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

• DOI: http://doi.org/10.1111/fire.12182
• Date: 01 May 2019
• Published date: 01 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

Abstract

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

squares

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: ehab.yamani@mavs.uta.edu.

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.

C2019 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