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The asymptotic and finite sample distributions of OLS and simple IV in simultaneous equations

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  • Kiviet, Jan F.
  • Niemczyk, Jerzy

Abstract

This discussion paper led to a publication in 'Computational Statistics & Data Analysis' 51(7) 3296-318. In practice structural equations are often estimated by least-squares, thus neglecting any simultaneity. This paper reveals why this may often be justifiable and when. Assuming data stationarity and existence of the first four moments of the disturbances we find the limiting distribution of the ordinary least-squares (OLS) estimator in a linear simultaneous equations model. In simple static and dynamic models we compare the asymptotic efficiency of this inconsistent estimator with that of consistent simple instrumental variable (IV) estimators and depict cases where -- due to relative weakness of the instruments or mildness of the simultaneity -- the inconsistent estimator is more precise. In addition, we examine by simulation to what extent these first-order asymptotic findings are reflected in finite sample, taking into account non-existence of moments of the IV estimator. By dynamic visualization techniques we enable to appreciate any differences in efficiency over a parameter space of a much higher dimension than just two, viz. in colored animated image sequences (which are not very effective in print, but much more so in live-on-screen projection).
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  • Kiviet, Jan F. & Niemczyk, Jerzy, 2007. "The asymptotic and finite sample distributions of OLS and simple IV in simultaneous equations," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3296-3318, April.
  • Handle: RePEc:eee:csdana:v:51:y:2007:i:7:p:3296-3318
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    2. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda, 2009. "Finite sample multivariate tests of asset pricing models with coskewness," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2008-2021, April.
    3. Firmin Doko Tchatoka, 2015. "On bootstrap validity for specification tests with weak instruments," Econometrics Journal, Royal Economic Society, vol. 18(1), pages 137-146, February.
    4. 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 Working Papers 2016-01, University of Adelaide, School of Economics.
    5. Doko Tchatoka, Firmin, 2011. "Testing for partial exogeneity with weak identification," MPRA Paper 39504, University Library of Munich, Germany, revised Mar 2012.
    6. Doko Tchatoka, Firmin, 2012. "Specification tests with weak and invalid instruments," Working Papers 15063, University of Tasmania, Tasmanian School of Business and Economics, revised 26 Jun 2012.
    7. 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.
    8. Jan F. Kiviet & Jerzy Niemczyk, 2014. "On the Limiting and Empirical Distributions of IV Estimators When Some of the Instruments are Actually Endogenous," Advances in Econometrics, in: Yoosoon Chang & Thomas B. Fomby & Joon Y. Park (ed.), Essays in Honor of Peter C. B. Phillips, volume 33, pages 425-490, Emerald Publishing Ltd.
    9. Kiviet, Jan F. & Niemczyk, Jerzy, 2012. "Comparing the asymptotic and empirical (un)conditional distributions of OLS and IV in a linear static simultaneous equation," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3567-3586.
    10. Michael Biggs & Thomas Mayer & Andreas Pick, 2009. "Credit and economic recovery," DNB Working Papers 218, Netherlands Central Bank, Research Department.
    11. Dufour, Jean-Marie & Khalaf, Lynda & Kichian, Maral, 2010. "Estimation uncertainty in structural inflation models with real wage rigidities," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2554-2561, November.
    12. 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.
    13. Bolduc, Denis & Khalaf, Lynda & Moyneur, Érick, 2008. "Identification-robust simulation-based inference in joint discrete/continuous models for energy markets," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3148-3161, February.
    14. Jean-Marie Dufour & Lynda Khalaf & Maral Kichian, 2009. "Structural Inflation Models with Real Wage Rigidities: The Case of Canada," Staff Working Papers 09-21, Bank of Canada.
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    JEL classification:

    • 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
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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