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Comparing the asymptotic and empirical (un)conditional distributions of OLS and IV in a linear static simultaneous equation

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  • Kiviet, Jan F.
  • Niemczyk, Jerzy

Abstract

In designing Monte Carlo simulation studies for analyzing finite sample properties of econometric inference methods, one can use either IID drawings in each replication for any series of exogenous explanatory variables or condition on just one realization of these. The results will usually differ, as do their interpretations. Conditional and unconditional limiting distributions are often equivalent, thus yielding similar asymptotic approximations. However, when an estimator is inconsistent, its limiting distribution may change under conditioning. These phenomena are analyzed and numerically illustrated for OLS (ordinary least-squares) and IV (instrumental variables) estimators in single static linear simultaneous equations. The results obtained supplement–and occasionally correct–earlier results. The findings demonstrate in particular that the asymptotic approximations to the unconditional and a conditional distribution of OLS are very accurate even in small samples, and that the actual absolute estimation errors of inconsistent OLS in finite samples are often much smaller than those of consistent IV, even when the instruments are not extremely weak. It is also shown that conditioning reduces the estimation errors of OLS, whereas it deranges the distribution of IV when instruments are weak. Finally it is indicated how OLS could be modified to produce accurate inference under assumptions regarding the degree of simultaneity.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:11:p:3567-3586
    DOI: 10.1016/j.csda.2010.07.028
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    References listed on IDEAS

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    1. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 38(2), pages 112-134.
    2. 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.
    3. Hillier, Grant, 2006. "Yet More On The Exact Properties Of Iv Estimators," Econometric Theory, Cambridge University Press, vol. 22(05), pages 913-931, October.
    4. Mikusheva, Anna, 2010. "Robust confidence sets in the presence of weak instruments," Journal of Econometrics, Elsevier, vol. 157(2), pages 236-247, August.
    5. Edgerton, David L., 1996. "Should stochastic or non-stochastic exogenous variables be used in Monte Carlo experiments?," Economics Letters, Elsevier, vol. 53(2), pages 153-159, November.
    6. Woglom, Geoffrey, 2001. "More Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 69(5), pages 1381-1389, September.
    7. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1130-1164, December.
    8. Jinyong Hahn & Jerry Hausman, 2003. "Weak Instruments: Diagnosis and Cures in Empirical Econometrics," American Economic Review, American Economic Association, vol. 93(2), pages 118-125, May.
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    Citations

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    Cited by:

    1. Doko Tchatoka, Firmin Sabro, 2012. "Specification Tests with Weak and Invalid Instruments," MPRA Paper 40185, University Library of Munich, Germany.
    2. 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.
    3. repec:eme:aecozz:s0731-905320140000033013 is not listed on IDEAS
    4. 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.
    5. 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: Essays in Honor of Peter C. B. Phillips, volume 33, pages 425-490 Emerald Publishing Ltd.

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