This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

Consistent Estimation with a Large Number of Weak Instruments

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
Chao, John Chao (University of Maryland)
Norman R. Swanson (Rutgers University)

Additional information is available for the following registered author(s):

Abstract

This paper conducts a general analysis of the conditions under which consistent estimation can be achieved in instrumental variables regression when the available instruments are weak in the local-to-zero sense. More precisely, the approach adopted in this paper combines key features of the local-to-zero framework of Staiger and Stock (1997) and the many-instrument framework of Morimune (1983) and Bekker (1994) and generalizes both of these frameworks in the following ways. First, we consider a general local-to-zero framework which allows for an arbitrary degree of instrument weakness by modeling the first-stage coefficients as shrinking toward zero at an unspecified rate, say b_{n}^{-1}. Our local-to-zero setup, in fact, reduces to that of Staiger and Stock (1997) in the case where b_{n} = sqrt{n}. In addition, we examine a broad class of single-equation estimators which extends the well-known k-class to include, amongst others, the Jackknife Instrumental Variables Estimator (JIVE) of Angrist, Imbens, and Krueger (1999). Analysis of estimators within this extended class based on a pathwise asymptotic scheme, where the number of instruments K_{n} is allowed to grow as a function of the sample size, reveals that consistent estimation depends importantly on the relative magnitudes of rn, the growth rate of the concentration parameter, and K_{n}. In particular, it is shown that members of the extended class which satisfy certain general conditions, such as LIML and JIVE, are consistent provided that sqrt{K_{n}n/r_{n}} -> 0, as n -> infinity. On the other hand, the two-stage least squares (2SLS) estimator is shown not to satisfy the needed conditions and is found to be consistent only if K_{n}/r_{n} -> 0, as n -> infinity. A main point of our paper is that the use of many instruments may be beneficial from a point estimation standpoint in empirical applications where the available instruments are weak but abundant, as it provides an extra source, by which the concentration parameter can grow, thus, allowing consistent estimation to be achievable, in certain cases, even in the presence of weak instruments. Our results, thus, add to the findings of Staiger and Stock (1997) who study a local-to-zero framework where K_{n} is held fixed and the concentration parameter does not diverge as sample size grows; in consequence, no single-equation estimator is found to be consistent under their setup.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. 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://cowles.econ.yale.edu/P/cd/d14a/d1417.pdf
File Format: application/pdf
File Function:
Download Restriction: no

Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1417.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length: 36 pages
Date of creation: May 2003
Date of revision:
Handle: RePEc:cwl:cwldpp:1417

Contact details of provider:
Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
More information through EDIRC

Order Information:
Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

For technical questions regarding this item, or to correct its listing, contact: (Glena Ames).

Related research
Keywords: Instrumental variables; k-class estimator; Local-to-zero framework; Pathwise asymptotics; Weak instruments;

Other versions of this item:

Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

This paper has been announced in the following NEP Reports:

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.:
  1. Blomquist, Soren & Dahlberg, Matz, 1999. "Small Sample Properties of LIML and Jackknife IV Estimators: Experiments with Weak Instruments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 69-88, Jan.-Feb.. [Downloadable!]
  2. Donald, Stephen G & Newey, Whitney K, 2001. "Choosing the Number of Instruments," Econometrica, Econometric Society, vol. 69(5), pages 1161-91, September.
  3. Jinyong Hahn & Whitney Newey, 2003. "Jackknife and analytical bias reduction for nonlinear panel models," CeMMAP working papers CWP17/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
    Other versions:
  4. James H. Stock & Motohiro Yogo, 2002. "Testing for Weak Instruments in Linear IV Regression," NBER Technical Working Papers 0284, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  5. Alastair Hall & Fernanda P. M. Peixe, 2000. "A Consistent Method for the Selection of Relevant Instruments," Econometric Society World Congress 2000 Contributed Papers 0790, Econometric Society. [Downloadable!]
  6. Angrist, J D & Imbens, G W & Krueger, A B, 1999. "Jackknife Instrumental Variables Estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 57-67, Jan.-Feb.. [Downloadable!]
    Other versions:
  7. Jinyong Hahn & Atsushi Inoue, 2002. "A Monte Carlo Comparison Of Various Asymptotic Approximations To The Distribution Of Instrumental Variables Estimators," Econometric Reviews, Taylor and Francis Journals, vol. 21(3), pages 309-336. [Downloadable!] (restricted)
  8. Peter C.B. Phillips, 1982. "Small Sample Distribution Theory in Econometric Models of Simultaneous Equations," Cowles Foundation Discussion Papers 617, Cowles Foundation, Yale University. [Downloadable!]
  9. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    Other versions:
  10. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September. [Downloadable!] (restricted)
  11. Peter C.B. Phillips, 1987. "Partially Identified Econometric Models," Cowles Foundation Discussion Papers 845R, Cowles Foundation, Yale University, revised Aug 1988. [Downloadable!]
  12. Choi, In & Phillips, Peter C. B., 1992. "Asymptotic and finite sample distribution theory for IV estimators and tests in partially identified structural equations," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 113-150. [Downloadable!] (restricted)
    Other versions:
  13. Koenker, Roger & Machado, Jose A. F., 1999. "GMM inference when the number of moment conditions is large," Journal of Econometrics, Elsevier, vol. 93(2), pages 327-344, December. [Downloadable!] (restricted)
  14. Morimune, Kimio, 1983. "Approximate Distributions of k-Class Estimators When the Degree of Overidentifiability Is Large Compared with the Sample Size," Econometrica, Econometric Society, vol. 51(3), pages 821-41, May. [Downloadable!] (restricted)
  15. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, vol. 59(2), pages 307-45, March. [Downloadable!] (restricted)
    Other versions:
  16. Peter C. B. Phillips & Chirok Han, 2004. "GMM with Many Moment Conditions," Econometric Society 2004 Far Eastern Meetings 525, Econometric Society. [Downloadable!]
    Other versions:
  17. Hahn, Jinyong & Kuersteiner, Guido, 2002. "Discontinuities of weak instrument limiting distributions," Economics Letters, Elsevier, vol. 75(3), pages 325-331, May. [Downloadable!] (restricted)
  18. Angrist, Joshua D & Krueger, Alan B, 1995. "Split-Sample Instrumental Variables Estimates of the Return to Schooling," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(2), pages 225-35, April.
  19. Joshua D. Angrist & Alan B. Krueger, 1995. "Split Sample Instrumental Variables," NBER Technical Working Papers 0150, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  20. Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, vol. 45(4), pages 939-53, May. [Downloadable!] (restricted)
  21. 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.
  22. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07. [Downloadable!] (restricted)
  23. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May. [Downloadable!] (restricted)
  24. Phillips, Garry D A & Hale, C, 1977. "The Bias of Instrumental Variable Estimators of Simultaneous Equation Systems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(1), pages 219-28, February. [Downloadable!] (restricted)
  25. Portnoy, Stephen, 1987. "A central limit theorem applicable to robust regression estimators," Journal of Multivariate Analysis, Elsevier, vol. 22(1), pages 24-50, June. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, 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.)

  1. 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. [Downloadable!]
  2. T. W. Anderson & Naoto Kunitomo & Yukitoshi Matsushita, 2006. "A New Light from Old Wisdoms : Alternative Estimation Methods of Simultaneous Equations with Possibly Many Instruments," CIRJE F-Series CIRJE-F-399, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  3. Peter C.B. Phillips, 2003. "Vision and Influence in Econometrics: John Denis Sargan," Cowles Foundation Discussion Papers 1393, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  4. Cizek, P., 2009. "Generalized Methods of Trimmed Moments," Discussion Paper 2009-25, Tilburg University, Center for Economic Research. [Downloadable!]
  5. Giovanni Forchini, 2006. "The Asymptotic distribution of the LIML Estimator in a Partially Identified Structural Equation," Monash Econometrics and Business Statistics Working Papers 1/06, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  6. Peter C. B. Phillips & Chirok Han, 2004. "GMM with Many Moment Conditions," Econometric Society 2004 Far Eastern Meetings 525, Econometric Society. [Downloadable!]
    Other versions:
  7. John Chao & Norman Swanson, 2004. "Estimation and Testing Using Jackknife IV in Heteroskedastic Regressions With Many Weak Instruments," Departmental Working Papers 200420, Rutgers University, Department of Economics. [Downloadable!]
    Other versions:
  8. Stanislav Anatolyev, 2007. "Inference about predictive ability when there are many predictors," Working Papers w0096, Center for Economic and Financial Research (CEFIR). [Downloadable!]
  9. Mehmet Caner, 2006. "Near Exogeneity and Weak Identification in Generlized Empirical Likelihood estimators : Fixed and Many Moment Asymptotics," Working Papers 212, University of Pittsburgh, Department of Economics, revised Jan 2006. [Downloadable!]
    Other versions:
  10. 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. [Downloadable!]
    Other versions:
  11. T. W. Anderson & Naoto Kunitomo & Yukitoshi Matsushita, 2008. "On the Asymptotic Optimality of the LIML Estimator with Possibly Many Instruments," CIRJE F-Series CIRJE-F-542, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  12. James H. Stock & Motohiro Yogo, 2002. "Testing for Weak Instruments in Linear IV Regression," NBER Technical Working Papers 0284, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  13. 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. [Downloadable!]
  14. Kazuhiko Hayakawa, 2006. "Efficient GMM Estimation of Dynamic Panel Data Models Where Large Heterogeneity May Be Present," Hi-Stat Discussion Paper Series d05-130, Institute of Economic Research, Hitotsubashi University. [Downloadable!]
  15. Stanislav Anatolyev & Nikolay Gospodinov, 2008. "Specification Testing in Models with Many Instruments," Working Papers w0124, Center for Economic and Financial Research (CEFIR). [Downloadable!]
  16. Ciccone, Antonio & Peri, Giovanni, 2003. "Skills' Substitutability and Technological Progress: U.S. States 1950-1990," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
  17. Mehmet Caner, 2005. "Higher Order Expansions in GMM with Nearly Weak and Many Nearly Weak Instruments," Working Papers 209, University of Pittsburgh, Department of Economics, revised Jan 2005. [Downloadable!]
  18. Mathias D. Cattaneo & Richard K. Crump & Michael Jansson, 2007. "Optimal Inference for Instrumental Variables Regression with non-Gaussian Errors," CREATES Research Papers 2007-11, School of Economics and Management, University of Aarhus. [Downloadable!]
  19. Whitney Newey & Frank Windmeijer, 2005. "GMM with many weak moment conditions," CeMMAP working papers CWP18/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  20. Christian Hansen & Jerry Hausman & Whitney Newey, 2006. "Estimation with many instrumental variables," CeMMAP working papers CWP19/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  21. T. W. Anderson & Naoto Kunitomo & Yukitoshi Matsushita, 2008. "On Finite Sample Properties of Alternative Estimators of Coefficients in a Structural Equation with Many Instruments," CIRJE F-Series CIRJE-F-577, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  22. Antonio Ciccone & Giovanni Peri, 2004. "Long-Run Substitutability between More and Less Educated Workers: Evidence from U.S. States 1950-1990," Economics Working Papers 764, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
    Other versions:
  23. Andreas Pick, 2007. "Financial contagion and tests using instrumental variables," DNB Working Papers 139, Netherlands Central Bank, Research Department. [Downloadable!]
Statistics
Access and download statistics

Did you know? You can create your own reading lists on IDEAS.

This page was last updated on 2009-11-9.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.