R square and Noise Trading: Evidence from Chinese Stock
Market1
Rong Zhu2
Guanghua School of Management,
Peking University,China
1
We thank Yaping Wang, Wei Jiang, Dong Wook Lee, Mark H.Liu, Randall Morck, Bernard Yeung, Brad
M.Barber , Jennifer Lynch Koski , Edward M.Rice and Ali Tarhouni for valuable help and comment.
Especially, we thank Jinghan Cai for help with cutoff of noise trading. We also thank seminar participants
at Peking University.
2
Address: 27 Jiyongzhuang, Peking University, China, 100871, Cell: 86-15116921064, email:
[email protected] and she will attend and present the paper.
R square and Noise Trading: Evidence from Chinese Stock Market
Abstract
Using data in Chinese stock market, this paper examines the empirical relationship
between R square and noise trading. Using small trades as measure of noise trading and
future earnings response coefficient, we test the relationship between noise trading and R
square by industry-matched-pairs methodology. We found noise trading has negative
effect on R square. Moreover, the effect is robust to alternative price informativeness
measure , modified sample. An examination of R square and price informativeness
measure does not support the result of Durnev , Morck et.al(2003).
1. Introduction
Extant research has been done on price synchronicity, R square obtained from a
regression of individual stock return on the market index or industry index. Since Roll
(1988), R square has been considered as a measure of price informativeness and has been
widely used. However, there are many other researches providing an opposing view
(Ashbaugh-Skaife et al.(2006) , Bhagat, Marr and Thompson (1985), Blackwell, Marr
and Spivey (1990), Krishnaswami and Subramaniam (1999), Kelly (2005) ). To reconcile
the two opposing views, Lee and Liu(2006) provide a model in a multi-asset, multiperiod noisy rational expectation equilibrium in which they document a U-shaped
relation between price informativeness and idiosyncratic return volatility. Their empirical
study support their theoretical findings.
Above is research on the information side of R square. What our paper is going to do is to
address a question different but related to this topic: R square and noise trading.
“Noise traders” are economic agents who trade in security markets for non-informationbased reasons. The existence of noise traders was theoretically posited as a solution to the
“no trade” or “ no speculation” results of Grossman and Stiglitz(1980) and Milgrom and
Stokey(1982). REE models assume that traders maximize expected utility with rational
beliefs, where rational beliefs are defined to be consistent with the model itself. The
notion of “noise” in REE literature corresponds to a random error term added to the
aggregate demand function.
Some papers address the relation between R square and Noise trading. West (1988)
provides a model in which low R square is associated with less firm-specific information
and more noise in return. In Roll (1988), he acknowledges that two explanation for his
findings are actually possible when he concludes by proposing that his finding seems “ to
imply the existence of either private information or else occasional frenzy unrelated to
concrete information”. Lee and Liu(2006) theoretically decompose idiosyncratic return
volatility into noise part and information part, which imply the relation between R square
and noise trading.
In this paper, using small trades as measure of noise trading and future earnings response
coefficient, we test the hypothesis that noise trading has negative effect on R square by
industry-matched-pairs methodology. We found noise trading has negative effect on R
square. Moreover, the effect is robust to alternative price informativeness measure ,
modified sample.
A related issue we address in this paper is the relation between R square and price
informativeness. Since Roll (1988), R square has been considered as a measure of
price informativeness. Morch, Yeung and Yu(2000) show that at country level, stock
prices in emerging markets show greater synchronicity than those in developed
countries and further that private property protection could explain that. They argue
that strong property right could promote informed arbitrage, which facilitates price
the discovery and utilization of firm-specific information. Durnev, Morck, Yeung,
and Zarowin (2003) directly test the relation between R square and price
informativeness using future earnings response coefficient and future earnings
incremental explanatory power at a firm level. Jin and Myers(2006) examine the
cross country stock returns and find R square is correlated with transparency of the
stock market. Wurgler (2000) finds that there is a higher elasticity of capital expenditure
with respect to value added in countries whose stock returns are less synchronous using
evidence from 65 countries.
However, there are many other researches providing an opposing view (Ashbaugh-Skaife
et al.(2006) , Bhagat, Marr and Thompson (1985), Blackwell, Marr and Spivey (1990),
Krishnaswami and Subramaniam (1999), Kelly (2005) ).West (1988) provides a model in
which low R square is associated with less firm-specific information and more noise in
return. More recently, Ashbaugh-Skaife et al.(2006) analyzes six of the largest equity
markets, including Australia, France, Germany, Japan , UK and US and find no evidence
in support of R square as a measure of firm-specific information impounded into stock
prices. Specifically, when using US data to examine the effect of R square on the
coefficients of future earnings in OLS, they find results contrary to Durnev et al.(2003).
Kelly (2005) finds that firms with a low R square has a worse information environment
as characterized by fewer institutional holdings, lower breadth of institutional ownership,
lower analyst coverage, lower liquidity, fewer information events, lower flow of
informed trades, and higher transaction costs. He concludes that a low R-square is not the
result of informed traders impounding firm-specific information in prices. In a research
by Yaping Wang, Liansheng Wu and Yunhong Yang(2009) where they investigate the
firm investment and stock price in Chinese stock market, they find there is no significant
difference in information content between high R square subgroup and low R square
subgroup.
To reconcile the two opposing views, Lee and Liu(2006) provide a model in a multiasset, multi-period noisy rational expectation equilibrium in which they document a Ushaped relation between price informativeness and idiosyncratic return volatility. Their
empirical study support their theoretical findings. We find that after controlling for noise
trading, R square is positively correlated with price informativeness , but coefficient is
not significant. Our result doesn’t support the first view.
Our view with regard to the relation between R square and firm-specific information is as
follows: On the one hand, low R square maybe represent more firm-specific information
impounded into the stock price. Since we assume firm-specific information is
uncorrelated with market return, the more firm-specific information, the higher
idiosyncratic volatility, the lower R square. On the other hand, noise trading of
individual stocks will also affect idiosyncratic volatility. The higher noise trading, the
lower R square. Thus, a lower R square may be attributed to firm-specific
information( higher or lower? ) or higher noise trading. (West 1988)
A recent paper have studied question as ours. Teoh, Yang and Zhang(2008) examine the debate
about R square as an indicator of information quality: Does low R-square indicate high resolution
of uncertainty through the arrival of firm-specific information or does it indicate a high level of
firm-specific uncertainty(noise). Test based on the accruals, net operating assets, post-earningsannouncement drift and V/P anomalies all reject high-information interpretation and meanwhile,
the direct test of the relation between R square and earnings response coefficient, also support the
noise interpretation instead of firm-specific information interpretation. But they address the
question from the information side, instead, we incorporate both measure of noise trading and
price informativeness and will do it more directly.
This paper contributes to the literature in several ways. Firstly, as far as we know, it is the first
paper that empirical test relation between R square and noise trading. Secondly, our result
provide new evidence for the two opposing views regarding the relation between R square and
price informativeness. In particular, this is new evidence after controlling for noise trading, an
important element in determining R square and also firm level evidence from Chinese market,
one of major emerging markets in the world. Thirdly, it provide evidence and idea for further
research, e.g. a better proxy for price informativeness.
The remainder of the paper proceeds as follows: Section 2 describes measurements for noise
trading and price informativeness. Section 3 describes sample selection, research design and
Section 4 presents the results of the empirical study. Section 5 presents some robust check and
Section 6 concludes
2. Measures of Noise Trading and Price Informativeness
2.1 Measures of Noise Trading
Following Barber, Odean and Zhu(2005), we use small trades as proxy for noise
trading. The reason for that is as follows:
Many recent papers argue that individual investor trading is often motivated by a
variety of psychological heuristics and biases. For example, a combination of mental
accounting (Thaler,1985) and risk seeking in the domain of losses (Kahneman and
Tversky,1979) may lead investors to hold onto losing investments and sell winners.
The representativeness heuristic (Tversky and Kahneman, 1974) may lead investors
to buy securities with strong recent returns because they view recent return patterns to
be representative of the underlying distribution of returns (see DeBondt and Thaler
(1987), DeLong, Shleifer, Summers, and Waldman (1990b), DeBondt (1993), and
Barberis, Shleifer, and Vishny (1998)). Overconfidence may cause investors to trade
too aggressively and, in combination with self-attribution bias, could contribute to
momentum in stock returns.(See Kyle and Wang (1997), Odean (1998b), Daniel,
Hirshleifer, and Subrahmanyam(1998, 2001), and Gervais and Odean (2001)).
Limited attention may constrain the set of stocks investors consider buying (Barber
and Odean, 2005) causing purchases to be artificially concentrated in attention
grabbing stocks. And the desire to avoid future regret may lead investors to
repurchase stocks that have gone down in price since they were previously sold or
purchased (Odean, Strahilevitz, and Barber, 2004).
Individual investors tend to place small trades, which is validated by Barber, Odean
and Zhu(2005) by a correlation study between proportion buys of TAQ/ISSM and
proportion buys at a large discount broker and a large retail broker.
In Chinese market, we use trades not greater than 10,000 share trades as proxy for
small trades following Cai and ouyang et al. (2007) .
2.2 Measures of Stock Price Informativeness
Following Durnev , Morck et.al (2003), we use future earnings response coefficient
and future earnings incremental explanatory power as measures for stock price
informativeness.
Collins et al. (1994) express current stock returns as a function of the current period’s
unexpected earnings and changes in expected future earnings. This ability of current
stock returns in tracking future earnings is a measure of stock price informativeness.
After proxy for current unexpected earnings using current changes in earnings, and
for changes in expected future earnings using changes in reported future earnings,
Durnev and Yeung(2003) estimate the following regression,
rt = a + b0 ∆ E t +
∑
τ
bτ ∆ E t + τ +
∑
τ
cτ rt + τ + u t
(1)
Where ∆ E t + τ is the earnings per share change τ period ahead, scaled by the price at
the beginning of the current year. Collins et al. recommend using future stock returns
rt + τ as control variables. Following Durnev and Yeung(2003), I include three future
years of earnings changes and returns .
The first future earnings response measure is future earnings response coefficient, the
sum of the coefficients on future earnings, defined as
FERC ≡
∑
τ
bτ
The second future earnings response measure is future earnings incremental
explanatory power, the increased R 2 of the regression (1) associated with including
the terms
∑
τ
bτ ∆ E t + τ and not
FINC ≡ Rr2 = a + b ∆ E +
t
0
t
∑
τ
bτ ∆ Et + τ +
∑
τ
cτ rt + τ + u t
− Rr2t = a + b0 ∆ Et + ut
3 Data and Sample Selection and Basic Empirical Design
3.1 Data, Sample Selection
We use all non-financial public companies listed on the Chinese A-share market from
2001 to 2005. We collect quarterly data from the China Economic Research Center
Sinofin database, including intraday transaction data. We use GICS ( Global Industry
Classification Standard) to classify industry. Using first two digit and deleting the sector
of financials and industry-quarter observations which have too less companies to estimate
price informativeness measure, our sample consists of 163 industry-quarter
observations .
3.2 Industry-Matched-Pairs Methodology
Our objective is to examine the relation between the noise trading measure and R
square. Yet, R square is affected by informativeness measures according to Durnev
and Yeung et al.(2003). Our approach is that, after controlling for informativeness,
we test if noise trading affects R square.
We use industry-matched-pairs methodology in Durnev and Yeung et al.(2003) and
Wang et al.(2009) to match pairs of high- and low- R square firms by industry and so
focus on intra-industry variation in noise trading measure and informativeness measure.
Each pair of matched firm contains some high-R-square firms and some low-R-square
firms that are similar in other critical dimensions. The method is as follows:
As the first step in our matched-pair procedure, we select 30% firms with the highest R
square and the 30% firms with the lowest R square each year in each industry,
maximizing the difference in R square within each industry in each year. We call the
highest 30% R-square firms H i and the lowest 30% R-square firms Li . We match firms
by industry, because many of the determinants of informativeness measure and noise
trading measures are industry specific and can thus be only controlled for using this
industry-matching procedure.
In step 2, in each industry, we use H i and Li to estimate earnings response coefficients
FERCiH , FERCiL and FINC iH , FINC iL for each year t. We take the difference in
earnings response measures3 between H i and Li in each industry as
3
Since there is no quarterly report in 2001, we should adjust the semi-annual report. First, we divide the
semi-annual net income by 2 , which can be compared with the quarterly net income. Then , if we still use
adjusted data for the following two quarters to get earnings surprise,
∆ E i ,t + 1 will be 0. Thus, we use data
for the following two period .For example, to investigate how much future earnings surprise is incorporated
into return of the first quarter of 2001, we use data of the first half year of 2001, the second half year of
2001 and the first quarter of 2002. Later we will do robust check regarding this problem.
∆ FERCi ,t ≡ FERCiH,t − FERCiL,t
∆ FINCi ,t ≡ FINCiH,t − FINC iL,t
We then aggregate noise trading for H i and Li for time t, respectively. We refer to noise
H
L
trading for H i and Li respectively as N i ,t and N i ,t .
∆ N i ,t = N iH,t − N iL,t
We then construct weighted –average R square for all the firms in H i and Li ,
respectively. We use simple average.
ψ
ψ
H
i ,t
L
i ,t
=
=
∑
j∈ H i
R 2j ,t
niH
∑
j∈ Li
R 2j ,t
niL
niH is the number of firms in H i and niL is the number of firms in Li
∆ψ
i ,t
=ψ
H
i ,t
−ψ
L
i ,t
3.3 Control Variables
3.3.1 Size
It is well documented in literature that larger firms tend to have higher R square( e.g. ,
Roll(1988); Durnev , Morck and Yeung(2000) and Kelly(2005)), which can be due to
non-informational reasons. Explanation might be that large firms tend to have many
divisions and operate in different industries and thus idiosyncratic volatility in different
divisions is diversified away in those large firms, resulting in higher R square.
Firm size at time t is measured as the market capitalization on the beginning date of the
quarter. If there is no data on the first trading date, we use data on the first available date.
3.2.2 Co-movement of fundamental variable
Since the more synchronous fundamentals are, the more synchronous stock returns are,
we include fundamental non-synchronicity as a control variable. We estimate the
fundamental non-synchronicity by regressing the following equation.
E i ,t = α
E
i ,t
E
+ β i ,t E m ,t + u iE,t
Where Ei ,t is the earnings scaled by total asset, and E m,t is the aggregate earnings of the
market portfolio (if we use value-weighed market index) scaled by aggregate total assets.
The variable
FRSQ is defined as the R square statistic from the above regression.
3.2.3 Number of companies in industry-quarter observation
Since we are adopting industry-matching methodology, the number of companies in a
industry might affect R square. Thus, we use this as a control variable.
3.4 Regression Framework
∆ψ
i ,t
= α + β ∆ N i ,t + γ ∆ FERCi ,t +
∑
k
(1)
θ k Z k + ei , t
Estimated across two-digit industries , indexed by I for year t, where Z k is a vector of
control variables discussed earlier. We perform panel regressions using a time-fixed
effects model, time and industry-fixed effect model and also report industry and time
clustered standard error, respectively.
4 Empirical Findings from the Industry-Matched Pairs Study
4.1 Univariate Statistics
Table 2 shows univariate statistics for the variables described previously through
2001 to 2005, using industry-matched-pairs approach. The mean of
than that of
ψ
L
, which is consistent with our prediction since ψ
square for the high noise trading subgroup while
ψ
L
ψ
H
H
is lower
is average R
corresponds to low noise
trading subgroup. This suggests that the lower noise trading, the higher noise trading.
4.2 Simple Correlations
Table 3 presents correlations of the differences in our key variables between
industry-matched pairs of firms grouped by high and low R square, estimated across
our sample of two-digit industries through 2001 to 2005. They key feature in the table
is the negative correlation between differential R square and differential noise trading.
We could also see the positive correlation between R square and price
informativeness measure.
4.3.Regressions
In the section, we test whether noise trading affect R square. Table 4 shows results of
regressions (1) using quarterly two-digit industry observations through 2001 to 2005.
In column 1, we regress our differential R square ∆ ψ on differential noise trading
∆ N . In column 2 and 3, measure of price informativeness is added. Column 1 and 2
only consider time fixed effect while column 3 considers both time and industry fixed
effect. Column 4 and 5 include noise trading measure, price informativeness measure
and other control variables----size, co-movement of fundamental variables and
number of companies in an industry. The difference between column 4 and column 5
is that Column 5 presents standard errors clustered by both firm and time.
Each column shows that noise trading is negatively correlated with R square, with the
coefficient significant at less than 5% or 1% level. This results support our hypothesis
that noise trading has a negative effect on R square.
Coefficient on FERC is positive , but not significant, which is contrary to the result
of Durnev, Morck, Yeung, and Zarowin (2003). Considering that we have controlled
for noise trading and used Chinese quarterly data, the result is not surprising.
Ashbaugh-Skaife et al.(2006) analyzes six of the largest equity markets, including
Australia, France, Germany, Japan , UK and US and find no evidence in support of R
square as a measure of firm-specific information impounded into stock prices.
Specifically, when using US data to examine the effect of R square on the coefficients
of future earnings in OLS, they find results contrary to Durnev et al.(2003). Using a
regression approach without matching scheme and employ rolling-regression method
as Ashbaugh-Skaife et al., Teoh, Yang and Zhang(2008) reached a conclusion contrary
to Durnev et al. Our result uses industry-matching methodology and get a result in
favor of Ashbaugh-Skaife et al.(2006) and Teoh, Yang and Zhang(2008) with Chinese
data, but the coefficient is not significant. So conclusion is not clear.
Result shows that size is positively correlatively with R square, which is consistent
with the literature. ，Roll (1988); Durnev, Morck and Yeung(2000) and Kelly(2005). The
reason for that might be that larger firms invest in more industries and thus more
idiosyncratic volatility is diversified away.
The result also shows that the number of companies in the industry is significantly
negatively correlated with the differential R square. The reason for that may be that
the more companies in an industry, the absolute differential R square should be
greater. But R square for H is lower than that for L, which means the differential R
square is negative. The above two reasons show that relation between differential R
square and number of companies in an industry should be negative.
Table 5 shows the result using alternative price informativeness measure, FINC .
The results are similar to those in Table 4. Noise trading is significantly negatively
correlated with R square while FINC is positively correlated with R square and the
coefficient is not significant. The coefficient on size is positive, coefficient on the
number of companies in the industry is significantly negative.
5. Robust
Check
The negative coefficients on noise trading documented above is consistent with the
idea that noise trading decrease R square. In this subsection, we attempt to strengthen
this result by deleting sample of 2001 , when only semi-annual accounting data are
available. Since we use adjusted accounting data to estimate price informativeness
measure and the earnings surprise is semi-annual in some cases, concern might rise
regarding the accuracy of estimation. Thus, we delete sample in 2001 and the
resulting sample is 131.
Table 6 shows that the result is similar to that in Table 4. It still shows a negative
coefficient estimate for noise trading, indicating a negative correlation between noise
trading and R square. The coefficient estimate for price informativeness is positive
and not significant, providing a slight support for the second view regarding
information role of R square(Ashbaugh-Skaife et al.(2006) , Bhagat, Marr and
Thompson (1985), Blackwell, Marr and Spivey (1990), Krishnaswami and
Subramaniam (1999), Kelly (2005) ).
5.2 Deleting observations with sample for estimating price informativeness less than
or equal to 10
Some industries don’t have many companies , which result in an accuracy estimate of
price informativeness measure. In this subsection, observations with sample size of H
or L less than or equal to 10 are deleted, in order to strengthen our result.
Table 7 shows the result after deleting those sample with H less than or equal to 10.
Coefficients estimate on the noise trading are all significant, which is quite similar to
the above results.
6. Conclusion
Price synchronicity (R square) has been widely considered and used as a proxy for
price informativeness and literature has contrary views regarding the relation between
R square and price informativeness. At the same time, relation between R square and
noise trading has been noticed by some papers, e.g., West(1988), Roll(1988), Lee and
Liu(2006). This paper provide the first empirical work to test the relation between R
square and noise trading, as far as we know.
Using data in Chinese stock market, this paper examines the empirical relationship
between R square and noise trading. Using small trades as measure of noise trading and
future earnings response coefficient, we test the relationship between noise trading and R
square by industry-matched-pairs methodology. We found noise trading has negative
effect on R square. Moreover, the effect is robust to alternative price informativeness
measure , modified sample. An examination of R square and price informativeness
measure does not support the result of Durnev , Morck et.al(2003).
This paper contributes to the literature in several ways. Firstly, as far as we know, it is the
first paper that empirical test relation between R square and noise trading. Secondly, our
result provide new evidence for the two opposing views regarding the relation between R
square and price informativeness. In particular, this is new evidence after controlling for
noise trading, an important element in determining R square and also firm level evidence
from Chinese market, one of major emerging markets in the world. Thirdly, it provide
evidence and idea for further research, e.g. a better proxy for price informativeness.
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Table 1: Variable Definitions
Variable
Definition
Panel A: R square
ψ
H
ψ
L
Simple average of R square for sample H in a two-digit industry
Simple average of R square for sample L in a two-digit industry
∆ψ
The difference between ψ
H
and ψ
L
Panel B: Future earnings response measures
FERC H
Sum of the coefficients on future changes in earnings for sample H
in rt = a + b0 ∆ E t +
FERC ≡
∑
τ
∑
τ
bτ ∆ E t + τ +
∑
τ
cτ rt + τ + u t ,
bτ
FERC L
Sum of the coefficients on future changes in earnings for sample L
in the above regression
∆ FERC
The difference between FERC H and FERC L
FINC H
Increase in coefficient of determination of
rt = a + b0 ∆ E t +
∑
τ
bτ ∆ E t + τ +
∑
τ
cτ rt + τ + u t
relative to the base regression rt = a + b0 ∆ Et + u t for H
FINC L
Same as FINC H , but for L
∆ FINC
The difference between FINC H and FINC L
Panel C: Noise trading measure
NH
Sum of trades not greater than 10,000 share over a quarter,
then average
for sample H
NL
∆N
Same as above , but for L
The difference between N H and N L
Panel D: Control variables
SH
then averaged
SL
∆S
FRSQ H
Market capitalization on the beginning date of a quarter ,
for over the sample H
Same as above, but for L
The difference between N H and N L
Co-movement of fundamental variables, measured as R square
statistics of the regression Ei ,t = α
E
i ,t
E
+ β i ,t E m ,t + u iE,t , where Ei ,t is the earnings scaled
by total asset, and E m,t is the aggregate earnings of the market portfolio (if we use valueweighed market index) scaled by aggregate total assets.
FRSQ L
∆ FRSQ
I
Same as above, but for L
H
L
The difference between FRSQ and FRSQ
Number of companies in an industry
Table 2 Univariate Statistics
Definition of the variables are in Table 1. Samples are from 2001 to 2005, using industry-matched-pairs
approach
Variable
N
Mean
Std Dev
Minimum
Maximum
_____________________________________________________________________________________
Panel A: R Square
ψ H
ψ L
∆ψ
163
0.4332272
0.1292492
0.1958962
0.6961254
163
0.4490807
0.1425975
0.2008540
0.7865648
163
-0.0158534
0.0911931
-0.2399912
0.3209809
Panel B: Noise Trading Measure
NH
NL
163
44388767.97
163
∆N
29139231.11
9976134.53
163
2341204.70
7985285.10
34412633.44
137625366
403979.93
22596635.78
48055900.55
1904625.11
97053033.25
Panel C: Future Earnings Response Measure
FERC H
FERC L
∆ FERC
163
-2.67759E-10
5.0959511E-9
-1.826148E-8
4.8449635E-8
163
2.3535436E-9
4.1684944E-8
-9.354696E-8
4.9930097E-7
163
-2.621303E-9
4.1213652E-8
-4.850325E-7
9.3537979E-8
163
0.2629686
0.2175931
0.0112045
0.9464525
163
0.2329471
0.1915039
0.0023837
0.8762855
163
0.0300215
0.1930272
-0.5920973
0.6456961
FINC H
FINC L
∆ FINC
Panel D: Control Variables
SH
SL
∆S
163
163
2572825508
163
FRSQ H _
FRSQ L
∆ FRSQ
I
8173885845
10319134581
1109733185
5601060337
163
163
163
163
0.0112028
140.9263804
1061773991
9842225471
0.3123198
0.3011170
1284949553
0.0992839
0.0999864
92.2655560
6755330047
-919493900
0.1062122
50154832847
45867112145
0.1585040
0.1404111
-0.2207119
21.0000000
0.6589024
0.6068099
0.2625018
307.0000000
Table 3: Simple Correlations
Simple Correlation Coefficients: All variables Constructed Using Industry Matched-Pairs Approach,
2001-2005
_NAME_
∆ψ
∆N
∆ FERC
∆S
∆ FINC
∆ FRSQ
∆ψ
∆N
1
∆ FERC
∆S
∆ FINC
∆ FRSQ
I
-0.1303
7
0.137088
-0.15301
0.059399
-0.17334
-0.08598
1
0.060187
0.133736
-0.00809
-0.09912
-0.00546
1
0.056969
-0.09833
0.088464
0.053403
1
0.02894
0.474075
-0.23275
1
0.078386
-0.06101
1
0.08289
I
1
Table 4: Relation between R Square and Noise Trading
Definition of all variables are listed in Table 1. The table reports the results of the following regression,
using industry-matched-pairs methodology, through 2001 to 2005. Sample size is 163.
∆ψ
i ,t
= α + β ∆ N i ,t + e i , t
∆ψ
i ,t
= α + β ∆ N i ,t + ∆ FERCi ,t + ei ,t
∆ψ
i ,t
= α + β ∆ N i ,t + ∆ FERCi ,t + ∆ S i ,t + ∆ FRSQi ,t + I i ,t + ei ,t
Where i indexes two-digit industry
Column 1 and Column 2 include time fixed effect while other columns include both industry and time fixed
effect. The last column reports adjusted standard error clustered both by industry and time. Coefficient
estimates are shown in bold and their standard errors are displayed right below.* indicate the coefficient
is significant at 5% level and ** indicate significant at 1% level
∆ψ
Dependent Variable
Specification
∆N
-1.80E-0
9*
-3.05E-09*
*
-3.34E-09**
-3.34E-09**
7.56E-10
8.53E-10
8.04E-10
8.09E-10
7.11E+04
126607
9.99E+04
118609
1.49E+05
111607
1.49E+05
83413
8.95E-13
8.73E-13
8.95E-13
9.16E-13
∆ FRSQ
-3.32E-01**
0.07367
-3.32E-01**
0.062
I
-8.11E-04*
0.000335
-1.00E-03**
0.0003
yes
yes
-1.80E
-09*
7.54E10
∆ FERC
∆S
industry effect
time effect
clustered standard error(by both
industry and time)
R square
no
yes
no
yes
yes
yes
no
0.6136
no
no
0.6144
yes
yes
no
0.6969
yes
0.7472
0.7472
Adj Rsq
0.5591
0.557
0.6336
0.6873
Table 5: Using Alternative Price Informativeness Measure
Definition of all variables are listed in Table 1. The table reports the results of the following regression,
using industry-matched-pairs methodology, through 2001 to 2005. Sample size is 163.
∆ψ
i ,t
= α + β ∆ N i ,t + e i , t
∆ψ
i ,t
= α + β ∆ N i ,t + ∆ FINC i ,t + ei ,t
∆ψ
i ,t
= α + β ∆ N i ,t + ∆ FINC i ,t + ∆ S i ,t + ∆ FRSQi ,t + I i ,t + ei ,t
Where i indexes two-digit industry
Column 1 and Column 2 include time fixed effect while other columns include both industry and time fixed
effect. The last column reports adjusted standard error clustered both by industry and time. Coefficient
estimates are shown in bold and their standard errors are displayed right below.* indicate the coefficient
is significant at 5% level and ** indicate significant at 1% level
∆ψ
Dependent Variable
∆N
-1.80E
-09*
7.54E10
-1.82E
-09*
7.50E10
-3.09E-09
**
-3.46E-09**
-3.46E-09**
8.45E-10
7.94E-10
7.82E-10
3.36E-02
0.024
4.00E-02
0.0225
4.00E-02
0.0234
6.30E-13
8.58E-13
6.30E-13
8.55-13
∆ FRSQ
-3.36E-01**
0.073
-3.36E-01
0.061
I
-8.00E-04*
-7.72E-04*
∆ FINC
∆S
4.20E02
0.026
0.00033
industry effect
time effect
clustered standard error(by both
industry and time)
R square
Adj Rsq
no
yes
no
yes
yes
yes
yes
yes
0.000298
yes
yes
no
0.6163
0.5591
no
0.6205
0.564
no
no
yes
0.6997
0.6369
0.7497
0.6904
0.7497
Table 6: Deleting Sample in 2001
Definition of all variables are listed in Table 1. The table reports the results of the following regression,
using industry-matched-pairs methodology, through 2002 to 2005. Sample size is 131.
∆ψ
i ,t
= α + β ∆ N i ,t + e i , t
∆ψ
i ,t
= α + β ∆ N i ,t + ∆ FERCi ,t + ei ,t
∆ψ
i ,t
= α + β ∆ N i ,t + ∆ FERCi ,t + ∆ S i ,t + ∆ FRSQi ,t + I i ,t + ei ,t
Where i indexes two-digit industry
Column 1 and Column 2 include time fixed effect while other columns include both industry and time fixed
effect. The last column reports adjusted standard error clustered both by industry and time. Coefficient
estimates are shown in bold and their standard errors are displayed right below.* indicate the coefficient
is significant at 5% level and ** indicate significant at 1% level
∆ψ
Dependent Variable
∆N
∆ FERC
∆S
∆ FRSQ
-1.73E
-09*
8.14E10
-1.66E-0
9*
-3.17E-0
9*
-3.81E-09**
-3.81E-09**
8.14E-10
8.73E-10
8.61E-10
8.44E-10
1.56E+06
1216556
8.30E+05
1079501
8.26E+05
1023944
8.26E+05
940241
-5.86E-13
1.12E-12
5.86E-13
9.99E-13
-2.80E-01**
0.084
-2.80E-01**
0.0744
I
-9.10E-04*
0.00044
industry effect
time effect
clustered standard error(by both
industry and time)
R square
no
yes
no
yes
yes
yes
yes
yes
no
0.2711
no
no
no
0.2815
-1.00E-03*
0.00039
yes
yes
yes
0.5097
0.5782
0.5782
Table 7: Deleting observations with sample for estimating price informativeness
less than or equal to 10
Definition of all variables are listed in Table 1. The table reports the results of the following regression,
using industry-matched-pairs methodology, through 2001 to 2005. We delete industry-quarter observations
with sample for estimating price informativeness less than 10. Sample size is 143.
∆ψ
i ,t
= α + β ∆ N i ,t + e i , t
∆ψ
i ,t
= α + β ∆ N i ,t + ∆ FERCi ,t + ei ,t
∆ψ
i ,t
= α + β ∆ N i ,t + ∆ FERCi ,t + ∆ S i ,t + ∆ FRSQi ,t + I i ,t + ei ,t
Where i indexes two-digit industry
Column 1 and Column 2 include time fixed effect while other columns include both industry and time fixed
effect. The last column reports adjusted standard error clustered both by industry and time. Coefficient
estimates are shown in bold and their standard errors are displayed right below.* indicate the coefficient
is significant at 5% level and ** indicate significant at 1% level
∆ψ
Dependent Variable
∆N
∆ FINC
-1.77E
-09*
8.36E10
-1.76E-9*
-2.21E-0
9*
-1.87E-09*
-1.87E-09*
8.37E-10
9.38E-10
8.99E-10
9.89E-10
105113
127429
181625
119601
147267
114440
147267
84393.4
∆S
∆ FRSQ
-8.42E-12*
2.35E-12
-8.42E-12*
2.35E-12
-6.26E-04
0.000356
I
industry effect
time effect
clustered standard error(by both
industry and time)
no
yes
No
Yes
Yes
Yes
yes
yes
-6.26E-04*
0.000314
yes
yes
no
No
No
no
yes
R square
Adj Rsq
0.6475
0.5897
0.6495
0.5887
0.7220
0.6567
0.7525
0.6889
0.7525