Instrumental variable estimation based on grouped data

Bekker, Paul; Ploeg, Jan van der

doi:10.1111/j.1467-9574.2005.00296.x

Cited by 44 publications

(54 citation statements)

References 45 publications

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“…The inconsistency of LIML was pointed out by Bekker and van der Ploeg (2005) and Chao and Swanson (2004) in special cases. We give a characterization of the inconsistency here, showing the precise restriction on the heteroskedasticity that would be needed for LIML to be consistent.…”

Section: Introductionmentioning

confidence: 99%

Instrumental variable estimation with heteroskedasticity and many instruments

Hausman¹,

Newey²,

Woutersen³

et al. 2007

Working Paper Series

104

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. This paper gives a relatively simple, well behaved solution to the problem of many instruments in heteroskedastic data. Such settings are common in microeconometric applications where many instruments are used to improve efficiency and allowance for heteroskedasticity is generally important. The solution is a Fuller (1977) like estimator and standard errors that are robust to heteroskedasticity and many instruments. We show that the estimator has finite moments and high asymptotic efficiency in a range of cases. The standard errors are easy to compute, being like White's (1982), with additional terms that account for many instruments. They are consistent under standard, many instrument, and many weak instrument asymptotics. We find that the estimator is asymptotically as efficient as the limited-information maximum likelihood (LIML) estimator under many weak instruments. In Monte Carlo experiments, we find that the estimator performs as well as LIML or Fuller (1977) under homoskedasticity, and has much lower bias and dispersion under heteroskedasticity, in nearly all cases considered. Terms of use: Documents in

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Section: Introductionmentioning

confidence: 99%

Instrumental variable estimation with heteroskedasticity and many instruments

Hausman¹,

Newey²,

Woutersen³

et al. 2007

Working Paper Series

104

View full text Add to dashboard Cite

show abstract

“…Bekker and van der Ploeg (2005), Ackerberg and Devereux (2009), Chao and Swanson (2006), and Hausman et al (2007)). The main objective of this paper is to develop asymptotic theory for the JIV estimators in a setting that includes the many instrument sequence of Kunitomo (1980), Morimune (1983), and Bekker (1994) and the many weak instrument sequence of Chao and Swanson (2005).…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Distribution of Jive in a Heteroskedastic Iv Regression With Many Instruments

Chao¹,

Swanson²,

Hausman³

et al. 2011

Econom. Theory

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in August, 2007Revised October, 2010 JEL classification: C13, C31.Keywords: heteroskedasticity, instrumental variables, jackknife estimation, many instruments, weak instruments. → 0 as n → ∞, where K n and r n denote, respectively, the number of instruments and the concentration parameter. This is in contrast to the asymptotic behavior of such classical IV estimators as LIM L, B2SLS, and 2SLS, all of which are inconsistent in the presence of heteroskedasticity, unless K n rn → 0. We also show that the rate of convergence and the form of the asymptotic covariance matrix of the JIV estimators will in general depend on the strength of the instruments as measured by the relative orders of magnitude of r n and K n .

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“…In the well known case of grouped data (Bekker and van der Ploeg, 2005), if the group sizes are not equal, the diagonal of the instrument projection matrix is generally asymptotically heterogeneous. Let us assume that all observations are split into l groups and proceed by brute force.…”

Section: Indicator Instruments With Unequal Group Sizesmentioning

confidence: 99%

“…A well-known example in the literature is the case of grouped data (Bekker and van der Ploeg, 2005) where the instruments are indicator variables. The instrument design in this example is deterministic and hence does not fit in our IID framework.…”

Section: Indicator Instruments With Equal Group Sizesmentioning

confidence: 99%

“…It is important to know the circumstances under which an asymptotically balanced design may or may not occur, on the one hand, and how much distortion a failure of this property may create, on the other. 2 One well-known example encountered in previous literature is the case of grouped data (Bekker and van der Ploeg, 2005) where the instruments are indicator variables. If group sizes are equal, it is known that the diagonal of the instrument projection matrix is asymptotically homogeneous (e.g., van Hasselt, 2010), and is asymptotically heterogeneous otherwise.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Asymptotics of Diagonal Elements of Projection Matrices Under Many Instruments/Regressors

Anatolyev

Yaskov

2016

Econom. Theory

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This article sheds light on the asymptotic behavior of diagonal elements of projection matrices associated with instruments or regressors under many instrument/regressor asymptotics. When the diagonal elements do not exhibit variation asymptotically, certain results in the many instrument/regressor literature lead to elegant solutions and conclusions. We establish conditions when this happens, provide relevant examples, and analyze instrument designs, for which this property does or does not hold.

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Instrumental variable estimation based on grouped data

Cited by 44 publications

References 45 publications

Instrumental variable estimation with heteroskedasticity and many instruments

Instrumental variable estimation with heteroskedasticity and many instruments

Asymptotic Distribution of Jive in a Heteroskedastic Iv Regression With Many Instruments

Asymptotics of Diagonal Elements of Projection Matrices Under Many Instruments/Regressors

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