# Improved Inference for the Instrumental Variable Estimator

## Abstract

It is now well known that standard asymptotic inference techniques for instrumental variable estimation perform very poorly in the presence of weak instruments. Specifically, standard asymptotic techniques give spuriously small standard errors, leading investigators to accept apparently tight confidence regions which unfortunately may be very far from the true parameter of interest. We present an improved technique for inference on structural parameters based on reduced form estimates. The "S-statistic" produces confidence regions based on a joint test of the structural hypothesis and the identification condition. The S- statistic converges to the standard asymptotic Wald statistic as identification becomes certain, has much better size properties when the instruments are weak, and may be inverted in closed form to conveniently compute confidence regions. In addition to providing improved inference for instrumental variable estimation, the technique suggested here may be useful in other applications where weak identification is important.## Download Info

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## Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 9905001.

**Length:**41 pages

**Date of creation:**25 May 1999

**Date of revision:**

**Handle:**RePEc:wpa:wuwpem:9905001

**Note:** Type of Document - MS Word; prepared on IBM PC; to print on PostScript; pages: 41 ; figures: included. Comments welcome**Contact details of provider:**

Web page: http://128.118.178.162

## Related research

**Keywords:**instrumental variables; Wald test; weak instruments;

**Other versions of this item:**

- Richard Startz & Charles Nelson & Eric Zivot, 1999.
"
**Improved Inference for the Instrumental Variable Estimator**," Working Papers 0039, University of Washington, Department of Economics. - Richard Startz & Charles Nelson & Eric Zivot, 1999.
"
**Improved Inference for the Instrumental Variable Estimator**," Discussion Papers in Economics at the University of Washington 0039, Department of Economics at the University of Washington. - Charles Nelson & Richard Startz & Eric Zivot, 2000.
"
**Improved Inference for the Instrumental Variables Estimator**," Econometric Society World Congress 2000 Contributed Papers 1600, Econometric Society.

**Find related papers by JEL classification:**

**C12**- Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General**C30**- Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

**This paper has been announced in the following NEP Reports:**

- NEP-ALL-1999-06-23 (All new papers)
- NEP-ECM-1999-06-23 (Econometrics)

## 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.:

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**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.**Cited by:**

- D.S. Poskitt & C.L. Skeels, 2002.
"
**Assessing Instrumental Variable Relevance:An Alternative Measure and Some Exact Finite Sample Theory**," Department of Economics - Working Papers Series 862, The University of Melbourne. - Dollar, David & Kraay, Aart, 2003.
"
**Institutions, trade, and growth : revisiting the evidence**," Policy Research Working Paper Series 3004, The World Bank. - Dufour, J.M., 2001.
"
**Logique et tests d'hypotheses: reflexions sur les problemes mal poses en econometrie**," Cahiers de recherche 2001-15, Centre interuniversitaire de recherche en économie quantitative, CIREQ.

- DUFOUR, Jean-Marie, 2001.
"
**Logique et tests d'hypotheses: reflexions sur les problemes mal poses en econometrie**," Cahiers de recherche 2001-15, Universite de Montreal, Departement de sciences economiques. - Jean-Marie Dufour, 2001.
"
**Logiques et tests d'hypothèses : réflexions sur les problèmes mal posés en économétrie**," CIRANO Working Papers 2001s-40, CIRANO.

- DUFOUR, Jean-Marie, 2001.
"
- Benoit Perron, 2002.
"
**Semi-Parametric Weak Instrument Regressions with an Application to the Risk-Return Trade-off**," CIRANO Working Papers 2002s-88, CIRANO.

- Benoit Perron, 2003.
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**Semiparametric Weak-Instrument Regressions with an Application to the Risk-Return Tradeoff**," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 424-443, May.

- Benoit Perron, 2000.
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**Semi-Parametric Weak Instrument Regressions with an Application to the Risk-Return Trade-off**," Cahiers de recherche 9901, Universite de Montreal, Departement de sciences economiques.

- Benoit Perron, 2003.
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- Kleibergen, F.R. & Zivot, E., 1998.
"
**Bayesian and classical approaches to instrumental variable regression**," Econometric Institute Research Papers EI 9835, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

- Kleibergen, Frank & Zivot, Eric, 2003.
"
**Bayesian and classical approaches to instrumental variable regression**," Journal of Econometrics, Elsevier, vol. 114(1), pages 29-72, May.

- Frank Kleibergen & Eric Zivot, 1998.
"
**Bayesian and Classical Approaches to Instrumental Variables Regression**," Econometrics 9812002, EconWPA. - Frank Kleibergen & Eric Zivot, 1998.
"
**Bayesian and Classical Approaches to Instrumental Variable Regression**," Discussion Papers in Economics at the University of Washington 0063, Department of Economics at the University of Washington. - Frank Kleibergen & Eric Zivot, 1998.
"
**Bayesian and Classical Approaches to Instrumental Variable Regression**," Working Papers 0063, University of Washington, Department of Economics. - Frank Kleibergen & Eric Zivot, 2003.
"
**Bayesian and Classical Approaches to Instrumental Variable Regression**," Working Papers UWEC-2002-21-P, University of Washington, Department of Economics.

- Kleibergen, Frank & Zivot, Eric, 2003.
"
- 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. - Paul A. Bekker & Jan van der Ploeg, 2000.
"
**Instrumental Variable Estimation Based on Grouped Data**," Econometric Society World Congress 2000 Contributed Papers 1862, Econometric Society. - D.S. Poskitt & C.L. Skeels, 2005.
"
**Small Concentration Asymptotics and Instrumental Variables Inference**," Department of Economics - Working Papers Series 948, The University of Melbourne.

- D. S. Poskitt & C. L. Skeels, 2005.
"
**Small Concentration Asymptotics and Instrumental Variables Inference**," Monash Econometrics and Business Statistics Working Papers 4/05, Monash University, Department of Econometrics and Business Statistics.

- D. S. Poskitt & C. L. Skeels, 2005.
"
- Dufour, Jean-Marie, 2001.
"
**Logique et tests d’hypothèses**," L'Actualité Economique, Société Canadienne de Science Economique, vol. 77(2), pages 171-190, juin. - Dufour, Jean-Marie & Taamouti, Mohamed, 2007.
"
**Further results on projection-based inference in IV regressions with weak, collinear or missing instruments**," Journal of Econometrics, Elsevier, vol. 139(1), pages 133-153, July.

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