Advanced Search
MyIDEAS: Login

Small Concentration Asymptotics and Instrumental Variables Inference

Contents:

Author Info

  • D. S. Poskitt

    ()

  • C. L. Skeels

Abstract

Poskitt and Skeels (2003) 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. A basic purpose of this paper is to provide the practitioner with easily implemented inferential tools based upon extensions to these small concentration asymptotic results. We present various approximations to the sampling distribution of functions of the IV estimator based upon small concentration asymptotics, and investigate hypothesis testing procedures and confidence region construction using these approximations. It is shown that the test statistics advanced are asymptotically pivotal and that the associated critical regions generate locally uniformly most powerful invariant tests. The confidence regions are also shown to be valid. The small-concentration asymptotic approximations lead to a non-standard application of standard distributions, facilitating numerical implementation using commonly available software.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2005/wp4-05.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 4/05.

as in new window
Length: 20 pages
Date of creation: Feb 2005
Date of revision:
Handle: RePEc:msh:ebswps:2005-4

Contact details of provider:
Postal: PO Box 11E, Monash University, Victoria 3800, Australia
Phone: +61-3-9905-2489
Fax: +61-3-9905-5474
Email:
Web page: http://www.buseco.monash.edu.au/depts/ebs/
More information through EDIRC

Order Information:
Email:
Web: http://www.buseco.monash.edu.au/depts/ebs/pubs/wpapers/

Related research

Keywords: IV estimator; concentration parameter; small concentration asymptotics; hypothesis testing; confidence region construction; valid inference.;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. 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.
  2. 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.
  3. Richard Startz & Charles Nelson & Eric Zivot, 1999. "Improved Inference for the Instrumental Variable Estimator," Working Papers 0039, University of Washington, Department of Economics.
  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. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
  6. Paul A. Bekker & Frank Kleibergen, 2001. "Finite-Sample Instrumental Variables Inference using an Asymptotically Pivotal Statistic," Tinbergen Institute Discussion Papers 01-055/4, Tinbergen Institute.
  7. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, 09.
  8. 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.
  9. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(02), pages 181-240, August.
  10. 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.
  11. Nelson, C. & Startz, R., 1988. "Some Furthere Results On The Exact Small Sample Properties Of The Instrumental Variable Estimator," Working Papers 88-06, University of Washington, Department of Economics.
  12. 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.
  13. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  14. 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.
  15. 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.
  16. 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.
  17. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
  18. 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.
  19. 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.
  20. 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.
  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. 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.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Russell Davidson & James MacKinnon, 2006. "Bootstrap Inference In A Linear Equation Estimated By Instrumental Variables," Departmental Working Papers 2006-21, McGill University, Department of Economics.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:msh:ebswps:2005-4. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Simone Grose).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.