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1. Introduction The Chinese equity market has become more attractive to both investors and academics, thanks to its rapid growth and progressive market liberalisation. For investors, the rapidly growing size and the resistance to market shocks make the Chinese capital market more attractive. According to an ambition survey from BDO International (2010), the Chinese capital market is the most attractive in the BRICs. Of their interviewees, 43% from 239 companies intend to invest in China, compared to 27% who chose India, 18% who chose Russia and 12% who chose Brazil. For academics, the unique structural and progressive liberalisation reforms provide a typical representative of emerging markets. Moreover, under the shadow of the
current global economic recession, international capital is setting its sights on the Asian market for new growth opportunities. The correlation between the Chinese stock market and developed stock markets contains critical information for investors who are planning to access the Chinese capital market, because all price formulas, risk management, and assets allocation depend on the perdition of further correlations between individual assets. In this paper, I will discuss the following issues: 1. Will the policies of the Qualified Foreign Institutional Investors system (QFII) and the Split Share Structure Reform in China impact the correlations across China, Hong Kong, and U.S. stock markets? 2. How do the exogenous variables, the excessive trading volume, and the daily high-low price differential of each stock market drive the correlations between the Chinese and developed markets? 3. Do the developed markets lead the Chinese market? This study is practical for both investors and policy makers. For investors, if the Chinese market is increasingly correlated with developed markets, shocks from
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the global market will have significant effects on the Chinese market. As a result, the diversification benefit from holding Chinese securities is diminishing. If the Chinese market is still segmented from the global market, foreign investors will benefit from lower diversification risks by adding Chinese stocks in their portfolios. This issue has been discussed in Li (2007), Hu (2010), and Tian (2007), but they did not find strong evidence on increasing cointegration between the Chinese and global markets. For policy makers, increasing cointegration would confirm the effectiveness of the international reformation of the Chinese stock market. More importantly, assessable policies would guide further policy developments. According to Phylaktis (1999), Henry (2000), Bekaert (2003), and Bekaert et al. (2005), the integration of emerging markets into the global market attracts foreign investors and further reduces costs on equities. Earlier literature on the comovement between the Chinese market and the global market emphasised the long-term common trend of cointegration, which does not tend to vary according to short-term shocks in the market. For example, Tian (2007) used Johansen’s cointegration test and did not find increasing cointegration between the Shanghai and Asian stock markets. Therefore, it is worth investigating the comovement of stock markets from a short-term and dynamic perspective. Furthermore, this study will investigate factors driving the short-term fluctuation of correlations according to market shocks and market liberalisation reform policies in China. In this study, I employ the DCC model which was proposed in Engle (2002), because the time-varying correlations coefficients estimated by the DCC model can reflect a dynamic track on the behaviour of correlations, which enable further analysis on how correlation coefficients fluctuate with market stocks, market regime changes, and financial crises. Since the DCC model estimates the correlation coefficients
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based on standardised residuals, it resolves the problem of heteroskedasticity. In addition, the DCC model can be used to estimation dynamic correlations on multiple asset returns without complex estimations on parameters. In this study, the Shanghai and Shenzhen stock markets represent the Chinese stock market. The Hong Kong and U.S. markets represent developed markets. Hong Kong is one of the major financial markets in Asia and also has essential geoeconomic relationships to the Chinese market. Several studies have found a linkage between the Chinese and Hong Kong stock markets, such as Tian (2007) and Li (2007). Although that linkage was relatively weak, it is significant for this study. On the other hand, the U.S. market is the major leading market in the world, so correlation with the U.S. stock market is the most appropriate proxy of the cointegration with the international market. In Tian (2007) and Li (2007), there is no evidence to support comovement between the Chinese and U.S. markets. In addition, since the U.S. stock market is the largest stock market in the world, it was used as a benchmark market in Tian (2007) and Li (2007). This study will discuss two reform policies in the China, the Qualified Foreign Institutional Investors system (QFII) 1 and the Split Share Structure Reform. The QFII regime allows qualified foreign investors to participate in the yuan-denominated security market in mainland China. Foreign investors are picked by the China
Securities Regulatory Commission (CSRC) according to certain criteria. QFII is a milestone in the opening-up of the Chinese security market, which lifted the ban on foreign investment and facilitated international participation of the Chinese capital market. Moreover, the participation of foreign institutional investors enhances the
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The QFII was first launched on 5 Nov 2002 to allow licensed foreign investors to trade yuandenominated stocks in both the A share and bond markets. Due to tight restrictions on movements of capital in and out of China, Chinese mainland stock markets were closed to foreign investors before QFII. The first licence was issued to UBS AG on 23 May 2003. As of October 2010, there were 103 licensed foreign institutional investors under the QFII regime.
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interaction between the Chinese and international markets, further affecting the cause relationship and integration between them. From a statistical perspective, QFII is expected to have a positive effect on the correlation between the Chinese and developed stock markets. Another policy is the Split Share Structure Reform, initiated by the CSRC on 29 April 2005. This reform involves transforming non-tradable stocks to tradable stocks. The non-tradable stocks refer to shares issued by state-owned corporations that do not trade in public. The split share structure means that the existence of both tradable and non-tradable shares in the Chinese A-share market. According to a report by CSRC (2005), the non-tradable stocks account for more than half of the aggregate value of the Chinese stock market. The split share structure distorted the price mechanism of Chinese stocks, because the price of non-tradable shares does not fully reflect the market supply-demand relationship. Moreover, the split share
structure damaged the power of substantial shareholders due to inefficient resource allocation in the market structure (CSRC, 2005). Since prices of non-tradable stocks are relatively lower than their market values, release of non-tradable stocks directly into the market will cause a dramatic drop in the aggregate value of existing stocks. According to CSRC (2005), a compensatory value will be added to the non-tradable stocks before they are released to the public. The compensatory value offsets the gap between the current price and the market price of non-tradable stocks, which ensures market stability in the stock reform process. In sum, the stock reform improves the price mechanism as well as the size of the Chinese stock market, and further improves market efficiency. In other words, stock prices reflect information shocks in the market more efficiently. As a result, the stock reform reduces the gap in institutional synchronisation between the Chinese
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stock market and the global stock market.
Therefore, I expect the Split Share
Structure Reform to improve the correlation between the Chinese stock markets and developed stock markets. Another objective of this study is to analyse the impact of exogenous variables (excessive trading volume and the daily high-low price differential of each stock market) on the correlations between the Chinese and developed markets. Since the trading volume correlates with the liquidity effect (Longin, 1997) and the daily highlow price reflects news shocks (Chiang et al., 2007a), I expect these two variables to drive the movement of correlations across stock markets. A similar issue has been studied in Chiang et al. (2007a), who supplemented the DCC model with OLS regressions to analyse the impact of these exogenous variables on the correlation between the Chinese A share and B share. Following Chiang et al. (2007a), I set up an OLS regression with two exogenous variables to explain the movement of each series of correlations. In this study, I find strong evidence that the QFII regime and the Split Share Structure Reform improve the correlation between Shanghai and Hong Kong stock markets, and significant evidence that these reform policies improve the correlation between Shanghai and U.S. stock markets and between the Shenzhen and Hong Kong stock markets. However, no evidence shows that these policies have any impact on the correlation between Shenzhen and the U.S. stock markets. In addition, the Split Share Structure Reform has more profound and lasting impacts than the QFII regime on market cointegration between the Chinese and developed markets, because the restriction on foreign capital flows in China weaken the effectiveness of the QFII regime by increasing the systematic risk of the Chinese stock market.
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Excessive trading volume and the daily high-low price differential from Hong Kong stock market have positive effects on the correlations with the Chinese markets, while these variables from the U.S. market have negative effect, which is attributed to that the Chinese stock markets resist to shocks from the U.S. market due to the geoeconomic bond between the Chinese and Hong Kong markets. In addition, excessive trading volume and daily high-low price differentials from the Chinese markets have weak explanatory power on the correlation with developed markets, because daily price limit rules on stocks and the ban on short-selling distort the market volatility in the Chinese stock markets. The remainder of this paper is organised thus: Section 2 provides literature reviews on both the topic and the DCC model. Section 3 discusses the data used in this study and delineates the descriptive statistics. Section 4 presents the estimation process of the DCC model and tests on structural breaks. Empirical results are
discussed in Section 5, followed by the conclusion in Section 6. Applications and limitations of this study are given in Section 7.
2. Literature Review 2.1 Studies Related to the Topic From a practical perspective, the financial market liberalisation will increase emerging markets’ integration into the global market, will further attract foreign investment, and will reduce the cost of equity capital, thereby ultimately increasing economic welfare. This common point of view can be summarised from Phylaktis (1999), Henry (2000), Bekaert & Harvey (2000), Bekaert (2003), and Bekaert et al. (2005). As far as the Chinese market is concerned, a variety of studies have
investigated the cointegration of the Chinese stock market. Chow & Lawler (2003)
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examined the integration between the Chinese and the U.S. markets from 1992 to 2002. They estimated a multiple regression which cantinas the return and the
volatility from both markets. They did not find any evidence of positive correlation between the Shanghai and New York stock markets, and concluded that the Shanghai and the New York markets were not integrated. However, they did not consider the possibility that the Chinese stock market integrates with the U.S. market indirectly through a regional developed market, such as the Hong Kong market. Li (2007) examined the linkages across the two stock markets in China, the Hong Kong stock market, and the U.S. stock market. The author has tested for the transmission of returns and volatility in the share price indices between these markets. The data in Li (2007) covered the time period from 01/2000 to 08/2005. The author did not find any evidence of direct linkage between the Chinese stock markets and the U.S. market. However, the author found a weak volatility spill-over from the Hong Kong market to the Chinese markets. Although the magnitude of that spill-over linkage was small, it indicated a weak integration between the Chinese stock markets and the Hong Kong market. For my study, the extension of the data period may lead to new findings due to the accelerating reform of Chinese stock markets. Similar results have been summarised by Hu (2010), who employed a timevarying conditional copula approach to compare the dependence structures across the Chinese, the U.S., and some other stock markets. The author found that the market segmentation between the Chinese stock market and international markets is relatively greater than the segmentation between the Chinese stock market and the U.S. market. In other words, Chinese stocks did not depend on any financial markets at all. A possible explanation why Li (2007) and Hu (2010) did not uncover any significant results is that they did not consider the effect of the market reform process
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of Chinese stock markets, such as the establish of QFII and the Split Share Structure Reform. Tian (2007) investigated the cointegration between Shanghai (A share and B share), Hong Kong, Taiwan, Japan, and U.S. markets by Johansen’s cointegration test. He has collected a longer and more recent sample period, from 1993 to 2007. More importantly, he has accounted for the effect of the QFII regime in 2002. He found that Shanghai A share was increasingly cointegrated with other Asian financial markets after the Asian financial crisis, which covered the period with the QFII regime. However, Tian did not find direct evidence that the QFII regime increased the cointegration between Shanghai and other Asian stock markets, which may be because Johansen’s cointegration test only considers the change of long-term cointegration. Nevertheless, the idea of taking into account the influence of Chinese stock market reform polices is valuable for this study.
2.2 Application of the DCC Model From the academic perspective, correlations are critical inputs in financial management. Engle (2002) proposed the Dynamic Conditional Correlation (DCC) multivariate GARCH model, which blends all the advantages of earlier correlation models. It incorporates the Constant Conditional Correlation (CCC) model while allowing the correlation to be time varying. It incorporates the two-stage estimation in univariate GARCH models while giving more weight to individual volatility. Most importantly, the DCC estimators inherit the flexibility from univariate GARCH and improve the complexity of multivariate GARCH. Substantial studies have employed and modified the DCC model to investigate correlations. Chiang, et al. (2007a) examined the correlation between Chinese A-share and B-share returns based on three different measurements: the rolling correlation model;
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the time-varying coefficient model, and the DCC model. The data period was from 1996 to 2003. They found an increasing correlation between A-share and B-share, which indicated that the DCC model provided the most appropriate measurement of correlations. Moreover, they supplemented the DCC model with OLS regressions to identify the impact of excess trading volume and abnormal price differentials on the correlation, which sheds lights on the impact of market volatility on the dynamic correlations. Chiang, et al. (2007b) applied the DDC model to series of stock returns from nine Asian markets, from 1990 to 2003. Their study confirmed an increasing
correlation across Asian stock markets. In addition, the variance of correlations shifted over the period of the Asian financial crisis, which reflecting the impact of financial crises on dynamic correlations. A new development of the DCC model was proposed in Li and Zou (2008). They used a new version of DCC model, the mix dynamic conditional correlation model (MADCC), to examine how policy and information shocks affect the correlation of Chinese T-bond and stock returns. This model captures the changes of covariance of standardised residuals in response to both positive and negative policy shocks. They found the correlation responded differently to positive and negative policy shocks. Specifically, correlations respond more to negative shocks than to positive ones. Li (2010) demonstrated another development of the asymmetric DCC model that incorporates the effect of interest rate differentials. The author found evidence that interest rate differentials reduce correlations. More importantly, the author
accounted for the impact of structural breaks in response to establishment of the Euro on exchange rate correlations, which gives this study the inspiration of employing the
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likelihood ratio tests to capture structural breaks in correlations corresponding to policy shocks. In sum, earlier studies on cointegration between the Chinese and global stock markets emphasised the long-term relationship, which does not tend to move according to market stocks. As a result, there was no solid evidence of an increasing cointegration between the Chinese and the global markets. Therefore, this study will investigate short-term cointegration between the Chinese and other stock markets corresponding to both policy and information shocks. From the methodology
perspective, the DCC model can immediately reflect market conditions by emphasising the impact of aggregate volatility as well as accounting for the dynamic of condition covariance and variance. Moreover, the latest studies of the DCC model have demonstrated its flexibility and reliability.
3. Data and Descriptive Statistics 3.1 Data The data in this study include daily stock price indices (high, low, and close prices) and trading volumes. The indices include the Shanghai composite index, the Shenzhen composite index, Standard & Poor’s 500 (S&P 500) composite index, and the Hang Seng index of Hong Kong. All prices are denominated in U.S. dollars to render the results more practical for foreign investors, and also to avoid distortion of the exchange rate fluctuations. Data are collected from Data Stream International and cover the period from 22/6/2000 to 10/8/2010. I did not consider a sample period before 2000 to avoid the market turbulence of the Asian financial crisis, and also because of the acceleration of Chinese stock market reform after 2000.
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3.2 Descriptive Statistics The daily index returns are calculated as and , where ,
represent the closing price on day and the closing price on day
respectively. I divided the sample period into three sub-periods corresponding to the establishment of QFII and the Split Share Structure Reform, respectively. In addition, I set 31/7/2003 as the break point of the QFII, as the first trade under the QFII regime was completed on that day. The break point of the Split Share Structure Reform is 29/4/2005, which is the day the policy was established. Because the Split Share Structure Reform started to intervene in the market price mechanism immediately after it was instituted. In Panel A in Table 1, the Shanghai and Shenzhen indices have higher returns and higher variance than the S&P 500 and Hang Sang indices. However, the variance of the Shanghai index is lower than that of the Shenzhen index. According to Panel C, which covers the period between 31/7/2003 and 29/4/2005, returns of Shanghai and Shenzhen indices are negative, while returns of S&P 500 and Hang Sang indices are positive. A possible interpretation is the impact of the deduction of state-owned nontradable stocks (an experimental policy used by the CSRC to solve the problem of the split share structure before the Split Share Structure Reform was instituted). Specifically, the deduction of state-owned stocks released large amount of underpriced non-tradable stocks into the market, which disturbed the supply-demand relationship of existing stocks. As a result, the aggregate stock price fell as did returns on stocks in China. In Panel D, returns on Chinese indices have dramatically improved, which may be attributed to the positive effect of the Split Share Structure Reform in stock prices.
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Table 1. A Summary of the Statistics of Stock Returns (22/6/2000 – 10/8/2010)
Mean Std. Dev Skewness Kurtosis Ljung Box(10) Ljung Box2 (10)
Panel A. Entire period (22/6/2000 - 10/8/2010) SH SZ SP HS 0.022 0.032 -0.012 0.014 1.720 1.839 1.429 1.679 -0.105 -0.346 -0.343 0.077 6.900 6.245 13.146 11.619 17.797* 30.125** 43.64*** 30.748*** 614.79*** 1041*** 622.40*** 719.39***
Panel B. Sub period 1 (22/6/2000 - 31/7/2003) SH -0.024 SZ SP -0.042 -0.059 1.329 1.389 1.443 1.433 0.843 0.616 0.213 0.229 11.917 10.700 3.938 3.890 2.99 5.328 6.239 15.784 179.72*** 180.43*** 175.73*** 203.41***
HS -0.063
Panel C. Sub period 2 (31/7/2003 - 29/4/2005) SH -0.063 SZ SP HS -0.085 0.041 0.065 1.260 1.329 0.737 1.019 0.677 0.473 0.0917 -0.056 4.013 4.001 4.13 5.310 12.117 11.947 8.531 11.112 115.63*** 115.52*** 128.02*** 86.87***
Panel D. Sub period 3 (29/4/2005 - 8/10/2010) SH SZ 0.075 0.112 2.021 2.175 1.584 1.958 -0.359 -0.635 -0.557 0.030 5.463 4.977 14.938 10.098 13.914 22.812** 47.973*** 28.22*** 332.20*** 266.32*** 353.97*** 422.48***
SP -0.0015 HS 0.0422
‘SH’ represents Shanghai composite index returns, ‘SZ’ represents Shenzhen composite index returns; ‘SP’ represents S&P 500 composite index returns, and ‘HS’ represents Hang Seng index returns. Ljung Box(10) and Ljung Box 2(10) test the dependency of index returns and squared index returns with 10 days lags, respectively. *, **, and *** represent statistical significance at 10%, 5%, and 1% respectively.
According to Chen et al. (2001), the negative skewness is a result of abnormal increases in trading volumes, because trading volumes reflect the degree of disagreement in stock markets. In situations of high disagreement, investors tend to
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under-react to information provided by bearish investors. This unrevealed (bearish) information leads the market to a negative skewness until bearish information forces it to come out. Skewness coefficients of SH, SZ, and SP in Panel D in Table 1 are negative, while they are positive in Panels B and C. Therefore, I suspect the existence of abnormal trading volumes in SH, SZ, and SP from 29/4/2005 to 8/10/2010. According to data in Panel B to Panel D in Table 1, the kurtosis coefficients of Chinese indices are diminishing over the three sub-periods while the kurtosis coefficients of SP and HS are increasing, which indicates that distributions of Chinese index returns have gradually become shorter in tails and smoother in peaks, further reflecting that the volatility of returns inherent in the Chinese stock markets is diminishing. In addition, all from test on squared index returns (Ljung-
Box2 (10)) in Table 1 are highly significant, which indicates a problem of heteroskedasticity, calling for the univariate GARCH model is proposed. Unconditional correlations contain useful information about the long-term relationship of market cointegration. Simple unconditional correlation matrices of four index returns are presented in Table 2. The sub-periods in Table 2 are the same as in Table 1. The unconditional correlation coefficient is computed based on
constant correlation coefficient formula in Equation 1.
According to Table 2, the correlation between the Shanghai and Shenzhen indices is extremely high throughout all periods. However, the Shanghai index is more correlated with the Hang Sang index and the S&P 500 index than is Shenzhen index. In addition, increasing correlations exist between Chinese indices and
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developed market indices. However, Chinese indices are more correlated with Hang Sang index than with the S&P 500 index. Table 2. Simple Correlation Matrix
SH SZ HS SP Entire period (22/6/2000 - 10/8/2010) SH 1 SZ 0.939741 1 HS 0.059376 0.042663 1 SP 0.365195 0.313271 0.254426 1 Sub period 1 (22/6/200 - 31/7/2003) SH 1 SZ 0.982292 1 HS -0.00861 -0.01106 1 SP 0.081126 -0.01106 0.187364 1 Sub period 2 (31/7/2003 - 29/4/2005) SH 1 SZ 0.959665 1 HS 0.007777 0.017527 1 SP 0.175045 0.177847 0.166456 1 Sub period 3 (29/4/2005 - 8/10/2010) SH 1 SZ 0.927087 1 HS 0.088408 0.063203 1 SP 0.464663 0.392373 0.288103 1 ‘SH’ represents Shanghai composite index returns, ‘SZ’ represents Shenzhen composite index returns, ‘SP’ represents S&P 500 composite index returns, and ‘HS’ represents Hang Seng index returns.
In Table 2, although an increasing correlation between Chinese indices and developed market can be found by the unconditional correlations, regarding the limitation of the constant correlation model, this only shows parametric information of the relationship in three sample periods. It cannot provide any information on the dynamic behaviour of correlations within each sub-period. At this stage, use of the dynamic correlation coefficient (DCC) model is proposed. The DCC model estimates the time-varying correlation coefficients and thus allows one to track the movements of correlations.
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4. Methodology 4.1 The DCC Model The DCC model was proposed in Engle (2002). I use it to estimate the dynamic conditional correlations across four stock index returns in this study. To start with, I specify each series of index returns as: (2) where ; is the residual for each index return, respectively. The AR(1) term
Equitation 2 is used to account for the autocorrelation in each index returns. Next, the conditional covariance matrix is specified as: (3) where is the (2× diagonal matrix of time varying standard deviations estimated 2) is the time-varying correlation
from univariate GARCH models, and matrix.
According to Engle (2002), the DCC model involves a two-stage estimation of the conditional covariance matrix conditional variance index returns: (4) where α is the weight of the lagged squared returns, β is the weight of the lagged variances, and ω is a constant. In the second stage, the index return residuals estimated in Equation 2 are transformed by the respective standard deviation estimated in Equation 4 in the first stage, which is: , where is the standardised residual which is . In the first stage, an estimate is made of the
by the univariate GARCH (1, 1) model for each series of
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used to estimate the conditional correlation parameters in latter processes. evolution of the correlation in DCC model is given in Equation (5).
The
(5) where: ; ; and ; ; , ; and , ,
is the unconditional correlation between . The elements of Equation (5) are:
(6) (7) (8) where correlation matrix , is given in Equation (9). (9) where , ). is a correlation matrix with ones on is , . The time-varying
diagonal and off diagonal elements less than one in absolutes value, given positive. A typical element of in a bivariable form is given in Equation (10).
According to Engle (2002), the coefficients in Equation (10) can be estimated by maximising the log-likelihood function, which is given is Equation (11).
(11)
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4.2 The Likelihood Ratio Tests Up to this point, the model we have discussed does not differ from that of Engle (2002). To test for structural breaks corresponding to the Chinese financial market reform policies, I follow Li (2010) and Gannon & Au-Yeung (2008) by importing the likelihood ratio test. The test statistic ‘LRT’ is twice the difference in two log-likelihoods: (12) where unrestricted model and represents the log-likelihoods estimated by the represents the log-likelihoods estimated by the restricted
model. The LRT statistic is measured by the chi-square distribution with the degrees of freedom equals to the number of restrictions (structural breaks). Specifically, I divide the unconditional correlation, which is in Equation (5),
into different time periods corresponding to the Chinese stock market reforms. Let: ‘A’ denote the start of the sample period, ‘B’ denote the break point of the QFII regime, which is 31/7/2003, ‘C’ denote the break point of the Split Share Structure Reform, and ‘D’ denote the end of the sample period. There are four different models corresponding to different unconditional correlations: ? ? Model 0 has no structural break in , and provides references for other models. Model 1 has two structural breaks in Structure Reform. Let 22/6/2000 to 31/7/2003, 1/8/2003 to 29/4/2005, and samples. , the QFII regime and the Split Share
be the unconditional correlation for samples from be the unconditional correlation for samples from be the unconditional correlation for the rest of
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?
Model 2 has one structural break in
, the QFII regime only. Let
be the be
unconditional correlation for samples from 22/6/2000 to 31/7/2003 and the ? for the rest of samples
Model 3 has one structural break in , the Split Share Structure Reform only. Let be the unconditional correlation for samples from 22/6/2000 to 29/4/2005, and be the unconditional correlation for the rest of samples. Next, I will apply the likelihood ratio tests to estimate the maximum
likelihood functions corresponding to different models.
For each series of
correlations, the null hypothesis is Model 0 (no structure breaks in ). First, I will test the likelihood for Model 0 versus Model 1. If both structural breaks are
significant, there will be no occasion to test Model 2 and Model 3 individually. If Model 1 is rejected, tests on Model 2 and Model 3 will be necessary to identify the significance of each individual structural break.
5. Empirical Results 5.1 Estimation of Structural Breaks The first objective is to identify the empirical evidence of significant structural breaks on the correlation between Chinese and developed stock markets corresponding to the Chinese stock market reforms. I set up four different models corresponding to the number of structural breaks to estimate the maximum likelihoods. Furthermore, I apply likelihood ratio tests on these likelihoods to test for existing of structural breaks. The Results are presented in Table 3. According to Table 3, strong evidence supports there being two structural breaks in the correlations between the Shanghai and Hang Sang indices. Significant
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evidence supports there being two structural breaks in the correlations between Shanghai and S&P 500 indices as well as in the correlation between Shenzhen and Hang Sang indices. However, both structural breaks are rejected in the correlations between Shenzhen and S&P 500 indices, which may be because the Shenzhen market is more attractive to Hong Kong investors due to the geo-economic bond between Shenzhen and Hong Kong. Similar results can be obtained from the graphic
presentations of estimated correlation coefficients in the next section. Table 3. Estimates of Maximum Log-likelihoods and Likelihoods Ratio Tests
Model 1 Model 2 Model 3 Model 0 (df=2) (df=1) (df=1) 7.71 10.92 0.0402** 144.28 159.71 0*** 7.633 9.101 8.118 8.667 0.230 0.325 0.150 117.73 120.84 0.0447** ‘SH-SP’ denotes the correlation between Shanghai and S&P 500 index returns; ‘SH-HS’ denotes the correlation between Shanghai and Hang Seng index returns; ‘SZ-SP’ denotes the correlation between Shenzhen and S&P 500 index returns; and ‘SZ-HS’ denotes the correlation between Shenzhen and Hang Seng index returns. ‘LLF’ denotes the log-likelihood function evaluated at the maximum. Each ‘p_value’ is estimated by the likelihoods ratio test, with null hypothesis of Model 0 (no structural break in ). ** and *** denotes significance at 5% and at 1%, respectively.
5.2 Estimation of Correlation Coefficients According to the results from Table 3, I use Model 1 to estimate the correlation coefficients for SH-SP, SH-HS, and SZ-HS. Meanwhile, I use Model 0 to estimate the correlation coefficients for SZ-SP because there is not a significant structural break in the unconditional correlations. (Parameters estimates of the DCC model are presented in Appendix A.)
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0.2 0.15 0.1 0.05 0 -0.05
Figure 1. Time varying correlation coefficients between Shanghai and S&P 500 index returns
0.6 0.5 0.4 0.3 0.2 0.1 0
Figure 2. Time varying correlation coefficients between Shanghai and Hang Seng index returns
0.07
0.06 0.05 0.04 0.03
0.02
0.01 0
Figure 3. Time varying correlation coefficients between Shenzhen and S&P 500 index returns
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0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0
Figure 4. Time varying correlation coefficients between Shenzhen and Hang Seng index returns
Table 4. Statistical Summary of Estimated Time Varying Correlation Coefficients
Mean SH-SP SH-HS SZ-SP SZ-HS 0.0623 0.271 0.0404 0.241 Variance 0.0044 0.0268 0.0017 0.0188 Skewness 2.53 0.35 13.06 0.39 Kurtosis 29.28 -1.3 249.18 -0.96
‘SH-SP’ denotes the correlation between Shanghai and S&P 500 index returns; ‘SH-HS’ denotes the correlation between Shanghai and Hang Seng index returns; ‘SZ-SP’ denotes the correlation between Shenzhen and S&P 500 index returns; and ‘SZ-HS’ denotes the correlation between Shenzhen and Hang Seng index returns.
In Figure 1, two obvious jumps in the movement of correlations are consistent with the two structure breaks in Model 2, which indicates that the significant change in the unconditional correlation corresponds to structural breaks. In addition, the volatility of correlation excluding the structure breaks in Figure 1 is relatively low, compared to the volatility of correlations in Figures 2, 3, and 4. Correlations in Figure 2 and Figure 4 follow a similar pattern, indicating that the Hang Seng index is equally correlated with two Chinese market indices. Moreover, there are constantly increasing correlations between Hang Seng and the
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Chinese indices after mid-2003, while such a trend cannot be clearly observed in correlations between the Chinese and S&P 500 indices. Furthermore, correlations between the Shenzhen and S&P 500 indices are rising dramatically before mid-2003 while staying relatively constant thereafter. These observations shed light on the impact of the QFII regime (started to issue licenses to foreign investors in July 2003) on the correlations between Hang Seng and the Chinese indices. This further
indicates that the QFII regime is more attractive to Hong Kong investors than to U.S. investors. In addition, all four series of correlations experienced abnormal fluctuations in late 2008. Specifically, there is a sudden drop in correlations in Figure 1 and Figure 3 around late-2008. Furthermore, the growing trend of correlations in Figure 2 and Figure 4 halt after late-2008. Therefore, I expect the subprime financial crisis has had considerable impact on correlations between Chinese and global stock markets. In Table 4, the correlations between the Chinese and Hang Seng indices have higher mean and higher variances than the correlation between Chinese and S&P 500 indices. The kurtosis coefficients of SH-SP and SZ-SP are much greater than the kurtosis coefficients of SH-HS and SZ-HS, which indicates greater density of volatility in correlations between the Chinese and S&P 500 indices than in correlations between the Chinese and Hang Seng indices. From the domestic point of view, SH-SP and SH-HS have greater means than SZ-SP and SZ-HS respectively, while SZ-SP and SZ-HS have lower variances than SH-SP and SH-HS respectively, reflecting that differences in market volatility occurred in the Shanghai and Shenzhen stock markets. To identify the impact of the movement of market volatility on the correlation coefficients across market indices, I will carry out regression estimations.
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5.3 Regression Estimation of Correlation Coefficients Although the correlation coefficients are derived from the DCC model and have incorporated the effect of structural breaks corresponding to reform policies, the conventional analysis of estimated time-varying correlation coefficients is insufficient to further investigate on the impact of reform policies and market volatility on correlations from a quantitative perspective. According to Engle (2002), the
correlation estimator in the DCC model has to be positive definite because the covariance matrix is a weighted average of a positive definite matrix. As a result, the DCC model may not allow one to incorporate the potential effects of lagged exogenous variables into the estimation of current correlation. However, the lagged exogenous variables are expected to have critical impacts on the movements of correlations across indices. Specifically, why is the Shenzhen index increasingly correlated with Hang Seng index while remained a roughly constant correlation with the S&P 500 index? Why do the correlations between the Chinese and Hang Seng indices follow a different pattern to correlations between the Chinese and S&P 500 indices? These observations lead to one question: What factors drive the time varying correlation coefficients? Following Chiang et al. (2007), who applied a regression to identify variables affecting the time varying correlation between Chinese A share and Chinese B share, I supplement the DCC model with OLS regression to see if any exogenous variables matter. First, I set up a preliminary regression model as: (13) where is the correlation coefficient between two index returns. and are
explanatory variables associated with market volatility.
Since the correlation
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coefficients in the DCC model are estimated based on past variances and residues of index returns, there is autocorrelation in estimated correlations, which would lead to understated standard deviations in regression estimation and further interfere with the . Therefore, I include in the regression to capture the
autocorrelation in each time series. A variety of studies have argued that trading volume is correlated with market volatility. Longin (1997) found positive correlations across liquidity, trading volume, and returns volatility. Wagner and Marsh (2005) found the surprise volume, which is above the average trading volume, has a positive correlation with the conditional market variance and return. Following these studies, I use the excess trading volumes as an explanatory variable in the regression. To accommodate the positive
definiteness of matrices in the DCC model, I take the absolute values of the excess trading volumes. Specifically:
where,
denotes the absolute value of excess trading volumes of either Shanghai or denotes the absolute value of excess trading volumes of ’ means moving average.
Shenzhen indices, and
either the S&P 500 or Hang Seng indices. ‘
The high and low prices during a trading day reflect the news shocks in a market (Chiang et al., 2007). Since the correlation coefficients are sensitive to
changes in volatilities during a particular day, shocks containing either good or bad news would be very likely to have significant potential influence on correlation coefficients. These news shocks are transmitted through the variation of the market volatility. Therefore, I introduce daily high-low price differentials as a proxy of news shocks in the regression:
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where and indices.
denotes the daily price differentials of either Shanghai or Shenzhen indices denotes the daily price differentials of either the S&P 500 or Hang Seng
Since the Chinese stock market is an emerging market, shocks from the global market are very likely to be lagged in spill-over to the Chinese market. To capture the lagged spill-over effect, I test each explanatory variable up to four lags. To capture the impact of Chinese stock market reform policies from a quantitative perspective, I set up two dummy variables in the regression: captures the impact of the QFII regime, unity after 31 July 2003, otherwise zero, and captures the effect of the Split Share Structure Reform, unity after 29 April 2005, otherwise zero. In addition, since the subprime financial crisis is expected to have considerable impact on the correlations between the Chinese and the global stock markets, I set up a dummy variable: , which unity starts from 1 June
2007 to 31 December 2008, otherwise zero. In sum, the general estimation regression is:
where
is the correlation coefficient between two index returns;
are are Each
explanatory variables from one of the Chinese indices; and explanatory variables from either the S&P 500 or Hang Seng indices. explanatory variable in Equation 14 is tested up to four lags (including
). I reject
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the lag variables with insignificant coefficients one by one, and only keep the lag variables with the most significant coefficients. If a variable is rejected at both lagged levels regression. and unlagged level , that variable will be rejected from the
In addition, only significant dummy variables are included in final
regressions. As a result, each final regression is different from the others. Table 5. Regression Estimates of Correlation Coefficients
Coefficients 0.775 -0.0013 -0.0751
t-statistic (71.8)*** (-2.66)*** (-10.9)***
Coefficients 0.996 0.00071 0.0188 0.0356 0.00068 0.00086
t-statistic (1141)*** (1.88)* (2.82)*** (4.26)*** (2.94)*** (2.74)***
0.0096 0.0194 -0.0014 F-stat 130755*** Coefficients 0.998 -0.00027 -0.0072
(19.2)*** (20.5)*** (-6.46)*** F-stat t-statistic (2160)*** (-3.65)*** (-8.45)***
778569*** Coefficients 0.995 0.00061 0.0374 0.00071 0.00089 t-statistic (1080)*** (1.96)* (5.70)*** (3.78)*** (3.42)***
F-stat
1614929***
F-stat
948961***
‘SH’ denotes the Shanghai index returns, ‘SZ’ denotes Shenzhen composite index returns; ‘SP’ denotes S&P 500 composite index returns, and ‘HS’ denotes Hang Seng index returns.* and *** denote significance at 10% and 1% respectively.
Table 5 reports the final estimation of four series of correlation coefficients based on Equation 14. Highly significant F-statistics indicate great overall joint significance of explanatory variables as a group. In general, results from Table 5
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suggest that correlation coefficients are sensitive to the explanatory variables. There are six findings summarised in Table 5 in the order of parameters. First finding. In all regressions, the daily price differential has much higher explanatory power than the excessive volume does, from both an economic and a statistical perspective. From an economic perspective, estimated coefficients of the price differential are more than 10 times greater than coefficients of the excessive volume in each regression. From the statistical perspective, all five coefficients of the price differential are significant at 1%, while only two coefficients of the excessive volume are significant at 1%. This finding is inconsistent with Chiang et al. (2007), they argued that excessive volume has same explanatory power in correlation estimation as the price differential, because the excessive volume proxies the liquidity effect while the price differential proxies the market volatility (shocks). My finding suggests that the
liquidity effect is not as significant as market volatility when they are used to estimate cross-nation correlations, because the liquidity effect from a foreign market impacts the correlation between two stock markets indirectly through the global financial market. On the other hand, information shocks from a foreign market may spill-over into the domestic stock market directly. In the other words, the liquidity effect from a foreign market has less effect than the market volatility (shocks) from a foreign market on the correlation between domestic and foreign markets. Second finding. In general, explanatory variables from Chinese markets have very weak explanatory power. There are nine significant explanatory variables in four regressions, and only one is from a Chinese market, which is the daily price differential of the Shanghai index in the regression of . The weak explanatory
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power of Chinese variables indicates that correlations between the Chinese and developed markets are mainly determined by the volatility from developed markets. The weak explanatory power of Chinese market variables is attributed to the restriction in the Chinese security market, such as the daily price limit rules and the ban on short-selling. The China Securities Regulatory Commission (CSRC) enforces a 10% daily price change limit on each individual security. If a stock hits the upper or the lower limit, it will be closed for trading. Stock price limits benefit by decreasing irrational stock price volatility, countering overreaction, and curbing speculation. For this reason, daily price limits are adopted in many countries. The Tokyo Stock Exchange Fact Book (2010) states that ‘daily price limits to prevent wild day-to-day swings in stock prices and provide a "time-out" in the event of a sharp rise or decline in price.’ According to George and Hwang (1995), under the daily price limit rules, stock prices are difficult to adjust according to substantial order imbalances at the end of a day. As a result, only part of the market value of stocks is reflected by the closing price. Therefore, index returns estimated by closing prices of Chinese indices cannot be fully explained by trading volumes and price differentials of Chinese indices, as are the correlations. Restrictions on short-selling have been practised in earlier stages or in emergency situations in developed markets. The uptick rule was adopted in the U.S. in 1938, which only allows short-selling when the uptick rule satisfied. The uptick rule is satisfied when the price of a short is above the last trading price (SEC, 1999). Several studies argued that short-selling encourages speculative investments and further increases aggregate market volatility (McGavin, 2010); (Bris, et al., 2007) Vivek (2010) found the volatility of the DOW and S&P 500 rose after the elimination of the uptick rule in 2007. Conversely, since short-selling is prohibited is China, the
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volatility of Chinese markets is expected to be less dense than the volatility of stock markets that allow short-selling, which may be another explanation of the weak explanatory power of Chinese market volatility. Third finding. Explanatory variables from the U.S. stock market have negative
impacts on the correlations between the Chinese and S&P 500 indices, while explanatory variables from the Hong Kong stock market have positive impacts on correlations between the Chinese and Hang Seng indices. These different spill-over effects from Hong Kong and the U.S. market reflect the volatility of Chinese market following shocks from Hong Kong market while countering shocks from the U.S. market, which may be attributed to the geo-economic bond between the Chinese and Hong Kong financial markets. Specifically, China and Hong Kong are geographically close, so they experience common shocks from the regional financial markets (Asian markets). Meanwhile, shocks from the U.S. market only interfere with the Asian market through the global market. Moreover, the price of the H share (shares issued by Chinese companies that trading on the Hong Kong Stock Exchange) are floating simultaneously on the Chinese and Hong Kong stock markets, which increases the interaction and the synchronisation between these two markets. Since the
comovement between the Chinese and the U.S. stock markets is less synchronous than the comovement between the Chinese and Hong Kong stock markets, the resistance of the Chinese markets to shocks from the U.S. market leads to opposite signs in the spill-over effects on the correlations. Fourth finding. All explanatory variables are lagged by either one or two time periods (days). Since the correlation coefficients are estimated by the DCC model which is based on previous variances and residues of index returns, it is reasonable to say that the explanatory variables should be lagged by one period to match the correlation coefficients estimated by the DCC model. In addition, and are lagged by two periods that reflect the non-synchronous trading time
between the Chinese stock market and the U.S. stock market. Specifically, the trading hours of the New York Security Exchange in the Eastern Time zone of the U.S. are 13
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hours later than Chinese standard time. Therefore, the market volatility of the U.S. stock market is lagged to spill over into the Chinese market. considering the lag in the DCC estimation, it is reasonable for lagged by two periods in the regression. developed markets lead the Chinese markets. Fifth finding. and In Table 5, the estimation of dummy variables ( Furthermore, and to be
In sum, there is no evidence that the
) are consistent with the structural breaks in the estimation of the DCC and are highly significant in regressions of .
model. Specifically, , , and
, while insignificant in the regression of
Moreover, all significant dummy variables are positive, indicating the Chinese stock market reforms have positive impact on the correlation with the developed markets. Furthermore, coefficients of of in Table 5 are greater than coefficients
, reflecting that the Split Share Structure Reform has greater impact on
the correlations than QFII does. The weaker impact of QFII on the correlations is attributed to the imperfect capital mobility in China. The State Administration of Foreign Exchange (SAFE) supervises all capital flows between the Chinese and foreign financial markets, which increases the systematic risk of the Chinese capital market, further reduces the benefits of holding the Chinese stocks. Although the QFII regime provides a path for foreign investors to participate in the Chinese financial market, restrictions on foreign capital flows have narrowed this path. On the other hand, the Split Share Structure Reform has improved the aggregate volume as well as the market price mechanism of Chinese stock markets, which makes the Chinese stock market more attractive to foreign investors and further increases interactions between the Chinese and foreign stock markets. Therefore, the Split Share Structure Reform has greater impact on the correlations than the QFII regime does.
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Sixth finding. The coefficients of
only show a weak and negative
impact on the correlations between Shanghai and the S&P 500 index returns. Although the coefficient is statistically significant, it has little economic significance in the regression.
6. Conclusion This paper investigates the structure of correlations between the Chinese and two developed stock markets, the U.S. market and the Hong Kong market. Based on earlier literature and a review of descriptive statistics, I employed the DCC model proposed in Engle (2002) to estimate the time varying conditional correlations, because the DCC model can immediately reflect market conditions by emphasising the impact of aggregate volatility as well as accounting for the dynamic condition covariances and variances. Moreover, I introduced the likelihood ratio tests to
identify structural breaks in unconditional correlations corresponding to the QFII regime and the Split Share Structure Reform. The results from the likelihood ratio tests on structure breaks have been incorporated into the estimation process of the DCC model. I further investigated the impact of the QFII regime and the Split Share Structure Reform as well as the impact of explanatory variables (the excessive trading volume and the daily high-low price differential) on the correlation coefficients by OLS regressions. Findings are summarised from the OLS regressions of dynamic correlation coefficients. First, the excessive volumes that proxy the liquidity effect have weaker explanatory power than the price differential that proxies the market shocks in a case of cross-nation stock markets. Second, weak explanatory power emanates from the excessive volumes and the price differentials of the Chinese markets on the
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correlations with developed markets, because the daily price limit rules and the ban on short-selling distort the market volatility of the Chinese stock markets. Third, the volatility of the Chinese stock markets follows shocks from Hong Kong market while it counters shocks from the U.S. market, due the geo-economic bond between the Chinese and Hong Kong financial markets. Fourth, no evidence suggests that the developed markets lead the Chinese markets. Fifth, the Split Share Structure Reform has greater impacts than the QFII regime on the cointegration between the Chinese and developed markets, because the restriction on foreign capital flows of Chinese markets weakens the effectiveness of the QFII regime by increasing the systematic risk of the Chinese stock market. Sixth, the subprime financial crisis has only a weak negative impact on the correlation between the Chinese and the U.S. stock markets.
7. Applications and Limitations Through this study, a few recommendations emerge for investors: although there are evidence of increasing correlations between the Chinese market and developed markets, the Chinese market is still relatively segmented from the global market. Investing in the Chinese stock market will provide considerable
diversification benefit, especially for U.S. investors. For policy makers in China, liberalisation reforms of the stock market will facilitate integration between Chinese market and the global market. However, considerable market imperfection still exists on issues such as the restriction on foreign capital flows and limitations on the market volatility. This study supplements the DCC model with OLS regressions to test the impact of exogenous variables. Although it has provided significant findings, it is not very rigorous. In addition, further robustness checks can be done by considering
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other models for estimating time-varying correlations, such as rolling regression models.
Acknowledgement I express my sincerest thanks to Prof. Xiaoming Li, who has provided great assistance and encouragement throughout the whole process of this study.
References
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Appendix A. Parameter Estimates of the DCC Model with Structure Breaks
SH-SP Model 1 Model 2 0.0188 0.0188 0.0967*** 0.0964 ? 0.0104 0.0104 0.995*** 0.995 ? 4.091E+13 ? 4.091E+13 ? 1.098E+7 1.098E+7 ? 4.156 4.257 LLF 10.921 10.116 SH-HS Model 0 Model 1 Model 2 0.0526** 0.0634** 0.0576*** 0.0621*** 0.0616*** 0.0611*** 0.996 ? 0.996*** 0.997*** 0.998 ? 0.998 ? 0.996*** 0.0434 ? 0.142 0.726** 0.251 0.251 ? 0.445 ? 6.76 ? 1.000 ? 0.789 ? LLF 144.276 159.708 151.583 SZ-SP Model 0 Model 1 Model 2 0.0038 0.0188 0.0281 0.0937 ? 0.0964 ? 0.0953 ? 0.400 0.0118 0.0617 0.994*** 0.995*** 0.994*** 6705 ? 4.091E+13 ? 28.8 10131 1.098E+7*** 12.2 20770 4.156? 7.9? LLF 7.633 9.101 8.118 SZ-HS Model 0 Model 1 Model 2 0.0727*** 0.114*** 0.0710 0.0640*** 0.0482** 0.0710*** 0.997*** 0.994*** 0.995*** 0.998*** 0.997*** 0.997 ? 0.0282 0.0667 0.110 0.399 ? 0.7068 0.899 10.695 ? 10.701 11.490 LLF 117.730 120.838 119.077 Parameters presente in this table are estimated by Equation (5) : Model 0 0.0583 0.0964 ? 0.01 0.995 ? 4.09E+13 ? 1.095E+7 ? 4.399 7.708 Model 3 0.0188 0.0966*** 0.0104 0.995? 4.091E+13 ? 1.098E+7 ? 4.265 10.686 Model 3 0.117 0.0614* 0.992*** 0.998 ? 0.142 0.258 ? 1.000 ? 160.708 Model 3 0.0531 0.0945 ? 0.249** 0.992 ? 39044*** 9519 ? 3359 8.667 Model 3 0.0946 0.0683 0.993*** 0.998*** 0.113 0.899 ? 10.000 120.074
. Model 0, 1, 2, 3 are DCC models with different structure breaks in the unconditional correlation corresponding to the QFII regime and the Split Share Structure Reform. LLT is the log-likelihood function evaluated at the maximum. ‘?’ denotes the significance of parameters is inconclusive, because the TSP4.5 cannot show standard errors less than 0.00001 (0.1E-3). Therefore, these inconclusive parameters are expected to be highly significant. *, **, *** denote significance at 10%, 5% and 1% respectively.
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