We provide analytical formulae for the asymptotic bias (ABIAS) and mean squared error (AMSE) of the IV estimator, and obtain approximations thereof based on an asymptotic scheme which essentially requires the expectation of the first stage F-statistic to converge to a finite (possibly small) positive limit as the number of instruments approaches infinity. The approximations so obtained are shown, via regression analysis, to yield good approximations for ABIAS and AMSE functions, and the AMSE approximation is shown to perform well relative to the approximation of Donald and Newey (2001). Additionally, the manner in which our framework generalizes that of Richardson and Wu (1971) is discussed. One consequence of the asymptotic framework adopted here is that consistent estimators for the ABIAS and AMSE can be obtained. As a result, we are able to construct a number of bias corrected OLS and IV estimators, which we show to be consistent under a sequential asymptotic scheme. These bias-corrected estimators are also robust, in the sense that they remain consistent in a conventional asymptotic setup, where the model is fully identified. A small Monte Carlo experiment documents the relative performance of our bias adjusted estimators versus standard IV, OLS, LIML estimators, and it is shown that our estimators have lower bias than LIML for various levels of endogeneity and instrument relevance.
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Paper provided by Rutgers University, Department of Economics in its series Departmental Working Papers with number
200316.
Find related papers by JEL classification: C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
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References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Christoffersen, Peter F, 1998.
"Evaluating Interval Forecasts,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
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