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The Instrument Variable Approach to Correct for Endogeneity in Finance

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Handbook of Quantitative Finance and Risk Management

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Abstract

The endogeneity problem has received a mixed treatment in corporate finance research. Although many studies implicitly acknowledge its existence, the literature does not consistently account for endogeneity using formal econometric methods. This chapter reviews the instrumental variables approach to endogeneity from the point of view of a finance researcher who is implementing instrumental variable methods in empirical studies. This review is organized into two parts. Part I discusses the general procedure of the instrumental variables approach, the related diagnostic statistics for assessing the validity of instruments, which are important but not frequently used in finance applications, and some recent advances in econometrics research on weak instruments. Part II surveys corporate finance applications of instrumental variables. We found that the instrumental variables used in finance studies are often chosen arbitrarily and very few diagnostic statistics are performed to assess the adequacy of IV estimation. The resulting IV estimates are thus questionable.

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Notes

  1. 1.

    Traditionally a variable is defined as endogenous if it is determined within the context of a model. However, in applied econometrics the “endogenous” variable is used more broadly to describe the situation where an explanatory variable is correlated with the disturbance and the resulting estimator is biased (Wooldridge 2002).

  2. 2.

    The finance literature using self-selection models has little interest in estimating the endogenous decision itself (the parameter β in Equation (1.1)), but is more interested in using self-selection models to reveal and test for the private information that influences the decision. In contrast, this chapter focuses on how to implement IV approach to estimate the parameter consistently. The readers interested in finance application of self-selection models are referred to Li and Prabhala (2005).

  3. 3.

    We follow Larcker and Rusticus (2007) to compare the squared terms to avoid the problem of sign flips.

  4. 4.

    If the instruments are only weakly related to the endogenous explanatory variables, the power of the test can be low.

  5. 5.

    A potential problem is that the test is not consistent against some failures of the orthogonality condition due to the loss of degrees of freedom from K to K–L.

  6. 6.

    If the assumption of homoskedasticity cannot be made, this standard error is invalid because the asymptotic variance of the difference is no longer the difference in asymptotic variances.

  7. 7.

    Since the robust (Hubert-White) standard errors are asymptotically valid to the presence of heteroskedasticity of unknown form including homoskedasticity, these standard errors are often reported in empirical research especially when the sample size is large. Several statistical packages such as Stata now report these standard errors with a simple command, so it is easy to obtain the heteroskedasticity-robust standard errors.

  8. 8.

    Stock, Wright, and Yogo (2002) defines weak-instrument asymptotics as the alternative asymptotics methods that can be used to analyze IV statistics in the presence of weak instruments. Weak-instrument asymptotics involves a sequence of models chosen to keep concentration parameters constant as sample size N → ∞ and the number of instruments held fixed.

  9. 9.

    Another reason we found a smaller number of finance papers using IV may be that we limit our key words to those appearing in the abstract. Thus, our data may be more representative of the general situation of the finance research using IV as their main tests.

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Authors and Affiliations

  1. Manhattan College, Riverdale, NY, USA

    Chia-Jane Wang

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  1. Chia-Jane Wang
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Correspondence to Chia-Jane Wang .

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Editors and Affiliations

  1. Department of Finance and Economics, Rutgers University, 94 Rockafeller Road, Janice H. Levin Bldg., New Brunswick, NJ, 08854-8054, USA

    Cheng-Few Lee

  2. State Street Corp., Boston, MA, 94132, USA

    Alice C. Lee

  3. Center for PBBEF Research, North Brunswick, NJ, USA

    John Lee

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Wang, CJ. (2010). The Instrument Variable Approach to Correct for Endogeneity in Finance. In: Lee, CF., Lee, A.C., Lee, J. (eds) Handbook of Quantitative Finance and Risk Management. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-77117-5_90

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