Kumhof, M., 2001. International capital mobility in emerging markets: new evidence from daily data. Review of International Economics 9 (4), 626 – 640. Levine, R., Zervos, S., 1998. Capital control liberalization and stock market development. World Development 26 (7), 1169 – 1183. Poon, S.-H., Granger, C.W.J., 2003. Forecasting volatility in financial markets: a review. Journal of Economic Literature 41 (2), 478 – 539.
Capital controls and stock market volatility in frequency domain Alexei G. Orlov * Department of Economics, Radford University, Radford, VA 24142, United States Received 20 December 2003; received in revised form 2 May 2005; accepted 7 September 2005 Available online 20 March 2006
Abstract The link between capital controls and stock market volatility is examined using frequency domain techniques. Conventional analyses of the second moments can produce spurious results if the high-frequency volatility is reduced (increased) while the overall volatility is increased (reduced). D 2006 Elsevier B.V. All rights reserved. Keywords: Capital controls; Stock market volatility; Spectral analysis JEL classification: F36; G15; C14
1. Capital controls and financial stability Researchers and policymakers debate whether restrictions on capital mobility can help to ensure financial stability (e.g., Fischer, 1998; Edwards, 1999; Errunza, 2001). Among the focal points of this debate is the ability of capital control policies to alleviate excessive stock market volatility (e.g., Levine and Zervos, 1998; Huang and Yang, 2000; Edison and Reinhart, 2001; Kumhof, 2001). On the one hand, a country’s integration with the world markets can lead to a higher efficiency of the domestic stock markets due to greater transparency and improved disclosure rules (Kim and Singal, 2000), so capital controls may increase stock market volatility. On the other hand, capital account liberalization can trigger an inflow of speculative hot money, which, in turn, can lead to a sharp increase in the volatility of returns (Henry, 2003); thus, capital controls may be associated with lower stock market volatility. This * Tel.: +1 540 831 5889; fax: +1 540 831 6209. E-mail address: [email protected]. 0165-1765/$ - see front matter D 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2005.09.014
A.G. Orlov / Economics Letters 91 (2006) 222–228
223
paper re-examines the issue in a frequency-domain framework, thereby taking a new step toward resolving this debate empirically. Spectral density estimation offers a valuable perspective on the potency of capital controls — a perspective which helps to refine results of the conventional time-domain analyses. In the extant literature, the study of volatility does not go beyond the analyses of the second moments. For instance, Edison and Reinhart (2001) test for the equality of first and second moments of the data between capital controls and free capital mobility periods. To see why this conventional time-domain approach can be misleading, suppose that the stock market volatility is higher for the period with capital controls than without. In this case the researcher would be tempted to conclude that capital controls are impotent at reducing stock market volatility. However, this conclusion should be deemed spurious if, with capital controls in place, most of the variability can be accounted for by the longer-period components.
2. Methodology This paper uses spectral analysis to determine relative importance of cycles of different frequencies in accounting for stock market volatility during two periods — with and without capital restrictions. Each time series is decomposed into a number of orthogonal components associated with various frequencies, and the power spectrum estimates the contribution of the components in a given frequency band to the total variance (Granger, 1966). Since stock market quotes arenonstationary processes, we first transform our data by defining stock market returns as r ¼ 100ln ppt1t , where p t is stock market closing quote at date t, and p t1 is date t 1 quote.1 To perform the spectral analysis, we use finite Fourier decomposition to describe the value of the time series as a weighed sum of periodic functions. We then form a periodogram, which gives us the contribution of the kth harmonic x k to the total sum of squares. Finally, since the periodogram is a volatile and inconsistent estimator of the spectrum, we produce spectral density estimates by smoothing the periodogram ordinates. Because such kernel estimate is an average over a number of frequencies, and because estimates of the power spectrum at x k and x l are independent for k p l (Hamilton, 1994), kernel estimates are less volatile and more consistent estimates of the spectrum than periodogram.
3. Empirical results The issue of stock market volatility has received very close attention in the wake of financial crises in Asia, Latin America and Russia. This section uses the methodology outlined above to study the effects of capital controls on stock market volatility in seven countries listed in Table 1. Our choice of countries was motivated by two main considerations. First, our sample is representative in that (i) it includes countries that regulated (Malaysia and Russia) and those that deregulated their capital accounts during the late 1990s (Brazil, Chile, China, India and Indonesia), and (ii) some countries placed an emphasis on restricting the inflows of capital, while others targeted capital outflows. Second, and more importantly, our sample includes only countries with no significant changes within 1
Applying the first difference filter to the stock market quotes produces results that are nearly identical to those for the returns.
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A.G. Orlov / Economics Letters 91 (2006) 222–228
Table 1 Changes in capital control policies and data summary Country Brazil Chile China India Indonesia Malaysia Russia a
Date of policy changea April 24, 1997 September 16, 1998 July 15, 1999 November 20, 1999 July 2, 1998 September 1, 1998 August 17, 1998
Liberalization or repression Lib. Lib. Lib. Lib. Lib. Rep. Rep.
Stock market index Bovesa Sao Paulo Santiago Stock Exchange Shanghai Composite BSE 30 Jakarta Composite KLSE Composite Moscow Times
Stock returns Mean
SD
0.61% 0.15% 0.26% 0.09% 0.26% 0.09% 0.50%
5.77 5.77 3.02 4.27 6.36 4.16 11.20
Based on the IMF’s Exchange Arrangements and Exchange Restrictions Annual Reports.
two and a half years prior to and two and a half years after the bmajorQ policy change reported in the second column of Table 1. Fig. 1 plots spectral densities of weekly returns on the stock market indices listed in the fourth column of Table 1 for the period from 1995 to 2001.2 Ultimately, we would like to know if capital controls are able to reduce the high-frequency volatility and magnify the low-frequency fluctuations. The shaded areas in Fig. 1 highlight the frequencies of 0 : 24 or lower (corresponding to the periodicity of 26 weeks or more) and frequencies higher than or equal to 1 : 57 (corresponding to the wavelength of 4 weeks or less). Fig. 1a reveals that after Brazil liberalized its capital account in 1997, the volatility of returns increased along all frequencies without exception. Chilean capital controls were able to reduce the volatility of stock market returns at high frequencies and magnify the low-frequency fluctuations (Fig. 1b). The spectral densities of Chinese stock market returns in Fig. 1c show that the removal of capital controls in 1999 shifted the weight away from low-frequency and toward higher-frequency components.3 The opposite is true for Indonesia (Fig. 1e): after the capital controls were lifted in 1998, we observe less volatility at the irregular components and more volatility near the trend. To produce accurate conclusions in the cases of India (Fig. 1d), Malaysia (Fig. 1f) and Russia (Fig. 1g) — and to quantify the results for the entire sample — we compute the exact percentage change in stock market volatility due to frequencies higher and lower than certain cut-off levels. The portion of the variance of stockR returns that is attributed to cycles with frequencies greater than or equal to x 1 can be k calculated as 2 x1 sˆ ðxÞdx, where sˆ (x) is the sample periodogram, or the sample analog of the population spectrum s(x) at frequency x. RSimilarly, the portion of the variance that is associated with x frequencies less than or equal to x 2 is 2 0 2 sˆ ðxÞdx. Thus, to calculate the contribution of various frequencies, we multiply the spectral density sˆ (x k ) from Fig. 1 by 4k n , where n is the number of observations in a time series, and sum over the relevant frequencies. We compare the contributions of x z 1.57 and x V 0.24 before and after imposing (lifting) capital controls.4 2 Weekly sampling frequency copes well with noise and spurious serial correlation caused by market microstructure and other effects (Poon and Granger, 2003). 3 One should, therefore, conclude that Chinese restrictions on capital mobility were successful, which (as we confirm below) cannot be inferred from the comparison of the second moments alone. 4 The results are largely invariant to choosing alternative cut-off frequencies.
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Table 2 reports the main findings and draws conclusions that emerge from the comparison of timeseries and frequency-domain analyses. In this table, columns two through four perform the comparison of second moments for two subperiods — with and without capital controls. A negative percent change indicates that variance is lower when capital controls are in place. The next six columns report the frequency-domain results. Columns five through seven show the volatility of returns due to frequencies x z 1.57 for the two subperiods, as well as the percent change relative to the no-controls subperiod. A positive (negative) sign in column seven indicates that the high-frequency volatility is higher (lower) for the period with capital controls. Columns eight through ten perform the analysis for the frequencies x V 0.24. The last column provides a comparison between the spectral and time-domain analyses. The timeseries results are deemed baccurateQ if the variance changes in the same direction as both the highfrequency and low-frequency volatility. If the variance changes in the opposite direction of the highfrequency volatility change, the time-series results are bspurious.Q We conclude that the time-domain results are bunderstatedQ (bexaggeratedQ) if the changes in the variance and high-frequency volatility are negative (positive), while the low-frequency change is positive (negative). We notice that for Brazil and India the time-series and spectral results paint an identical picture. For these two countries, capital controls are able to reduce both high- and low-frequency volatility, which drives the negative percent change in variance. At the other extreme is China as an example of a gross inconsistency between the time-domain conclusions and the true potency of capital controls. For this country, we observe a 17% increase in variance relative to the no-controls subperiod, which prompts one to believe that Chinese capital controls are incapable of reducing stock market volatility. However, such conclusion is erroneous, as high-frequency fluctuations are 15% lower with capital controls as compared to the no-controls subperiod. The fact that Chinese capital restrictions lead to a 57% increase in the lowfrequency volatility should be viewed in a positive light. However, the standard time-series analysis fails to recognize this and, worse, a variance-based study interprets this positive impact of capital controls as a failure! While the time-series results for Chile, Indonesia, Malaysia and Russia are broadly consistent with the spectral analysis (in that high-frequency volatility changes in the same direction as the overall volatility), frequency-domain results are much more informative, as for these countries low-frequency volatility changes in the opposite direction relative to the variance. Thus, in these instances timedomain results overstate or understate the true effectiveness of capital controls. Chile and Malaysia provide examples of how capital controls can be more effective than what can be judged from the second moments. Chilean stock market overall volatility is only 21% lower when capital controls are in place relative to the no-controls subperiod. However, the high-frequency volatility is 48% lower with capital controls. So although the time-series analysis correctly predicts that Chilean capital controls were effective, it severely underestimates the true effectiveness of Chilean policies. The explanation lies in the fact that lifting capital controls led to a whooping 131% decrease in lowfrequency volatility. The imposition of capital controls in Russia and Indonesia in 1998 led to an increase in variance and high-frequency volatility, and a reduction in the low-frequency (bgoodQ) volatility. As it turns out, our sample is representative in one additional way: it includes countries for which the time-series results are quite accurate (Brazil and India), a country for which timedomain conclusions should be deemed spurious (China), countries for which the second-moment analysis understates the true potency of capital controls (Chile and Malaysia), and countries for
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(a) Brazil
(b) Chile
12
6
spectral density
spectral density
no cc 8
4
cc
0 0.4
2.4
0.8
1.2
1.6
2.0
2.4
2.8
4 3
no cc
2
3.2
0.0
0.4
0.8
1.2
1.6
2.0
frequency
frequency
(c) China
(d) India 4.0
cc
spectral density
spectral density
cc
1 0.0
2.0 1.6
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1.6
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0.8
1.2
1.6
2.0
frequency
frequency
(e) Indonesia
(f) Malaysia
16
6
cc
12
spectral density
spectral density
5
8
no cc 4 0
cc
5
no cc 4 3 2 1
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
frequency
0.0
0.4
0.8
1.2
1.6
2.0
2.4
frequency
(g) Russia
spectral density
28
cc
24
The shaded areas indicate (i) periodicity of 26 weeks or more, and (ii) wavelength of 4 weeks or less
20 16
no cc 12 8 0.0
0.4
0.8
1.2
1.6
2.0
frequency
2.4
2.8
3.2
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Table 2 Capital controls and volatility of stock market returns: a comparison of time- and frequency-domain results Country
Brazil Chile China India Indonesia Malaysia Russia a b
Volatility due to x z 1.57a
Volatility due to x V 0.24b
Without CC
With CC
Percent change
Without CC
With CC
Percent change
Without CC
With CC
Percent change
Assesment of time-domain results
50.71 18.16 8.45 19.63 30.82 19.31 106.56
15.99 14.31 9.87 17.09 61.02 14.24 125.75
68.46% 21.24% +16.86% 12.92% +97.99% 26.24% +18.01%
22.82 10.05 4.82 9.73 14.77 10.12 54.28
9.33 5.22 4.10 8.83 40.29 6.50 65.63
59.12% 48.04% 15.06% 9.25% + 172.80% 35.77% +20.90%
6.06 1.14 0.69 1.63 5.41 2.15 10.86
1.30 2.63 1.08 1.45 5.39 2.50 9.20
78.60% + 130.60% + 57.18% 10.93% 0.25% + 16.59% 15.27%
Accurate Understated Spurious Accurate Exaggerated Understated Exaggerated
Variance
Frequencies xz 2k 4 c1:57 corresponds to the periodicity of 4 weeks or less. Frequencies xV 2k 26 c0:24 corresponds to the periodicity of 26 weeks or more.
which the time-series studies exaggerate the true effectiveness of capital restrictions (Indonesia and Russia).
4. Conclusions This paper contributes to the body of research that explores the link between capital restrictions and financial stability. The conventional time-domain approach can lead to spurious results if the highfrequency volatility of the financial data is reduced (increased) at the same time as the overall volatility is increased (reduced). The results reported for China exemplify this possibility. Capital controls should be viewed in a positive light if they shift the weight away from irregular components and toward the trend component of volatility — even if the overall volatility is intact. Needless to say, in this scenario a second-moment study would conclude that the volatility of financial markets is immune to changes in capital control policies. These potentially misleading results, as well as ensuing policy implications, of the time-domain analyses necessitate a detailed examination of all frequency components. This logic — and our examples — prompts re-examination of results reported in Levine and Zervos (1998); Huang and Yang (2000); Kim and Singal (2000); Edison and Reinhart (2001); Kumhof (2001) and elsewhere. Even if the frequency-domain conclusions are generally consistent with the timedomain results, spectral analysis offers a deeper understanding of the effects of capital controls on stock market volatility. We show that time-domain techniques can exaggerate or understate the true potency of capital controls. For instance, if capital restrictions are able to dampen the high-frequency volatility while boosting the low-frequency components (as was the case in Chile and Malaysia), the true potency of capital controls will exceed the estimation based on the simple examination of the second moments.
Fig. 1. Spectral densities of stock market returns with (solid lines) and without (dashed lines) capital controls. The shaded areas indicate (i) periodicity of 26 weeks or more, and (ii) wavelength of 4 weeks or less.
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A.G. Orlov / Economics Letters 91 (2006) 222–228
Acknowledgement I would like to thank, without implicating, an anonymous referee for helpful comments on an earlier draft.
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