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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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    1. Bun, Maurice J.G. & Kiviet, Jan F., 2006. "The effects of dynamic feedbacks on LS and MM estimator accuracy in panel data models," Journal of Econometrics, Elsevier, vol. 132(2), pages 409-444, June.
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    7. Hillier, Grant, 2006. "Yet More On The Exact Properties Of Iv Estimators," Econometric Theory, Cambridge University Press, vol. 22(05), pages 913-931, October.
    8. West, Kenneth D & Wilcox, David W, 1996. "A Comparison of Alternative Instrumental Variables Estimators of a Dynamic Linear Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 281-293, July.
    9. Hall, Alastair R. & Inoue, Atsushi, 2003. "The large sample behaviour of the generalized method of moments estimator in misspecified models," Journal of Econometrics, Elsevier, vol. 114(2), pages 361-394, June.
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    11. Jinyong Hahn & Atsushi Inoue, 2002. "A Monte Carlo Comparison Of Various Asymptotic Approximations To The Distribution Of Instrumental Variables Estimators," Econometric Reviews, Taylor & Francis Journals, vol. 21(3), pages 309-336.
    12. Maasoumi, Esfandiar & Phillips, Peter C. B., 1982. "On the behavior of inconsistent instrumental variable estimators," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 183-201, August.
    13. Jan F. Kiviet & Garry D. A. Phillips, 2000. "Improved Coefficient and Variance Estimation in Stable First-Order Dynamic Regression Models," Econometric Society World Congress 2000 Contributed Papers 0631, Econometric Society.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Dufour, Jean-Marie & Khalaf, Lynda & Kichian, Maral, 2010. "On the precision of Calvo parameter estimates in structural NKPC models," Journal of Economic Dynamics and Control, Elsevier, vol. 34(9), pages 1582-1595, September.
    7. 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.
    8. Michael Biggs & Thomas Mayer & Andreas Pick, 2009. "Credit and economic recovery," DNB Working Papers 218, Netherlands Central Bank, Research Department.
    9. 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.
    10. 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.

    More about this item

    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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