IDEAS home Printed from https://ideas.repec.org/p/cir/cirwor/2003s-49.html
   My bibliography  Save this paper

Identification, Weak Instruments and Statistical Inference in Econometrics

Author

Listed:
  • Jean-Marie Dufour

Abstract

We discuss statistical inference problems associated with identification and testability in econometrics, and we emphasize the common nature of the two issues. After reviewing the relevant statistical notions, we consider in turn inference in nonparametric models and recent developments on weakly identified models (or weak instruments). We point out that many hypotheses, for which test procedures are commonly proposed, are not testable at all, while some frequently used econometric methods are fundamentally inappropriate for the models considered. Such situations lead to ill-defined statistical problems and are often associated with a misguided use of asymptotic distributional results. Concerning nonparametric hypotheses, we discuss three basic problems for which such difficulties occur: (1) testing a mean (or a moment) under (too) weak distributional assumptions; (2) inference under heteroskedasticity of unknown form; (3) inference in dynamic models with an unlimited number of parameters. Concerning weakly identified models, we stress that valid inference should be based on proper pivotal functions —a condition not satisfied by standard Wald-type methods based on standard errors — and we discuss recent developments in this field, mainly from the viewpoint of building valid tests and confidence sets. The techniques discussed include alternative proposed statistics, bounds, projection, split-sampling, conditioning, Monte Carlo tests. The possibility of deriving a finite-sample distributional theory, robustness to the presence of weak instruments, and robustness to the specification of a model for endogenous explanatory variables are stressed as important criteria assessing alternative procedures.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Jean-Marie Dufour, 2003. "Identification, Weak Instruments and Statistical Inference in Econometrics," CIRANO Working Papers 2003s-49, CIRANO.
  • Handle: RePEc:cir:cirwor:2003s-49
    as

    Download full text from publisher

    File URL: https://cirano.qc.ca/files/publications/2003s-49.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. James G. MacKinnon, 2002. "Bootstrap inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 35(4), pages 615-645, November.
    2. Phillips, Peter C B, 1985. "The Exact Distribution of LIML: II," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(1), pages 21-36, February.
    3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    4. Lynda Khalaf, 2000. "Simulation Based Inference in Simultaneous Equations," Econometric Society World Congress 2000 Contributed Papers 1078, Econometric Society.
    5. McManus, Douglas A. & Nankervis, John C. & Savin, N. E., 1994. "Multiple optima and asymptotic approximations in the partial adjustment model," Journal of Econometrics, Elsevier, vol. 62(2), pages 91-128, June.
    6. Maddala, G S & Jeong, Jinook, 1992. "On the Exact Small Sample Distribution of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 60(1), pages 181-183, January.
    7. Banerjee, Anindya & Dolado, Juan J. & Galbraith, John W. & Hendry, David, 1993. "Co-integration, Error Correction, and the Econometric Analysis of Non-Stationary Data," OUP Catalogue, Oxford University Press, number 9780198288107.
    8. Benoit Perron, 2003. "Semiparametric Weak-Instrument Regressions with an Application to the Risk-Return Tradeoff," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 424-443, May.
    9. Kleibergen, Frank & Zivot, Eric, 2003. "Bayesian and classical approaches to instrumental variable regression," Journal of Econometrics, Elsevier, vol. 114(1), pages 29-72, May.
    10. Hillier, Grant H, 1990. "On the Normalization of Structural Equations: Properties of Direct Estimators," Econometrica, Econometric Society, vol. 58(5), pages 1181-1194, September.
    11. Bekker, Paul & Kleibergen, Frank, 2003. "Finite-Sample Instrumental Variables Inference Using An Asymptotically Pivotal Statistic," Econometric Theory, Cambridge University Press, vol. 19(5), pages 744-753, October.
    12. Alastair R. Hall & Fernanda P. M. Peixe, 2003. "A Consistent Method for the Selection of Relevant Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 22(3), pages 269-287, January.
    13. Joshua D. Angrist & Alan B. Krueger, 1993. "Split Sample Instrumental Variables," Working Papers 699, Princeton University, Department of Economics, Industrial Relations Section..
    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 283-298, May.
    15. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    16. John Bound & David A. Jaeger & Regina Baker, 1993. "The Cure Can Be Worse than the Disease: A Cautionary Tale Regarding Instrumental Variables," NBER Technical Working Papers 0137, National Bureau of Economic Research, Inc.
    17. Dufour, J.M., 1979. "Rank Tests for Serial Dependence," Cahiers de recherche 7815, Universite de Montreal, Departement de sciences economiques.
    18. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    19. E. J. Working, 1927. "What Do Statistical "Demand Curves" Show?," The Quarterly Journal of Economics, Oxford University Press, vol. 41(2), pages 212-235.
    20. Zivot, Eric & Startz, Richard & Nelson, Charles R, 1998. "Valid Confidence Intervals and Inference in the Presence of Weak Instruments," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1119-1146, November.
    21. Hahn, Jinyong & Hausman, Jerry, 2002. "Notes on bias in estimators for simultaneous equation models," Economics Letters, Elsevier, vol. 75(2), pages 237-241, April.
    22. DUFOUR, Jean-Marie & JASIAK, Joanna, 1998. "Finite-Sample Inference Methods for Simultaneous Equations and Models with Unobserved and Generated Regressors," Cahiers de recherche 9812, Universite de Montreal, Departement de sciences economiques.
    23. repec:dgr:rugsom:01f38 is not listed on IDEAS
    24. Benedikt M. Poetscher, 2002. "Lower Risk Bounds and Properties of Confidence Sets for Ill-Posed Estimation Problems with Applications to Spectral Density and Persistence Estimation, Unit Roots, and Estimation of Long Memory Parame," Econometrica, Econometric Society, vol. 70(3), pages 1035-1065, May.
    25. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
    26. Jean-Marie Dufour & Jan F. Kiviet, 1998. "Exact Inference Methods for First-Order Autoregressive Distributed Lag Models," Econometrica, Econometric Society, vol. 66(1), pages 79-104, January.
    27. Horowitz, Joel L., 2001. "The bootstrap and hypothesis tests in econometrics," Journal of Econometrics, Elsevier, vol. 100(1), pages 37-40, January.
    28. 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.
    29. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    30. 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 225-235, April.
    31. Dufour, Jean-Marie & Jasiak, Joann, 2001. "Finite Sample Limited Information Inference Methods for Structural Equations and Models with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(3), pages 815-843, August.
    32. 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.
    33. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    34. Campbell, Bryan & Dufour, Jean-Marie, 1995. "Exact Nonparametric Orthogonality and Random Walk Tests," The Review of Economics and Statistics, MIT Press, vol. 77(1), pages 1-16, February.
    35. Jean-Marie Dufour, 2000. "Économétrie, théorie des tests et philosophie des sciences," CIRANO Working Papers 2000s-47, CIRANO.
    36. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    37. Jean-Marie Dufour, 2001. "Logiques et tests d'hypothèses : réflexions sur les problèmes mal posés en économétrie," CIRANO Working Papers 2001s-40, CIRANO.
    38. Dufour, J.M., 2000. "Econometrie, theorie des tests et philosophie des sciences," Cahiers de recherche 2000-14, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    39. Jean‐Marie Dufour, 1981. "Rank Tests For Serial Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 2(3), pages 117-128, May.
    40. John Shea, 1997. "Instrument Relevance in Multivariate Linear Models: A Simple Measure," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 348-352, May.
    41. 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.
    42. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    43. Sims, Christopher A, 1971. "Discrete Approximations to Continuous Time Distributed Lags in Econometrics," Econometrica, Econometric Society, vol. 39(3), pages 545-563, May.
    44. DUFOUR, Jean-Marie, 2001. "Logique et tests d'hypotheses: reflexions sur les problemes mal poses en econometrie," Cahiers de recherche 2001-15, Universite de Montreal, Departement de sciences economiques.
    45. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    46. Marc Hallin & Jean-Marie Dufour & Ivan Mizera, 1998. "Generalized run tests for heteroscedastic time series," ULB Institutional Repository 2013/2077, ULB -- Universite Libre de Bruxelles.
    47. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
    48. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    49. 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.
    50. Phillips, P.C.B., 1983. "Exact small sample theory in the simultaneous equations model," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 8, pages 449-516, Elsevier.
    51. Dufour, Jean-Marie, 1990. "Exact Tests and Confidence Sets in Linear Regressions with Autocorrelated Errors," Econometrica, Econometric Society, vol. 58(2), pages 475-494, March.
    52. Cochrane, John H., 1991. "A critique of the application of unit root tests," Journal of Economic Dynamics and Control, Elsevier, vol. 15(2), pages 275-284, April.
    53. repec:dgr:rugccs:200109 is not listed on IDEAS
    54. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-1633, November.
    55. Maddala, G S, 1974. "Some Small Sample Evidence on Tests of Significance in Simultaneous Equations Models," Econometrica, Econometric Society, vol. 42(5), pages 841-851, September.
    56. Blough, Stephen R, 1992. "The Relationship between Power and Level for Generic Unit Root Tests in Finite Samples," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(3), pages 295-308, July-Sept.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jean‐Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 36(4), pages 767-808, November.
    2. Dufour, Jean-Marie, 2001. "Logique et tests d’hypothèses," L'Actualité Economique, Société Canadienne de Science Economique, vol. 77(2), pages 171-190, juin.
    3. Jean-Marie Dufour, 2001. "Logiques et tests d'hypothèses : réflexions sur les problèmes mal posés en économétrie," CIRANO Working Papers 2001s-40, CIRANO.
    4. Jean-Marie Dufour & Mohamed Taamouti, 2005. "Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments," Econometrica, Econometric Society, vol. 73(4), pages 1351-1365, July.
    5. 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.
    6. Richard Startz & Charles Nelson & Eric Zivot, 1999. "Improved Inference for the Instrumental Variable Estimator," Working Papers 0039, University of Washington, Department of Economics.
    7. Dufour, Jean-Marie & Khalaf, Lynda & Kichian, Maral, 2006. "Inflation dynamics and the New Keynesian Phillips Curve: An identification robust econometric analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1707-1727.
    8. Donald W.K. Andrews & James H. Stock, 2005. "Inference with Weak Instruments," NBER Technical Working Papers 0313, National Bureau of Economic Research, Inc.
    9. Chao, John & Swanson, Norman R., 2007. "Alternative approximations of the bias and MSE of the IV estimator under weak identification with an application to bias correction," Journal of Econometrics, Elsevier, vol. 137(2), pages 515-555, April.
    10. DUFOUR, Jean-Marie & JASIAK, Joanna, 1998. "Finite-Sample Inference Methods for Simultaneous Equations and Models with Unobserved and Generated Regressors," Cahiers de recherche 9812, Universite de Montreal, Departement de sciences economiques.
    11. Mardi Dungey & Vitali Alexeev & Jing Tian & Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91, pages 1-24, June.
    12. Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91(S1), pages 1-24, June.
    13. Doko Tchatoka, Firmin Sabro, 2012. "Specification Tests with Weak and Invalid Instruments," MPRA Paper 40185, University Library of Munich, Germany.
    14. Russell Davidson & Victoria Zinde‐Walsh, 2017. "Advances in specification testing," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 50(5), pages 1595-1631, December.
    15. Bekker, Paul A. & Lawford, Steve, 2008. "Symmetry-based inference in an instrumental variable setting," Journal of Econometrics, Elsevier, vol. 142(1), pages 28-49, January.
    16. 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.
    17. Lynda Khalaf & Maral Kichian, 2004. "Estimating New Keynesian Phillips Curves Using Exact Methods," Staff Working Papers 04-11, Bank of Canada.
    18. Paul A. Bekker & Jan van der Ploeg, 2000. "Instrumental Variable Estimation Based on Grouped Data," Econometric Society World Congress 2000 Contributed Papers 1862, Econometric Society.
    19. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, September.
    20. 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.

    More about this item

    Keywords

    hypothesis testing; confidence set; confidence interval; identification; testability; asymptotic theory; exact inference; pivotal function; nonparametric model; Bahadur-Savage; heteroskedasticity; serial dependence; unit root; simultaneous equations; structural model; instrumental variable; weak instrument; weak identification; simultaneous inference; projection; split-sample; conditional test; Monte Carlo test; bootstrap; test d'hypothèse; région de confiance; intervalle de confiance; identification; testabilité; théorie asymptotique; inférence exacte; fonction pivotale; modèle non-paramétrique; Bahadur-Savage; hétéroscédasticité; dépendance sérielle; racine unitaire; équations simultanées; modèle structurel; variable instrumentale; instrument faible; inférence simultanée; projection; subdivision d'échantillon; test conditionnel; test de Monte Carlo; bootstrap;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

    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:cir:cirwor:2003s-49. 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: . General contact details of provider: https://edirc.repec.org/data/ciranca.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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Webmaster (email available below). General contact details of provider: https://edirc.repec.org/data/ciranca.html .

    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.