1932

Abstract

When instruments are weakly correlated with endogenous regressors, conventional methods for instrumental variables (IV) estimation and inference become unreliable. A large literature in econometrics has developed procedures for detecting weak instruments and constructing robust confidence sets, but many of the results in this literature are limited to settings with independent and homoskedastic data, while data encountered in practice frequently violate these assumptions. We review the literature on weak instruments in linear IV regression with an emphasis on results for nonhomoskedastic (heteroskedastic, serially correlated, or clustered) data. To assess the practical importance of weak instruments, we also report tabulations and simulations based on a survey of papers published in the from 2014 to 2018 that use IV. These results suggest that weak instruments remain an important issue for empirical practice, and that there are simple steps that researchers can take to better handle weak instruments in applications.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-economics-080218-025643
2019-08-02
2024-07-23
Loading full text...

Full text loading...

/deliver/fulltext/economics/11/1/annurev-economics-080218-025643.html?itemId=/content/journals/10.1146/annurev-economics-080218-025643&mimeType=html&fmt=ahah

Literature Cited

  1. Anderson T, Rubin H 1949. Estimators for the parameters of a single equation in a complete set of stochastic equations. Ann. Math. Stat. 21:570–82
    [Google Scholar]
  2. Andrews D 2017. Identification-robust subvector inference Discuss. Pap. 2105, Cowles Found., Yale Univ., New Haven, CT
    [Google Scholar]
  3. Andrews D, Cheng X, Guggenberger P 2018. Generic results for establishing the asymptotic size of confidence sets and tests Work. Pap. 1813, Cowles Found. Res. Econ., Yale Univ., New Haven, CT
    [Google Scholar]
  4. Andrews D, Guggenberger P 2009. Asymptotic size and a problem with subsampling and the m out of n bootstrap. Econom. Theory 26:426–68
    [Google Scholar]
  5. Andrews D, Guggenberger P 2015. Identification- and singularity-robust inference for moment condition models Discuss. Pap. 1978, Cowles Found., Yale Univ., New Haven, CT
    [Google Scholar]
  6. Andrews D, Guggenberger P 2017. Asymptotic size of Kleibergen's LM and conditional LR tests for moment condition models. Econom. Theory 33:1046–80
    [Google Scholar]
  7. Andrews D, Marmer V, Yu Z 2019. On optimal inference in the linear IV model. Quant. Econ. 102457–85
    [Google Scholar]
  8. Andrews D, Moreira M, Stock J 2004. Optimal invariant similar tests of instrumental variables regression Discuss. Pap. 1476, Cowles Found., Yale Univ., New Have, CT
    [Google Scholar]
  9. Andrews D, Moreira M, Stock J 2006. Optimal two-sided invariant similar tests of instrumental variables regression. Econometrica 74:715–52
    [Google Scholar]
  10. Andrews D, Moreira M, Stock J 2008. Efficient two-sided nonsimilar invariant tests in IV regression with weak instruments. J. Econom. 146:241–54
    [Google Scholar]
  11. Andrews I 2016. Conditional linear combination tests for weakly identified models. Econometrica 84:2155–82
    [Google Scholar]
  12. Andrews I 2018. Valid two-step identification-robust confidence sets for GMM. Rev. Econ. Stat. 100:337–48
    [Google Scholar]
  13. Andrews I, Armstrong TB 2017. Unbiased instrumental variables estimation under known first-stage sign. Quant. Econ. 8:479–503
    [Google Scholar]
  14. Andrews I, Mikusheva A 2016. Conditional inference with a functional nuisance parameter. Econometrica 84:1571–612
    [Google Scholar]
  15. Angrist J, Krueger A 1991. Does compulsory school attendance affect schooling and earnings. Q. J. Econ. 106979–1014
    [Google Scholar]
  16. Baum C, Schaffer M, Stillman S 2007. Enhanced routines for instrumental variables/generalized method of moments estimation and testing. Stata J. 7:465–506
    [Google Scholar]
  17. Bound J, Jaeger D, Baker R 1995. Problems with instrumental variables estimation when the correlation between the instruments and the endogeneous explanatory variable is weak. J. Am. Stat. Assoc. 90:443–50
    [Google Scholar]
  18. Breusch T, Pagan A 1980. The Lagrange multiplier test and its applications to model specifications in econometrics. Econometrica 47:239–53
    [Google Scholar]
  19. Chaudhuri S, Zivot E 2011. A new method of projection-based inference in GMM with weakly identified nuisance parameters. J. Econom. 164:239–51
    [Google Scholar]
  20. Chernozhukov V, Jansson M, Hansen C 2009. Admissible invariant similar tests for instrumental variables regression. Econom. Theory 25:806–18
    [Google Scholar]
  21. Conley T, Hansen C, Rossi P 2012. Plausibly exogenous. Rev. Econ. Stat. 94:260–72
    [Google Scholar]
  22. Cragg J, Donald S 1993. Testing identifiability and specification in instrumental variable models. Econom. Theory 9:222–40
    [Google Scholar]
  23. Davidson R, MacKinnon J 2014. Bootstrap confidence sets with weak instruments. Econom. Rev. 33:651–75
    [Google Scholar]
  24. Dufour J 1997. Some impossibility theorems in econometrics with applications to structural and dynamic models. Econometrica 65:1365–87
    [Google Scholar]
  25. Dufour J, Jasiak J 2001. Finite sample limited information inference methods for structural equations and models with generated regressors. Int. Econ. Rev. 42:815–44
    [Google Scholar]
  26. Dufour J, Taamouti M 2005. Projection-based statistical inference in linear structural models with possibly weak instruments. Econometrica 73:1351–65
    [Google Scholar]
  27. Favara G, Imbs J 2015. Credit supply and the price of housing. Am. Econ. Rev. 105:958–92
    [Google Scholar]
  28. Fieller E 1954. Some problems in interval estimation. J. R. Stat. Soc. B 16:175–85
    [Google Scholar]
  29. Gleser L, Hwang J 1987. The nonexistence of 100(1)% confidence sets of finite expected diameter in errors-in-variables and related models. J. Am. Stat. Assoc. 15:1341–62
    [Google Scholar]
  30. Guggenberger P 2012. On the asymptotic size distortion of tests when instruments locally violate the exogeneity assumption. Econom. Theory 28:387–421
    [Google Scholar]
  31. Guggenberger P, Kleibergen F, Mavroeidis S 2019. A more powerful subvector Anderson Rubin test in linear instrumental variable regression. Quant. Econ. 102487–526
    [Google Scholar]
  32. Guggenberger P, Kleibergen F, Mavroeidis S, Chen L 2012. On the asymptotic sizes of subset Anderson–Rubin and Lagrange multiplier tests in linear instrumental variables regression. Econometrica 80:2649–66
    [Google Scholar]
  33. Hausman JA 1983. Specification and estimation of simultaneous equation models. Handbook of Econometrics Z Grilliches, M Intriligator391–448 Amsterdam: North-Holland
    [Google Scholar]
  34. Hirano K, Porter J 2015. Location properties of point estimators in linear instrumental variables and related models. Econom. Rev. 34:720–33
    [Google Scholar]
  35. Hornung E 2014. Immigration and the diffusion of technology: the Huguenot diaspora in Prussia. Am. Econ. Rev. 104:84–122
    [Google Scholar]
  36. Imbens G, Angrist J 1994. Identification and estimation of local average treatment effects. Econometrica 62:467–75
    [Google Scholar]
  37. Kleibergen F 2002. Pivotal statistics for testing structural parameters in instrumental variables regression. Econometrica 70:1781–803
    [Google Scholar]
  38. Kleibergen F 2005. Testing parameters in GMM without assuming they are identified. Econometrica 73:1103–23
    [Google Scholar]
  39. Kleibergen F 2007. Generalizing weak instrument robust IV statistics towards multiple parameters, unrestricted covariance matrices, and identification statistics. J. Econom. 139:181–216
    [Google Scholar]
  40. Kleibergen F, Paap R 2007. Generalized reduced rank tests using the singular value decomposition. J. Econom. 133:97–126
    [Google Scholar]
  41. Lee J 2015. Asymptotic sizes of subset Anderson-Rubin tests with weakly identified nuisance parameters and general covariance structure Unpublished manuscript, Mass. Inst. Technol., Cambridge, MA
    [Google Scholar]
  42. Lee S 2018. A consistent variance estimator for 2SLS when instruments identify different LATEs. J. Bus. Econ. Stat. 36:400–10
    [Google Scholar]
  43. Lehmann E, Romano J 2005. Testing Statistical Hypotheses Berlin: Springer. 3rd ed.
    [Google Scholar]
  44. Magnusson L 2010. Inference in limited dependent variable models robust to weak identification. Econom. J. 13:S56–79
    [Google Scholar]
  45. Mariano R, Sawa T 1972. The exact finite-sample distribution of the limited-information maximum likelihood estimator in the case of two included endogenous variables. J. Am. Stat. Assoc. 67:159–63
    [Google Scholar]
  46. Mikusheva A 2010. Robust confidence sets in the presence of weak instruments. J. Econom. 157:236–47
    [Google Scholar]
  47. Montiel Olea J 2018. Admissible, similar tests: a characterization Unpublished manuscript, Columbia Univ., New York
    [Google Scholar]
  48. Montiel Olea J, Pflueger C 2013. A robust test for weak instruments. J. Bus. Econ. Stat. 31:358–69
    [Google Scholar]
  49. Moreira H, Moreira M 2013. Contributions to the theory of optimal tests Unpublished manuscript, FGV/EPGE, Rio de Janeiro
    [Google Scholar]
  50. Moreira H, Moreira M 2015. Optimal two-sided tests for instrumental variables regression with heteroskedastic and autocorrelated errors Work. Pap. CWP25/16, Cent. Microdata Methods Pract., London
    [Google Scholar]
  51. Moreira M 2003. A conditional likelihood ratio test for structural models. Econometrica 71:1027–48
    [Google Scholar]
  52. Moreira M 2009. Tests with correct size when instruments can be arbitrarily weak. J. Econom. 152:131–40
    [Google Scholar]
  53. Moreira M, Porter J, Suarez G 2009. Bootstrap validity for the score test when instruments may be weak. J. Econom. 149:52–64
    [Google Scholar]
  54. Moreira M, Ridder G 2017. Optimal invariant tests in an instrumental variables regression with heteroskedastic and autocorrelated errors Unpublished manuscript, FGV/EPGE, Rio de Janeiro
    [Google Scholar]
  55. Nagar A 1959. The bias and moment matrix of the general k-class estimators of the parameters in simultaneous equations. Econometrica 27:575–95
    [Google Scholar]
  56. Nelson C, Startz R. 1990a. The distribution of the instrumental variable estimator and its t-ratio when the instrument is a poor one. J. Bus. 635125–40
    [Google Scholar]
  57. Nelson C, Startz R 1990b. Some further results on the exact small sample properties of the instrumental variable estimator. Econometrica 58967–76
    [Google Scholar]
  58. Sanderson E, Windmeijer F 2016. A weak instrument f-test in linear IV models with multiple endogenous variables. J. Econom. 190:212–21
    [Google Scholar]
  59. Sawa T 1969. The exact sampling distribution of ordinary least squares and two-stage least squares estimators. J. Am. Stat. Assoc. 64:923–37
    [Google Scholar]
  60. Staiger D, Stock J 1997. Instrumental variables regression with weak instruments. Econometrica 65:557–86
    [Google Scholar]
  61. Stock J, Wright J 2000. GMM with weak identification. Econometrica 68:1055–96
    [Google Scholar]
  62. Stock J, Yogo M 2005. Testing for weak instruments in linear IV regression. Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg DWK Andrews, JH Stock80–108 Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  63. Wang W, Tchatoka FD 2018. On bootstrap inconsistency and Bonferroni-based size-correction for the subset Anderson–Rubin test under conditional homoskedasticity. J. Econom. 207:188–211
    [Google Scholar]
  64. Young A 2014. Structural transformation, the mismeasurement of productivity growth, and the cost disease of services. Am. Econ. Rev. 104:3635–67
    [Google Scholar]
  65. Young A 2018. Consistency without inference: instrumental variables in practical application Unpublished manuscript, London School Econ.
    [Google Scholar]
  66. Zhu Y 2015. A new method for uniform subset inference of linear instrumental variables models Unpublished manuscript, Univ. Oregon, Eugene
    [Google Scholar]
  67. Zivot E, Startz R, Nelson CR 1998. Valid confidence regions and inference in the presence of weak instruments. Int. Econ. Rev. 39:1119–46
    [Google Scholar]
/content/journals/10.1146/annurev-economics-080218-025643
Loading
/content/journals/10.1146/annurev-economics-080218-025643
Loading

Data & Media loading...

Supplementary Data

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error