How Does Social Media Impact Bitcoin Value? A Test of the Silent Majority Hypothesis

Abstract

Bitcoin’s emergence has the potential to pave the way for a technological revolution in financial markets. What determines its valuation is an important open question with far-reaching business and policy implications. Building on information systems and finance literature, we examine the dynamic interactions between social media and the monetary value of bitcoin using textual analysis and vector error correction models. We show that more bullish forum posts are associated with higher future bitcoin values. Interestingly, social media’s effects on bitcoin are driven primarily by the silent majority, the 95 percent of users who are less active and whose contributions amount to less than 40 percent of total messages. In addition, messages on an Internet forum, relative to tweets, have a stronger impact on future bitcoin value. Overall, our findings reveal that social media sentiment is an important predictor in determining bitcoin’s valuation, but not all social media messages are of equal impact. This study offers new insights into the digital currency market and the economic impact of social media.

Full text

How Does Social Media Impact Bitcoin
Value? A Test of the Silent Majority
Hypothesis
FENG MAI, ZHE SHAN, QING BAI, XIN (SHANE) WANG, AND
ROGER H.L. CHIANG
FENG MAI (feng.mai@stevens.edu; corresponding author) is an assistant professor of
information systems in the School of Business at Stevens Institute of Technology. He
received his Ph.D. from the University of Cincinnati. His research interests include
social media, electronic commerce, and business analytics.
ZHE SHAN (zhe.shan@uc.edu) is an assistant professor in the Department of
Operations, Business Analytics, and Information Systems in the Lindner College
of Business at the University of Cincinnati. He earned his Ph.D. in business
administration and operations research from Penn State University’s Smeal
College of Business. His research interests include fintech innovation, information
security, patient-center health care, and business process analytics.
QING BAI (baiq@dickinson.edu) is an assistant professor of finance in the
Department of International Business & Management, Dickinson College. She
received her Ph.D. in finance from the University of Cincinnati. Her current research
focuses on asset return predictability, patent-based indicators of technological inno-
vation, and financial innovation.
XIN (SHANE)WANG (xwang@ivey.uwo.ca) is an assistant professor in marketing
and statistics, and the MBA ’80 Faculty Fellow at the Ivey Business School of
Western University, Canada. He received his Ph.D. in marketing from the
University of Cincinnati. His research focuses on machine learning with applica-
tions in marketing, social media analytics, the marketing-information systems
interface, and Bayesian statistics.
ROGER H.L. CHIANG (roger.chiang@uc.edu) is a professor of information systems at
Carl H. Lindner College of Business, University of Cincinnati. He received his Ph.D.
in computers and information systems from the University of Rochester. His research
interests focus on business intelligence and analytics, data and knowledge manage-
ment, and intelligent systems. He has published over fifty refereed articles in journals
and conference proceedings, including ACM Transactions on Database Systems, ACM
Transactions on Management Information Systems, Communications of the ACM,
Color versions of one or more of the figures in the article can be found online at www.
tandfonline.com/mmis.
Journal of Management Information Systems / 2018, Vol. 35, No. 1, pp. 19–52.
Copyright © Taylor & Francis Group, LLC
ISSN 0742–1222 (print) / ISSN 1557–928X (online)
DOI: https://doi.org/10.1080/07421222.2018.1440774

Journal of Management Information Systems, Marketing Science, MIS Quarterly,and
others. He has also served as a senior editor or associate editor of some leading
journals.
ABSTRACT: Bitcoin’s emergence has the potential to pave the way for a technological
revolution in financial markets. What determines its valuation is an important open
question with far-reaching business and policy implications. Building on information
systems and finance literature, we examine the dynamic interactions between social
media and the monetary value of bitcoin using textual analysis and vector error
correction models. We show that more bullish forum posts are associated with higher
future bitcoin values. Interestingly, social media’s effects on bitcoin are driven
primarily by the silent majority, the 95 percent of users who are less active and
whose contributions amount to less than 40 percent of total messages. In addition,
messages on an Internet forum, relative to tweets, have a stronger impact on future
bitcoin value. Overall, our findings reveal that social media sentiment is an impor-
tant predictor in determining bitcoin’s valuation, but not all social media messages
are of equal impact. This study offers new insights into the digital currency market
and the economic impact of social media.
KEY WORDS AND PHRASES: bitcoin, cryptocurrencies, digital currency, fintech, social
media, text mining, vector error correction model.
Digital currency was first introduced in the 1990s in the form of stored value cards
for peer-to-peer (P2P) payments that did not require bank authorization [12]. Bitcoin
represents a new form of digital currency that uses cryptography and information
technology (IT) to facilitate P2P transactions. Since its invention in 2008, bitcoin has
captured the attention of the business world. In August 2017, the market capitaliza-
tion of all bitcoins in the world surpassed US$73 billion.
1
The New York Stock
Exchange has created a bitcoin index; well-known retailers such as Dell, Newegg,
and Overstock accept bitcoin, as do online payment gateways such as PayPal; and
hundreds of bitcoin ATMs operate on four continents. According to one estimate
[13], 12 million trading accounts and over 100,000 retailers worked with bitcoin in
the fourth quarter of 2015. In less than a decade, bitcoin has emerged from the
fringes of the Internet to become a thriving fintech innovation, disrupting existing
payment and monetary systems [5].
Accompanying the rising popularity of bitcoin is a vexing question with no clear
answer: What determines its value? Finding the factors that influence bitcoin’s
monetary value (the market price on major bitcoin exchanges) has important prac-
tical and theoretical implications. Investors need predictors to estimate future price
swings and calculate the expected return. Policymakers need to unpack the forces
behind bitcoin to devise regulations and curb financial stability risks [31].
Businesses need to understand the price movement patterns before adopting bitcoin
or even launching their own digital currency—what is known as an initial coin
offering [48]. For information systems (IS) researchers, bitcoin’s value can be
viewed as a proxy for the market’s confidence and perceived usefulness of the
20 MAI, SHAN, BAI, WANG, AND CHIANG

digital currency. Therefore, revealing influential factors affecting bitcoin’s value can
advance theory by identifying the roles of different parties in the dispersion of new
financial technology.
We study whether and to what extent social media can impact bitcoin’s value.
Prior literature in economics provides models that can explain the worth of currency
using a nation’s monetary policies, macroeconomic conditions, and inflation and
interest rates, among other variables [43]. However, as bitcoin is a digital currency
with no government or central bank backing, traditional explanatory variables for
currency valuation fall short. Recently, IS researchers suggest that bitcoin resembles
a financial investment instrument like stock, rather than a currency [22]. We there-
fore draw from the theory on the connection between social media and equity value
[37,38] and hypothesize that social media can exert an impact on the bitcoin market.
Social media can reveal information that is unobtainable from traditional media. The
discussions on social media are also more timely and abundant compared with
traditional media, especially in bitcoin’s fledgling stages. Thus, establishing the
linkage between social media and bitcoin’s value could offer investors, regulators,
and businesses a new indicator of digital currencies’future value.
Further, bitcoin provides a unique opportunity to understand the economic value
of social media and its role in catalyzing the spread of fintech innovations. Thanks to
the focus of the media and a generation of investors who are vocal on social media,
emotions of bitcoin investors are increasingly visible online. Online discussions
about bitcoin are also abundant in quantity and diverse in form. These characteristics
make bitcoin an ideal laboratory for testing new theories. Previous literature typi-
cally considers social media as a whole, disregarding the mixed signals from various
users and channels. This study explicitly analyzes the heterogeneous effects of users
with different levels of activity [8]: the active users who contribute most content (the
vocal minority), and the relatively inactive users who contribute less often (the silent
majority). We also reveal how messages on two major platforms (an Internet forum
and Twitter) affect the bitcoin market differently. Integrating these new aspects into
economic models can improve our understanding of how social media interacts with
the markets. We investigate two research questions:
Is there a predictive relationship between social media and bitcoin value?
Does social media information created by different user cohorts and published on
different platforms exhibit the same effect?
To answer these questions, we assembled diverse data from bitcoin trading
markets, traditional Internet measures, and social media. We conduct sentiment
analyses of messages on an Internet forum (Bitcointalk.org) and Twitter. We use
vector error correction models (VECMs) to empirically test the relationship between
bitcoin value and social media variables. VECM extends the traditional vector
autoregression (VAR) models that are used to study a system of interdependent
variables [37]. VECM shares many of the benefits of VAR models. Specifically,
VECM accounts for endogeneity, autocorrelation, and reverse causality. It allows us
to model the bidirectional causality between pairs of variables. Also, VECM controls
for cointegration—a form of long-run dependencies between variables.
HOW DOES SOCIAL MEDIA IMPACT BITCOIN VALUE? 21

Overall, our findings show that social media is an important predictor of future
values of bitcoin. More bullish (or bearish) forum posts are significantly associated
with higher (or lower) next-day bitcoin market price. Yet not all social media are
created equal. Content contributed by relatively inactive users has a larger effect than
that from active users. Furthermore, at a daily frequency, forum sentiment offers a
better indicator of future values than Twitter sentiment. Variance decomposition
analyses suggest that social media metrics explain a significant amount of future
variations of bitcoin value. Finally, our social media metrics can improve out-of-
sample forecasts of bitcoin values in a three-month test period. Our findings are
robust to alternative sentiment metrics, different sampling periods, and fluctuations
caused by local government policies.
This research makes two main contributions. First, we develop a more compre-
hensive understanding of the various factors behind the monetary value of bitcoin.
We show that social media sentiment is a meaningful source of variation that can
explain and predict bitcoin value. These findings offer a new perspective on the
emergence of bitcoin and the diffusion of fintech innovations—for example, prices
of digital currencies are subject to the same Keynesian “animal spirits”observed in
traditional markets. Theories and empirical models on fintech adoptions should take
this perspective into consideration.
Second, we contribute to IS theory by highlighting the different influences of
various social media users and platforms. We extend prior findings in Gao et al. [20]
to the domain of financial markets and quantify the dynamic effects of different user
cohorts. We show that the volume of user contributions and platform differences
correlate with the impact of the messages. Therefore, in addition to asking generic
questions such as “Does social media affect X?”researchers should pay closer
attention to the complex and subtle forces that lead to the creation of various social
media messages.
Research Background and Hypothesis Development
This research draws primarily on two streams of research in IS and finance: (1)
market characteristics of bitcoin, and (2) the impact of social media on the financial
markets. We begin by reviewing studies on bitcoin’s exchange market and lay out
the reasons for incorporating social media metrics in predicting Bitcoin’s value (H1).
We then highlight the gaps in social media research that motivate our investigation
of user cohorts (H2) and platform (H3) differences.
Predictive Relationship Between Social Media and Bitcoin Value
Although the literature on bitcoin has underscored the need to model bitcoin as a
financial asset [5], there is no consensus on how bitcoin’s monetary value should be
determined. One main reason is whether bitcoin—or digital currencies in general—
qualifies as currency is in dispute. Government agencies have not provided clear
22 MAI, SHAN, BAI, WANG, AND CHIANG

guidelines on how to treat virtual currencies.
2
Yermack [62] tests bitcoin in terms of
the three functions of money—as a measure of exchange, store of value, and unit of
account—and concludes that it faces challenges in meeting all three criteria. Böhme
et al. [5] compare the coefficient of variation for the daily USD–BTC (bitcoin)
exchange rate with other currency exchanges; they find that bitcoin is 41 times more
volatile than the USD–EUR exchange rate. This extreme price volatility makes it
even more important to find meaningful predictors because such predictors could
protect individual and business adopters against future price swings.
Bitcoin’s market characteristics hint at the possibility that we can study bitcoin
using models for stocks. Glaser et al. [22] examine users’motivations for holding
bitcoin and conclude that most users treat their bitcoin investment as an asset rather
than as a means of payment. In addition, Kristoufek [33,34] has shown that bitcoin’s
price correlates with conventional online behavioral metrics such as Google search.
The popularity of the search term “Bitcoin”among U.S. Google users correlates
highly with both Bitcoin exchange rates (80.6 percent) and weekly total transaction
volume at the four largest exchanges (89.1 percent). The strong contemporaneous
relationship between attention from Internet users and Bitcoin valuation is similar to
the relationship between Web visits and firm equity value [15].
If bitcoin’s price formation process indeed resembles that of stock, can we use
social media to predict its value? Financial theory asserts that new information will
change expectations of investors and thereby affect the stock price [18]. In other
words, theory would predict that Bitcoin’s price movements follow new information.
In modern society, social media has fundamentally changed how information dis-
seminates and has become a valuable source of novel information. Internet forums
can disclose new or private information that fundamentally alters bitcoin evalua-
tions, such as when new stores accept bitcoin or forthcoming regulations limit its
use. Thus, it is plausible that social media serves as a channel through which
information and expectations become reflected in the bitcoin price.
A growing body of empirical studies has examined the interactions between social
media and asset value. An analysis of articles published on a social media platform
indicates that the opinions expressed in both articles and comments predict future
stock prices and earnings surprises [9]. In another examination of the dynamic
relationship between social media (online consumer ratings and Web blogs) and
firm equity value, social media metrics are found to have significant predictive
power for firm equity value [38]. In contrast, in their study of Internet stocks,
Tumarkin and Whitelaw [57] find that message board activity cannot predict stock
prices, but instead, the causality appears to run from the market to the forums.
Antweiler and Frank [1] further indicate that a positive shock to message board
posting predicts negative stock returns on the next day. Overall, the relationship
between social media and financial market is inconsistent across prior studies.
What is more, there are salient differences between bitcoin and stock. For exam-
ple, bitcoin has no discounted future cash flows (e.g., dividends) and hence no
intrinsic value to speak of. The bitcoin market also has limited depth and a lack of
short-selling or derivative instruments, meaning that it is costly to trade. Therefore,
HOW DOES SOCIAL MEDIA IMPACT BITCOIN VALUE? 23

the connection between social media information and bitcoin’s value cannot be
automatically assumed from previous research.
On the other hand, several unique features of bitcoin lead us to hypothesize that
social media metrics will have a significant predictive relationship to bitcoin’s value.
First, in bitcoin’s earlier stages, social media has been the most prominent channel
through which new information is shared and discussed. If social media can predict
the stock price of firms [37] for which many other information disclosure channels
(annual reports, financial analysts, etc.) are available, we may expect the same to
apply for bitcoin. Second, the design of bitcoin’s algorithm ensures that the supply
of new coins gets created at a known, geometrically decaying rate, so demand from
businesses and individuals represents the main driver of its value. As a new fintech
product with strong network effects [47], the attention bitcoin garners on social
media can translate to new adopters and positive externalities, consequently increas-
ing its value. The third reason concerns the demographics of users. A survey shows
that bitcoin users largely exhibit the demographic characteristics of heavy social
media users [17]. Social media messages may naturally have an impact on the
bitcoin users’behavior due to more exposure [61]. In addition, peer influence
plays a crucial role in how social media impacts asset prices [9]. Such a peer
influence effect should be stronger among investors with more shared characteristics
because of the homophily in the network [21]. For these reasons, we postulate:
Hypothesis 1: (The Social Media Metrics Effects Hypothesis). Social media
metrics have significant effects on future bitcoin prices, such that increased
positive (negative) sentiments indicate higher (lower) future bitcoin prices.
Distinctive Impacts of User Cohorts and Platforms on Social Media
When considering the influence of social media, the existing literature tends to use
social media as an all-inclusive term even though content is generated on multiple
platforms by users with varying behavior. In the previous section, we mentioned that
studies examining the relationship between social media and financial markets report
inconsistent findings. The mixed results may be an artifact of treating content
generated by all users, and from different platforms, as a single source. A few recent
studies that dissect social media show that user behaviors correlate with the content
they generated. For example, Ludwig et al. [36] show that a user’s linguistic style
correlates with posting quantity and quality. In the health-care domain, patients who
have lower-quality physicians are also less likely to post online reviews [20]. Yet
critical gaps remain, especially with regard to whether differences within the social
media realm have any bearing on their predictive value in financial markets. With a
growing interest in developing online media strategies and integrating social media
metrics in business decision making, the distinctive impacts of different user cohorts
and platforms are worth investigating. The vast digital footprints created by bitcoin
users allow us to test these differences.
24 MAI, SHAN, BAI, WANG, AND CHIANG

We first look at the differences associated with user activities. The power law
nature of social media suggests that most users contribute little content as the silent
majority, and a small proportion of highly active users contribute the most as the
vocal minority. This phenomenon has been empirically verified for online social
media such as Twitter and online reviews [41,44]. Yet the evidence about which
cohort is more valuable in terms of reflecting market sentiments and affecting future
prices remains inconclusive.
On the one hand, critical mass theory [41]predictsthat“the group of active
contributors is a minority of the population, but this minority makes the most useful
contributions,”thus indicating the vocal minority’s contribution should be of higher
quantity and higher quality. Quality aside, the sheer quantity of content produced by
the vocal minority should amplify its messages, resulting in disproportional influence
[10]. This is because for the online community, more posts are associated with a
higher probability of becoming a leader [30]. Early bitcoin adopters who also elect to
post large amounts naturally should emerge as community leaders. Research based on
social network theory and word-of-mouth theory highlight the importance of these
influential users through social media. As Trusov et al. [56] show, community
members differ in the frequency, volume, type, and quality of digital content they
generate and consume. Leaders have a disproportionate influence on others [23],
partly because they have greater exposure to mass media than their followers [49].
Further, from a financial market point of view, the vocal minority also has a crucial
role for information cascades, which can lead to herding behavior. That is, opinions
and decisions by community leaders are widely observed and assumed to be con-
veying localized or private information by followers [14]. For instance, groups of
mutual funds tend to adopt the investment choices of their successful counterparts
[19]. Jiao and Ye [26] show strong evidence that mutual funds collectively enter or
exit stocks, following the herd of hedge funds. Thus, the vocal minority may be
more influential as an information source.
On the other hand, the opinions of the silent majority may be just as important, if
not more so, than those of the vocal minority. First, by definition, the silent majority
users contribute to conversations sporadically, usually after highly salient events, and
they are not particularly interested in generating buzz [44]. The sentiments of the
silent majority, as market measures, thus tend to be more concise and relevant.
Second, the decentralized nature of bitcoin has meant that most grassroots users
can be categorized as the silent majority. If its market price reflects the valuation of
crowds, then the diversity prediction theorem [45]—collective error diminishes as
the diversity of the crowd increases—may apply to the bitcoin market. When it
comes to predicting the future movement of asset prices, the silent majority that
consists of many independent individuals may outperform the collective of like-
minded experts and fanatics.
Third, the silent majority users are less likely to engage in groupthink [25], defined
as self-deception, wishful thinking, and conformity to group values that lead to
willful blindness and collective denial [3]. Bitcoin has been subjected to criticism
that its value may depend on its most zealous users [42]. It is plausible that the vocal
HOW DOES SOCIAL MEDIA IMPACT BITCOIN VALUE? 25

minority users engage in numerous discussions of bitcoin, get caught up in glorified
ideas, and are more prone to groupthink. If so, they may hold biased views of the
future return of the investment and deny any downside risk [54]. In sum, any or a
combination of these mechanisms may lead to the result that messages from the
silent majority is a more compelling metric for actual investors. Recognizing both
sides of the argument, we propose two competing hypotheses:
Hypothesis 2a: (The Vocal Minority Hypothesis). The vocal minority has a
stronger impact than the silent majority on bitcoin value.
Hypothesis 2b: (The Silent Majority Hypothesis). The silent majority has a
stronger impact than the vocal minority on bitcoin value.
In addition to the differences brought by user activity levels, we propose that
various social media platforms affect financial markets differently. The mechanisms
of information diffusion, visibility, and representation differ by platform. As exam-
ples, we use an Internet forum and Twitter, which differ in three main ways. First,
Internet forums generally seek diverse opinions, and reaching consensus is not a
primary objective. In contrast, on Twitter, most communications propagate from the
sender to followers, who spread the information further by retweeting. Limited by
length restrictions, these followers may add brief, general sentiments, but they
cannot engage in thorough discussions of the original content. Any dissent can be
expressed only via a reply, which is unlikely to receive the same publicity as the
original tweet. On forums though, the act of reading a message brings up all replies
to that message. According to the theory of social exchange motivations [51], the
lack of latent benefit of publicity should suppress critical, in-depth discussions on
Twitter. Thus, forum discussions are likely to reflect the complete picture.
Second, a forum is designed to be an archive of all messages; by design, Twitter
focuses more on timeliness. It is not uncommon for forum users to engage in a
discussion that was started days or months ago, whereas the average life cycle of a
tweet is much shorter, and it is difficult for users to trace earlier tweets from an
active account. The Twitter search function, for example, does not return messages
that are more than a few weeks old. In turn, the information search cost for a
nonrecent tweet is much higher, which should reduce the efficiency of the market for
information at the intraday level. In addition, behavioral finance scholars note that
investors have limited attention capacities, so they respond asymmetrically to more
visible information [2]. Since aggregate daily information is more visible and
accessible on forums in the form of discussion threads, investors are more likely
to respond to it.
Third, a tweet is limited to 140 characters, so information generally must be
condensed. A forum does not have this strict limitation. This condensing process
creates two limitations in terms of analyzing the impact of these social media. For
one, adding external URLs to tweets is a common practice [11], and essential
information then gets encapsulated at an external site; it cannot be decoded solely
by analyzing (or reading) the tweets themselves. Apart from the URLs, because of
26 MAI, SHAN, BAI, WANG, AND CHIANG

the length limitation, contributors on Twitter also are more likely to use numerical
expressions to present information in an exact form. Yet numbers lack inherent
meaning; they are clear only when used relative to other numerical information [58].
To determine the full implications of a current trading price on Twitter, users would
need to know the linguistic context (e.g., increased/decreased) and/or temporal
context (e.g., last available price, momentum). If numerical information is indeed
more salient on Twitter, whereas verbal information is more salient on forums, we
expect the aggregated sentiment measure on Twitter to have less impact. Formally,
Hypothesis 3: (The Internet Forum-Content Bitcoin Value Impact Hypothesis).
User-generated content from Internet forums, rather than Twitter, has a stron-
ger impact on bitcoin value at a daily level.
Data
Measures for Monetary Value of Bitcoin
The focal point of our empirical analysis is the monetary value (market price) of
bitcoin. We study the dynamic relationship between the natural logarithm of price
and other variables. A nice property of ln (price) is that the continuously com-
pounded return in bitcoin is the first difference of ln (price). If Ptis the bitcoin
market price at the end of day t, then the daily continuously compounded return is:
rt¼ln Pt
Pt1

¼ln Pt
ðÞln Pt1
ðÞ:(1)
This specification means that our model is constant returns to scale; in other words,
the model coefficients can be interpreted as the effects of one-unit changes in
explanatory variables on investment outcomes, measured by the continuously com-
pounded percentage rate of return. Changes in log price have been widely used in
asset pricing studies [7].
Our data set comprises daily market prices (BTC–USD exchange rates) from
BitStamp Ltd., the top bitcoin exchange by volume. To control for other observable
variations in the bitcoin trading market, we also include transaction volume, trading
volume, and volatility in our model. We collected bitcoin-to-bitcoin transaction
volume, defined as the total value of all transaction outputs per day,
3
from
Bitcoincharts.com. Transaction volume indicates the amount transferred within the
bitcoin economy, while the trading volume measure refers to the amount of bitcoin
traded for U.S. dollars. We denote the trading volume and transaction volume of day
tas Vtand VTX
t.
To capture the effects on bitcoin price brought about by uncertainty, we include a
risk measure of bitcoin value using the volatility of bitcoin returns. To measure the
volatility of the return, we apply the exponentially weighted moving average model,
which tracks changes in volatility with the formula σ2
t¼λσ2
t1þ1λðÞr2
t1. The
HOW DOES SOCIAL MEDIA IMPACT BITCOIN VALUE? 27

estimate of volatility on day t,σ2
t, is calculated from σ2
t1and the most recent daily
percentage change in price. The value of λgoverns the responsiveness of the
estimate to the most recent daily percentage change. We chose λ= .94, the same
value used by RiskMetrics (previously a JPMorgan subsidiary, and now owned by
MCSI Inc., which changed its name from Morgan Stanley Capital International and
MSCI Barra), which has demonstrated that, across a range of market variables, this
value of λresults in variance rate forecasts that come closest to the realized variance
rate.
Social Media Metrics
We implemented a Python-based Web crawler to collect discussion content from
Bitcointalk.org between January 1, 2012, and December 31, 2014. We chose this
forum for two reasons: it was rated the most popular bitcoin community in a recent
survey [52], and it appears first in the community section of the official Bitcoin
website. We limited our data collection to the Bitcoin discussion board, to which
users post general news, community developments, innovations, and so forth. After
filtering out content beyond our study period, we gathered 343,769 posts and 15,420
topics for further analysis. Each post contained textual content, an author, and a time
stamp. Among the 17,215 unique users who posted, the most active 5 percent of
users generated 63.11 percent of the content. The average number of posts generated
by a single user in the sample period was 19.97; the median was 3. As Figure 1
reveals, the distribution of the number of messages by users follows a typical power
law distribution. Most users belong to the silent majority, and a small proportion of
the vocal minority generated most of the content.
For the sentiment analysis, we applied a finance sentiment dictionary [35], which
includes 2,329 negative and 297 positive sentiment words. We used Natural
Language Toolkit 3.0 [4] for the language-processing tasks, such as sentence
Figure 1. Distribution of Posting Activities among Forum Users (Log-Log Scale)
28 MAI, SHAN, BAI, WANG, AND CHIANG

segmentation, word tokenization, and lemmatization. We counted the number of
positive and negative words for each message. If a message contains more positive
than negative words, it constitutes a positive post, and vice versa.
To compare the impacts of Twitter and the Internet forum, we also collected tweets
that contained the hashtag (#Bitcoin) from the public application program interfaces
(API) of Twitter. Twitter’s search APIs allow queries within the indices of recent or
popular tweets, and also can collect a wider range of data, such as latest favored or
retweeted counts. Using a Python-based Web crawler, we collected data from the
search API at its highest frequency (limited to 180 queries per 15-minute window)
between September 16 and December 16, 2014. We thus gathered 3,348,965 unique
tweets from 339,295 unique users. On average, 21,910 users tweeted 27,227 mes-
sages per day. With these data, we again applied the sentiment dictionary [35]to
count the number of positive and negative words in each tweet. If the number of
positive words is greater than the negative words, the tweet is classified as positive,
and vice versa.
Other Variables
We included a set of traditional Internet activity measures and control variables from
the financial market. To measure search interest related to bitcoin, we collected data
from Google Trends. The measure of interest over time indicated the popularity of a
given keyword (in our case, Bitcoin) in Google’s search engine, using a 0–100 scale
and normalized values. We also obtained the Web traffic measure website rank
(traffic rankings of the website) related to Bitcoin.org from the Alexa Web
Information Service. External instruments from the financial market include the
S&P 500 index, stock market volatility (VIX index from Chicago Board Options
Exchange), COMEX gold price, and AAII investor sentiment survey. Because
Google Trends and AAII Investor Sentiment provide only weekly data, we used
the previous week’s measure applied to each day in the subsequent week. Finally, we
searched the Thomson Reuters News Analytics (TRNA) database for news articles
that contained the word “bitcoin”in the title or full text. We included daily TRNA
news sentiment scores in our analyses; these scores are calculated using a proprietary
system to give financial professionals an idea of how average sentiment is shifting in
the news. Table 1 summarizes the key measures.
Empirical Methodology
To study the dynamic relationship between bitcoin and social media, we use VECMs
to capture the interdependencies across time-series. These models extend the VAR
system when cointegration is present, meaning that there are long-term common
trends among the nonstationary time series [28]. We chose VECM rather than a more
traditional multiple regression (cf. [1,60]), for several reasons. First, as an extension
of the VAR model, VECM also allows us to model the recursive relationship
HOW DOES SOCIAL MEDIA IMPACT BITCOIN VALUE? 29

Table 1. Key Measures and Summary Statistics
Variable Definition Mean SD Median Min Max
Bitcoin Market Variables
ln(P) Bitcoin price (log) 4.32 1.84 4.17 1.47 7.05
σVolatility of bitcoin returns 0.05 0.03 0.04 0.01 0.21
VLog daily trading volume 11.96 0.48 11.97 10.58 13.74
V
TX
Log daily transaction volume 14.40 1.51 14.51 11.09 18.09
Social Media Activities
POS
F
Number of positive posts 55.58 32.38 49 3 225
NEG
F
Number of negative posts 88.30 58.19 75 3 509
POS
T
Number of positive tweets 3,669 761.9 3,604 955 5,780
NEG
T
Number of negative tweets 3,050 956.9 2,862 1,009 6,716
Control Variables
rank Bitcoin.org web traffic rank (log) 9.66 0.94 9.49 7.14 11.64
googletrend Google Trend for bitcoin 16.33 18.53 12 2 100
sp500 Log S&P 500 closing price 7.40 0.15 7.41 7.15 7.65
vix COBE Volatility Index 15.33 2.88 14.68 10.32 26.66
gold Log COMEX gold price 6.73 0.13 6.69 6.50 6.95
investor_sentiment AAII investor sentiment 13.70 8.94 0 0 38.60
news_sentiment TRNA Bitcoin news sentiment 0.02 0.14 0 −0.76 0.81
30 MAI, SHAN, BAI, WANG, AND CHIANG

between interdependent variables. We can treat the variables as jointly endogenous,
without creating ad hoc model restrictions by separating them as endogenous and
exogenous variables. Nor do we need a priori knowledge about the mechanisms
influencing a variable, as required by structural models with simultaneous equations.
Second, the model allows for both autocorrelation and cross-correlation, so we can
better understand the dynamic relationships among the variables. Third, as a time-
series model, we can interpret an estimated VECM model using Granger causality.
This allows us to test whether the past values of social media variables are useful for
predicting the bitcoin market variables and establish the causality between variables.
In our empirical study, we examine models in which the variables include daily
observations of bitcoin market activities, namely, price (ln PtÞ,volatility(σ2
tÞ,transac-
tion volume (VTX
tÞ, and trading volume (VtÞ. The models also include measures of
relevant social media activities: number of forum posts or tweets expressing both
positive/bullish opinions (POSF;POST) and negative/bearish opinions
(NEGF;NEGT). Last, we include the relevant control variables defined in Table 1 .
We now outline how we determine the appropriate model. Appendix A provides
more details on the model specification tests. We first test the stationarity of the
variables. Conventional regression estimators, including VAR, encounter problems
when applied to nonstationary processes. The regression of two independent ran-
dom-walk processes would yield a spurious significant coefficient, even if they were
not related [24]. We used an augmented Dickey–Fuller unit root test on each
variable. Among the time series in the model, news sentiment, VIX, and investor
sentiments are stationary; the others are nonstationary with one order of integration.
Next, we determined the appropriate lag length pusing the Akaike information
criterion, which is standard in econometrics literature [40].
Given nonstationary variables, we can model their relationship using VAR by
taking the first differences of each time series. Yet this approach can suffer mis-
specification biases if cointegration is present [40]. Instead, VECM yields more
efficient estimators of cointegrating time series using a vector of error correction
terms that is equal in length to the number of cointegrating relationships added to the
relationship [29]. We performed a Johansen test [27] and confirmed the presence of
cointegration in our daily frequency data and concluded that VECM is the appro-
priate model. We estimated the order of cointegration rank = 5 using Johansen’s
multiple trace test procedure.
Formally, a VECM with pvariables, klags, and cointegration order rhas the
following form:
ΔYt¼X
k1
j¼1
ΓjΔYttkþαβ0Ytt1þμþt;(2)
where Δis the first difference operator, Ytis a p1 vector with order of integration
1, μis a p1 constant vector representing the linear trend, kis the lag length, and 
is the residual vector. Furthermore, Γjis a ppmatrix that indicates short-term
relationships among variables, βis a prmatrix that represents the long-term
HOW DOES SOCIAL MEDIA IMPACT BITCOIN VALUE? 31

relationships between the cointegrating vectors, and αis a prmatrix denoting the
speed with which the variables adjust to the long-term equilibria. The difference
between the VECM and the VAR model with first-differenced variables is the
additional β0Yt1, known as the error correction term. Thus, the VECM model is a
special case of the general VAR system expressed as an equivalent VAR:
Yt¼Ikþαβ0þΓ1
ðÞYt1þX
k1
j¼2
ðΓjΓj1ÞYtjþΓk1Ytkþμþt;(3)
where Ikis a kkidentity matrix.
Analyses and Results
VECM Analyses
To test the Social Media Metrics Effects Hypothesis (H1), we examine the effects of
the bullishness of forum messages using a VECM. The model includes daily
measures of the bitcoin market variables ln(P),σ,V, and V
TX
and the social media
variables POS
F
and NEG
F
, as well as all the controls in Table 1. We selected the
model with lag length k= 3, according to the Akaike information criteria. Table 2
presents the estimated coefficients in the VECM, highlighting the relationship
between social media metrics and bitcoin market variables.
We can observe several characteristics of the bitcoin market in Table 2.
First, price and volatility exhibit a strong autoregressive relationship: days
with higher prices and volatility tend to precede days of higher prices and
volatility. Trading and transaction volume exhibit a strong negative autoregres-
sive relationship, such that higher trading (transaction) volume days tend to
precede days of lower trading (transaction) volume. Second, the two social
media metrics work as we predicted in H1. Days with unexpected increases in
the number of positive (bullish) posts tend to precede days with higher prices
and high transaction volume. One more positive forum post is associated with
an increase in bitcoin price by 3.53 basis points (1 basis point = one-hundredth
of a percentage) next day. Days with unexpected increases in the number of
negative (bearish) posts tend to be followed by days with lower bitcoin prices
(1.63 basis points). All these relationships are statistically significant. To con-
firm this result, we also performed a Granger causality test between bitcoin price
changes and lagged social media metrics. The social media metrics are indivi-
dually (χ
2
=6.37,p= 0.012 for POS
F
;χ
2
= 5.48, p=0.019forNEG
F
)and
jointly (χ
2
=7.00,p= 0.030) significant, meaning the past values of forum
sentiments cause the changes in bitcoin value. Finally, the Google Trend mea-
sure is the only control variable that affects future bitcoin value. Therefore,
forum posts contain new information about the monetary value of bitcoin and
provide a better indication of general market sentiment than what is already
contained in the trading record, in support of H1.
32 MAI, SHAN, BAI, WANG, AND CHIANG

To test the Vocal Minority and Silent Majority Hypotheses (H2a, H2b), we
estimate two separate VECM models by splitting the forum messages according to
user posting activities. One model uses sentiment measures generated from messages
posted by the silent majority of users (bottom 95 percent by posting volume); the
other model uses the vocal minority (top 5 percent by posting volume). The silent
minority generated a mere 36.89 percent of the messages, whereas the vocal
minority generated 63.11 percent. Table 3 presents the split sample results.
For the posts by the silent majority, the estimates for their impacts on bitcoin
prices are much greater than those in the full sample model (Table 2). An unexpected
increase in positive forum posts will predict a surge in bitcoin price by 8.74 basis
points (p<0.01). The effect of their posts grows stronger, even though posts from
Table 2. VECM Estimates for Forum Sentiments and Bitcoin
Dependent Variables (Bitcoin Market)
Indep Vars ln(P)σVV
TX
ln(P)(t–1) 0.138*** −0.007*** −0.017 0.152
(0.030) (0.002) (0.346) (0.190)
σ(t–1) 0.380 0.140*** 4.464 −4.203
(0.544) (0.030) (6.165) (3.382)
V(t–1) −0.009** 5.76E-4*** −0.209*** 0.128***
(0.004) (2.10E-4) (0.043) (0.024)
V
TX
(t–1) −2.84E-4 2.48E-4 0.304*** −0.207***
(0.006) (3.15E-4) (0.065) (0.036)
POS
F
(t–1) 3.53E-4** −8.15E-6 6.02E-5 0.004***
(1.40E-4) (7.68E-6) (0.002) (8.70E-4)
NEG
F
(t–1) −1.63E-4** −1.61E-6 −4.66E-4 −3.94E-4
(6.98E-5) (3.83E-6) (7.91E-4) (4.34E-4)
rank(t–1) 0.012 −5.90E-4 −0.029 0.086
(0.009) (4.88E-4) (0.101) (0.055)
googletrend(t–1) 0.002*** 5.67E-6 0.012* −0.002
(5.36E-4) (2.94E-5) (0.006) (0.003)
sp500(t–1) −0.557 0.021 9.895* 5.340*
(0.448) (0.025) (5.086) (2.790)
vix(t–1) −0.002 1.92E-4 0.055 0.050***
(0.003) (1.64E-4) (0.034) (0.019)
gold(t–1) 0.066 0.015 0.770 −1.125
(0.170) (0.009) (1.928) (1.058)
investor_sent(t–1) 6.42E-4 4.76E-6 −0.004 9.41E-4
(4.61E-4) (2.53E-5) (0.005) (0.003)
news_sent(t–1) −0.003 2.32E-4 0.212 −0.022
(0.016) (8.75E-4) (0.181) (0.099)
Notes: T = 1,901. Lag length k= 3. The first lag estimates are displayed. The controls are not
displayed among the dependent variables. Standard errors are in parentheses.
*** p< 0.01, ** p< 0.05, * p< 0.1.
HOW DOES SOCIAL MEDIA IMPACT BITCOIN VALUE? 33

Table 3. VECM Estimates for Comparing the Silent Majority and Vocal Minority
Dependent Variables (Bitcoin Market)
ln(P)σVV
TX
Indep Vars
Silent
Majority
Vocal
Minority
Silent
Majority
Vocal
Minority
Silent
Majority
Vocal
Minority
Silent
Majority
Vocal
Minority
ln(P)(t–1) 0.136*** 0.143*** −0.007*** −0.007*** 0.084 −0.052 0.175 0.186
(0.030) (0.030) (0.002) (0.002) (0.347) (0.345) (0.191) (0.189)
σ(t–1) 0.417 0.333 0.139*** 0.142*** 3.523 4.869 −4.314 −4.491
(0.543) (0.544) (0.030) (0.030) (6.181) (6.159) (3.399) (3.379)
V(t–1) −0.009** −0.008** 5.51E-4*** 5.94E-4*** −0.218*** −0.209*** 0.138*** 0.125***
(0.004) (0.004) (2.09E-4) (2.10E-4) (0.043) (0.043) (0.024) (0.024)
V
TX
(t–1) −1.59E-4 −0.002 1.90E-4 2.89E-4 0.313*** 0.311*** −0.217*** −0.197***
(0.006) (0.006) (3.13E-4) (3.13E-4) (0.065) (0.065) (0.036) (0.035)
POS
F
(t–1) 8.74E-4*** 2.50E-4 −1.79E-5 −8.89E-6 −0.003 0.001 0.005*** 0.005***
(2.61E-4) (2.09E-4) (1.44E-5) (1.14E-5) (0.003) (0.002) (0.002) (0.001)
NEG
F
(t–1) −4.27E-4*** −1.31E-4 3.65E-6 −5.93E-6 −5.95E-4 −9.93E-4 9.02E-5 −5.58E-4
(1.52E-4) (1.03E-4) (8.34E-6) (5.62E-6) (0.002) (0.001) (9.50E-4) (6.38E-4)
rank(t–1) 0.011 0.014 −5.70E-4 −6.47E-4 −0.049 −0.025 0.096* 0.081
(0.009) (0.009) (4.86E-4) (4.89E-4) (0.101) (0.101) (0.055) (0.056)
googletrend(t–1) 0.002*** 0.002*** 9.67E-6 3.11E-6 0.012* 0.012* −0.002 −0.002
(5.35E-4) (5.37E-4) (2.94E-5) (2.94E-5) (0.006) (0.006) (0.003) (0.003)
sp500(t–1) −0.571 −0.476 0.022 0.019 9.404* 9.897* 5.578** 5.345*
(0.447) (0.449) (0.025) (0.025) (5.082) (5.084) (2.794) (2.789)
vix(t–1) −0.002 −0.002 2.10E-4 1.81E-4 0.057* 0.054 0.051*** 0.052***
(0.003) (0.003) (1.64E-4) (1.64E-4) (0.034) (0.034) (0.019) (0.019)
gold(t–1) 0.083 0.056 0.014 0.015 1.023 0.651 −1.144 −1.068
34 MAI, SHAN, BAI, WANG, AND CHIANG

(0.170) (0.170) (0.009) (0.009) (1.931) (1.925) (1.062) (1.056)
investor_sent(t–1) 6.86E-4 6.08E-4 3.44E-6 4.27E-6 −0.004 −0.004 8.27E-4 7.18E-4
(4.61E-4) (4.61E-4) (2.53E-5) (2.52E-5) (0.005) (0.005) (0.003) (0.003)
news_sent(t–1) −0.001 −9.35E-4 2.04E-4 2.01E-4 0.225 0.193 0.014 −0.037
(0.016) (0.016) (8.75E-4) (8.73E-4) (0.181) (0.180) (0.100) (0.099)
Notes: T = 1,901. Lag length k= 3. The first lag estimates are displayed. Standard errors are in parentheses.
*** p< 0.01, ** p< 0.05, * p< 0.1.
HOW DOES SOCIAL MEDIA IMPACT BITCOIN VALUE? 35

these users account for a smaller proportion of the total posting volume. In contrast,
posts by the vocal minority instead provide indicators of future transaction volumes
only, not of prices.
The estimates for POS
F
and NEG
F
are lower in value (2.5 and 1.31 basis points,
respectively) and are not statistically significant on prices. The effects of bullishness
of messages on future transaction volume are similar between the two groups: an
increase in the number of bullish posts predicts higher transaction volume in the
following day. Overall, these results support the Silent Majority Hypothesis (H2b):
the predictability available from social media depends mostly on content created by
the silent majority.
Having established the overall impact of social media and the stronger effects of
the silent majority users’sentiment on bitcoin prices, we can study platform differ-
ences and test the Internet Forum-Content Bitcoin Value Impact Hypothesis (H3). To
determine whether forum messages and tweets have the same impacts, we look at
observational days when we collected both forum and Twitter data. By modifying
the VECM model, we can include the normalized number of bullish and bearish
messages on both the forum and Twitter. The relevant estimates in Table 4 reveal
that, when aggregated at the interday level, the sentiments on forum messages are
more telling indicators of future bitcoin prices than are tweets. The forum variables
(POS
F
and NEG
F
) predict the prices one day in the future. A 1-standard deviation
increase in bullish forum posts is associated with 2.2 percent higher price, and a 1-
standard deviation increase in bearish forum posts is associated with a 3.6 percent
decrease in price. Both coefficient estimates are statistically significant. In contrast,
the Twitter variables (POS
T
and NEG
T
) have no significant predictive power for
bitcoin prices. The Granger causality tests confirm this finding. The forum sentiment
of the previous day Granger causes changes in future bitcoin prices (χ
2
= 18.58,
p< 0.01), whereas there is no Granger causality from Twitter sentiment to daily
bitcoin prices (χ
2
= 2.60, p= 0.27). In addition, no social media variables exhibit
significant predictive power for trading volume and transaction volume during the
sample period, though days with more bearish tweets precede days with high
volatility. Overall, these results lend support to Internet Forum-Content Bitcoin
Value Impact Hypothesis (H3): user-generated content from Internet forums, rather
than from Twitter, has a stronger impact on bitcoin value at the daily level.
Forecast Error Variance Decomposition and Forecast Accuracy
Given the estimated effects of forum social media on bitcoin value, we now examine
two more practical questions: To what extent does forum sentiment explain the
future variance of bitcoin values? More important, do social media help forecast
future bitcoin value?
To answer the first question, we derive the forecast-error variance decomposition
(FEVD) measures [39]. FEVD can measure the percentage contribution of each type
of shock to the forecast error of bitcoin value. Therefore, it is comparable to R
2
in
36 MAI, SHAN, BAI, WANG, AND CHIANG

regression models and provides insights into the relative importance of the variables.
FEVD is defined as:
FEVDjk ;s¼X
s1
i¼0
p2
jk;i
MSEksðÞ
:(4)
The MSEksðÞis the mean squared error of s-step forecast of variable k, and pjk;iis the
effect of a one-unit shock to variable jon kgiven by the impulse responses function.
Table 4. VECM Estimates for Comparing Forum and Twitter
Dependent Variables
Independent Variables ln(P)σVV
TX
ln(P)(t–1) −0.077 0.013 −1.736 −0.434
(0.109) (0.008) (1.752) (1.031)
σ(t–1) 0.128 0.135 21.750 13.320
(1.847) (0.136) (29.750) (17.510)
V(t–1) −0.022 0.002* 0.349 0.415***
(0.016) (0.001) (0.256) (0.151)
V
TX
(t–1) 0.014 −0.002 0.108 −0.466**
(0.020) (0.001) (0.319) (0.188)
POS
T
(t–1) 0.012 −6.54E-4 0.007 0.041
(0.008) (5.64E-4) (0.123) (0.073)
NEG
T
(t–1) −0.004 7.21E-4* −0.030 −0.050
(0.005) (3.68E-4) (0.081) (0.047)
POS
F
(t–1) 0.022*** 7.86E-4 0.119 0.027
(0.008) (6.02E-4) (0.132) (0.077)
NEG
F
(t–1) −0.036*** −2.31E-4 −0.159 0.033
(0.009) (6.29E-4) (0.137) (0.081)
rank(t–1) −0.009 0.002 0.628 0.500**
(0.027) (0.002) (0.431) (0.254)
googletrend(t–1) 0.001 −5.56E-4 −0.115 0.008
(0.007) (4.88E-4) (0.107) (0.063)
sp500(t–1) −1.156 −0.067 −3.668 −5.462
(1.357) (0.100) (21.850) (12.860)
vix(t–1) 0.002 −1.57E-4 0.107 −0.021
(0.007) (5.05E-4) (0.110) (0.065)
gold(t–1) 0.315 −0.009 −12.250 0.244
(0.541) (0.040) (8.712) (5.127)
investor_sent(t–1) 0.003** 5.12E-5 0.008 −0.006
(0.001) (9.44E-5) (0.021) (0.012)
news_sent(t–1) −0.140*** −0.003 −0.620 −0.085
(0.035) (0.003) (0.559) (0.329)
Notes: T = 89. Lag length k= 3. The first lag estimates are displayed. Estimates for controls are not
displayed. Standard errors are in parentheses. *** p< 0.01, ** p< 0.05, * p< 0.1.
HOW DOES SOCIAL MEDIA IMPACT BITCOIN VALUE? 37

FEVD has recently been used in a number of VAR/VECM applications in the IS
literature [37,55]. We follow Luo and Zhang [37] and evaluate the FEVD values at
20 days. We calculate FEVD for three models: a model that includes metrics from all
forum messages, a model that includes forum metrics from the silent majority users,
and a model that includes forum metrics from the vocal minority.
Table 5 provides a breakdown of forecast error variance of Bitcoin value that can
be attributed to shocks to itself or other variables in our system. As would be
expected, the Bitcoin price variable accounts for the largest fraction of its own
forecast error variance (84.25 percent to 86.66 percent). Consistent with prior
research, shocks to search and Internet traffic together can explain between 5.64
percent to 6.27 percent of the variation. When all forum messages are used, the
shock in forum sentiment explains 3.60 percent of the variance, which is the third
strongest source among all variables. The explanatory power for the social media
variables increases to 4.54 percent when we select only the silent majority group.
Given that only about 12 percent of the variance can be explained using variables
outside of the bitcoin market, these findings point to an economically significant
effect. In terms of explaining the variation in future price swings, sentiment on a
single forum is comparable in scale to the aggregate behavior of all Google users.
On the contrary, the sentiment of vocal minority users only accounts for 0.45 percent
of the total variation of bitcoin value—about one-tenth that of the silent majority.
Overall, the FEVD analysis further emphasizes that social media sentiments add
meaningful explanatory power for bitcoin value, after controlling for bitcoin market
variables, Internet and search traffic, and other control variables.
Table 5. Variance of Bitcoin Value Explained by Different Variables
Model
All Forum Messages (percent) Silent Majority Vocal Minority
Bitcoin Market
Price (log) 85.49 84.25 86.66
Volatility 1.86 2.18 1.79
Trading Vol 0.29 0.23 0.38
Transaction Vol 1.00 0.97 1.11
Total 88.64 87.62 89.94
Social Media
Positive Posts 2.29 2.64 0.02
Negative Posts 1.31 1.90 0.43
Total 3.60 4.54 0.45
Search and Internet
Traffic
Google Trend 5.19 5.07 5.83
Website Rank 0.52 0.57 0.44
Total 5.71 5.64 6.27
Other Controls 2.06 2.20 3.33
38 MAI, SHAN, BAI, WANG, AND CHIANG

To answer the second question, we test the predictive power of social media
variables by conducting out-of-sample forecasting. Out-of-sample forecasting is
regarded as the ultimate test of a model [53, p. 571]. In this test, we reserve the
last quarter of our observations period, from October 1 to December 31, 2014, as the
test period. First the model is estimated with the observations prior to the test period.
The model is then reestimated period by period through to the last day of the entire
sample as the updated parameters are used to generate new one-day ahead forecasts.
Such recursive rolling forecasts mimic the actual behavior of a practitioner in real
time and are routinely used in economics [43]. We measure the forecasting accuracy
using root mean square error (RMSE) and the mean absolute error (MAE). The
RMSE is defined as ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
nPactual predictedðÞ
2
q, and the MAE is defined as
1
nPactual predicted
jj
, where nis the number of forecasting periods (92 days).
Smaller RMSE and MAE indicate better model performance.
A three-day moving average model is used as a benchmark for judging the
accuracy of VECM forecasts. We estimate two VECMs for each forecast, one uses
all the variables but excludes the forum sentiments, and another is the full model that
includes the number of positive and negative forum posts generated by the silent
majority users. Table 6 presents the results.
In our test period, VECM with social media metrics has the lowest RMSE and MAE.
When compared with the three-day moving average model, the RMSE and MAE are
reduced by approximately 16 percent (from 16.60 to 13.92) and 14 percent (from 10.89
to 9.35). When compared with the VECM model with no social media metrics, the
RMSE and MAE are reduced by 10 percent (from 15.47 to 13.92) and 6 percent (from
9.96 to 9.35). Again, the results provide compelling evidence that social media senti-
ment has an important bearing on the determination of future bitcoin values.
Robustness Checks
We conducted a series of robustness checks for our results. To remove bias from the
specific sentiment measures we used, we considered a combined measure of
Table 6. Comparison of Forecasting Accuracy
Model
3-Day Moving Average
VECM
(No Social Media)
VECM
(With Social Media)
RMSE 16.60 15.47 13.92
MAE 10.89 9.96 9.35
Notes: The forecasting accuracy measures are calculated using a 92-day period from October 1,
2014 to December 31, 2014. For each day, a model is estimated using all the data prior to that day.
The model’s parameters are used to forecast next day’s bitcoin monetary value.
HOW DOES SOCIAL MEDIA IMPACT BITCOIN VALUE? 39

bullishness [1]. We define the bullishness measure as (POS –NEG)/(POS + NEG)
and reestimate our models using this single measure. Table 7 shows that all the
coefficients are in line with our findings using both POS
F
and NEG
F
: social media
bullishness on the forum is associated with future bitcoin returns, and the result is
mainly driven by the silent majority users. When we combine forum and Twitter
bullishness measures, the forum measure is the more important predictor.
To ensure that our results are not driven by certain events in a specific time frame,
we interacted a time dummy with social media metrics and estimated our model
again. The time dummy takes a value of one if it is after July 2013. The estimates in
Table 8 are largely consistent with our main findings.
Also, the interaction effects are not significant, thereby ruling out the possibility
that our results are time specific. As a check of the robustness of our results with
respect to the definition of the vocal minority and the silent majority, we adopted 10
percent and 2.5 percent user activity cutoff levels, in addition to the 5 percent level
in our main study. The results in Table 9 show that the impact of the vocal minority
and that of the silent majority exhibit similar disparities with the new definitions:
posts from less active users carry more weight for indicating future price changes.
Finally, recent evidence suggests that the monetary value of bitcoin may be impacted
by government regulations and laws. Although we control for news sentiment in our
model using the TRNA database, it is possible that actions of foreign governments—
especially the Chinese government—are not promptly included in English news. We
include bitcoin-related Baidu news trend (data provided by Baidu, the largest search
engine in China) in our model as a robustness check. We find that our results still stand
with this alternative control. (See Appendix B for details.)
Discussion and Conclusions
Bitcoin and other digital currencies provide unique benefits, including lower trans-
action costs and stimulus for financial innovation [6]. By breaking down existing
Table 7. Robustness Checks Using the Alternative Sentiment Measure
(1) (2) (3) (4)
All Users Silent Majority Vocal Minority All Users
Forum Bullishness 1.10E-4** 2.80E-4*** 8.35E-5 0.012***
(4.45E-5) (8.17E-5) (6.96E-5) (0.004)
Twitter Bullishness 0.003
(0.005)
Notes: This table shows the VECM estimates of previous day’s social media bullishness on bitcoin
prices. The first lag estimates are displayed. T = 1,901 for Models 1–3; T = 89 for Model 4. Lag
length k= 3. Estimates for controls are not displayed. Standard errors are in parentheses. ***
p< 0.01, ** p< 0.05, * p< 0.1.
40 MAI, SHAN, BAI, WANG, AND CHIANG

payment barriers and liberating global trades, they have the potential to generate
enormous wealth and social welfare for the economy. Lack of understanding of their
price fluctuations, however, could hold back bitcoin and other digital currencies
from achieving their full potential. We have accordingly sought to quantify the
dynamic relationship between social media and the monetary value of bitcoin. To
Table 9. Robustness Checks: Posting Volume Thresholds
Cutoff = top 10 percent Cutoff = top 2.5 percent
ln(P) ln(P)
Independent
Variables
Silent
Majority
Vocal
Minority
Silent
Majority
Vocal
Minority
POS
F
(t–1) 0.000995*** 0.000364** 0.000805*** 0.000139
(0.000363) (0.000181) (0.000222) (0.000248)
NEG
F
(t–1) −0.000467** −0.000145 −0.000328*** −0.000142
(0.000209) (8.91e-05) (0.000124) (0.000120)
Notes: T = 1,901. Lag length k= 3. The first lag estimates are displayed. Estimates for controls are
not displayed. Standard errors are in parentheses. *** p< 0.01, ** p< 0.05, * p< 0.1.
Table 8. Robustness Checks: Effect of Time Periods
Dependent Variables
ln(P)
Independent Variables Silent Majority Vocal Minority
ln(P)(t–1) 0.133*** 0.143***
(0.031) (0.031)
σ(t–1) 0.423 0.376
(0.546) (0.546)
V(t–1) −0.008** −0.008**
(0.004) (0.004)
V
TX
(t–1) −0.005 −0.004
(0.005) (0.006)
POS
F
(t–1) 0.001*** 3.89E-4
(3.05E-4) (3.58E-4)
NEG
F
(t–1) −4.69E-4*** −1.63E-4
(1.67E-4) (1.06E-4)
POS
F
(t–1) × post-07/2013 −4.26E-4 −1.61E-5
(5.53E-4) (5.50E-4)
NEG
F
(t–1) × post-07/2013 1.46E-5 −2.33E-4
(4.33E-4) (3.41E-4)
Notes: T = 1,901. Lag length k= 3. The first lag estimates are displayed. Estimates for controls are
not displayed. Standard errors are in parentheses. *** p< 0.01, ** p< 0.05, * p< 0.1.
HOW DOES SOCIAL MEDIA IMPACT BITCOIN VALUE? 41

the best of our knowledge, this study is the first research that systemically explores
the economic impact of social media information on bitcoin valuation. The results
suggest that social media sentiment is an important leading indicator of future
bitcoin price swings. Yet the relationship is complex, because the silent majority
exerts a more significant effect, and forum sentiment appears to be a better indicator
at the interday level than tweets. Evidence from the Granger causality test, error
variance decomposition, and out-of-sample forecasting suggests that forum senti-
ment has a strong predictive power for bitcoin value.
The findings also have implications for virtual currency adopters, investors, and
policymakers. First, the predictive relationship suggests that social media offer
substantial novel information about bitcoin’s demand among the general public as
well as daily fluctuations in its market sentiments. These signals are factored into the
price-formation process and influence future returns. Investors thus can discern
bitcoin’s monetary value from this rich information source. Greater predictability
of digital currency values can improve their reliability as a regular component of
investment portfolios. For regulators, social media monitoring also offers timely
indicators of impending movements of bitcoin prices, which can be used to address
the potential systemic risks associated with this unprecedented financial innovation.
Second, companies should strategically evaluate their decision to adopt bitcoin
payments. An important motivation for early institutional bitcoin adopters was to
capture positive public relations through social media, because “being noted as a
Bitcoin innovator can potentially generate favorable press and social media men-
tions”[46, p. 2]. Our results suggest that companies must think through more than
just the marketing consideration of generating positive buzz. The dynamic relation-
ship between social media content and bitcoin value means the future value of
accounts receivable can also be affected. This self-fulfilling feedback loop is new
for payment systems and could be a distinct feature of similar blockchain-based
financial technologies such as Ripple and Ethereum. If leveraged thoughtfully, social
media also can drive other fintech innovation in the future.
Although our study focuses on bitcoin, a fintech innovation, the broader implica-
tions also can influence general business practices in online social media.
Companies should analyze user behaviors and activities on social media while
monitoring the content. We have shown that social media messages are not created
equal and therefore should not be treated in the same way. The practice of exploiting
emotions and influences for marketing purposes is not novel; businesses have long
recognized the value of lead users [59] and opinion leaders [32], for example. But
our empirical findings highlight the value of the silent, yet influential majority of
inactive users. Despite the vocal minority dominating social media, the silent
majority users’opinions cannot be overlooked. More marketing and analytic efforts
should seek to identify this “heavy tail”of the online community. Moreover,
companies can benefit from monitoring discussions on various social media plat-
forms and devising unique strategies for them. For example, the instantaneous buzz
on mobile-oriented media (e.g., Twitter) may prompt interactions, but in-depth
42 MAI, SHAN, BAI, WANG, AND CHIANG

discussions on Internet forums can paint a more comprehensive picture of partici-
pants and thus are more likely to trigger final adoption or purchase decisions.
Our research has several limitations in its data sources and analysis methods,
which suggest possible extensions to this study. We used secondary data to identify
the association between social media sentiments and future bitcoin prices. Well-
designed, randomized experiments could enhance our understanding of the specific
findings. Second, we collected data from an English-language Internet forum and
limited our Twitter data to messages in English. Bitcoin prices across the globe are
highly correlated, and the market consists of investors and adopters worldwide.
Comparing messages written in other languages may lead to insights about the
potential effects of cultural differences. Moreover, we used financial sentiment as
the sole indicator of information in social media. Further studies might identify
subtle human emotions (e.g., fear, surprise) in the textual data and investigate their
role. Finally, we did not explore the mechanisms that may explain the prominence of
the silent majority and the stronger impact of the forum messages. Subsequent
analyses of text mining, user social networks, and information diffusion may create
new perspectives in understanding this unique phenomenon.
NOTES
1 Calculated as the number of coins in existence available to the public multiplied by the
U.S. dollar market price.
2 For example, the U.S. Internal Revenue Service treats bitcoin and other virtual curren-
cies like property, similar to stocks, whereas the Australian Taxation Office regards bitcoin
transactions as akin to barter arrangements.
3 A transaction is a signed section of data, broadcast to the network and collected in
blocks. It typically references previous transaction(s) and dedicates a certain number of
bitcoins to one or more new public key(s) (i.e., Bitcoin address). It is not encrypted; nothing
in Bitcoin is encrypted.
ORCID
Feng Mai http://orcid.org/0000-0001-6897-8935
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Appendix A: VECM Model Specifications
Step 1: Stationarity of variables. We first test the variables for unit roots and
determine if the variables are stationary. We perform the augmented Dickey–Fuller
(ADF) test [16]. The null hypothesis is that a variable contains a unit root, which
indicates that the variable follows a nonstationary process. If the series is station-
ary after differencing once, it is integrated of order 1 or I(1). The alternative
hypothesis is that the series was generated by a stationary process; the series is
integrated of order zero of I(0). When performing the ADF test, we include a lag
using the rule of thumb p=12T=100ðÞ
1=4as recommended by Schwert [50]. As
Tab le A1 shows, we cannot reject the null hypotheses for bitcoin market variables
and social media variables. We conclude that these time-series exhibit a unit root.
Among the control variables, we reject null hypothesis of a unit root for VIX,
46 MAI, SHAN, BAI, WANG, AND CHIANG

investor sentiment, and news sentiment, and failed to reject the null hypothesis for
rank, google trend, and gold index.
Step 2: Number of lags. We use the Akaike information criterion (AIC) to
choose the optimal lag length in the model. We estimate VAR models with length
varying from 0 to 12 and compute the log-likelihood and the AIC. AIC for a
VAR model is defined as 2Lþ2kþ2kpðÞ,whereLis the log-likelihood, kis
the number of coefficients, and pis the lag length. A smaller AIC indicates better
trade-off between model fits and complexity. Based on results in Ta ble A2 ,we
select the model with p¼3.
Step 3: Cointegration Tests.Ta ble A3 reports the results from the Johansen
trace test [27] for cointegration rank. The trace test is a sequential hypothesis
testing procedure. It starts from the null hypothesis of no integration (maximum
rank = 0), and compares the log-likelihood of the unconstrained model that
includes one more cointegrating equation with the constrained model. The test
is repeated until the first null hypothesis is not rejected. From Tab le A3,we
reject the null hypothesis of no cointegration, which confirms that VECM is the
appropriate model. The trace test stops at the null hypothesis that there are five
cointegration relations in the bitcoin market. Therefore, we proceed to estimate
our VECM with rank = 5.
Table A1. Results of Unit Root Tests
Variables Meaning
Test
Stats p-value
Order of
Integration
Bitcoin Market Variables
ln(P) Bitcoin price (log) −1.171 0.6859 I(1)
σVolatility of bitcoin returns −1.931 0.3177 I(1)
VLog daily trading volume −1.825 0.3679 I(1)
V
TX
Log daily transaction
volume
−3.039 0.1215 I(1)
Social Media Activities
POS
F
Number of positive posts −1.664 0.4500 I(1)
NEG
F
Number of negative posts −2.358 0.1540 I(1)
POS
T
Number of positive tweets −2.204 0.4878 I(1)
NEG
T
Number of negative tweets −3.112 0.1033 I(1)
Control Variables
rank Bitcoin.org web traffic rank
(log)
googletrend Google Trend for Bitcoin −1.732 0.4145 I(1)
sp500 Log S&P 500 closing price −0.829 0.8104 I(1)
vix COBE Volatility Index −5.649 < 0.001 I(0)
gold Log COMEX gold price −0.815 0.8147 I(1)
investor_sentiment AAII investor sentiment −6.379 < 0.001 I(0)
news_sentiment TRNA Bitcoin news
sentiment
−5.503 < 0.001 I(0)
HOW DOES SOCIAL MEDIA IMPACT BITCOIN VALUE? 47

Appendix B: VECM with Baidu Trend
This section shows that our results are robust when we control for the recent Chinese
government meddling with bitcoin. We used the data from Baidu news monitoring
(zhishu.baidu.com) and downloaded the Chinese news intensity data for bitcoin
(Figure B1). Baidu is the largest search engine in China. Its news aggregation
service provides broad coverage of government policy announcements through the
major Chinese news outlets.
We replicated VECM analyses to examine the relationship between social media
and bitcoin values. As Table B1 demonstrates, with the added control of Baidu news
intensity, the social media variables remain to have a significant predictive relation-
ship with future bitcoin prices in the Social Media Metrics Effects Hypothesis (H1).
In addition, Table B2 shows the distinct effects hold in the Vocal Minority and Silent
Majority Hypotheses (H2a, H2b). Finally, Table B3 suggests that when both forum
Table A2. Selecting Optimal Lag Length
Lag Log-Likelihood AIC
0−17,762.2 32.86
1−2,226.1 4.45
2−1,930.1 4.22
3−1,711.1 4.12*
4−1,555.2 4.15
5−1,422.0 4.21
6−1,214.5 4.14
7−1,080.1 4.21
8−928.6 4.24
9−792.0 4.30
10 −675.7 4.40
11 −554.3 4.49
12 −432.8 4.57
Table A3. Trace Test for Cointegration
Rank Log Likelihood Eigenvalue Trace Statistic 5 percent Critical Value
0 777.9 —909.0 233.13
1 914.7 0.22 635.4 192.89
2 1,025.0 0.18 414.8 156.00
3 1,105.0 0.14 254.9 124.24
4 1,164.2 0.10 136.3 94.15
5 1,199.4 0.06 66.1* 68.52
* Indicates the first null hypothesis that is not rejected
48 MAI, SHAN, BAI, WANG, AND CHIANG

Table B1. VECM Estimates for Forum Sentiments and Bitcoin
Dependent Variables (Bitcoin Market)
Indep Vars ln(P)σVV
TX
ln(P)(t–1) 0.133*** −0.007*** −0.064 0.199
(0.031) (0.002) (0.349) (0.193)
σ(t–1) 0.631 0.159*** 4.158 −3.532
(0.543) (0.030) (6.099) (3.374)
V(t–1) −0.007* 7.07E-4*** −0.180*** 0.136***
(0.004) (2.15E-4) (0.044) (0.024)
V
TX
(t–1) −0.002 −1.72E-4 0.243*** −0.202***
(0.006) (3.28E-4) (0.067) (0.037)
POS
F
(t–1) 0.001*** −2.28E-5 −0.002 0.007***
(3.66E-4) (2.02E-5) (0.004) (0.002)
NEG
F
(t–1) −4.42E-4** 1.50E-5 2.89E-4 3.29E-4
(2.10E-4) (1.16E-5) (0.002) (0.001)
Rank(t–1) 1.84E-7 −1.64E-8 1.97E-7 1.30E-6
(3.20E-7) (1.77E-8) (3.60E-6) (1.99E-6)
Baidunews(t–1) 1.07E-7 7.05E-9 6.68E-7 6.18E-7
(1.28E-7) (7.09E-9) (1.44E-6) (7.97E-7)
googletrend(t–1) 0.002*** 2.21E-5 0.014** −0.002
(5.44E-4) (3.01E-5) (0.006) (0.003)
sp500(t–1) −0.481 0.026 10.550** 5.205*
(0.450) (0.025) (5.059) (2.798)
vix(t–1) −0.002 2.20E-4 0.054 0.053***
(0.003) (1.66E-4) (0.034) (0.019)
gold(t–1) 0.069 0.014 0.555 −0.977
(0.171) (0.009) (1.926) (1.066)
investor_sent(t–1) 5.01E-4 −6.41E-6 −0.006 3.42E-4
(4.66E-4) (2.58E-5) (0.005) (0.003)
news_sent(t–1) −9.74E-4 1.47E-4 0.203 0.010
(0.016) (8.85E-4) (0.180) (0.100)
Notes: T = 1,901. Lag length k= 3. The first lag estimates are displayed. The controls are not
displayed among the dependent variables. Standard errors are in parentheses.
*** p< 0.01, ** p< 0.05, * p< 0.1.
Figure B1. Baidu News Intensity
HOW DOES SOCIAL MEDIA IMPACT BITCOIN VALUE? 49

Table B2. VECM Estimates for Comparing the Silent Majority and Vocal Minority
Dependent Variables (Bitcoin Market)
ln(P)σVV
TX
Independent Variables
Silent
Majority
Vocal
Minority
Silent
Majority
Vocal
Minority
Silent
Majority
Vocal
Minority
Silent
Majority
Vocal
Minority
ln(P)(t–1) 0.129*** 0.143*** −0.007*** −0.008*** −0.072 −0.138 0.193 0.190
(0.031) (0.031) (0.002) (0.002) (0.348) (0.346) (0.193) (0.191)
σ(t–1) 0.625 0.570 0.159*** 0.159*** 4.351 5.104 −3.468 −3.651
(0.540) (0.543) (0.030) (0.030) (6.081) (6.085) (3.366) (3.350)
V(t–1) −0.007* −0.007* 7.24E-4*** 7.33E-4** −0.180*** −0.191*** 0.135*** 0.126***
(0.004) (0.004) (2.14E-4) (2.12E-4) (0.043) (0.043) (0.024) (0.024)
V
TX
(t–1) −0.002 −0.002 −1.61E-4 −6.51E-5 0.241*** 0.257*** −0.203*** −0.188***
(0.006) (0.006) (3.29E-4) (3.28E-4) (0.067) (0.067) (0.037) (0.037)
POS
F
(t–1) 9.61E-4*** 2.47E-4 −9.54E-6 −5.21E-6 −8.67E-4 0.002 0.004** 0.005***
(2.65E-4) (2.14E-4) (1.47E-5) (1.18E-5) (0.003) (0.002) (0.002) (0.001)
NEG
F
(t–1) −4.11E-4*** −1.17E-4 6.64E-6 −3.87E-6 9.13E-5 −6.07E-4 2.69E-4 −4.01E-4
(1.53E-4) (1.04E-4) (8.46E-6) (5.71E-6) (0.002) (0.001) (9.51E-4) (6.40E-4)
rank(t–1) 1.77E-7 1.68E-7 −1.68E-8 −2.05E-8 2.28E-7 1.61E-7 1.27E-6 9.81E-7
(3.19E-7) (3.23E-7) (1.77E-8) (1.77E-8) (3.59E-6) (3.62E-6) (1.99E-6) (1.99E-6)
baidunews(t–1) 8.29E-8 9.42E-8 7.16E-9 8.47E-9 6.63E-7 7.64E-7 5.35E-7 6.55E-7
(1.28E-7) (1.29E-7) (7.10E-9) (7.09E-9) (1.44E-6) (1.44E-6) (7.99E-7) (7.95E-7)
googletrend(t–1) 0.002*** 0.002*** 2.25E-5 1.95E-5 0.014** 0.014** −0.002 −0.002
(5.43E-4) (5.47E-4) (3.01E-5) (3.01E-5) (0.006) (0.006) (0.003) (0.003)
sp500(t–1) −0.501 −0.453 0.025 0.022 10.530** 10.600** 5.220* 5.116*
(0.449) (0.453) (0.025) (0.025) (5.058) (5.074) (2.799) (2.793)
vix(t–1) −0.002 −0.002 2.13E-4 1.91E-4 0.055 0.054 0.053*** 0.054***
50 MAI, SHAN, BAI, WANG, AND CHIANG

(0.003) (0.003) (1.66E-4) (1.66E-4) (0.034) (0.034) (0.019) (0.019)
gold(t–1) 0.055 0.048 0.014 0.015 0.582 0.443 −1.081 −1.029
(0.171) (0.172) (0.009) (0.009) (1.924) (1.924) (1.065) (1.059)
investor_sent(t–1) 5.40E-4 4.83E-4 −6.31E-6 −7.48E-6 −0.006 −0.006 5.03E-4 4.12E-4
(4.65E-4) (4.67E-4) (2.58E-5) (2.57E-5) (0.005) (0.005) (0.003) (0.003)
news_sent(t–1) −0.002 −4.03E-4 1.64E-4 1.44E-4 0.207 0.179 0.012 −0.035
(0.016) (0.016) (8.87E-4) (8.85E-4) (0.180) (0.180) (0.100) (0.099)
Notes: T = 1,901. Lag length k= 3. The first lag estimates are displayed. Standard errors are in parentheses.
*** p< 0.01, ** p< 0.05, * p< 0.1.
HOW DOES SOCIAL MEDIA IMPACT BITCOIN VALUE? 51

and Twitter sentiments are included, only forum variables have significant relation-
ships with future Bitcoin price, as in the Internet Forum-Content Bitcoin Value
Impact Hypothesis (H3). The evidence supports that our main results hold when
we account for shocks in Chinese government regulations.
Table B3. VECM Estimates for Comparing Forum and Twitter
Dependent Variables (Bitcoin Market)
Indep Vars ln(P)σVV
TX
ln(P)(t–1) −0.017 0.023** 0.525 0.306
(0.148) (0.009) (1.966) (1.215)
σ(t–1) 1.662 0.116 −19.910 3.294
(2.636) (0.160) (35.100) (21.690)
V(t–1) −0.020 0.001 −0.090 0.277*
(0.018) (0.001) (0.240) (0.149)
V
TX
(t–1) 0.033 −0.001 −0.196 −0.518**
(0.026) (0.002) (0.341) (0.211)
POS
T
(t–1) 0.007 −5.36E-4 −0.053 0.019
(0.006) (4.90E-4) (0.108) (0.067)
NEG
T
(t–1) −0.009 5.36E-4 0.034 −0.046
(0.007) (4.03E-4) (0.088) (0.055)
POS
F
(t–1) 0.013* −6.83E-5 0.025 0.003
(0.008) (4.45E-4) (0.098) (0.060)
NEG
F
(t–1) −0.023** 1.12E-4 −0.246* 0.013
(0.010) (6.30E-4) (0.138) (0.086)
rank (t–1) 1.24E-6 1.87E-7 3.59E-5 3.25E-5
(2.46E-6) (1.49E-7) (3.28E-5) (2.03E-5)
baidunews (t–1) 0.005 −3.27E-4 0.015 0.035
(0.008) (4.95E-4) (0.109) (0.067)
googletrend (t–1) 6.34E-6 5.82E-7* 1.44E-4* 6.61E-5
(5.55E-6) (3.37E-7) (7.39E-5) (4.57E-5)
sp500 (t–1) −0.679 −0.023 18.630 −2.615
(1.696) (0.103) (22.580) (13.960)
vix (t–1) 0.007 5.12E-5 0.154 −0.014
(0.008) (4.74E-4) (0.104) (0.064)
gold (t–1) 0.145 0.005 −10.270 0.258
(0.649) (0.039) (8.643) (5.341)
investor_sent (t–1) 0.001 3.52E-7 −4.80E-4 −0.010
(0.001) (8.89E-5) (0.019) (0.012)
news_sent (t–1) −0.036 −5.53E-4 −0.353 −0.103
(0.033) (0.002) (0.442) (0.273)
Notes: T = 89. Lag length k= 3. The first lag estimates are displayed. Estimates for controls are not
displayed. Standard errors are in parentheses. *** p < 0.01, ** p< 0.05, * p< 0.1.
52 MAI, SHAN, BAI, WANG, AND CHIANG