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Identification and inference in a simultaneous equation under alternative information sets and sampling schemes

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  • Jan F. Kiviet

Abstract

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 setting in which (in practice often incredible) assumptions regarding the zero correlation between instruments and disturbances are replaced by (generally more credible) interval 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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Article provided by Royal Economic Society in its journal Econometrics Journal.

Volume (Year): 16 (2013)
Issue (Month): 1 (02)
Pages: S24-S59

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Handle: RePEc:wly:emjrnl:v:16:y:2013:i:1:p:s24-s59

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  1. Jan F. Kiviet & Jerzy Niemczyk, 2006. "The Asymptotic and Finite Sample Distributions of OLS and Simple IV in Simultaneous Equations," Tinbergen Institute Discussion Papers 06-078/4, Tinbergen Institute.
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Cited by:
  1. Firmin Doko Tchatoka & Jean‐Marie Dufour, 2014. "Identification‐robust inference for endogeneity parameters in linear structural models," Econometrics Journal, Royal Economic Society, vol. 17(1), pages 165-187, 02.
  2. Denizer, Cevdet & Kaufmann, Daniel & Kraay, Aart, 2013. "Good countries or good projects? Macro and micro correlates of World Bank project performance," Journal of Development Economics, Elsevier, vol. 105(C), pages 288-302.
  3. Bun, Maurice J.G. & Harrison, Teresa D., 2014. "OLS and IV estimation of regression models including endogenous interaction terms," School of Economics Working Paper Series 2014-3, LeBow College of Business, Drexel University.
  4. Skeels, Christopher L. & Taylor, Larry W., 2014. "Prediction after IV estimation," Economics Letters, Elsevier, vol. 122(3), pages 420-422.

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