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Small Concentration Asymptotics and Instrumental Variables Inference

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  • D.S. Poskitt
  • C.L. Skeels

Abstract

Poskitt and Skeels (2005) provide a new approximation to the sampling distribution of the IV estimator in a simultaneous equations model, the approximation is appropriate when the concentration parameter associated with the reduced form model is small. We present approximations to the sampling distributions of various functions of the IV estimator based upon small-concentration asymptotics, and investigate hypothesis testing procedures and confidence region construction using these approximations. We explore the relationship between our work and the K statistic of Kleibergen (2002) and demonstrate that our results can be used to explain the sampling behaviour of the K statistic in simultaneous equations models where identification is weak.

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Bibliographic Info

Paper provided by The University of Melbourne in its series Department of Economics - Working Papers Series with number 948.

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Length: 31 pages
Date of creation: 2005
Date of revision:
Handle: RePEc:mlb:wpaper:948

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Keywords: simultaneous equations model; IV estimator; weak identification; weak instruments; small-concentration asymptotics;

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References

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  1. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-29, October.
  2. John Chao & Norman Swanson, 2004. "Consistent Estimation with a Large Number of Weak Instruments," Departmental Working Papers 200421, Rutgers University, Department of Economics.
  3. Anderson, T W & Sawa, Takamitsu, 1973. "Distributions of Estimates of Coefficients of a Single Equation in a Simultaneous System and Their Asymptotic Expansions," Econometrica, Econometric Society, vol. 41(4), pages 683-714, July.
  4. Nelson, C. & Startz, R., 1988. "The Distribution Of The Instrumental Variables Estimator And Its T-Ratio When The Instrument Is A Poor One," Discussion Papers in Economics at the University of Washington 88-07, Department of Economics at the University of Washington.
  5. D. S. Poskitt & C. L. Skeels, 2004. "Approximating the Distribution of the Instrumental Variables Estimator when the Concentration Parameter is Small," Monash Econometrics and Business Statistics Working Papers 19/04, Monash University, Department of Econometrics and Business Statistics.
  6. Sargan, J D & Mikhail, W M, 1971. "A General Approximation to the Distribution of Instrumental Variables Estimates," Econometrica, Econometric Society, vol. 39(1), pages 131-69, January.
  7. Charles R. Nelson & Richard Startz, 1988. "Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," NBER Technical Working Papers 0068, National Bureau of Economic Research, Inc.
  8. In Choi & Peter C.B. Phillips, 1989. "Asymptotic and Finite Sample Distribution Theory for IV Estimators and Tests in Partially Identified Structural Equations," Cowles Foundation Discussion Papers 929, Cowles Foundation for Research in Economics, Yale University.
  9. Jinyong Hahn & Jerry Hausman, 2002. "A New Specification Test for the Validity of Instrumental Variables," Econometrica, Econometric Society, vol. 70(1), pages 163-189, January.
  10. 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.
  11. Bekker, Paul & Kleibergen, Frank, 2003. "Finite-Sample Instrumental Variables Inference Using An Asymptotically Pivotal Statistic," Econometric Theory, Cambridge University Press, vol. 19(05), pages 744-753, October.
  12. Frank Kleibergen, 2000. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Tinbergen Institute Discussion Papers 00-055/4, Tinbergen Institute.
  13. Richard Startz & Charles Nelson & Eric Zivot, 1999. "Improved Inference for the Instrumental Variable Estimator," Working Papers 0039, University of Washington, Department of Economics.
  14. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
  15. Phillips, P C B, 1980. "The Exact Distribution of Instrumental Variable Estimators in an Equation Containing n + 1 Endogenous Variables," Econometrica, Econometric Society, vol. 48(4), pages 861-78, May.
  16. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(02), pages 181-240, August.
  17. Rothenberg, Thomas J., 1984. "Approximating the distributions of econometric estimators and test statistics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 15, pages 881-935 Elsevier.
  18. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
  19. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  20. Jiahui Wang & Eric Zivot, 1998. "Inference on Structural Parameters in Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 66(6), pages 1389-1404, November.
  21. John C. Chao & Norman R. Swanson, 2003. "Asymptotic Normality of Single-Equation Estimators for the Case with a Large Number of Weak Instruments," Departmental Working Papers 200312, Rutgers University, Department of Economics.
  22. Anderson, T W & Sawa, Takamitsu, 1979. "Evaluation of the Distribution Function of the Two-Stage Least Squares Estimate," Econometrica, Econometric Society, vol. 47(1), pages 163-82, January.
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Cited by:
  1. Russell Davidson & James G. MacKinnon, 2008. "Bootstrap Inference in a Linear Equation Estimated by Instrumental Variables," Working Papers 1157, Queen's University, Department of Economics.

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