The Endogeneity of Trading Volume in Stock and Bond Returns: An Instrumental Variable Approach

Date01 May 2019
Published date01 May 2019
The Financial Review 54 (2019) 303–344
The Endogeneity of Trading Volume in
Stock and Bond Returns: An Instrumental
Variable Approach
Ehab Yamani
Chicago State University and TantaUniversity (Egypt)
David Rakowski
University of Texasat Arlington
This paper investigates the joint determination of trading volume and returns. Our ap-
proach follows from the argument that trading activity depends on security returns, thus
resulting in a reverse causality from returns to trading activity. Using exogenous instruments
for security trading activity,we estimate a system of two-stage simultaneous equations to better
model the return-volume relationship. Our results confirm that returns and trading volume are
determined simultaneously in both stock and corporate bond markets and that conclusions
about the direction and significance of causality between volume and returns can be reversed
once one corrects for the endogeneity of volume.
Keywords: endogeneity, simultaneity, trading volume, security returns, two-stage least
JEL Classifications: C18, C30, C36, G10, G12
Corresponding author: Department of Accounting and Finance, Chicago State University,9501 S. King
Drive, Chicago, IL 60628; Phone: (817) 673-6883; E-mail:
Wewould like to thank Srinivasan Krishnamurthy (the Editor), two anonymous referees, Larry Lockwood,
Darren Hayunga, Peter Lung and Mahmut Yasar for their helpful comments and suggestions, as well
as seminar participants at Chicago State University, California State University at Bakersfield, Central
Connecticut State University,and Bloomsburg University of Pennsylvania.
C2019 The Eastern Finance Association 303
304 E. Yamani and D. Rakowski/The Financial Review54 (2019) 303–344
1. Introduction
Price and quantity are the fundamental building blocks of any theory of market
interactions. As a result, the relationship between the volume of trading in a security
and its return has always interested market practitioners, as well as the academic
community. The conventional empirical approach taken is to estimate a model in
which return (volume) is a function of volume (return). Although this approach has
found a functional relationship between return and volume, it potentially leads one to
neglect correcting for endogeneity by explicitly assuming that volumeis exogenous to
returns. In this paper, we present intuitive theoretical argumentsand empirical results
that suggest that return and volume are endogenously related. We then propose an
instrumental variable (IV) approach to alleviate these endogeneity concerns and we
demonstrate how corrections for endogeneity can lead to a reversal in the direction
and significance of the estimated relationship between returns and volume.
From a statistical point of view,we distinguish between two potential sources of
endogeneity. The first source of endogeneity is simultaneity, where price and volume
are simultaneously determined in equilibrium, with whatever process that generates
returns also giving rise to trading volume. Theoretically,the “mixture of distributions
hypothesis” (MDH) predicts that security returns increase in any period when trading
activity increases (Clark, 1973; Epps and Epps, 1976; Tauchen and Pitts, 1983;
Anderson, 1996). While return may be associated with volume, the reverse will also
be true—volume will also be affected by return (Lee and Rui, 2002). Our suggestion
is that ordinary least squares (OLS) estimates can be biased and inconsistent in the
presence of simultaneity.
The second source of endogeneity is dynamic endogeneity, which arises when
current values of the explanatory variables are related to past valuesof the dependent
variables. To illustrate, previous research on volume-based momentum strategies
suggests a causal relationship running from past volume to current returns (as implied
by Campbell, Grossman and Wang, 1993; Blume, Easley and O’Hara, 1994; Wang,
1994; Datar, Naik and Radcliffe, 1998; Chordia and Swaminathan, 2000; Lee and
Swaminathan, 2000). The empirical approach in these studies assumes that volume is
exogenous and the history of returns thus does not affectvolume. However, theoretical
models of overconfidence (Kyleand Wang, 1997; Benos, 1998; Odean, 1998b; Wang,
1998; Gervais and Odean, 2001; Caball´
e and Sakovics, 2003); and positive feedback
trading (De Long, Bradford, Shleifer, Summers and Waldman, 1990; Hirshleifer,
Subrahmanyam and Titman, 1994, 2006) suggest a causal relation running from past
returns to current volume. We thus suggest that many studies may have overlooked
dynamic endogeneity when evaluatingthe relation between lagged return and volume.
In this paper, we are motivated by these two sources of endogeneity, and we
propose an IV approach to alleviate these endogeneity concerns, using data from both
stock and corporate bond markets. Given that theories and empirical studies suggest
that return and volume are simultaneously determined, we use a system of two-
stage simultaneous equations to better estimate the contemporaneous return-volume
E. Yamani and D. Rakowski/The Financial Review54 (2019) 303–344 305
relation. In stage one, security trading volume in one period is allowed to depend on
security return in that period, control variables, and instruments for security trading.
We use five IVs for stock trading: firm age, the number of analysts following a stock,
analyst forecast dispersion, earnings surprises, and earnings volatility; and two IVs
for bond trading: bond age and the firm’sdebt size. In stage two, returns depend on the
fitted values of volume from stage one, control factors, and a predetermined variable
to correctly specify our model. Given that previousstudies also suggest that return and
volume are dynamically determined, we include lagged return and lagged volume to
serve as control factors, among others, that jointly affect current returns and volume.
Our central finding in this paper is that the magnitude and/or direction of the
return-volume relation can be reversed once we account for endogeneity using our IV
approach. Put differently, many of our return and volume coefficients flip sign when
switching from OLS to two-stage least squares (2SLS) using various regression
specifications and three measures of volume. Consider first the contemporaneous
relations. Our OLS regression estimates show that there is a significant positive
bidirectional contemporaneous relation between number of shares traded and stock
return. In contrast, 2SLS estimates report a significant negative contemporaneous
relation between both variables. When corporate bond data are considered, OLS esti-
mates predict a significant negative bidirectional contemporaneous relation between
numbers of bonds traded and bond return, while 2SLS estimates predict a signifi-
cant positive relation between both variables. Generalized across different security
markets, our 2SLS results depart from previous evidence reported by Clark (1973),
Rogalski (1978), Tauchen and Pitts (1983), Jain and Joh (1988), Gallant, Rossi and
Tauchen (1992), Lee and Rui (2002), Chuang, Hsiang-His and Susmel (2012).
Turning to the dynamic return-volume relation, many of our OLS results are
again at odds with 2SLS results. For the impact of lagged stock return on current
volume, the OLS estimates are significantly negative for all three volume measures
while the 2SLS estimates are significantly positive for two out of three volume
measures. Our OLS findings differ from those of Gallant, Rossi and Tauchen (1992),
Chordia and Swaminathan (2000), Barber and Odean (2002), Statman, Thorley and
Vorkink (2006), Griffin, Nardari and Stulz (2007), Kim and Nofsinger (2007), Glaser
and Weber (2009), Goyenko and Ukhov (2009), and Nicolosi, Peng and Zhu (2009).
However, the positive 2SLS coefficients are in line with the predictions of previous
research on the overconfidence theory (e.g., Kyle and Wang, 1997; Benos, 1998;
Odean, 1998b; Wang, 1998; Gervais and Odean, 2001; Caball´
e and Sakovics, 2003),
the disposition effect (Shefrin and Statman, 1985), differences of opinion theory
(Harris and Raviv, 1993; Kandel and Pearson, 1995; Bamber, Barron and Stober,
1999), and positive feedback trading (e.g., De Long, Bradford, Shleifer,Summers and
Waldman, 1990; Hirshleifer, Subrahmanyam and Titman, 1994, 2006) that suggest
that high returns make investors trade more frequently.
When considering the impact of lagged stock volume (measured by number
of shares traded) on current stock return, our OLS results suggest a significant
negative relationship between lagged volumeand current returns. After correcting for

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