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Identification and Inference in a Simultaneous Equation Under Alternative Information Sets and Sampling Schemes

  • Jan F. KIVIET

    (Division of Economics, Nanyang Technological University, Singapore 637332, Singapore)

In simple static linear simultaneous equation models the empirical distributions of IV and OLS are examined under alternative sampling schemes and compared with their first-order asymptotic approximations. We demonstrate that the limiting distribution of consistent IV is not affected by conditioning on exogenous regressors, whereas that of inconsistent OLS is. The OLS asymptotic and simulated actual variances are shown to diminish by extending the set of exogenous variables kept fixed in sampling, whereas such an extension disrupts the distribution of IV and deteriorates the accuracy of its standard asymptotic approximation, not only when instruments are weak. Against this background the consequences for the identification of parameters of interest are examined for a set- ting in which (in practice often incredible) assumptions regarding the zero correlation between instruments and disturbances are replaced by (generally more credible) inter- val assumptions on the correlation between endogenous regressor and disturbance. This yields OLS-based modified confidence intervals, which are usually conservative. Often they compare favorably with IV-based intervals and accentuate their frailty.

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Paper provided by Nanyang Technological University, School of Humanities and Social Sciences, Economic Growth Centre in its series Economic Growth Centre Working Paper Series with number 1207.

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Length: 38 pages
Date of creation: Jul 2012
Date of revision:
Handle: RePEc:nan:wpaper:1207
Contact details of provider: Postal: Nanyang Drive, Singapore 637332
Fax: 6795 5797
Web page: http://egc.hss.ntu.edu.sg/
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