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Specification Tests with Weak and Invalid Instruments

  • Doko Tchatoka, Firmin Sabro

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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 40185.

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Date of creation: 20 Jul 2012
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Handle: RePEc:pra:mprapa:40185
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  1. 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.
  2. Doko Tchatoka, Firmin & Dufour, Jean-Marie, 2012. "Identification-robust inference for endogeneity parameters in linear structural models," MPRA Paper 40695, University Library of Munich, Germany.
  3. 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.
  4. Doko Tchatoka, Firmin, 2013. "On bootstrap validity for specification tests with weak instruments," Working Papers 16875, University of Tasmania, School of Economics and Finance, revised 05 Aug 2013.
  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. 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.
  7. Jean-Marie Dufour, 2003. "Identification, Weak Instruments and Statistical Inference in Econometrics," CIRANO Working Papers 2003s-49, CIRANO.
  8. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  9. Daniel Berkowitz & Mehmet Caner & Ying Fang, 2013. "The Validity of Instruments Revisited," Papers 2013-10-14, Working Paper.
  10. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, vol. 29(3), pages 229-256, September.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, 07.
  16. 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.
  17. David H. Romer & Jeffrey A. Frankel, 1999. "Does Trade Cause Growth?," American Economic Review, American Economic Association, vol. 89(3), pages 379-399, June.
  18. Chmelarova, Viera & Hill, R. Carter, 2010. "The Hausman pretest estimator," Economics Letters, Elsevier, vol. 108(1), pages 96-99, July.
  19. 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.
  20. Mankiw, N Gregory & Romer, David & Weil, David N, 1992. "A Contribution to the Empirics of Economic Growth," The Quarterly Journal of Economics, MIT Press, vol. 107(2), pages 407-37, May.
  21. Engle, Robert F., 1982. "A general approach to lagrange multiplier model diagnostics," Journal of Econometrics, Elsevier, vol. 20(1), pages 83-104, October.
  22. Berkowitz, Daniel & Caner, Mehmet & Fang, Ying, 2008. "Are "Nearly Exogenous Instruments" reliable?," Economics Letters, Elsevier, vol. 101(1), pages 20-23, October.
  23. 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.
  24. Farebrother, R W, 1976. "A Remark on the Wu Test," Econometrica, Econometric Society, vol. 44(3), pages 475-77, May.
  25. 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.
  26. Chaudhuri, Saraswata & Rose, Elaina, 2009. "Estimating the Veteran Effect with Endogenous Schooling When Instruments Are Potentially Weak," IZA Discussion Papers 4203, Institute for the Study of Labor (IZA).
  27. Wong, Ka-fu, 1997. "Effects on inference of pretesting the exogeneity of a regressor," Economics Letters, Elsevier, vol. 56(3), pages 267-271, November.
  28. Christopher F Baum & Mark E. Schaffer & Steven Stillman, 2002. "Instrumental variables and GMM: Estimation and testing," North American Stata Users' Group Meetings 2003 05, Stata Users Group.
  29. 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.
  30. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-33, November.
  31. Harrison, Ann, 1991. "Openness and growth : a time series, cross-country analysis for developing countries," Policy Research Working Paper Series 809, The World Bank.
  32. 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.
  33. 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.
  34. 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.
  35. 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.
  36. DUFOUR, Jean-Marie, 2005. "Monte Carlo Tests with Nuisance Parameters: A General Approach to Finite-Sample Inference and Nonstandard Asymptotics," Cahiers de recherche 03-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  37. 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.
  38. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  39. 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.
  40. 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.
  41. 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.
  42. Hausman, Jerry A, 1978. "Specification Tests in Econometrics," Econometrica, Econometric Society, vol. 46(6), pages 1251-71, November.
  43. 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.
  44. 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.
  45. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September.
  46. 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.
  47. Holly, Alberto, 1982. "A Remark on Hausman's Specification Test," Econometrica, Econometric Society, vol. 50(3), pages 749-59, May.
  48. 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.
  49. 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.
  50. Wong, Ka-fu, 1996. "Bootstrapping Hausman's exogeneity test," Economics Letters, Elsevier, vol. 53(2), pages 139-143, November.
  51. 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.
  52. Guildo W. Imbens, 2003. "Sensitivity to Exogeneity Assumptions in Program Evaluation," American Economic Review, American Economic Association, vol. 93(2), pages 126-132, May.
  53. Ruud, Paul A., 2000. "An Introduction to Classical Econometric Theory," OUP Catalogue, Oxford University Press, number 9780195111644.
  54. 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.
  55. 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.
  56. 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.
  57. 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.
  58. 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.
  59. 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.
  60. 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.
  61. 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.
  62. 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.
  63. 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.
  64. 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.
  65. Wu, De-Min, 1973. "Alternative Tests of Independence Between Stochastic Regressors and Disturbances," Econometrica, Econometric Society, vol. 41(4), pages 733-50, July.
  66. 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.
  67. 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.
  68. 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.
  69. 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.
  70. Hausman, Jerry A. & Taylor, William E., 1981. "A generalized specification test," Economics Letters, Elsevier, vol. 8(3), pages 239-245.
  71. 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.
  72. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07.
  73. 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.
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