IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Specification tests with weak and invalid instruments

We investigate the size of the Durbin-Wu-Hausman tests for exogeneity when instrumental variables violate the strict exogeneity assumption. We show that these tests are severely size distorted even for a small correlation between the structural error and instruments. We then propose a bootstrap procedure for correcting their size. The proposed bootstrap procedure does not require identification assumptions and is also valid even for moderate correlations between the structural error and instruments, so it can be described as robust to both weak and invalid instruments.

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://eprints.utas.edu.au/15063/1/2012-06__DP_Doko.pdf
Download Restriction: no

Paper provided by University of Tasmania, School of Economics and Finance in its series Working Papers with number 15063.

as
in new window

Length: 27 pages
Date of creation: 26 Jun 2012
Date of revision: 26 Jun 2012
Publication status: Published by the University of Tasmania. Discussion paper 2010-06
Handle: RePEc:tas:wpaper:15063
Contact details of provider: Postal: Private Bag 85, Hobart, Tasmania 7001
Phone: +61 3 6226 7672
Fax: +61 3 6226 7587
Web page: http://www.utas.edu.au/economics-finance/

More information through EDIRC

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. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 38(2), pages 112-134.
  2. Ann Harrison, 1995. "Openness and Growth: A Time-Series, Cross-Country Analysis for Developing Countries," NBER Working Papers 5221, National Bureau of Economic Research, Inc.
  3. Smith, Richard J., 1985. "Wald tests for the independence of stochastic variables and disturbance of a single linear stochastic simultaneous equation," Economics Letters, Elsevier, vol. 17(1-2), pages 87-90.
  4. Doko Tchatoka, Firmin, 2012. "On the Validity of Durbin-Wu-Hausman Tests for Assessing Partial Exogeneity Hypotheses with Possibly Weak Instruments," MPRA Paper 40184, University Library of Munich, Germany.
  5. Nakamura, Alice & Nakamura, Masao, 1981. "On the Relationships among Several Specification Error Tests Presented by Durbin, Wu, and Hausman," Econometrica, Econometric Society, vol. 49(6), pages 1583-88, November.
  6. Wu, De-Min, 1974. "Alternative Tests of Independence between Stochastic Regressors and Disturbances: Finite Sample Results," Econometrica, Econometric Society, vol. 42(3), pages 529-46, May.
  7. Dufour, Jean-Marie, 2006. "Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics," Journal of Econometrics, Elsevier, vol. 133(2), pages 443-477, August.
  8. Donald W.K. Andrews, 1999. "Higher-Order Improvements of a Computationally Attractive-Step Bootstrap for Extremum Estimators," Cowles Foundation Discussion Papers 1230R, Cowles Foundation for Research in Economics, Yale University, revised Jan 2001.
  9. Doko Tchatoka, Firmin Sabro & Dufour, Jean-Marie, 2008. "Instrument endogeneity and identification-robust tests: some analytical results," MPRA Paper 29613, University Library of Munich, Germany.
  10. 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.
  11. Ruud, Paul A., 2000. "An Introduction to Classical Econometric Theory," OUP Catalogue, Oxford University Press, number 9780195111644, March.
  12. Daniel Berkowitz & Mehmet Caner & Ying Fang, 2006. "Are "Nearly Exogenous" Instruments Reliable?," Working Papers 219, University of Pittsburgh, Department of Economics, revised Jan 2006.
  13. Kiviet, Jan F. & Niemczyk, Jerzy, 2007. "The asymptotic and finite sample distributions of OLS and simple IV in simultaneous equations," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3296-3318, April.
  14. Saraswata Chaudhuri & Elaina Rose, 2009. "Estimating the Veteran Effect with Endogenous Schooling when Instruments are Potentially Weak," Working Papers UWEC-2009-07, University of Washington, Department of Economics.
  15. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
  16. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, vol. 29(3), pages 229-256, September.
  17. Li, Jing, 2006. "The block bootstrap test of Hausman's exogeneity in the presence of serial correlation," Economics Letters, Elsevier, vol. 91(1), pages 76-82, April.
  18. Smith, Richard, 1983. "On the classical nature of the Wu-Hausman statistics for the independence of stochastic regressors and disturbance," Economics Letters, Elsevier, vol. 11(4), pages 357-364.
  19. Doko Tchatoka, Firmin & Dufour, Jean-Marie, 2012. "Identification-robust inference for endogeneity parameters in linear structural models," Working Papers 15064, University of Tasmania, School of Economics and Finance, revised 01 Aug 2012.
  20. Thurman, Walter N, 1986. "Endogeneity Testing in a Supply and Demand Framework," The Review of Economics and Statistics, MIT Press, vol. 68(4), pages 638-46, November.
  21. 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.
  22. 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.
  23. Nakamura, Alice & Nakamura, Masao, 1985. "On the performance of tests by Wu and by Hausman for detecting the ordinary least squares bias problem," Journal of Econometrics, Elsevier, vol. 29(3), pages 213-227, September.
  24. Spencer, David E & Berk, Kenneth N, 1981. "A Limited Information Specification Test [Specification Tests in Econometrics]," Econometrica, Econometric Society, vol. 49(4), pages 1079-85, June.
  25. Revankar, Nagesh S & Hartley, Michael J, 1973. "An Independence Test and Conditional Unbiased Predictions in the Context of Simultaneous Equation Systems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(3), pages 625-31, October.
  26. Doko Tchatoka, Firmin, 2010. "Subset hypotheses testing and instrument exclusion in the linear IV regression," MPRA Paper 29611, University Library of Munich, Germany, revised 02 Feb 2012.
  27. Firmin Doko Tchatoka, 2015. "On bootstrap validity for specification tests with weak instruments," Econometrics Journal, Royal Economic Society, vol. 18(1), pages 137-146, 02.
  28. DUFOUR, Jean-Marie, 2003. "Identification, Weak Instruments and Statistical Inference in Econometrics," Cahiers de recherche 10-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  29. Kadane, Joseph B & Anderson, T W, 1977. "A Comment on the Test of Overidentifying Restrictions," Econometrica, Econometric Society, vol. 45(4), pages 1027-31, May.
  30. Christopher F Baum & Mark E. Schaffer & Steven Stillman, 2002. "Instrumental variables and GMM: Estimation and testing," Boston College Working Papers in Economics 545, Boston College Department of Economics, revised 14 Feb 2003.
  31. Berkowitz, Daniel & Caner, Mehmet & Fang, Ying, 2012. "The validity of instruments revisited," Journal of Econometrics, Elsevier, vol. 166(2), pages 255-266.
  32. Hwang, Hae-shin, 1985. "The equivalence of Hausman and Lagrange Multiplier tests of independence between disturbance and a subset of stochastic regressors," Economics Letters, Elsevier, vol. 17(1-2), pages 83-86.
  33. Pesaran, M. Hashem & Smith, Richard J., 1990. "A unified approach to estimation and orthogonality tests in linear single-equation econometric models," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 41-66.
  34. Jean-Marie Dufour, 2003. "Identification, Weak Instruments and Statistical Inference in Econometrics," CIRANO Working Papers 2003s-49, CIRANO.
  35. Chmelarova, Viera & Hill, R. Carter, 2010. "The Hausman pretest estimator," Economics Letters, Elsevier, vol. 108(1), pages 96-99, July.
  36. Small, Dylan S., 2007. "Sensitivity Analysis for Instrumental Variables Regression With Overidentifying Restrictions," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1049-1058, September.
  37. Wong, Ka-fu, 1996. "Bootstrapping Hausman's exogeneity test," Economics Letters, Elsevier, vol. 53(2), pages 139-143, November.
  38. Samuel Bazzi & Michael A. Clemens, 2013. "Blunt Instruments: Avoiding Common Pitfalls in Identifying the Causes of Economic Growth," American Economic Journal: Macroeconomics, American Economic Association, vol. 5(2), pages 152-86, April.
  39. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07.
  40. Michael P. Murray, 2006. "Avoiding Invalid Instruments and Coping with Weak Instruments," Journal of Economic Perspectives, American Economic Association, vol. 20(4), pages 111-132, Fall.
  41. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  42. Farebrother, R W, 1976. "A Remark on the Wu Test," Econometrica, Econometric Society, vol. 44(3), pages 475-77, May.
  43. Jan F. KIVIET, 2012. "Identification and Inference in a Simultaneous Equation Under Alternative Information Sets and Sampling Schemes," Economic Growth Centre Working Paper Series 1207, Nanyang Technological University, School of Humanities and Social Sciences, Economic Growth Centre.
  44. 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.
  45. Hausman, Jerry A. & Taylor, William E., 1981. "A generalized specification test," Economics Letters, Elsevier, vol. 8(3), pages 239-245.
  46. Smith, Richard J, 1984. "A Note on Likelihood Ratio Tests for the Independence between a Subset of Stochastic Regressors and Disturbances," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 263-69, February.
  47. Mikusheva, Anna, 2013. "Survey on statistical inferences in weakly-identified instrumental variable models," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 29(1), pages 117-131.
  48. Richard Ashley, 2009. "Assessing the credibility of instrumental variables inference with imperfect instruments via sensitivity analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(2), pages 325-337, 03.
  49. Hall, Alastair R & Rudebusch, Glenn D & Wilcox, David W, 1996. "Judging Instrument Relevance in Instrumental Variables Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(2), pages 283-98, May.
  50. Jinyong Hahn & Jerry Hausman, 2010. "Estimation with Valid and Invalid Instruments," NBER Chapters, in: Contributions in Memory of Zvi Griliches, pages 25-57 National Bureau of Economic Research, Inc.
  51. Reynolds, Roger A, 1982. "Posterior Odds for the Hypothesis of Independence between Stochastic Regressors and Disturbances," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(2), pages 479-90, June.
  52. Wong, Ka-fu, 1997. "Effects on inference of pretesting the exogeneity of a regressor," Economics Letters, Elsevier, vol. 56(3), pages 267-271, November.
  53. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-33, November.
  54. David H. Romer & Jeffrey A. Frankel, 1999. "Does Trade Cause Growth?," American Economic Review, American Economic Association, vol. 89(3), pages 379-399, June.
  55. Holly, Alberto, 1982. "A Remark on Hausman's Specification Test," Econometrica, Econometric Society, vol. 50(3), pages 749-59, May.
  56. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September.
  57. N. Gregory Mankiw & David Romer & David N. Weil, 1990. "A Contribution to the Empirics of Economic Growth," NBER Working Papers 3541, National Bureau of Economic Research, Inc.
  58. Engle, Robert F., 1982. "A general approach to lagrange multiplier model diagnostics," Journal of Econometrics, Elsevier, vol. 20(1), pages 83-104, October.
  59. Richard A. Ashley., 2006. "Assessing the Credibility of Instrumental Variables Inference With Imperfect Instruments Via Sensitivity Analysis," Working Papers e06-9, Virginia Polytechnic Institute and State University, Department of Economics.
  60. Guggenberger, Patrik, 2012. "On The Asymptotic Size Distortion Of Tests When Instruments Locally Violate The Exogeneity Assumption," Econometric Theory, Cambridge University Press, vol. 28(02), pages 387-421, April.
  61. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  62. Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, 07.
  63. Ruud, Paul A., 1984. "Tests of Specification in Econometrics," Department of Economics, Working Paper Series qt4kq8m0hf, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  64. Guildo W. Imbens, 2003. "Sensitivity to Exogeneity Assumptions in Program Evaluation," American Economic Review, American Economic Association, vol. 93(2), pages 126-132, May.
  65. Patrik Guggenberger & Frank Kleibergen & Sophocles Mavroeidis & Linchun Chen, 2012. "On the Asymptotic Sizes of Subset Anderson–Rubin and Lagrange Multiplier Tests in Linear Instrumental Variables Regression," Econometrica, Econometric Society, vol. 80(6), pages 2649-2666, November.
  66. James H. Stock & Francesco Trebbi, 2003. "Retrospectives: Who Invented Instrumental Variable Regression?," Journal of Economic Perspectives, American Economic Association, vol. 17(3), pages 177-194, Summer.
  67. 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.
  68. Jan F. KIVIET & Milan PLEUS, 2012. "The performance of tests on endogeneity of subsets of explanatory variables scanned by simulation," Economic Growth Centre Working Paper Series 1208, Nanyang Technological University, School of Humanities and Social Sciences, Economic Growth Centre.
  69. Wu, De-Min, 1973. "Alternative Tests of Independence Between Stochastic Regressors and Disturbances," Econometrica, Econometric Society, vol. 41(4), pages 733-50, July.
  70. Revankar, Nagesh S, 1978. "Asymptotic Relative Efficiency Analysis of Certain Tests of Independence in Structural Systems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(1), pages 165-79, February.
  71. 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.
  72. Hwang, Hae-Shin, 1980. "Test of Independence between a Subset of Stochastic Regressors and Disturbances," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(3), pages 749-60, October.
  73. Ahn, Seung C, 1997. "Orthogonality Tests in Linear Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 59(1), pages 183-86, February.
Full references (including those not matched with items on IDEAS)

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

When requesting a correction, please mention this item's handle: RePEc:tas:wpaper:15063. 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: (Derek Rowlands)

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.