IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/40185.html
   My bibliography  Save this paper

Specification Tests with Weak and Invalid Instruments

Author

Listed:
  • Doko Tchatoka, Firmin Sabro

Abstract

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.

Suggested Citation

  • Doko Tchatoka, Firmin Sabro, 2012. "Specification Tests with Weak and Invalid Instruments," MPRA Paper 40185, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:40185
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/40185/1/MPRA_paper_40185.pdf
    File Function: original version
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Wu, De-Min, 1973. "Alternative Tests of Independence Between Stochastic Regressors and Disturbances," Econometrica, Econometric Society, vol. 41(4), pages 733-750, July.
    2. 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.
    3. 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.
    4. Christopher F Baum & Mark E. Schaffer & Steven Stillman, 2003. "Instrumental variables and GMM: Estimation and testing," Stata Journal, StataCorp LP, vol. 3(1), pages 1-31, March.
    5. Kiviet, Jan F. & Pleus, Milan, 2017. "The performance of tests on endogeneity of subsets of explanatory variables scanned by simulation," Econometrics and Statistics, Elsevier, vol. 2(C), pages 1-21.
    6. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    7. Jean-Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 36(4), pages 767-808, November.
    8. Firmin Doko Tchatoka, 2015. "On bootstrap validity for specification tests with weak instruments," Econometrics Journal, Royal Economic Society, vol. 18(1), pages 137-146, February.
    9. Berkowitz, Daniel & Caner, Mehmet & Fang, Ying, 2008. "Are "Nearly Exogenous Instruments" reliable?," Economics Letters, Elsevier, vol. 101(1), pages 20-23, October.
    10. Firmin Doko Tchatoka & Jean‐Marie Dufour, 2014. "Identification‐robust inference for endogeneity parameters in linear structural models," Econometrics Journal, Royal Economic Society, vol. 17(1), pages 165-187, February.
    11. Donald W. K. Andrews, 2002. "Higher-Order Improvements of a Computationally Attractive "k"-Step Bootstrap for Extremum Estimators," Econometrica, Econometric Society, vol. 70(1), pages 119-162, January.
    12. 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.
    13. Guildo W. Imbens, 2003. "Sensitivity to Exogeneity Assumptions in Program Evaluation," American Economic Review, American Economic Association, vol. 93(2), pages 126-132, May.
    14. 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.
    15. Ruud, Paul A., 2000. "An Introduction to Classical Econometric Theory," OUP Catalogue, Oxford University Press, number 9780195111644.
    16. Wu, De-Min, 1974. "Alternative Tests of Independence between Stochastic Regressors and Disturbances: Finite Sample Results," Econometrica, Econometric Society, vol. 42(3), pages 529-546, May.
    17. Engle, Robert F., 1982. "A general approach to lagrange multiplier model diagnostics," Journal of Econometrics, Elsevier, vol. 20(1), pages 83-104, October.
    18. 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 283-298, May.
    19. Farebrother, R W, 1976. "A Remark on the Wu Test," Econometrica, Econometric Society, vol. 44(3), pages 475-477, May.
    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 638-646, November.
    21. Kadane, Joseph B & Anderson, T W, 1977. "A Comment on the Test of Overidentifying Restrictions," Econometrica, Econometric Society, vol. 45(4), pages 1027-1031, May.
    22. 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.
    23. 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 183-186, February.
    24. Wong, Ka-fu, 1996. "Bootstrapping Hausman's exogeneity test," Economics Letters, Elsevier, vol. 53(2), pages 139-143, November.
    25. Tchatoka, Firmin Doko, 2015. "Subset Hypotheses Testing And Instrument Exclusion In The Linear Iv Regression," Econometric Theory, Cambridge University Press, vol. 31(06), pages 1192-1228, December.
    26. 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.
    27. repec:adr:anecst:y:2005:i:79-80:p:02 is not listed on IDEAS
    28. Jan F. Kiviet, 2013. "Identification and inference in a simultaneous equation under alternative information sets and sampling schemes," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 24-59, February.
    29. Harrison, Ann, 1996. "Openness and growth: A time-series, cross-country analysis for developing countries," Journal of Development Economics, Elsevier, vol. 48(2), pages 419-447, March.
    30. 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.
    31. David H. Romer & Jeffrey A. Frankel, 1999. "Does Trade Cause Growth?," American Economic Review, American Economic Association, vol. 89(3), pages 379-399, June.
    32. N. Gregory Mankiw & David Romer & David N. Weil, 1992. "A Contribution to the Empirics of Economic Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 407-437.
    33. 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.
    34. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 38(2), pages 112-134.
    35. Holly, Alberto, 1982. "A Remark on Hausman's Specification Test," Econometrica, Econometric Society, vol. 50(3), pages 749-759, May.
    36. 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 1583-1588, November.
    37. 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.
    38. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    39. 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.
    40. Berkowitz, Daniel & Caner, Mehmet & Fang, Ying, 2012. "The validity of instruments revisited," Journal of Econometrics, Elsevier, vol. 166(2), pages 255-266.
    41. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-1070, September.
    42. Doko Tchatoka, Firmin, 2012. "On the validity of Durbin-Wu-Hausman tests for assessing partial exogeneity hypotheses with possibly weak instruments," Working Papers 15061, University of Tasmania, Tasmanian School of Business and Economics, revised 06 Jul 2012.
    43. Hausman, Jerry A. & Taylor, William E., 1981. "A generalized specification test," Economics Letters, Elsevier, vol. 8(3), pages 239-245.
    44. Chmelarova, Viera & Hill, R. Carter, 2010. "The Hausman pretest estimator," Economics Letters, Elsevier, vol. 108(1), pages 96-99, July.
    45. 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.
    46. 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, March.
    47. 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.
    48. Wong, Ka-fu, 1997. "Effects on inference of pretesting the exogeneity of a regressor," Economics Letters, Elsevier, vol. 56(3), pages 267-271, November.
    49. 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 152-186, April.
    50. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    51. 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 263-269, February.
    52. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, vol. 29(3), pages 229-256, September.
    53. Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, July.
    54. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
    55. Spencer, David E & Berk, Kenneth N, 1981. "A Limited Information Specification Test [Specification Tests in Econometrics]," Econometrica, Econometric Society, vol. 49(4), pages 1079-1085, June.
    56. 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 749-760, October.
    57. 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.
    58. 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 518-529, October.
    59. 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.
    60. 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.
    61. 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 165-179, February.
    62. 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 479-490, June.
    63. 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.
    64. 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.
    65. 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.
    66. 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 625-631, October.
    67. 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.
    68. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-1633, November.
    69. 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.
    70. 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.
    71. Hansen, Christian & Hausman, Jerry & Newey, Whitney, 2008. "Estimation With Many Instrumental Variables," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 398-422.
    72. Holly, Alberto & Monfort, Alain, 1986. "Some useful equivalence properties of Hausman's test," Economics Letters, Elsevier, vol. 20(1), pages 39-43.
    Full references (including those not matched with items on IDEAS)

    Citations

    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. What I Learned Last Week
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-10-13 09:19:00

    More about this item

    Keywords

    Exogeneity tests; weak instruments; instrument endogeneity; bootstrap technique;

    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
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:40185. 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: (Joachim Winter). General contact details of provider: http://edirc.repec.org/data/vfmunde.html .

    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 CitEc recognized a reference but did not link an item in RePEc 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 RePEc Author Service 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.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.