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

  • Kiviet, Jan F.
  • Niemczyk, Jerzy

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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File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(06)00344-6
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Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 51 (2007)
Issue (Month): 7 (April)
Pages: 3296-3318

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Handle: RePEc:eee:csdana:v:51:y:2007:i:7:p:3296-3318
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  1. Joseph, Agnes S. & Kiviet, Jan F., 2005. "Viewing the relative efficiency of IV estimators in models with lagged and instantaneous feedbacks," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 417-444, April.
  2. DUFOUR, Jean-Marie, 2003. "Identification, Weak Instruments and Statistical Inference in Econometrics," Cahiers de recherche 2003-12, Universite de Montreal, Departement de sciences economiques.
  3. 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.
  4. 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.
  5. Hillier, Grant, 2006. "Yet More On The Exact Properties Of Iv Estimators," Econometric Theory, Cambridge University Press, vol. 22(05), pages 913-931, October.
  6. 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.
  7. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  8. Kenneth D. West & David W. Wilcox, 1994. "A Comparison of Alternative Instrumental Variables Estimators of Dynamic Linear Model," Macroeconomics 9410001, EconWPA.
  9. 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.
  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. 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.
  12. 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.
  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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