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Pacific-Basin Finance Journal xx (2004) xxx – xxx
www.elsevier.com/locate/econbase
A note on price limit performance: The case of
illiquid stocks
Gong-Meng Chena, Kenneth A. Kimb,*, Oliver M. Ruic
b
a
Department of Accountancy, Hong Kong Polytechnic University, Kowloon, Hong Kong
School of Management, State University of New York at Buffalo, Jacobs Management Center,
Buffalo, NY 14260, USA
c
Faculty of Business Administration, Chinese University of Hong Kong, Shatin, Hong Kong
Received 22 January 2003; accepted 24 May 2004
Abstract
In the Chinese stock markets, there are A-shares and B-shares. Both share-types have identical
cash flow rights but different ownership structures (i.e., A-shares are owned by local Chinese citizens
and B-shares are owned primarily by foreigners), causing B-shares to be less liquid relative to Ashares. However, even though B-shares have much wider bid–ask spreads than A-shares, both sharetypes are subject to the same 10% daily price limit regulation. As such, B-shares, simply due to their
wider spreads, may be more inclined than A-shares to hit price limits. Our empirical results support
this contention. The findings have policy implications. First, given wide spreads for illiquid stocks,
exchanges may consider using midpoint prices (between bid and ask prices) to establish price limit
ranges for illiquid stocks. In addition, and perhaps more importantly, exchanges may consider using
wider price limits for less liquid classes of stocks.
D 2004 Elsevier B.V. All rights reserved.
JEL classification: G10; G14
Keywords: China; Stock market; Price limits; Liquidity
* Corresponding author. Tel.: +1 716 645 3266; fax: +1 716 645 3823.
E-mail address: kk52@buffalo.edu (K.A. Kim).
0927-538X/$ - see front matter D 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.pacfin.2004.05.002
PACFIN-00328; No of Pages 12
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1. Introduction
Price limits exist in many stock markets around the world. The contended benefits for
using price limits are numerous and they vary. For example, price limits may be able to
bcool downQ markets during times of panic, they may be able to moderate excessive
volatility, and they may help identify market manipulation.1 Despite the potential cited
benefits of price limits, almost all of the recent empirical literature criticizes them for their
obvious impediment to market efficiency.2 For example, as shown by Kim and Rhee
(1997), when security prices are prevented from going beyond their price limit, desired
trading activities are postponed. Consequently, equilibrium price discovery is delayed and,
at the same time, stock price volatility is merely temporarily contained.
In this research note, we contribute to the growing list of price limit criticisms by
suggesting that price limits may be particularly restrictive for illiquid stocks. Illiquid
stocks usually have bid and ask prices that are relatively farther away from their mid price.
Therefore, if a price limit band is dnarrow,T then illiquid stocks may hit price limits often
simply due to their wide bid–ask spreads. A systematic relationship between limit-hit
frequencies and spread size is problematic because stock characteristics, in and of
themselves, should not result in predictable price-limit-hits, especially if price limits are
designed to be hit during times of unexpected excessive volatility and/or unique events
(see Kim and Limpaphayom, 2000 for a similar argument).
To investigate whether illiquid stocks are especially vulnerable to price limits, we use
data from the Chinese stock exchanges. The daily price limit in the Chinese stock markets
are set at 10%, for both upper and lower price movements, based on the previous day’s
closing price. What makes Chinese markets uniquely useful for our research purposes is as
follows. There are two types of shares traded on the Chinese stock markets: class A-shares
and class B-shares. A-shares are owned by and traded among Chinese citizens, while Bshares are owned primarily by and traded among non-Chinese citizens or overseas Chinese
citizens.3 Other than their ownership differences, A- and B-shares are identical in every
other important way. For example, both shares have the same claims on cash flows and the
same voting rights. However, due to their differences in their ownership type, B-shares are
dramatically less liquid than A-shares (see Chen et al., 2001). Here, price limits may be
particularly binding for B-shares, as compared to their effects on A-shares. If so, then a
1
For example, the Tokyo Stock Exchange believes that price limits provide a bcooling downQ effect (Tokyo
Stock Exchange, 1997), while the Taiwan Stock Exchange and the Athens Stock Exchange believe that price
limits moderate excessive volatility and destabilize speculation, respectively (Yang and Kim, 2001; Phylaktis et
al., 1999).
2
Chen (1998) and Park (2000) find that price limits in the U.S. futures markets delay equilibrium price
discovery. Similar findings have also been found for non-US stock exchanges (e.g., Kim and Rhee, 1997) using
Tokyo Stock Exchange data and Yang and Kim (2001) using Taiwan Stock Exchange data). In addition, price
limits do not appear to moderate excessive volatility in a meaningful way (Kim, 2001; Kim and Rhee, 1997).
Instead, volatile stocks are simply those that are hitting price limits (Kim and Limpaphayom, 2000). Recently,
Chan et al. (2004) find that price limits do not improve information asymmetry, delay the arrival of informed
traders, and exacerbate order imbalance.
3
Since 2001, domestic Chinese investors who have access to foreign currencies (U.S. dollars and Hong
Kong dollars) have been allowed to own B-shares. We address this regime shift later in the paper.
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policy prescription that stock markets may wish to consider is to adopt wider price limits
for their less liquid stock classes.
In our empirical examination, where we confine our study sample to firms that have
both A-shares and B-shares, we document a large number of occasions where B-shares hit
their price limit while the firm’s companion A-shares do not. As liquidity is the primary
difference (with regard to stock quality) between the same firm’s A-shares and B-shares,
this finding importantly suggests that illiquid stocks hit price limits more often than liquid
stocks, and hence stocks with wide bid–ask spreads, in particular, are constrained by
narrow price limits. We also find that B-shares typically close at the ask price, causing the
next day’s price limit to be upward biased. Note that this bias is significant for illiquid
stocks as their spreads are wide.
To further show that a stock’s wide spread causes it to hit price limits frequently, we
conduct regression analysis. Specifically, we test the relationship between a stock’s
propensity to hit price limits and its spread. If price-limit-hits are supposed to occur only
during periods of unusual volatility and/or events, then a stock’s intrinsic characteristics,
such as spread size, should not cause it to hit price limits more often (Kim and
Limpaphayom, 2000). However, our regression results do reveal a positive significant
relationship between spreads and limit-hit frequencies.
The rest of our research note proceeds as follows. In the next section, we provide a brief
overview of China’s stock exchanges. In the third section, we discuss our data. In Section
4, we discuss our results. Section 5 concludes the research note.
2. China’s stock exchanges
The two stock markets in China, the Shanghai Stock Exchange (SHSE) and the
Shenzhen Stock Exchange (SZSE), were established on December 1990 and July 1991,
respectively. To allow foreign investors to participate in China’s stock market, B-shares
were introduced in 1992, but not all firms list both classes of shares. In 1992, there were
53 A-shares and 14 B-shares on both exchanges combined. At the end of 2002, there were
1211 A-shares (725 in SHSE and 486 in SZSE) and 111 B-shares (54 in SHSE and 57 in
SZSE). There are two trading sessions on both exchanges. The morning session runs from
9:30 to 11:30 and the afternoon session runs from 1:00 to 3:00. The tick size is one cent,
regardless of the stock price. Both markets are completely order-driven, with no specialists
or market makers.
Since December 16, 1996, both markets have used a daily price limit of 10% based on
the previous day’s closing price. When a stock hits a price limit, there is no special
announcement; instead, this information is simply posted on the exchange’s trading
screens. Like most price limit systems, trading in the stock is allowed to continue after it
hits a price limit, but only trades at or within the limit-prices are executed. Finally, Ashares are denominated in RMB, and B-shares are denominated in US dollars (Hong Kong
dollars) in the SHSE (SZSE). Because price limits are based on a percentage, the different
denominations do not affect our analyses. This contention is confirmed by separate
analyses of SHSE and SZSE subsamples, where we find consistent results between the
subsamples despite the different denominations.
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3. Data
We use daily stock data retrieved from the China Stock Market and Accounting
Research Database, which is compiled and maintained at the Hong Kong Polytechnic
University. The database contains daily opening, closing, high, and low bid and ask prices
on all individual shares. In addition, the database contains daily trading volume and daily
shares outstanding for each firm. For our study sample, we use the period from July 1999
to December 2002, as this represents the entire period for which bid and ask data are
available in our database.
For illustrative purposes, Fig. 1 and 2 report the A-share and B-share composite index
of the Shanghai and Shenzhen Stock Exchanges, respectively, during March 1999 through
June 2003. With respect to our paper, and with respect to our subsequent empirical tests,
two noteworthy observations can be made from these figures. First, there is a dramatic runup in B-shares during the first half of 2001. On February 19, 2001, domestic Chinese
investors with US or Hong Kong dollars were allowed to purchase B-shares. Therefore,
since February 2001, B-shares became more like A-shares, which explains B-shares’ runup. Second, A-share returns and B-share returns appear to be strongly positively
correlated, thus confirming our earlier implicit contention that A-shares and B-shares
should share the same dtrueT price changes. Specifically, the correlation coefficients
between A-share returns and B-share returns during the period before and after February
2001 are 0.404 and 0.652, respectively.
As we focus on B-shares, we restrict our sample to firms that have both A- and Bshares. We have 83 firms (i.e., 166 stocks) in our final sample. Table 1 reports some
descriptive statistics of our sample. Specifically, we report bid–ask spreads for both Ashares and B-shares. Relative spread is measured as follows:
relative spread ¼ ðask price bid priceÞ=½ðbid þ ask priceÞ=2:
ð1Þ
An alternative spread measure, using trading price minus the mid price as the
numerator,4 yields nearly identical results to the reported results throughout the entire
paper, so we choose not to report on it. We report spread statistics separately for two
subperiods surrounding February 19, 2001. A bpre-event subperiodQ is from July 1, 1999
to December 29, 2000. A bpost-event subperiodQ is from July 1, 2001 to December 29,
2002. Data from the first 6 months for the year 2001 are excluded as it represents a
transitional phase, where B-shares were hitting their price limits almost every day (Chen et
al., 2003).5 Note also that our subperiods are equal in length, thus facilitating direct
comparisons between subperiods.
From Table 1, we see that during the pre-event period, the average B-share spread is
nearly ten times larger than the average A-share spread. Chen et al. (2001) confirm that
this difference in liquidity between A-shares and B-shares is due to their difference in
ownership structure. During the post-event period, where ownership restrictions were
lifted from B-shares, we see that B-shares have become more liquid, however, B-shares are
4
The logic of this alternative measure (otherwise known as beffectiveQ spread) is that trades can often occur
inside the posted bid and ask quotes. For example, see Christie et al. (1994) and Huang and Stoll (1994).
5
From January 2001 to June 2001, the return on B-shares was 163%.
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Fig. 1. The A-share and B-share composite index of the Shanghai Stock Exchange.
G.-M. Chen et al. / Pacific-Basin Finance Journal xx (2004) xxx–xxx
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Fig. 2. The A-share and B-share composite index of the Shenzhen Stock Exchange.
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Table 1
Descriptive statistics: bid–ask spreads
Pre-event period
Post-event period
A-shares
B-shares
Difference
0.0024
[0.0023]
(0.0008)
0.0023
[0.0022]
(0.0007)
0.0227
[0.0228]
(0.0094)
0.0054
[0.0049]
(0.0025)
0.0203***
0.0205***
0.0031***
0.0027***
This table reports means, medians (in [brackets]), and standard deviations (in (parentheses)) of bid–ask spreads
during two subperiods. The first subperiod, denoted as the pre-event period, is from July 1, 1999 to December 29,
2000, and the second subperiod, denoted as the post-event period, is from July 1, 2001 to December 29, 2002.
The sample is restricted to firms with both A and B shares. Statistically significant differences between A-shares
and B-shares are determined by a t-test (for means) and a Wilcoxon test (for medians). ***Denotes statistical
significance at the 1% level.
still significantly less liquid than A-shares. The persisting difference in liquidity may be
due to the fact that domestic shareholders must use US or Hong Kong dollars to trade in Bshares, or it may be due to a factor associated with foreign investors. Overall, Table 1
confirms that B-shares are less liquid than A-shares.
4. Empirical findings
4.1. Sample sizes of price limit hits
Table 2 presents sample sizes of limit-hit-days during our study period. Specifically, we
report the number of occasions where (i) a firm’s A-share and its B-share both hit their
upper price limit on the same day (denoted as A-up-hit and B-up-hit), and we similarly
report sample sizes for (ii) A-up-hit and B-no-hit, (iii) A-no-hit and B-up-hit, (iv) A-downhit and B-down-hit, (v) A-down-hit and B-no-hit, and (vi) A-no-hit and B-down-hit. We
also differentiate these samples by the exchange.
From Table 2, we see that it is rare for a firm’s A-shares and B-shares to both hit price
limits on any given day. During our study sample period, this only occurred 82 times. It
was more often the case that one of the shares hit a price limit and the firm’s other share
did not. Perhaps what is most striking in Table 2 is the fact that B-shares hit their lower
price limit, when their companion A-shares do not, a relatively very large number of times.
This pattern occurs on both stock exchanges. One possible explanation for this unusual
asymmetry between down-hits and up-hits is that B-shares typically close at their ask
prices (this occurs about 62% (55) of the time during the pre-event (post-event)
subperiod),6 thus causing the next day’s price limit to be upwardly biased.7 We investigate
this possible explanation further and find supporting evidence. Specifically, we find that
6
For A-shares, they close at their ask prices 46% (45) of the time during the pre-event (post-event)
subperiod.
7
We acknowledge our referee for pointing this out to us.
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Table 2
Sample sizes of limit-hit days
Shanghai Stock Exchange
Shenzhen Stock Exchange
Event
Sample size
Event
Sample size
Pre-event period
(i) A-up-hit and B-up-hit
(ii) A-up-hit and B-no-hit
(iii) A-no-hit and B-up-hit
(iv) A-down-hit and B-down-hit
(v) A-down-hit and B-no-hit
(vi) A-no-hit and B-down-hit
10
137
116
35
169
554
(i) A-up-hit and B-up-hit
(ii) A-up-hit and B-no-hit
(iii) A-no-hit and B-up-hit
(iv) A-down-hit and B-down-hit
(v) A-down-hit and B-no-hit
(vi) A-no-hit and B-down-hit
24
97
258
32
187
913
Post-event period
(i) A-up-hit and B-up-hit
(ii) A-up-hit and B-no-hit
(iii) A-no-hit and B-up-hit
(iv) A-down-hit and B-down-hit
(v) A-down-hit and B-no-hit
(vi) A-no-hit and B-down-hit
26
72
76
41
50
289
(i) A-up-hit and B-up-hit
(ii) A-up-hit and B-no-hit
(iii) A-no-hit and B-up-hit
(iv) A-down-hit and B-down-hit
(v) A-down-hit and B-no-hit
(vi) A-no-hit and B-down-hit
22
75
75
36
48
299
This table presents sample sizes for six different event combinations: (i) a firm’s A share hits its upper price limit
and its companion B share hits its upper price limit, (ii) a firm’s A share hits its upper price limit, but its
companion B share does not hit its upper price limit, (iii) a firm’s A share does not hit its upper price limit, but its
companion B share does not hit its upper price limit, and (iv–vi) repeats (i–iii), but using the lower price limits.
The sample sizes are reported for each stock exchange, and by subperiods. The first subperiod, denoted as the preevent period, is from July 1, 1999 to December 29, 2000, and the second subperiod, denoted as the post-event
period, is from July 1, 2001 to December 29, 2002.
when B-shares close at the bid price, they hit a down-limit on the next day 28 percent of
the time. In contrast, when B-shares close at the ask price, they hit a down-limit on the
next day 72% of the time. These findings are remarkably robust across subperiods. Note
that this finding has policy implications. Perhaps exchanges should set price limits based
on the previous day’s closing midpoint price (between the bid and the ask) rather than the
realized closing price, especially for illiquid stocks whose spreads are wide.
Most importantly (from the view of our paper), the sample sizes in Table 2 suggest the
following. When a class of stocks is illiquid, compared to other stocks, it appears to be
more inclined to hit price limits. Note that this is probably an unintended outcome for
stock exchanges that impose a uniform price limit regulation for all of its stocks. The next
subsection conducts an important direct test that investigates the relationship between a
stock’s spread and its propensity to hit price limits.
4.2. Regression analyses
Kim and Limpaphayom (2000) find that firms with high beta, high residual risk, high
trading volume, and small market capitalization, are more likely to hit price limits. That is,
they find that stocks with certain characteristics and qualities cause them to be
systematically more biased toward hitting price limits. Their finding reveals a significant
problem with price limits if price limits are supposed to be hit primarily during times of
unexpected excess volatility and/or unexpected events (e.g., stock market crashes), as most
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Table 3
Descriptive statistics
Pre-event period
Beta
RR
TV
Size
BM
Post-event period
A-shares
B-shares
A-shares
B-shares
0.8249
(1.0741)
0.0697
(0.0295)
0.0201
(0.0075)
22.3714
(0.6447)
0.2206
(0.1076)
0.8728
(0.5696)
0.0710
(0.0340)
0.0040
(0.0022)
20.8729
(0.7477)
1.0812
(0.5545)
0.9833
(0.3631)
0.0520
(0.0223)
0.0117
(0.0058)
22.3078
(0.6030)
0.2666
(0.1387)
0.9336
(0.2755)
0.0404
(0.0186)
0.0101
(0.0070)
21.6897
(0.6073)
0.4803
(0.2269)
This table reports means and standard deviations (in parentheses) of the control variables used in the regression
analyses. Beta is the market beta, RR is residual risk, TV represents average trading volume (daily trading volume
divided by total shares outstanding), Size is the log of market capitalization, and BM is the book-to-market value
of equity. Beta is calculated from the standard market model using monthly stock and equally weighted market
returns over the sample period, and the market model’s residual standard deviation is residual risk. The descriptive
statistics are differentiated by subperiods. The first subperiod, denoted as the pre-event period, is from July 1,
1999 to December 29, 2000, and the second subperiod, denoted as the post-event period, is from July 1, 2001 to
December 29, 2002.
exchange regulators contend. For our study, we will test to see if firms with wider spreads
are more likely to hit price limits, while controlling for other factors that have been found
to explain a stock’s propensity to hit price limits. Specifically, we estimate the following
regression model:
log %Hitj = 1 %Hitj ¼ a þ b1 Spreadj þ b2 Betaj þ b3 RRj þ b4 TVj
þ b5 Sizej þ b6 BMj þ e
ð2Þ
where %Hit represents the frequency that each stock j hits a price limit (calculated as the
number of days a limit-hit occurs divided by the total number of trading days for each
subperiod),8 Spread is the average relative bid–ask spread, Beta is the market beta, RR is
residual risk, TV represents average trading volume (daily trading volume divided by total
shares outstanding), Size is the log of market capitalization, and BM is the book-to-market
value of equity. Spread is our key variable of concern. The other explanatory (control)
variables are motivated by Kim and Limpaphayom (2000). Beta is calculated from the
standard market model using monthly stock and equally weighted market returns over the
sample period, and the market model’s residual standard deviation is residual risk. In
estimating the parameter coefficients for our regression model, we follow Kim and
8
Alternatively, %Hit could be our dependent variable (in fact, the results are qualitatively the same using
%Hit). However, %Hit is a bounded dependent, and a variable that has values between 0 and 1 has a beta
distribution (here, beta refers to a statistical term, not the usual market model beta). One way to accommodate this
problem is a logit transformation where we take the log of (%Hit/(1%Hit)). See, for example, Demsetz and
Lehn (1985) for additional explanations, and for another example of how this transformation is used.
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Table 4
Regression results
Intercept
Spread
Beta
RR
TV
Size
BM
F-value
Adj. R 2
Pre-event period
Post-event period
3.839
(2.24)**
31.104
(2.80)***
0.025
(1.45)
5.852
(3.95)***
11.002
(1.55)
0.372
(4.93)***
0.123
(1.03)
14.58***
0.262
6.573
(4.50)***
101.214
(5.88)***
0.170
(1.38)
2.194
(2.15)**
48.003
(6.65)***
0.041
(0.63)
0.108
(0.55)
30.56***
0.407
This table reports generalized method of moments (GMM) parameter coefficients for the following models:
log %Hitj = 1 %Hitj
¼ a þ b1 Spreadj þ b2 Betaj þ b3 RRj þ b4 TVj þ b5 Sizej þ b6 BMj þ e
ð2Þ
where %Hit represents the frequency that each stock j hits a price limit (calculated as the number of days a
limit-hit occurs divided by the total number of trading days), Spread is the relative bid–ask spread, Beta is
the market beta, RR is residual risk, TV represents average trading volume (daily trading volume divided by
total shares outstanding), Size is the log of market capitalization, and BM is the book-to-market value of
equity. The study sample is split into two subperiods. The pre-event subperiod is from July 1, 1999 to
December 29, 2000, and the post-event subperiod is from July 1, 2001 to December 29, 2002. t-Statistics
are reported in the (parentheses). ***, **, and * denote statistical significance at the 1%, 5%, and 10%
levels, respectively.
Limpaphayom (2000) and use the generalized method of moments (GMM) estimation
procedure.9 Table 3 shows summary statistics of our control variables.
Table 4 reports our regression results. From the first column of results, we see that
stocks with wider spreads, more residual risk, and smaller market capitalizations hit
price limits more often. The residual risk and market capitalization findings are
consistent with Kim and Limpaphayom (2000). The spread finding, which is our paper’s
focus, is consistent with our contention that stocks with wider spreads hit price limits
more often.
When we turn to the post-event sample period, the key result is qualitatively similar.
Specifically, in the second column of results we again see that stocks with wider
spreads hit price limits often. With regard to the other explanatory variables, stocks
9
Following Kim and Limpaphayom (2000), we use the Parzen kernel estimator to specify the appropriate
weighting matrix; and for the instrumental variables we include a constant, all of our explanatory variables, and
the squares of the explanatory variables. See Kim and Limpaphayom (2000) for more details. Furthermore,
similar to Kim and Limpaphayom, we also find that our results are robust to the choice of instrumental variables,
and using ordinary-least-squares to estimate our model.
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with more trading volume hits price limits more often, which is also consistent with
Kim and Limpaphayom (2000) overall findings, but firms with smaller market
capitalization are no longer more likely to hit price limits. Perhaps most importantly,
when we assess both of the regression results together, it appears that the primary factor
that explains limit-hits (in terms of robustness and statistical significance) is spread size.
We conclude that stocks with wider spreads are more inclined to hit their price limits,
ceteris paribus.
5. Conclusion
Price limits may be especially restrictive for illiquid classes of stocks. Illiquid stocks
have wider bid–ask spreads, which may cause them to hit price limits more often than
liquid stocks. Using liquid A-shares and less liquid B-shares that trade on the Chinese
stocks markets, our empirical evidence confirms this contention. Specifically, we find that
the less liquid B-shares hit price limits more often than A-shares, even though both share
classes have identical claims on cash flows. In regression analysis, we further document a
positive systematic relationship between a stock’s spread and its propensity to hit price
limits.
This study contends, and documents, that a less liquid class of stocks is more
susceptible to hitting price limits. Unless this is the intended goal of stock exchanges to
impose a uniform price limit across all of its stock classes, we suggest a re-evaluation of
this policy prescription. For a class of stocks that are less liquid than other classes of
stocks, perhaps the exchange should impose a wider price limit (if the exchange uses price
limits in the first place). Furthermore, perhaps the exchange should use the prior day’s
closing midpoint prices (between the closing ask and bid prices) to establish the next day’s
price limit range, as illiquid stocks have wider spreads.
Acknowledgements
We are deeply indebted to an anonymous referee and to Ghon Rhee (the editor) for
providing detailed comments, guidance, and important insights. We also thank Andreas
Andrikopoulos, Pat Conroy, Amy Edwards, Pat Fishe, Piman Limpaphayom, and Qinghai
Wang for discussions and/or for answering questions. We alone assume responsibility for
errors herein. Part of this work was undertaken while the second author was visiting the
Hong Kong Polytechnic University, for which he expresses his sincere appreciation for
their kind hospitality.
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