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The Asymptotic and Finite Sample Distributions of OLS and Simple IV in Simultaneous Equations

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  • Jan F. Kiviet

    ()
    (Universiteit van Amsterdam)

  • Jerzy Niemczyk

    ()
    (Universiteit van Amsterdam)

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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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 06-078/4.

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Date of creation: 18 Sep 2006
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Handle: RePEc:dgr:uvatin:20060078

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Related research

Keywords: efficiency of an inconsistent estimator; invalid instruments; simultaneity bias; weak instruments; 4D diagrams;

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References

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  1. 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.
  2. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  3. Jean-Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 36(4), pages 767-808, November.
  4. Maurice J.G. Bun & Jan F. Kiviet, 2002. "The Effects of Dynamic Feedbacks on LS and MM Estimator Accuracy in Panel Data Models," Tinbergen Institute Discussion Papers 02-101/4, Tinbergen Institute, revised 19 Feb 2004.
  5. 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.
  6. Agnes S. Joseph & Jan F. Kiviet, 2004. "Viewing the Relative Efficiency of IV Estimators in Models with Lagged and Instantaneous Feedbacks," Tinbergen Institute Discussion Papers 04-056/4, Tinbergen Institute.
  7. Elliott, Graham & Stock, James H., 2001. "Confidence intervals for autoregressive coefficients near one," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 155-181, July.
  8. Kenneth D. West & David W. Wilcox, 1994. "A Comparison of Alternative Instrumental Variables Estimators of Dynamic Linear Model," Macroeconomics 9410001, EconWPA.
  9. Hillier, Grant, 2006. "Yet More On The Exact Properties Of Iv Estimators," Econometric Theory, Cambridge University Press, vol. 22(05), pages 913-931, October.
  10. 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.
  11. Woglom, Geoffrey, 2001. "More Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 69(5), pages 1381-89, September.
  12. 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.
  13. Kenneth D. West & David W. Wilcox, 1995. "A Comparison of Alternative Instruments Variables Estimators of a Dynamic Linear Model," NBER Technical Working Papers 0176, National Bureau of Economic Research, Inc.
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Citations

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Cited by:
  1. Peter C. B. Phillips, 2005. "A Remark on Bimodality and Weak Instrumentation in Structural Equation Estimation," Cowles Foundation Discussion Papers 1540, Cowles Foundation for Research in Economics, Yale University.
  2. 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 S24-S59, 02.
  3. Michael Biggs & Thomas Mayer & Andreas Pick, 2009. "Credit and economic recovery," DNB Working Papers 218, Netherlands Central Bank, Research Department.
  4. Doko Tchatoka, Firmin & Dufour, Jean-Marie, 2012. "Identification-robust inference for endogeneity parameters in linear structural models," MPRA Paper 40695, University Library of Munich, Germany.
  5. 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.
  6. Doko Tchatoka, Firmin, 2011. "Testing for partial exogeneity with weak identification," MPRA Paper 39504, University Library of Munich, Germany, revised Mar 2012.
  7. 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.
  8. Jean-Marie Dufour & Lynda Khalaf & Maral Kichian, 2009. "Structural Inflation Models with Real Wage Rigidities: The Case of Canada," Working Papers 09-21, Bank of Canada.
  9. 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.
  10. 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.

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