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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

    (University of Amsterdam)

Abstract

This discussion paper led to a publication in 'The Econometrics Journal' , 2013, 16(1), S24-S59. 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.

Suggested Citation

  • Jan F. Kiviet, 2012. "Identification and Inference in a Simultaneous Equation under Alternative Information Sets and Sampling Schemes," Tinbergen Institute Discussion Papers 12-128/III, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20120128
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    Cited by:

    1. Kiviet, Jan F., 2020. "Testing the impossible: Identifying exclusion restrictions," Journal of Econometrics, Elsevier, vol. 218(2), pages 294-316.
    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. Kiviet, Jan, 2019. "Instrument-free inference under confined regressor endogeneity; derivations and applications," MPRA Paper 96839, University Library of Munich, Germany.
    6. Wang, Haining & Cheng, Zhiming, 2022. "Kids eat free: School feeding and family spending on education," Journal of Economic Behavior & Organization, Elsevier, vol. 193(C), pages 196-212.
    7. Ahsan, Md Nazmul & Emran, M. Shahe & Shilpi, Forhad, 2024. "Complementarities and intergenerational educational mobility: Theory and evidence from Indonesia," Journal of Economic Behavior & Organization, Elsevier, vol. 225(C), pages 170-191.
    8. Richard A. Ashley & Christopher F. Parmeter, 2020. "Sensitivity Analysis of an OLS Multiple Regression Inference with Respect to Possible Linear Endogeneity in the Explanatory Variables, for Both Modest and for Extremely Large Samples," Econometrics, MDPI, vol. 8(1), pages 1-24, March.
    9. Firmin DOKO TCHATOKA & Jean-Marie DUFOUR, 2016. "Exogeneity Tests, Incomplete Models, Weak Identification and Non-Gaussian Distributions : Invariance and Finite-Sample Distributional Theory," Cahiers de recherche 14-2016, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    10. Kiviet, Jan F., 2023. "Instrument-free inference under confined regressor endogeneity and mild regularity," Econometrics and Statistics, Elsevier, vol. 25(C), pages 1-22.
    11. Jan Kiviet & Milan Pleus & Rutger Poldermans, 2017. "Accuracy and Efficiency of Various GMM Inference Techniques in Dynamic Micro Panel Data Models," Econometrics, MDPI, vol. 5(1), pages 1-54, March.
    12. Seitz, Michael & Watzinger, Martin, 2017. "Contract enforcement and R&D investment," Research Policy, Elsevier, vol. 46(1), pages 182-195.
    13. 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.
    14. Maurice J. G. Bun & Teresa D. Harrison, 2019. "OLS and IV estimation of regression models including endogenous interaction terms," Econometric Reviews, Taylor & Francis Journals, vol. 38(7), pages 814-827, August.
    15. 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.
    16. Sunjae Won & Roderick M. Rejesus & Barry K. Goodwin & Serkan Aglasan, 2024. "Understanding the effect of cover crop use on prevented planting losses," American Journal of Agricultural Economics, John Wiley & Sons, vol. 106(2), pages 659-683, March.
    17. Richard Ashley & Christopher F. Parmeter, 2018. "A Correction/Update to “When Is It Justifiable to Ignore Variable Endogeneity In A Regression Model?â€," Working Papers 2018-01, University of Miami, Department of Economics.
    18. 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.
    19. Skeels, Christopher L. & Taylor, Larry W., 2014. "Prediction after IV estimation," Economics Letters, Elsevier, vol. 122(3), pages 420-422.
    20. Firmin Doko Tchatoka & Jean-Marie Dufour, 2016. "Exogeneity tests, weak identification, incomplete models and non-Gaussian distributions: Invariance and finite-sample distributional theory," School of Economics and Public Policy Working Papers 2016-01, University of Adelaide, School of Economics and Public Policy.
    21. Aglasan, Serkan & Rejesus, Roderick M., 2022. "Do Cover Crops Reduce Production Risk?," 2022 Annual Meeting, July 31-August 2, Anaheim, California 324776, Agricultural and Applied Economics Association.
    22. Hirschberg, Joe & Lye, Jenny, 2017. "Inverting the indirect—The ellipse and the boomerang: Visualizing the confidence intervals of the structural coefficient from two-stage least squares," Journal of Econometrics, Elsevier, vol. 199(2), pages 173-183.
    23. 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.
    24. Doko Tchatoka, Firmin & Dufour, Jean-Marie, 2020. "Exogeneity tests, incomplete models, weak identification and non-Gaussian distributions: Invariance and finite-sample distributional theory," Journal of Econometrics, Elsevier, vol. 218(2), pages 390-418.
    25. Serkan Aglasan & Roderick M. Rejesus & Stephen Hagen & William Salas, 2024. "Cover crops, crop insurance losses, and resilience to extreme weather events," American Journal of Agricultural Economics, John Wiley & Sons, vol. 106(4), pages 1410-1434, August.

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    More about this item

    Keywords

    partial identification; weak instruments; (un)restrained repeated sampling; (un)conditional (limiting) distributions; credible robust inference;
    All these keywords.

    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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