Sample selection bias and Heckman models in strategic management research

• DOI: http://doi.org/10.1002/smj.2475
• Published date: 01 December 2016
• Date: 01 December 2016

Strategic Management Journal

Strat. Mgmt. J.,37: 2639–2657 (2016)

Published online EarlyView 9 February 2016 in WileyOnline Library (wileyonlinelibrary.com) DOI: 10.1002/smj.2475

Received 29 January 2015;Final revisionreceived 5 October 2015

SAMPLE SELECTION BIAS AND HECKMAN MODELS

IN STRATEGIC MANAGEMENT RESEARCH

S. TREVIS CERTO, JOHN R. BUSENBARK, HYUN-SOO WOO,

and MATTHEW SEMADENI*

Department of Management, W. P. Carey School of Business, Arizona State

University, Tempe, Arizona, U.S.A.

Research summary: The use of Heckman models by strategy scholarsto resolve sample selection

bias has increased by more than 700percent over the last decade, yet signicant inconsistencies

exist in how theyhave applied and interpreted these models. In view of these differences, we explore

the drivers of sample selection bias and review how Heckmanmodels alleviate it. We demonstrate

three important ndings for scholars seeking to use Heckman models: First, the independent

variable of interest must be a signicant predictor in the rststage of a model for sample selection

bias to exist. Second, the signicance of lambda alone does not indicate sample selection bias.

Finally,Heckman models account for sample-induced endogeneity, butare not effective when other

sources of endogeneity are present.

Managerial summary: When nonrandom samples are used to test statistical relationships,sample

selection bias can lead researchers to awed conclusions that can, in turn, negatively impact

managerial decision-making. We examine the use of Heckman models, which were designed to

resolve sample selection bias, in strategic management research and highlight conditions when

sample selection bias is present as well as when it is not. We also distinguish sample selection

bias, a form of omitted variable (OV) bias, from more traditional OV bias, emphasizing that it

is possible for models to have sample selection bias, traditional OV bias, or both. Accurately

identifying the type(s) of OV bias present is essential to effectively correcting it. We close with

several recommendationsto improve practice surrounding the use of Heckman models. Copyright

© 2015 John Wiley & Sons, Ltd.

Selection bias is not well understood by prac-

titioners. (Kennedy, 2006: 286)

INTRODUCTION

Empirical studies in strategy research rely on sam-

ples of observations that represent fractions of

underlying populations. Biases may arise when

Keywords: sample selection bias; Heckman models; endo-

geneity; research methods

*Correspondence to: Matthew Semadeni, Ofce BA 323H,

PO Box 874006, Tempe, AZ 85287, U.S.A. E-mail:

semadeni@asu.edu

Copyright © 2015 John Wiley & Sons, Ltd.

researchers use samples instead of populations to

test hypotheses. In particular, sample selection bias

may occur when values of a study’s dependent

variable are missing as a result of another process

(Greene, 2011; Sartori, 2003). The central objec-

tive of this article is to explore the drivers of sample

selection bias and review how different analytical

tools can correct it.

Scholars routinely describe the intuition of sam-

ple selection bias as requiring a two-stage approach

(e.g., Wooldridge, 2010). Determining whether or

not an observation in an overall population appears

in its nal representative sample is the rst stage,

and modeling the relation between the hypothesized

dependent and independent variables in the nal

sample is the second stage. When an omitted vari-

able (i.e., an unmeasured variable not included in a

2640 S. T. Certo et al.

model) creates a correlation between the error terms

in these two stages, traditional techniques such as

ordinary least squares (OLS) regression may report

biased coefcient estimates. To resolve this poten-

tial bias, Heckman (1976) introduced the Heckman

model, a two-step process for data analysis.1

To better understand how strategy scholars

approach potential sample selection bias, we

reviewed 63 articles appearing in the Strategic

Management Journal (SMJ) between 2005 and

2014 that utilized Heckman models. In recent

years, strategy scholars have employed Heckman

models to study areas, including upper echelons

and board membership (e.g., Quigley and Ham-

brick, 2012), diversication and M&A activity

(e.g., Kim, Hoskisson, and Lee, 2015), executive

compensation (e.g., Chen, 2015), capital market

activity (e.g., Arikan and Capron, 2010), and com-

petition and factor markets (e.g., Ndofor, Sirmon,

and He, 2011).

Despite the signicant growth in the use of

Heckman models in strategy research (more than

700 percent over the last decade), we noted incon-

sistencies in how strategy scholars implemented and

reported the results they derived. We also found that

scholars often justied the use of Heckman models

on the basis of concerns about endogeneity from

a source other than sample selection. This is per-

haps to be expected, however, as some econometrics

textbooks list sample selection as a potential cause

of endogeneity (e.g., Kennedy, 2006). This prac-

tice may cause some researchers to (mistakenly)

equate the effects of sample selection bias with the

effects of other sources of endogeneity. These dis-

crepancies suggest that, as strategy scholars, we

need a more rigorous understanding of (1) how sam-

ple selection bias varies across study conditions, (2)

when sample selection bias affects statistical results,

(3) how to apply Heckman models, and (4) how to

account for effects resulting from sample selection

bias versus other sources of endogeneity.

Accordingly, the rst objective of this article is

to explain how sample selection bias varies across

study conditions. We explain that sample selection

bias is the result of a special case of endogeneity,

which we label sample-induced endogeneity. This

1By “the Heckman model,” we are referring to the Heckman

two-stage model. There is an alternative Heckman model known

as the Heckman full information maximum likelihood (FIML)

model, but the more ubiquitous is the two-stage model. Of the 63

reviewed articles published in the SMJ between 2005 and 2014,

only one article used the Heckman FIML model.

special case occurs when omitted variables create a

correlation between the error term in the selection

equation (i.e., the rst stage of a study’s statistical

model) and the error term in the equation of interest

(i.e., the second stage). We explain that the magni-

tude and direction of the bias depends on two fac-

tors: (1) whether the true relationship between the

independent and dependent variable is positive or

negative, and (2) whether the correlation between

the error terms in the two stages is positive or

negative.

To address our rst objective, we create four

gures (Figure 1a– d) to demonstrate that, in some

cases, sample selection bias can lead researchers to

nd signicant relationships that do not exist, or in

other cases, it can lead researchers to fail to nd sig-

nicant relationships that do exist. Then, we report

on the three studies in which we used simulations

to address our other three objectives. Study 1 exam-

ines the conditions necessary to understand when

sample selection processes bias results. We exam-

ine two factors related to the sample selection pro-

cess: (1) the strength of the correlation between the

error terms from rst- and second-stage equations,

and (2) the extent to which the independent variable

of interest is related to the probability of an obser-

vation’s entering the nal sample. Our literature

review revealed a great deal of confusion regarding

the role of lambda. Our simulations illustrate that

a signicant lambda does not always denote sam-

ple selection bias. Specically, our results indicate

that traditional techniques (e.g., OLS) remain unbi-

ased when the independent variable from the second

stage is not also a signicant predictor in the rst

stage.

Study 2 uses simulations to clarify how

researchers should implement Heckman models.

In this study, our ndings illustrate that lambda

can be insignicant even when sample selection

bias exists, if model specications are improper.

This nding is important as our review uncovered

numerous strategy research interpreting an insignif-

icant lambda as evidence of no sample selection

bias. Taken together, the simulations illustrate

the complex role of lambda in explaining sample

selection bias and help researchers understand how

to use Heckman models.

Finally, Study 3 addresses how researchers

should approach different sources of endogeneity

when employing Heckman models. We distin-

guish between sample-induced and other forms of

endogeneity. Our simulations reveal that Heckman

Copyright © 2015 John Wiley & Sons, Ltd. Strat. Mgmt. J.,37: 2639–2657 (2016)

DOI: 10.1002/smj