endogeneity in accounting and finance research: natural ... · endogeneity in accounting and...

JENNIFER GIPPEL, TOM SMITH, AND YUSHU ZHU

Endogeneity in Accounting and FinanceResearch: Natural Experiments as a

State-of-the-Art Solution

This paper provides a discussion of endogeneity as it relates to finance andaccounting research. We discuss the textbook solutions: two-stage leastsquares, instrumental variables, differenced generalized method ofmoments (GMM) and system GMM and provide a unifying frameworkshowing how they are related. We consider the limitations of these tech-niques and then detail a state-of-the-art solution, utilizing a natural experi-ment as a way of mitigating endogeneity and building stronger theory.

Key words: Corporate governance; Endogeneity; Natural or quasiexperiment.

Endogeneity is more than a problem of econometrics. It is also a problem of theory.The issue for researchers is that often variables included in the structural equationsare simultaneously determined, mismeasured and/or the theory is incomplete and soimportant variables are omitted. More sophisticated econometric techniques areonly part of the solution. Better theory is also necessary to help researchers buildmore complete and accurately specified models.

In finance and accounting research it is important that empirical work is under-pinned by theory. Accordingly a well-designed study must be clear about how andwhy variables influence one another and the logic and direction of the relationshipmust be specified (Larcker and Rusticus, 2007). However, much of the accountingand finance empirical literature is plagued by endogeneity, particularly in corporategovernance studies (Roberts and Whited, 2012). A spate of recent articles address-ing the concerns of endogeneity in the finance and accounting literature is puttingthis issue firmly on the table. For example, Chenhall and Moers (2007), Larcker andRusticus (2007), and Van Lent (2007) in accounting. And in finance, Robertsand Whited (2012) and Brown et al. (2011). Endogeneity has always been presentand recognized as a problem that undermines causal inference. However, it is oftena problem that researchers either do not address at all, or simply note in passing that

Jennifer Gippel ([email protected]) is a visiting Fellow at the Australian National University;the University of Sydney Business School; and Macquarie University. Tom Smith ([email protected]) is Frank Finn Professor in Finance at the University of Queensland Business School.Yushu Zhu ([email protected]) is a Lecturer in Finance at the University of Queensland Busi-ness School.

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ABACUS, Vol. 51, No. 2, 2015 doi: 10.1111/abac.12048

143© 2015 Accounting Foundation, The University of Sydney

mailto:[email protected]




the problem exists. Table 1 selects the papers with endogeneity issues pub-lished in 2013 and 2014 in Asian Pacific journals including: Australian Journal ofManagement (9), Accounting and Finance (11), Abacus (1), Pacific Basin FinanceJournal (2), and International Review of Finance (1). Out of the 24 papers listedin the table, only two performed all specification tests and more than half (13)performed no tests.

Ignoring the problem, however, does not mitigate the implications—endogeneitylimits the validity of empirical testing of models. Here, we do not question thevalidity of finance and accounting research to date to the extent that it should bedisregarded. We argue that endogeneity has become more of a concern as we modelincreasingly complex relationships. Accordingly, the power of our theories is morekeenly scrutinized and tested.

While all agree the problem is pervasive there is some disagreement about howbest to deal with it. Chenhall and Moers (2007) and Larcker and Rusticus (2007)argue that theory development is critical. Van Lent (2007) on the other hand, arguesthat theory is never likely to be complete and good instruments are hard to find andso there is little a researcher can do to mitigate endogeneity. He argues that goodresearch should be judged by how stimulating the research question is and it is amistake to pretend that models are fully specified. Researchers should rather defendwhy they chose that particular misspecification and articulate how the results wouldchange had they chosen another misspecification of the model. Roberts and Whited(2012) emphasize the importance of researchers discussing endogeneity along withgood empirical design using high-quality data and robust testing of empirical pre-dictions. Researchers should not be discouraged from empirical testing because evenif endogeneity is known to be present, such studies provide the foundation for futurework (Roberts and Whited, 2012).

Where researchers recognize endogeneity as a limitation to their research, howthey deal with it is constrained by current thinking on appropriate techniques.Commonly used research designs to deal with endogeneity include two-stage leastsquares (2SLS), instrumental variables (IV), differenced GMM (generalized methodof moments), and system GMM as we can see from Table 1. In the next section weprovide a unifying framework that illustrates and encompasses all of theseapproaches.

Looking beyond the textbook solutions, one research design that helps miti-gate the problem of endogeneity is that utilizing a natural experiment. A studyincorporating a natural experiment provides the researcher leverage over thecommonly used textbook solutions to endogeneity because it involves makinguse of a plausibly exogenous source of variation in the independent variablesof interest (Meyer, 1995). If the naturally occurring event is convincingly exogenous,and the study well implemented, then researchers have a way to isolate causallinks, build new theory and clarify (confirm/disconfirm) existing theory by mitigat-ing the issue of endogeneity. In this paper, we provide researchers with a roadmap for designing research based on natural experiments and in this way wecontribute to the evolution of more rigorous research techniques in finance andaccounting.

A BAC U S


Tabl

e1

PAP

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SP

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LIS

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DIN

2013

AN

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ES

OF

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ifica

tion

Test

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),(3

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etho

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aff,

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(201

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sex

plan

ator

yva

riab

les:

mar

ket

disc

iplin

e,ba

nkca

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l,an

dch

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(1),

(2),

(3)

Two-

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di,K

rish

nam

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vari

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E N D O G E N E I T Y I N AC C O U N T I N G A N D F I NA N C E R E S E A R C H


ENDOGENEITY AND CURRENT TEXTBOOK SOLUTIONS

The current textbook solutions to endogeneity include 2SLS, IV, differenced GMM,and system GMM.1 In the section that follows, we work through these methods andprovide a unified framework showing how these approaches are related.

What is Endogeneity?In terms of econometrics we can think of endogeneity as having several dimensions.First, it is a problem of omitted variables,that is,variables other than the ones specifiedprovide alternative or additional explanation for the relationship modelled. Forexample, the relationship between executive compensation and firm value intuitivelydepends on executives’ abilities, which is difficult to quantify (Roberts and Whited,2012).Further, if looking at the value of independent directors,again, the ability of thedirectors would be important but also it is difficult to measure independence, surely afunction of director and CEO networks, which are not easy to establish.

Second, endogeneity is a problem of simultaneity, that is, when the dependentvariable and one or more of the explanatory variables are jointly determined. Forexample, more police officers might reduce crime but cities with higher crime ratesmight demand more police officers; more diffuse firm ownership might affect per-formance but firms with strong performance might attract diffuse ownership; bankswith adequate capital reserves might have good performance but good performingbanks might have stronger capital reserves, etc. In all such cases, results from regres-sion analysis might confound these relationships because the direction of causality ismost likely two ways.

A third problem is that related to measurement error when proxies are used forunobservable or difficult to measure independent or dependent variables (Robertsand Whited, 2012). For example, looking at the relationship between firm value andboard independence, researchers must proxy for the degree of independence fromthe CEO.

The following works through the current textbook approaches to endogeneitybeginning with the errors in variables problem, which is familiar to most students orresearchers in finance.

Errors in Variables ProblemTo understand endogeneity we can first liken it to the errors in variables problem.The following greatly simplifies this problem. Let’s define the relationship:

Y X= + +α β μ

where: X = X* + ε

i.e., X* = True value and X measures X* with error

1 Roberts and Whited (2012) discuss in great detail the issue of endogeneity and how it relates to thecorporate governance literature.

A BAC U S


This implies that the X variable is not independent of the error and that omittedvariables, which may be variables we are unaware of or simply cannot be quantified,are correlated with the error term.

Ordinary least squares (OLS) minimizes the sum of the squared errors:

L E Y X= − +[ ]α β 2

This has the following first-order conditions known as the normal equations ofOLS:

∂∂

→ − −[ ] =L

E Y Xα

α β 0 (1)

∂∂

→ − −[ ] =L

E Y X Xβ

α β 0 (2)

We will show in this section that all of the econometric methods to addressendogeneity can be thought of in terms of these normal equations of OLS. Theywill be the basis for moment conditions that define the GMM estimators.The approach will nest the maximum likelihood approach with the advantage thatthe coefficients and standard errors will be the same if the maximum likelihoodassumptions are correct but that the standard errors of the GMM approach willbe valid whether or not the maximum likelihood assumptions are correct. Solvingthe normal equations of OLS—equations (1) and (2) above—yields the normalβ estimate:

→ =( )

( )β Cov Y X

Var X,

Since X is measured with error: X = X* + ε

β εε ε

=+( )

+( )=

( )( ) + ( )

Cov Y XVar X

Cov Y XVar X Var

, ,**

**

whereas the true **

*β =

( )( )

Cov Y XVar X

,

Hence, the calculated Beta is a biased and inconsistent estimator of the trueBeta. This comes about because the X variable is not independent of the errorterm.

Two-stage Least Squares (2SLS), Instrumental Variable (IV)The standard solution to the errors in variable problem is to use an IV z, which is (1)not correlated with the error term ε (i.e., exogenous) and (2) is relevant to X* (i.e.,non-zero correlation).



The IV estimator is:

β =( )( )

Cov YCov X

,,ZZ

We can think of this as a two-stage procedure:

Stage 1: Run the regression X a bz bCov X z

Var z= + ⇒ =

( )( )

,

Now define the instrument to be: X a bz= +

Stage 2: Run the regression Y X= +α β ˆ

This implies that:

⇒ =( )

( ) =+( )

+( )=

( )( )

βCov Y X

Var X

Cov Y a bzVar a bz

bCov Y zb Var z

, , ,ˆ

ˆ 2==

( )( )

Cov Y zbVar z

,

Now substitute: bCov X z

Var z=

( )( )

,from the first stage regression and we have:

⇒ =( )

( )( )

( )=

( )( )

β Cov Y zCov X z

Var zVar z

Cov Y zCov X z

,,

,,

We can see that 2SLS gives us the familiar measurement error IV estimator.Now we will show how 2SLS and IV estimators can be thought of in a general GMM

framework. Think of the normal equations of OLS (equations (1) and (2) above):

E Y XE Y X X

− −( ) =− −( ) = }α β

α β0

0

Solving for β we obtain:

β =( )

( )Cov Y X

Var X,

If we replace X with z in the 2nd equation:

E Y XE Y X z

− −( ) =− −( ) = }α β

α β00

This implies that β =( )( )

Cov Y zVar X z

,,

the instrumental variable estimator.We will show

how the GMM moment conditions based on the normal equations of OLS, that is,equations (1) and (2), will nest all of the endogeneity estimators.

The GMM moment conditions based on the normal equations of OLS gives usanother way to think of the IV estimator. Take the following example:

A BAC U S


The simultaneous equations are:

Y Y X1 0 1 2 2 1 1= + + +α α α μ (3)

Y Y X2 0 1 1 2 2 2= + + +β β β μ (4)

where the Ys are endogenous variables and the Xs are exogenous variables. Theproblem is similar to the measurement error issue, that is, where Y is correlated withμ.This can be seen from equation (4) where Y2 contains the error term μ2, which theninduces in equation (3) a problem similar to measurement error and with similarconsequences, that is, biased and inconsistent estimators.

Now consider estimating (3) with 2SLS:

(1) 1st stage: Regress Y2 on the exogenous variables:

Y X X2 0 1 1 2 2 2= + + +α α α ε .

Now define the instrument as:

Y X X2 0 1 1 2 2= + +α α α

(2) 2nd stage: In the regression for Y1 use the instrument Y2instead of Y2 as follows:

Y Y X1 0 1 2 2 1= + +α α αˆ

Now consider estimating (4) with 2SLS:

(1) 1st stage: Regress Y1 on the exogenous variables:

Y b b X b X1 0 1 1 2 2 1= + + + ε

Now define the instrument as:

Y b b X b X1 0 1 1 2 2= + +

(2) 2nd stage: In the regression for Y2 use the instrument Y1instead of Y1:

Y Y X2 0 1 1 2 2= + +β β βˆ

The above will give the standard 2SLS estimators. To see how this can be done inGMM consider the following moment conditions. The first three conditions are thenormal equations (equations (1) and (2) above) for the Y1 regression, with the firstbeing the condition that the error term is mean zero and the second and thirdimposing the condition that the error term is uncorrelated with the independentvariables. The fourth through sixth moment conditions are the normal equations forthe Y2 regression:2

2 The GMM moment conditions provide a system approach to testing both equations, thus the unifiedapproach encompasses three-stage least squares (3SLS) in addition to 2SLS.



E

Y Y XY Y X YY Y X X

Y

1 0 1 2 2 1

1 0 1 2 2 1 2

1 0 1 2 2 1 1

2

− − −− − −( )( )− − −( )

α α αα α αα α α

−− − −− − −( )( )− − −( )

⎡

⎣

⎢⎢

β β ββ β ββ β β

0 1 1 2 2

2 0 1 1 2 2 1

2 0 1 1 2 2 2

Y XY Y X YY Y X X

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥

= 0

You will notice the endogenous variables are in brackets. To get IV estimatorssimply replace the endogenous variables Y1 and Y2 with instruments. Here wechoose X1 and X2, the exogenous variables in the equation system. This yields thefollowing GMM moment conditions:

E

Y Y XY Y X XY Y X X

Y

1 0 1 2 2

1 0 1 2 2 1 2

1 0 1 2 2 1 1

2

− − −− − −( )( )− − −( )

−

α α αα α αα α αββ β ββ β ββ β β

0 1 1 2 2

2 0 1 1 2 2 1

2 0 1 1 2 2 2

− −− − −( )( )− − −( )

⎡

⎣

⎢⎢⎢ Y X

Y Y X XY Y X X

⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥

= 0

In this way we can see that the system is identified. Textbooks spend many pageson rank and order conditions but basically all you need is to be able to write out theIV system as above and have a unique equation for every parameter.

The following presents an example where there is no identification:

Y Y X1 0 1 2 2 1= + +α α αY Y X2 0 1 1 2 1= + +β β β

The normal equations are:

E

Y Y XY Y X YY Y X XY

1 0 1 2 2 1

1 0 1 2 2 1 2

1 0 1 2 2 1 1

2

− − −− − −( )( )− − −( )


−− − −( )− − −( )( )− − −( )

⎡

⎣


0 1 1 2 1

2 0 1 1 2 1 1

2 0 1 1 2 1 1

Y XY Y X YY Y X X

⎢⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥

= 0

When we go to replace the endogenous variables with instruments we see that wehave no more exogenous variables in the system. This leaves two equations that arenot separately identified.

E

Y Y XY Y XY Y X X=

− + −( )− + −( )( )− + −( )

1 0 1 2 2 1

1 0 1 2 2 1

1 0 1 2 2 1 1


?(( )

− − −( )− − −( )( )− − −( )

Y Y XY Y XY Y X X

2 0 1 1 2 1

2 0 1 1 2 1

2 0 1 1 2 1


?11

0

( )

⎡

⎣

⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥

⎫

⎬

⎪⎪⎪

⎭

⎪⎪⎪

=

System is notidentified as tthese twoequations do not have

an instrument.

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Differenced General Method of Moments (GMM)Graham (1996) was the first to apply dynamic models to issues in corporate finance.He looked at the difference in leverage as the dependent variable and the marginaltax rate as the independent variable. The logical extension is to look at the wholeequation in changes and add a lagged Y variable to take account of the dynamics ofthe relationship.

Y Y Y Xt t t t t1 0 1 1 1 2 2 3 1 1= + + + +−α α α α μ (5)

Taking the first difference of equation (5):

Y Y Y Xt t t t t1 1 0 1 1 2 2 2 1 3 1 1 1 1− − − − −= + + + +α α α α μ (6)

That is, equation (5) minus equation (6) gives:

Δ Δ Δ Δ ΔY Y Y Xt t t t t1 1 1 1 2 2 3 1 1= + + +−α α α μ

Note that the intercept term cancels and also that the error term will now becorrelated. The estimated moment conditions for this differenced GMM approachare:

EY Y Y XY Y Y X Y

t t t t

t t t t

Δ Δ Δ ΔΔ Δ Δ Δ

1 1 1 1 2 2 3 1

1 1 1 1 2 2 3 1

− − −− − −( )

−

−

α α αα α α 22 2

1 1 1 1 2 2 3 1 1 2

0t

t t t t tY Y Y X X−

− −− − −( )

⎡

⎣⎢⎢

⎤

⎦⎥⎥

=Δ Δ Δ Δα α α

The instruments are at t-2 as the change in the X variables is from t-1 to t.

System GMMThe above treats all of the explanatory variables as endogenous and is known asdifferenced GMM. It can be run in STATA as a Dynamic Panel. STATA also lets yourun system GMM, which is the equation in difference form, instrumented in laggedlevels and the equations in levels, instrumented with lagged differences. The levelequations would accordingly appear as follows:

EY Y Y XY Y Y X YY

t t t t

t t t t t

1 1 1 1 2 2 3 1

1 1 1 1 2 2 3 1 2 2

1

− − −− − −( ) )

−

− −

α α αα α α Δ

tt t t t tY Y X X− − −( )

⎡

⎣⎢⎢

⎤

⎦⎥⎥

=− −α α α1 1 1 2 2 3 1 1 2

0Δ

The above are known as Arellano and Bond estimators.3 An excellent example ofthe application in corporate governance is Wintoki et al. (2012). However, in theGMM approach you can run your own GMM program and use whatever instru-ments you like. It is not necessary to use the lagged values that STATA employs.

3 Stephen Bond has an excellent site (www.nuffield.ox.ac.uk/users/bond) on the use of differencedGMM and system GMM.



http://www.nuffield.ox.ac.uk/users/bond

Specification TestsThere are several important specification tests that are related to endogeneity. Herewe cover three of the most important. First, a test for whether endogeneity is indeeda concern for your research, that is, the Hausman Wu test for endogeneity. Thesecond and third specification tests deal with how good your instruments are. Thesecond test examines whether your instrument is correlated with your endogenousvariable and the third specification test examines whether your instrument isuncorrelated with the error.

Testing for Endogeneity: The Hausman-Wu TestThe Hausman-Wu test of endogeneity is as follows:

Test: H0 : βOLS is efficient and consistent andH1 : βIV is consistent.

This hypothesis is tested by the following statistics, which has a χ2 distribution withdegrees of freedom equal to the number of elements in β:

β β β β χ βOLS IVT

IV OLS OLS IV elementsV V− − −( ) [ ] ( )−1 2∼ #

The variance in the above test is a point of interest. One would think that thevariance of βOLS − βIV would be the normal expression for variance including cova-riance terms:

Var CovIV IVβ β β βOLS OLS OLS IVV V−( ) = − ( ) +2 ,

And it is. However, because OLS is a maximum likelihood estimator, it is anefficient estimator, meaning that it has minimum variance. We know fromMarkowitz’s mean variance frontier analysis that the covariance of the minimumvariance portfolio with any other portfolio is the variance of the minimum varianceportfolio, and the same rule applies for efficient estimators. So here the Cov(βOLS,βIV) term equals VOLS as the OLS estimator has the minimum variance property. Theresulting cancellations lead to Var(βOLS − βIV) = VIV − VOLS.

Testing that Instruments are Correlated with Endogenous Variables: F TestTo verify that the instruments you employ are valid you conduct an F test as follows.

Perform first-stage regression of the endogenous variable on the instruments:

Y b b X b X1 0 1 1 2 2 1= + + + ε

Check the R2 and F statistic of the regression. The rule of thumb is F>10 (Staigerand Stock, 1997). More formal tests are given in Stock et al. (2002) and Kleibergenand Paap (2006).

Testing that Instruments are Uncorrelated with the Error Term: Hansen’sOver-identifying Chi-squared TestThe over-identifying J test is a chi-squared test of whether the instruments areuncorrelated with the error. Many textbook solutions use lagged values of thevariables as the identifying instruments.

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E

Y Y XY Y X XY Y X X

Y

1 0 1 2 2

1 0 1 2 2 1 2

1 0 1 2 2 1 1

2

− − −− − −( )( )− − −( )

−

α α αα α αα α αββ β ββ β ββ β β

0 1 1 2 2

2 0 1 1 2 2 1

2 0 1 1 2 2 2

− −− − −( )( )− − −( )

⎡

⎣

⎢⎢⎢ Y X

Y Y X XY Y X X

⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥

= 0

In using IVs the researcher must first identify a suitable instrument. Using eco-nomically meaningful instruments is the best way to go but it is much more difficultthan using lagged values of the variables in the system. Such instruments, as well asbeing economically meaningful, should be correlated with the endogenous predictorvariable but uncorrelated with the error term. The researcher should provide justi-fication for the use of any particular instrument (Larcker and Rusticus, 2010). Ininvestigating potential and valid instruments, Roberts and Whited (2012) suggestasking the question: ‘Does the instrument affect the outcome only via its effect onthe endogenous regressor?’ (p. 27). Researchers in finance and accounting have useda variety of creative instruments. Some examples used in the finance, accounting, andeconomics literature are shown in Table 2.

There are many instrumental variables available—perhaps limited only by theresearcher’s imagination. Other creative instruments could be: local sports starssalaries as an IV for CEO salaries; and women on local councils as an IV for womenon corporate boards. However, there are limitations to using IVs, such as refocusingthe argument away from the presence of endogeneity to the appropriateness of theIV chosen (Brown et al., 2011).

Again referring to the 24 papers cited in Table 1, only two of the papers conductthe three specification tests and the most common method is 2SLS with only onenatural experiment as the research design.

Table 2

SOME EXAMPLES OF INSTRUMENTAL VARIABLES USED IN FINANCE ANDACCOUNTING RESEARCH

Study Focus Instrumental variable

Angrist (1990) Future earnings prospects Vietnam War randomlottery draw

Molina (2005) Leverage and default probability Marginal tax rate

Bennedsen, Nielsen, andPerez-Gonzalez and Wolfenzon(2006)

Family succession and firm value Gender of first child

Bennedsen, Kongsted, and Nielsen(2008)

Board size on the performance ofsmall to medium firms

Number of children of theCEO

Bamber, Jiang, and Wang (2010) Disclosure policy Top mangers prior militaryservice

Bouwman (2013) Executive compensation

King and Williams (2013) Executive compensation Local sports star salaries



ENDOGENEITY IN FINANCE AND ACCOUNTING

Much of the empirical corporate governance literature lacks formal theory(Hermalin and Weisbach, 2003) and there is little consensus in this literature onissues relating to performance and governance (Schultz et al., 2010). Yet corporategovernance studies, of which there are many, showing a relationship between cor-porate governance and firm value, have impacted policy, for example, policy relatingto board composition and executive compensation included in the Sarbanes-OxleyAct (SOX).4 Are such regulations justified in terms of the costs imposed on firmswho have to adjust governance structures to be in compliance? Krishnan et al. (2008)estimate that $1.4 trillion has been spent on compliance with SOX.This translates toan average firm compliance cost of over $3 million (Financial Executives Institute,2007) and reflects the high cost of restructuring corporate governance mechanisms,which involves the formation of committees and the hiring of additional directors.Such costs may well be justified if we had compelling causal evidence to supportlegislated governance restructuring.

Many studies show corporate governance structure to be a largely endogenouscharacteristic of the firm (Coles et al., 2012; Demsetz, 1983; Demsetz and Lehn, 1985;Hoang et al., 2014; Wintoki et al., 2012). So for the vast number of corporate gover-nance studies showing a relation between governance and performance, even ifrigorously designed, it is safe to say they are fraught with issues of endogeneity, thatis, the optimal level of corporate governance is endogenously determined at the firmlevel (Demsetz, 1983). So if firms are at an internal equilibrium, then a forced changein governance structure may be detrimental to firm performance as sub-optimalgovernance structures may reduce performance.

Schultz et al. (2010) compare a variety of econometric techniques to examine thegovernance/performance relationship. They point out that there is a lack of consen-sus in the literature regarding the relationship. When they use OLS and fixed effectspanel methodologies they find that there is a significant relationship between cor-porate governance variables and performance. OLS will give biased and inconsistentresults in the presence of endogeneity but will give efficient estimation if theendogeneity is not present and the assumptions underlying OLS hold.To resolve thistension, Schultz et al. (2010) conduct a test for endogeneity using the Hausman-Wutest:

β β β β χ βOLS IVT

IV OLS OLS IV elementsV V− − −( ) [ ] ( )−1 2∼ #

The Hausman-Wu test for endogeneity will be significant when the OLS estima-tors are significantly different from the instrumental variables estimators. They findthat the test is significant, indicating a significant difference in the OLS and IVcoefficients and then proceed to estimate the governance/performance relationship

4 The Sarbanes-Oxley Act of 2002 set new standards for corporate governance including number ofindependent directors.

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using differenced GMM and system GMM approaches. Under both of theseapproaches, they no longer find a significant relationship between governance andperformance.

Arguably, it is much better to model the ownership–performance relationship atthe firm level, for example, model the pay–performance relationship at the firm leveland observe the pay–performance sensitivity that maximizes performance. Coleset al. (2012) model the relationship at the firm level by looking at the productivityparameters for managerial input and investment that would give rise to the observedlevel of ownership and investment. Their results seem intuitive. They find that theproductivity of managerial input is high in personal and business services andequipment industries such as education, software, networking, and computers. Theyalso find that the productivity of managerial input is low in metal mining andutilities. Also, they model Tobin Q values and find that they are highly correlatedwith observed Q.

Graphic Example of the Detrimental Effects of Mandating Insider QwnershipIf firms are at an internal equilibrium, then a forced change in governance structurewill not improve firm performance. In fact, not only is restructuring costly to imple-ment but it may also be directly detrimental to firm performance.This is because theoptimal level of ownership is endogenously determined at the firm level (Demsetz,1983). Figure 1 graphically illustrates the cost to firms when forced to adopt asub-optimal ownership structure, and a similar illustration appears in Larcker andRusticus (2007). In Panel A, each firm internally optimizes their insider ownership–performance relationship. For Firm A that is 3%, for Firm B it is 7%, and for FirmC it is 5%.

Assume now a senate committee commissions a study to examine the corporategovernance and performance relationship. Based on this study, all firms arerequired (forced by regulation) to adopt the ‘optimal level’ of insider ownership.In Panel B, 5% ownership is considered the optimal ownership level. Firm A hasbeen forced to increase its board size beyond its optimal 3%. Firm B is forced toreduce its size and is also no longer at its optimal level. Only Firm C is at itsoptimal structure post-regulation. We can see from Panel C the loss in perfor-mance to A and B if they have 5% ownership. In contrast an instrumental vari-ables estimation approach tends to find no relationship. This is illustrated in PanelD of Figure 1. So if the optimal level of ownership is endogenously determined atthe firm level, that is, the value maximizing governance choices of one firm may bevery different to the value maximizing governance choices of another firm(Demsetz, 1983); then if firms are at an internal equilibrium a forced change ingovernance structure will not improve firm performance. In fact, it may be detri-mental to firm performance. Policy prescriptions based on conflicting research willinevitably prove suboptimal in many cases. Developing better theory and morecompelling evidence to fully describe the relationship between insider ownershipand performance is accordingly part of the solution and this is where naturalexperiments can be valuable.



NATURAL EXPERIMENTS: STATE-OF-THE-ARTSOLUTIONS TO ENDOGENEITY

A natural experiment can be one of two things: (1) a randomized controlled trial(RCT) set up by the researcher in a natural setting5 to induce controlled variance; or(2) a naturally occurring state (event) resulting from a social or political situationand thus not intentionally set up by the researcher. This second type of experiment

5 This excludes experiments in a laboratory or other artificial environments.

Figure 1

OPTIMAL INSIDER OWNERSHIP/PERFORMANCE RELATION

Panel A: Each firm internally optimizes the insider ownership/ performance relationship

3% 5% 7%

Panel B Level of insider ownership mandated at 5%

3% 5% 7%

Panel C: Loss of performance due to mandated ownership level

3% 5% 7%

Arrows show loss of performance from mandated ownership levels

Panel D: IV Estimation finds no relation between insider ownership and performance

3% 5% 7%

A

Insider Ownership

C

B

APerfo

rman

ce

Insider Ownership

C

B

A

C

Insider Ownership

B A

Insider Ownership

C

B

Perfo

rman

ce

Perfo

rman

ce

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is often referred to as a quasi-experiment (Meyer, 1995). Proponents of experimen-tal research argue that such research designs avoid a criticism often levelled ateconometric studies, that is, they are based on questionable economic theories.

A randomized trial in a natural setting is set up and controlled by the researcher.Economists regularly use randomized trials to study a multitude of issues. Thesestudies are designed to measure outcomes based on observations of a treatmentgroup and a control (or comparison) group that have been randomly assigned. Ifimplemented correctly the researcher creates two (or more) groups that are onaverage probabilistically similar so that any observed differences are due to thetreatment and not to other differences in the groups (Shadish et al., 2002). Angristand Pischke (2010) detail some influential randomized experiments in economics,for example, the ‘Moving to Opportunity’ program,6 or the Progresa7 program inMexico.

The advantage of randomized trials is that when the research design is robust theycan provide more convincing evidence. For example, randomized clinical trialsprovide Grade I evidence in the field of medicine (Leigh, 2010). Leigh (2010) arguesthat policy makers in Australia should make more use of randomized trials to bettertarget policies and improve outcomes. He gives several examples that would lendthemselves to this type of study, for example, is job training or wage subsidies bestfor long-term youth unemployed? And, would more generous post-release pay-ments reduce criminal relapse?

Not everyone agrees that randomized controlled experiments necessarily provideany better evidence than econometric studies. Deaton (2010), for example, in thecontext of economic development and foreign aid, goes into detail about the validityof results from RCT. One inherent problem is that their results provide the popu-lation mean of the treatment effects. Policies then put in place based on populationmeans can be misconceived if the averages are skewed by a small number of verypositive outcomes when in fact most of the population is negatively affected by thepolicy. Deaton further addresses problems of external validity with RCT, that is,making generalizations from largely local results and it is important RCTs focus, notjust on program evaluation, but also on developing theory. Further, not all policyquestions lend themselves to randomized experiments as ethical issues are para-mount. Randomized trials actually come with a multitude of practical difficulties,apart from ethical issues, in dealing with human subjects. Problems in randomizing

6 This program randomly selected low-income families in Baltimore, Boston, Chicago, Los Angeles, andNew York City to be offered housing vouchers specifically limited to low-poverty areas (Kling et al.,2007 as cited in Angrist and Pischke, 2010). The idea of the program was to determine ifneighbourhood effects are a primary determinant of low earnings by the residents of poorneighbourhoods (p. 4).

7 The Progresa program in Mexico offered cash transfers to randomly selected mothers, contingent onparticipation in prenatal care, nutritional monitoring of children, and the children’s regular schoolattendance. As a direct consequence of this program 30 countries worldwide have conditional cashtransfer programs. Further, the results of this program have influenced the move to random assignmentpolicy evaluations in development economics (p. 3).



group assignments, as well as gaining access to subjects, can be virtually impossibleto overcome. Such trials are also expensive and time-consuming to implement.

In questions of finance, randomized experiments are difficult to implement. Forexample, it is neither feasible nor ethical to conduct randomized trials of bankfailures, corporate governance changes, or tax changes. Thus there are relativelyfew examples of randomized trials in a natural setting in the finance literature.One notable exception is Kaplan et al. (2013), who examine the impact of shortselling in stock markets. Specifically, they investigate whether short sellingmakes markets more efficient by improving price discovery, or if short selling dis-torts markets and adversely affects prices. The authors, with the cooperation of alarge money manager, randomly made available or withheld stocks from thelending market. While such experiments provide novel results they require thecooperation of practitioners and investors and such cooperation may be difficult toattain.

Arguably, the next tier of evidence involves natural experiments in naturallyoccurring states or events (Leigh, 2010). This type of experiment provides moreopportunities for finance and accounting researchers. A naturally occurring stateoften comes about from a social or political situation (Dunning, 2007) such as agovernment policy change. Natural experiments are not ‘true’ experiments and aresometimes referred to as ‘quasi’ experiments (Meyer, 1995). This is because theso-called naturally occurring state is not intentionally set up by the researcher and sothe treatment group is not randomly assigned. Such experiments are more likeobservational studies where the researcher cannot manipulate the environment,although the researcher must choose the comparison or control group. In these typesof research design, control groups and treatment groups may differ in systematicways other than in regard to the treatment. The researcher therefore has to beconcerned about ruling out such effects.

Some examples of naturally occurring events of interest to finance and accountingresearchers may include legislated corporate governance changes (e.g., SOX), or taxchanges across jurisdictions that can justifiably be seen as exogenous sources ofvariation in the explanatory variables of interest. Meyer (1995) gives the example ofthe Vietnam era draft mechanism, which depended on date of birth as an exogenousevent to study the effects of military service on earnings. Research utilizing naturalexperiments is growing in the field of economics (Dunning, 2007), although it is notvery common in finance and accounting.

Finance and accounting researchers may see an obvious roadblock to designingresearch around a natural event, that is, how often will issues yield themselves to thekind of actual randomization that Heider and Ljungqvist (2014), for example,exploit? Researchers though, may not be aware of the number of situations ornaturally occurring events that could be used in natural experimental research andthus many more natural experiments may be available than researchers realize.Generally studies making use of natural experiments are motivated by existingevidence and thus address issues fundamental to a discipline. Table 3 provides asample of finance and accounting research that utilizes natural experiments. Alladdress issues fundamental in the disciplines. Using such events as exogenous factors

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in a model helps researchers to provide a constructive link between the real worldand econometric methodology (Angrist and Pischke, 2010).

Quasi-natural experiments have some advantages over randomized trials. First,they minimize ethical dilemmas involved in using human subjects. They also mini-mize problems that can be attributed to the researcher’s influence when setting upa randomized trial stemming from the researcher’s interaction with participants, forexample, paternalism, inequity, and deception—even though these things are notintentional, they are difficult to completely avoid. Additionally, natural experimentsremove the problem of access to practitioners, which can be a particular problem infinancial markets, and generally they are useful when random assignment is neitherpossible nor ethical.

Table 3

RECENT RESEARCH IN FINANCE AND ACCOUNTING UTILIZINGNATURAL EXPERIMENTS

Study Focus Source of naturalexperiment

Haselmann, Pistor, andVig (2010)

Creditor rights and the size ofcreditor markets

Reforms of creditor rights across 12transition economies

Kisgen and Strahan (2010) Credit ratings and firms’ cost ofcapital

Dominion Bond Rating Servicebecoming a recognized ratingagency in 2003

Iyer and Peydro (2011) Financial contagion due tointerbank linkages

Large bank failure outside offinancial crisis

Nguyen and Nielsen (2010) Corporate governance and firmvalue

Sudden death of CEO

Puri, Rocholl, and Steffen(2011)

Credit crises and supply of creditto retail customers

German retail banks pre- andpost-GFC

Heider and Ljungqvist(2014)

Tax changes on capital structure 25 US states: 67 corporate taxdecreases and 35 corporate taxincreases 1990–2011

Kaplan, Moskowitz, andSensoy (2013)

Effects of stock lending onsecurity prices

Randomized stock lendingexperiment

Kelly and Ljungqvist(2012)

Information asymmetry and assetprices

Brokerage closures due to: 4429coverage terminations due to 43US brokerage firms closingresearch departments between Q1,2000, and Q1, 2008, and 356coverage terminations due toSeptember 11 terrorist attacks

Gropp, Gruendl, andGuettler (2014)

Public guarantees on bankrisk-taking

EU court ruling to removegovernment guarantee for savingsbanks

Gormley, Matsa, andMilbourn (2013)

CEO compensation andcorporate left-tail risk

Workplace exposures to carcinogensand newly classified carcinogens

Note: This table is not exhaustive and is intended to provide the reader with examples of the types ofevents used as natural experiments in recent finance and accounting research.



The inferences drawn from natural experiments are often criticized as beinglimited to a particular time and place. However, this is not necessarily the case.Angrist and Pischke (2010) cite several examples where natural experiments havebeen used to address issues, including those that affect the entire world or the marchof history. For example, Nunn (2008) uses a wide range of historical evidence,including sailing distances on common trade routes, to estimate the long-termgrowth effects of the African slave trade. Deschênes and Greenstone (2007) look atrandom year-to-year fluctuations in temperature to estimate effects of climatechange on energy use and mortality. In a study of the effects of foreign aid ongrowth, Rajan and Subramanian (2008) construct instruments for foreign aidfrom the historical origins of donor–recipient relations. Natural experiments havealso provided the basis for significant policy choices for centuries. Dunning (2007)provides the example of cholera outbreaks in 19th-century London. This, and theexamples above, speaks eloquently for the wide applicability of a natural experi-ment, design-based approach.

The advantage of using natural experiments, when well considered, is that they arean exogenous event. At least the researcher should convince her audience this is so.Studies using such events make a strong case for a causal interpretation of theresults. Meyer (1995) argues that the main contribution of such research designs is inproviding an understanding of the source of the causal relationship. The disadvan-tage is the time spent collecting data particularly considering there are often a lot ofevents. Another problem is validating the ‘as if’ random assignment of the compari-son and control groups (Dunning, 2007).

DESIGNING RESEARCH AROUND A NATURAL EXPERIMENT

To lay the foundation or road map for researchers wanting to utilize a naturalexperiment, we now detail two concrete applications. Both studies, which we offer asexemplars, make use of a natural experiment providing an exogenous source ofvariation in the main explanatory variable. The first study is that of Heider andLjungqvist (2014). These authors exploit jurisdictional variation in tax changesacross the United States to estimate the tax sensitivity of leverage from exogenousstate tax changes. As the authors note, in an ideal world the researcher could set upa truly randomized experiment. In this case that would involve ‘randomly assigningdifferent tax rates to firms and then comparing their debt policies to see if higher taxrates lead to higher leverage’. Random assignment would ensure that ‘observeddifferences in leverage could not be caused by unobserved firm-level heterogeneity’(Heider and Ljungqvist 2014, p. 2). However, we do not live in an ideal world andsuch truly random experiments with a treatment and control group are not possible.The next best method is to seek tax changes that are plausibly exogenous. Thesecond study we offer as an exemplar of utilizing a naturally occurring event is thatof Nguyen and Nielsen (2010). Nguyen and Nielsen (2010) use the sudden death ofindependent directors as an exogenous event impacting firm value. Their focus is onthe value of independent directors to shareholder value.

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To date, the research on these two fundamental issues is plagued by problems ofendogeneity, including a lack of solid theory. For example, do high-profit firmsborrow more because debt offers valuable tax shields or because their marginal costof debt is lower? The perplexing issue of endogeneity in the corporate governanceliterature has been discussed above.

Road Map Illustrated with Two Recent StudiesThe following steps provide a guide to an ideal approach to this type of researchdesign.

1. Lay a solid foundation for the research design/methodology As is desirable forany research design, first outline the current thinking or theory related to theresearch question and in this case establish the existence and possible sources ofendogeneity. The goal is to substantiate how a natural experiment could over-come such problems. In Heider and Ljungqvist (2014), we know from previousliterature that taxes are important in capital structure, but to what degree? Thesources of endogeneity noted by the authors include high-profit firms are inhigher tax brackets, and such firms may borrow more to take advantage of taxshields, or high-profit firms may borrow more because their default risk is lower.‘A simple comparison cannot tell if high-profit firms borrow more because debtoffers valuable tax shields or because their marginal cost of debt is lower. Unob-served differences across firms would impart a positive bias in the estimated taxbenefit’ (p. 3).

In the second study of Nguyen and Nielsen (2010), intuitively researchers knowthat board composition is determined endogenously, for example, we can argue thatpoor performance is a result of previous board decisions as well as a factor thatinfluences subsequent appointments of more independent board members. Theresearch thus far provides scant evidence of any cross-sectional relationshipbetween firm performance and board composition or the ratio of insiders to outsid-ers (Hoang et al., 2014). Some studies, as reviewed by Hermalin and Weisbach(2003), use lagged performance measures to correct for endogeneity and still find noevidence of a causal relationship between board independence and firm perfor-mance. Given recent legislation governing board composition the link between thenumber of independent directors and firm value is a significant one. The authorsaccordingly lay the foundation for the research design.

2. Identify the natural event(s) This step determines the treatment group, that is,the group affected by the event. Here it is important to use as many data pointsas are available. Having multiple treatment groups, which may be affected by theevent in different time periods, different locales, or with different intensities,strengthens the external validity of the results. Heider and Ljungqvist (2014)exploit the natural event of staggered changes in US state corporate income taxrates. State tax changes are used in preference to federal tax changes becausestate changes occur more frequently and at different times. Their data include 38corporate tax increases in 25 states affecting 1,824 firms over 1990–2011, and 67



corporate tax decreases in 29 states affecting 7,021 firms. Nguyen and Nielsen(2010) use the sudden death of independent directors identified from companieslisted on Amex, NASDAQ, and NYSE from 1994–2007. They identify 229 (out of772 director deaths) cases that satisfy the strict definition of sudden death of adirector. Of this 229, 108 are identified as independent directors.

3. Verify the natural event is plausibly exogenous The researcher is obliged toprovide the reader with clearly identified and understood exogenous events andthereby rule out other explanations. This part of the research is critical to theinternal validity of the results. As Heider and Ljungqvist (2014) note, state taxchanges occur for a reason and this could make them endogenous (simultane-ously determined) to capital structure. For instance, tax changes could result fromeconomic downturns and firms could borrow more in economic downturns. Inthis study the authors control for various confounds such as unobserved variationin local business conditions or investment opportunities, union power, and states’political leanings.

In Nguyen and Nielsen (2010) the definition of independence is critical. Theauthors follow the previous literature and use length of tenure and length of tenurerelative to tenure of CEO as two measures of independence. Further, deaths of theindependent directors are required to be both sudden and unanticipated by themarket to justify these events as random and exogenous to current firm or marketconditions. The authors are conservative in trying to exclude any deaths that couldhave been foreseen by the market, for example, excluding the death of elderlydirectors, or those with known prolonged illnesses where it is likely the death isanticipated. Also excluded are observations where other confounding news couldaffect firm value at the time of sudden death. Sudden death also alleviates theargument that appointments of independent directors could be driven by the needfor change.

4. Comparison of treatment group pre and post event As a method of preliminaryanalysis, the research design may include a simple comparison of the treatmentgroup pre and post the event. By itself this is not likely to lead to strong inferencesbecause it is difficult to determine that the treatment group would have been thesame over time in the absence of the event. If this is the extent of the researchdesign then the researcher would need to provide strong evidence that thetreatment group would have been the same over time in the absence of the event(Meyer, 1995). This is essentially the approach taken by Nguyen and Nielsen(2010). They use an event study to look at CAR pre and post an independentdirector dying suddenly.

5. Determine the control or comparison group The control or comparison groupshould not be affected by the exogenous change in the explanatory variable. Thestudy is strengthened by identifying a comparison group that is similar to thetreatment group in relevant dimensions; however, only randomly different acrossthe variables under study. Heider and Ljungqvist (2014) use firms in neighbouringstates not affected by tax changes, for example, firms in North Carolina affectedby a tax rise are compared to firms in the same industry in the neighbouring state

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of South Carolina. Nguyen and Nielsen (2010) identify stock price reactionsagainst director type, that is, inside and gray as well as the independent directors.

6. Comparison of treatment and control group These groups may be comparedusing a number of approaches, for example, a difference-in-differences techniqueor an event study. Heider and Ljungqvist (2014) corroborate the exogenousnature of the tax changes by looking at what happens to firms in the same industryin neighbouring states where there are no tax changes. Nguyen and Nielsen(2010) use an event study to examine stock returns in the −5 day to +5 day eventwindow coincident with the sudden death of an independent director. The resultsshow pre- and post-event returns on the overall sample and separately for inde-pendent, gray, and inside directors.

7. Control for standard variables found in the literature Including control variablesis a standard way to allow for observable differences across the treatment andcontrol groups. In this case Heider and Ljungqvist (2014) control for standardvariables in the debt literature including: profitability (return on assets); firm size(total assets); tangibility (the ratio of fixed to total assets); and investment oppor-tunities (market-to-book). In our second study Nguyen and Nielsen (2010) use amultivariate approach to control for director and firm characteristics. Suchcontrol variables include: director age; firm size; firm age; market-to-book; andboard size. Further, the study applies a fixed effects approach to isolate andcontrol for independent director ability and skill.

8. Determine if the magnitude of the effects is economically meaningful Thestrength of the results and thus the conclusions regarding economic magnitudeare reliant on having ruled out confounding influences. Heider and Ljungqvist(2014) include industry-year effects to eliminate time-varying industry shocks.Robustness tests also show that the results hold within-firm (ruling out that theyare driven by time-invariant firm heterogeneity). Further tests also show that theresults are robust to the inclusion of state fixed effects and changes in localeconomic conditions, changes in local labour market conditions, and changes in astate’s political leanings. Nguyen and Nielsen (2010) investigate alternative speci-fications such as ruling out firms that may have been affected by confoundingnews at the time of the director’s death and ruling out firms where the age of thedirector may increase the probability of mortality.

9. Reversal of the initial event Findings are strengthened by investigating theeffects of a reversal in the treatment (Meyer, 1995). For example, Heider andLjungqvist (2014) look at reversals of tax increases and find leverage increasespermanently. Not all events will lend themselves to reversal. The (2010) Nguyenand Nielsen study does not investigate the situation where independent boardmembers are later replaced with inside directors.

The true test of research designs using natural experiments as sources of exog-enous variation partly rests with the significance of the results. Heider andLjungqvist (2014) find a positive relation between increases in taxes and leverage,that is, firms increase leverage on average by 114 basis points in response to a rise intheir home state taxes. This effect is asymmetric, that is, firms do not decrease their



leverage in response to tax cuts. This paper provides compelling evidence that taxesare a first-order determinant of capital structure choices. Importantly, the papercontributes to capital structure theory by providing strong evidence that the taxsensitivity of leverage is asymmetric, which is contrary to current belief.

Nguyen and Nielsen (2010) find that stock prices fall by 0.85%, which translatesinto an average of a $35 million decrease in firm value as a result of the sudden deathof an independent director. The study more specifically shows that the value of anindependent director is susceptible to the influence of powerful CEOs and also tothe number of independent directors on the board. Further, this study shows thatthere is value added if independent board members perform a particular boardfunction such as chairman or member of the audit committee. Previous studies oncorporate governance and firm value fail to reach convincing and meaningful con-clusions because corporate governance structure is endogenously determined. Thisstudy adds to a deeper understanding of the effects of corporate governance on firmvalue.

Limitations of Natural (Quasi) ExperimentsIn any research design, researchers need to be aware of issues that undermine thecausal inferences. A natural experiment that is plausibly exogenous may diminishproblems of omitted variable bias and simultaneity. However, in utilizing naturalexperiments researchers face other threats to internal and external validity.

External validity Evidence provided by natural experiments is most convincingwith more complex research designs, for example, using multiple exogenous changesin corporate governance. Using one event leaves the results open to criticisms thatthey are local and derived from a particular time and place. The response to this isto look for more evidence. It is possible, for example, to exploit national or jurisdic-tional borders since a policy shift on one side of a border may not affect groups onthe other side of the border. Jurisdictional boundaries provide the most convenientbasis for natural experiments (Dunning, 2007). Using multiple treatment and com-parison groups allows further checks on hypotheses and strengthens the validity ofthe inferences (Meyer, 1995).

Internal validity The researcher must provide a convincing argument that thesource of the natural experiment is truly exogenous, for example, that policy changesare not in response to changes in the variables under study.Also, the researcher mustperform exhaustive robustness tests to convince the reader of the validity of theresults.

CONCLUSION

This paper provided a discussion of endogeneity in finance and accounting empiricalresearch: the problem, its scope, and current textbook solutions. We note thatendogeneity is increasingly seen as a concern and it is insufficient for researchers tolabel some variables endogenous and others exogenous without providing strong

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‘institutional or empirical support for these identifying assumptions’ (Angrist andPischke, 2010, p. 17). We provide a road map for research design using a-state-of-the-art solution—a natural experiment. Researchers can utilize such experiments tomitigate the problem of endogeneity and in doing so build better theory to justifytheir model. This technique involves using naturally occurring exogenous events.

However, there are two caveats. First, not all regulation or policy changes aresources of exogenous variation. Calling a policy change a natural experiment doesnot make it an exogenous source of variation (Meyer, 1995). Second, researchers, inlooking for and using natural experimental events, should retain a clear focus onresearch design to improve empirical work and avoid seeking good answers overgood questions. There is a chance that researchers will look for good experimentsregardless of the importance of the questions they ask. On a positive note, well-designed studies around natural experiments will progress theory and thus thesetypes of studies will get the most weight in the compiling of evidence, while otherevidence, which we know is subject to issues of endogeneity, is likely to be treated asmore provisional (Angrist and Pischke, 2010).

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