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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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Bibliographic Info

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. 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.
  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. Kenneth D. West & David W. Wilcox, 1994. "A Comparison of Alternative Instrumental Variables Estimators of Dynamic Linear Model," Macroeconomics 9410001, EconWPA.
  5. Esfandier Maasoumi & Peter C.B. Phillips, 1980. "On the Behavior of Inconsistent Instrumental Variable Estimators," Cowles Foundation Discussion Papers 568, Cowles Foundation for Research in Economics, Yale University.
  6. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  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. Alastair R. Hall & Atsushi Inoue, 2005. "The Large Sample Behaviour of the Generalized Method of Moments Estimator in Misspecified Models," Econometrics 0505002, EconWPA.
  9. 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.
  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. 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.
  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. 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.
  14. DUFOUR, Jean-Marie, 2003. "Identification, Weak Instruments and Statistical Inference in Econometrics," Cahiers de recherche 10-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
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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 & Jean-Marie DUFOUR, 2014. "Identification-Robust Inference for Endogeneity Parameters in Linear Structural Models," Cahiers de recherche 03-2014, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  3. Doko Tchatoka, Firmin, 2012. "Testing for partial exogeneity with weak identification," Working Papers 14565, University of Tasmania, School of Economics and Finance, revised 31 May 2012.
  4. 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.
  5. 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.
  6. Jan F. KIVIET, 2012. "Identification and Inference in a Simultaneous Equation Under Alternative Information Sets and Sampling Schemes," Economic Growth centre Working Paper Series 1207, Nanyang Technolgical University, School of Humanities and Social Sciences, Economic Growth centre.
  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. 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. 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.

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