Two-Stage Least Squares as Minimum Distance

Frank Windmeijer

Bristol Economics Discussion Papers from School of Economics, University of Bristol, UK

Abstract: The Two-Stage Least Squares instrumental variables (IV) estimator for the parameters in linear models with a single endogenous variable is shown to be identical to an optimal Minimum Distance (MD) estimator based on the individual instrument specific IV estimators. The 2SLS estimator is a linear combination of the individual estimators, with the weights determined by their variances and covariances under conditional homoskedasticity. It is further shown that the Sargan test statistic for overidentifying restrictions is the same as the MD criterion test statistic. This provides an intuitive interpretation of the Sargan test. The equivalence results also apply to the efficient two-step GMM and robust optimal MD estimators and criterion functions, allowing for general forms of heteroskedasticity. It is further shown how these results extend to the linear overidentified IV model with multiple endogenous variables.

Keywords: Instrumental Variables; Two-Stage Least Squares; Minimum Distance; Overidentification Test. (search for similar items in EconPapers)
JEL-codes: C12 C13 C26 (search for similar items in EconPapers)
Pages: 14 pages.
Date: 2017-06-07, Revised 2018-06-13
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (1)

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Journal Article: Two-stage least squares as minimum distance (2019)
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