Estimation with Valid and Invalid Instruments
AbstractWe demonstrate analytically that for the widely used simultaneous equation model with one jointly endogenous variable and valid instruments, 2SLS has smaller MSE error, up to second order, than OLS unless the R², or the F statistic of the reduced form equation is extremely low. We also consider the relative bias of estimators when the instruments are invalid, i.e. the instruments are correlated with the stochastic disturbance. Here, both 2SLS and OLS are biased in finite samples and inconsistent. We investigate conditions under which the approximate finite sample bias or the MSE of 2SLS is smaller than the corresponding statistics for the OLS estimator. We again find that 2SLS does better than OLS under a wide range of conditions, which we characterize as functions of observable statistics and one unobservable statistic.
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Bibliographic InfoArticle provided by ENSAE in its journal Annals of Economics and Statistics.
Volume (Year): (2005)
Issue (Month): 79-80 ()
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- Laffers, Lukas, 2013. "Identification in Models with Discrete Variables," Discussion Paper Series in Economics 1/2013, Department of Economics, Norwegian School of Economics.
- Doko Tchatoka, Firmin, 2012.
"Specification tests with weak and invalid instruments,"
15063, University of Tasmania, School of Economics and Finance, revised 26 Jun 2012.
- Doko Tchatoka, Firmin Sabro, 2012. "Specification Tests with Weak and Invalid Instruments," MPRA Paper 40185, University Library of Munich, Germany.
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