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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 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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Suggested Citation

  • Jan F. Kiviet, 2013. "Identification and inference in a simultaneous equation under alternative information sets and sampling schemes," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 24-59, February.
  • Handle: RePEc:wly:emjrnl:v:16:y:2013:i:1:p:s24-s59
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    Citations

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    Cited by:

    1. Jan F. Kiviet, 2016. "Testing the impossible: identifying exclusion restrictions," UvA-Econometrics Working Papers 16-03, Universiteit van Amsterdam, Dept. of Econometrics.
    2. Doko Tchatoka, Firmin Sabro, 2012. "Specification Tests with Weak and Invalid Instruments," MPRA Paper 40185, University Library of Munich, Germany.
    3. 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.
    4. 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, February.
    5. Firmin Doko Tchatoka & Jean-Marie Dufour, 2016. "Exogeneity tests, incomplete models, weak identification and non-Gaussian distributions: invariance and finite-sample distributional theory," CIRANO Working Papers 2016s-62, CIRANO.
    6. Jan Kiviet & Milan Pleus & Rutger Poldermans, 2017. "Accuracy and Efficiency of Various GMM Inference Techniques in Dynamic Micro Panel Data Models," Econometrics, MDPI, Open Access Journal, vol. 5(1), pages 1-54, March.
    7. Kiviet, Jan F., 2016. "When is it really justifiable to ignore explanatory variable endogeneity in a regression model?," Economics Letters, Elsevier, vol. 145(C), pages 192-195.
    8. Maurice J.G. Bun & Teresa D. Harrison, 2014. "OLS and IV estimation of regression models including endogenous interaction terms," UvA-Econometrics Working Papers 14-02, Universiteit van Amsterdam, Dept. of Econometrics.
    9. Joe Hirschberg & Jenny Lye, 2017. "Alternative Graphical Representations of the Confidence Intervals for the Structural Coefficient from Exactly Identified Two-Stage Least Squares," Department of Economics - Working Papers Series 2026, The University of Melbourne.
    10. Jan F. Kiviet & Qu Feng, 2014. "Efficiency Gains by Modifying GMM Estimation in Linear Models under Heteroskedasticity," UvA-Econometrics Working Papers 14-06, Universiteit van Amsterdam, Dept. of Econometrics.
    11. Skeels, Christopher L. & Taylor, Larry W., 2014. "Prediction after IV estimation," Economics Letters, Elsevier, vol. 122(3), pages 420-422.
    12. repec:eee:econom:v:199:y:2017:i:2:p:173-183 is not listed on IDEAS
    13. Jan F. Kiviet & Milan Pleus & Rutger Poldermans, 2014. "Accuracy and efficiency of various GMM inference techniques in dynamic micro panel data models," UvA-Econometrics Working Papers 14-09, Universiteit van Amsterdam, Dept. of Econometrics.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials

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