Dominance of doublek-class estimators in simultaneous equations

Srivastava, V. K.; Agnihotri, B. S.; Dwivedi, T. D.

doi:10.1007/bf02480343

“…Nagar [24] and Brown et al [10] were unable to find fixed values of k t and k 2 for which the double Ic-class estimator dominates other estimators. Srivastava et al [30] investigated the same problem assuming that the error covariance matrix 12 of the reduced form is known. Any uniform domination of one estimator over others does not seem obtainable in the small-disturbance asymptotics because h t (i = 1 , .…”

Section: Theorem 62 As T -» Go Under Assumption B 9 the Asymptotic mentioning

confidence: 99%

Comparing Single-Equation Estimators in a Simultaneous Equation System

Anderson

¹

,

Kunitomo

²

,

Morimune

³

1986

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Comparisons of estimators are made on the basis of their mean squared errors and their concentrations of probability computed by means of asymptotic expansions of their distributions when the disturbance variance tends to zero and alternatively when the sample size increases indefinitely. The estimators include k-class estimators (limited information maximum likelihood, two-stage least squares, and ordinary least squares) and linear combinations of them as well as modifications of the limited information maximum likelihood estimator and several Bayes' estimators. Many inequalities between the asymptotic mean squared errors and concentrations of probability are given. Among medianunbiasedestimators, the limited information maximum likelihood estimator dominates the median-unbiased fixed k-class estimator.

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“…The double k-class of IV estimators has received very limited attention over the years (Nagar, 1962;Srivastava, Agnihotri and Dwivedi, 1980;Dwividi and Srivastava, 1984;Gao and Lahiri, 2002) and to our knowledge has never been considered as an option for the estimation of systems of equations with weak and/or many instruments. The double k-class is also a generalization of a now-forgotten class of estimators proposed by Theil (1958) and called the h-class, and which appears to correspond to the case of k 1 = h 2 and k 2 = h for a real valued parameter h.…”

Section: Finite Sample Bias Correction In the Double K-classmentioning

confidence: 99%

Finite Sample BIAS Corrected IV Estimation for Weak and Many Instruments

Harding

¹

,

Hausman

²

,

Palmer

³

2016

Advances in Econometrics

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This paper considers the finite sample distribution of the 2SLS estimator and derives bounds on its exact bias in the presence of weak and/or many instruments. We then contrast the behavior of the exact bias expressions and the asymptotic expansions currently popular in the literature, including a consideration of the no-moment problem exhibited by many Nagar-type estimators. After deriving a finite sample unbiased k-class estimator, we introduce a double k-class estimator based on Nagar (1962) that dominates k-class estimators (including 2SLS), especially in the cases of weak and/or many instruments. We demonstrate these properties in Monte Carlo simulations showing that our preferred estimators outperforms Fuller (1977) estimators in terms of mean bias and MSE.JEL: C31, C13, C15

show abstract

“…The double k-class of IV estimators has received very limited attention over the years (Nagar, 1962;Srivastava, Agnihotri and Dwivedi, 1980;Dwividi and Srivastava, 1984;Gao and Lahiri, 2002) and to our knowledge has never been considered as an option for the estimation of systems of equations with weak and/or many instruments. The double kclass is also a generalization of a now-forgotten class of estimators proposed by Theil (1958) and called the h-class, and which appears to correspond to the case of k 1 = h 2 and k 2 = h for a real valued parameter h.…”

Section: Finite Sample Bias Correction In the Double K-classmentioning

confidence: 99%

Finite sample bias corrected IV estimation for weak and many instruments

Harding

¹

,

Hausman

²

,

Palmer

³

2015

View full text Add to dashboard Cite

This paper considers the finite sample distribution of the 2SLS estimator and derives bounds on its exact bias in the presence of weak and/or many instruments. We then contrast the behavior of the exact bias expressions and the asymptotic expansions currently popular in the literature, including a consideration of the no-moment problem exhibited by many Nagar-type estimators. After deriving a finite sample unbiased k-class estimator, we introduce a double k-class estimator based on Nagar (1962) that dominates k-class estimators (including 2SLS), especially in the cases of weak and/or many instruments. We demonstrate these properties in Monte Carlo simulations showing that our preferred estimators outperforms Fuller (1977) estimators in terms of mean bias and MSE.JEL: C31, C13, C15

show abstract

Dominance of doublek-class estimators in simultaneous equations

Cited by 6 publications

References 3 publications

Comparing Single-Equation Estimators in a Simultaneous Equation System

Comparing Single-Equation Estimators in a Simultaneous Equation System

Finite Sample BIAS Corrected IV Estimation for Weak and Many Instruments

Finite sample bias corrected IV estimation for weak and many instruments

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