IDEAS home Printed from https://ideas.repec.org/a/taf/emetrv/v36y2017i6-9p818-839.html
   My bibliography  Save this article

Reduced forms and weak instrumentation

Author

Listed:
  • Peter C. B. Phillips

Abstract

This paper develops exact finite sample and asymptotic distributions for a class of reduced form estimators and predictors, allowing for the presence of unidentified or weakly identified structural equations. Weak instrument asymptotic theory is developed directly from finite sample results, unifying earlier findings and showing the usefulness of structural information in making predictions from reduced form systems in applications. Asymptotic results are reported for predictions from models with many weak instruments. Of particular interest is the finding that, in unidentified and weakly identified structural models, partially restricted reduced form predictors have considerably smaller forecast mean square errors than unrestricted reduced forms. These results are related to the use of shrinkage methods in system-wide reduced form estimation.

Suggested Citation

  • Peter C. B. Phillips, 2017. "Reduced forms and weak instrumentation," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 818-839, October.
    • Handle: RePEc:taf:emetrv:v:36:y:2017:i:6-9:p:818-839
    DOI: 10.1080/07474938.2017.1307578
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/07474938.2017.1307578
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/07474938.2017.1307578?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chernozhukov, Victor & Hansen, Christian, 2008. "The reduced form: A simple approach to inference with weak instruments," Economics Letters, Elsevier, vol. 100(1), pages 68-71, July.
    2. Kotlyarova, Yulia & Zinde-Walsh, Victoria, 2006. "Non- and semi-parametric estimation in models with unknown smoothness," Economics Letters, Elsevier, vol. 93(3), pages 379-386, December.
    3. Nelson, Charles R & Startz, Richard, 1990. "The Distribution of the Instrumental Variables Estimator and Its t-Ratio When the Instrument Is a Poor One," The Journal of Business, University of Chicago Press, vol. 63(1), pages 125-140, January.
    4. 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.
    5. Phillips, P C B, 1980. "The Exact Distribution of Instrumental Variable Estimators in an Equation Containing n + 1 Endogenous Variables," Econometrica, Econometric Society, vol. 48(4), pages 861-878, May.
    6. Fan, Yanqin & Ullah, Aman, 1999. "Asymptotic Normality of a Combined Regression Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 191-240, November.
    7. 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.
    8. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    9. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(2), pages 181-240, August.
    10. Emma M. Iglesias & Garry D. A. Phillips, 2012. "Almost Unbiased Estimation in Simultaneous Equation Models With Strong and/or Weak Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 505-520, June.
    11. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    12. Bruce E. Hansen, 2014. "Model averaging, asymptotic risk, and regressor groups," Quantitative Economics, Econometric Society, vol. 5(3), pages 495-530, November.
    13. Knight, John L., 1977. "On the existence of moments of the partially restricted reduced-form estimators from a simultaneous-equation model," Journal of Econometrics, Elsevier, vol. 5(3), pages 315-321, May.
    14. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
    15. Carlo V. Fiorio & Vassilis A. Hajivassiliou & Peter C. B. Phillips, 2010. "Bimodal t-ratios: the impact of thick tails on inference," Econometrics Journal, Royal Economic Society, vol. 13(2), pages 271-289, July.
    16. Maasoumi, Esfandiar, 1978. "A Modified Stein-like Estimator for the Reduced Form Coefficients of Simultaneous Equations," Econometrica, Econometric Society, vol. 46(3), pages 695-703, May.
    17. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Christopher L. Skeels & Frank Windmeijer, 2018. "On the Stock–Yogo Tables," Econometrics, MDPI, vol. 6(4), pages 1-23, November.
    2. Phillips, Peter C.B. & Gao, Wayne Yuan, 2017. "Structural inference from reduced forms with many instruments," Journal of Econometrics, Elsevier, vol. 199(2), pages 96-116.

    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. Phillips, Peter C.B. & Gao, Wayne Yuan, 2017. "Structural inference from reduced forms with many instruments," Journal of Econometrics, Elsevier, vol. 199(2), pages 96-116.
    2. D.S. Poskitt & C.L. Skeels, 2005. "Small Concentration Asymptotics and Instrumental Variables Inference," Department of Economics - Working Papers Series 948, The University of Melbourne.
    3. D. S. Poskitt & C. L. Skeels, 2004. "Approximating the Distribution of the Instrumental Variables Estimator when the Concentration Parameter is Small," Monash Econometrics and Business Statistics Working Papers 19/04, Monash University, Department of Econometrics and Business Statistics.
    4. Poskitt, D.S. & Skeels, C.L., 2007. "Approximating the distribution of the two-stage least squares estimator when the concentration parameter is small," Journal of Econometrics, Elsevier, vol. 139(1), pages 217-236, July.
    5. Keisuke Hirano & Jack R. Porter, 2015. "Location Properties of Point Estimators in Linear Instrumental Variables and Related Models," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 720-733, December.
    6. Phillips, Peter C.B., 2003. "Vision And Influence In Econometrics: John Denis Sargan," Econometric Theory, Cambridge University Press, vol. 19(3), pages 495-511, June.
    7. Christopher L. Skeels & Frank Windmeijer, 2018. "On the Stock–Yogo Tables," Econometrics, MDPI, vol. 6(4), pages 1-23, November.
    8. Emma M. Iglesias & Garry D. A. Phillips, 2012. "Almost Unbiased Estimation in Simultaneous Equation Models With Strong and/or Weak Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 505-520, June.
    9. 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.
    10. Chirok Han & Peter C. B. Phillips, 2006. "GMM with Many Moment Conditions," Econometrica, Econometric Society, vol. 74(1), pages 147-192, January.
    11. 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.
    12. Iglesias Emma M., 2011. "Constrained k-class Estimators in the Presence of Weak Instruments," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(4), pages 1-13, September.
    13. Guilhem Bascle, 2008. "Controlling for endogeneity with instrumental variables in strategic management research," Post-Print hal-00576795, HAL.
    14. Ali Habibnia & Esfandiar Maasoumi, 2021. "Forecasting in Big Data Environments: An Adaptable and Automated Shrinkage Estimation of Neural Networks (AAShNet)," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 363-381, December.
    15. Ribeiro, André L.P. & Hotta, Luiz K., 2013. "An analysis of contagion among Asian countries using the canonical model of contagion," International Review of Financial Analysis, Elsevier, vol. 29(C), pages 62-69.
    16. Bun, Maurice J.G. & Windmeijer, Frank, 2011. "A comparison of bias approximations for the two-stage least squares (2SLS) estimator," Economics Letters, Elsevier, vol. 113(1), pages 76-79, October.
    17. 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.
    18. Cai, Zongwu & Fang, Ying & Su, Jia, 2012. "Reducing asymptotic bias of weak instrumental estimation using independently repeated cross-sectional information," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 180-185.
    19. Wang, Wenjie, 2021. "Wild Bootstrap for Instrumental Variables Regression with Weak Instruments and Few Clusters," MPRA Paper 106227, University Library of Munich, Germany.
    20. Phillips, Peter C.B., 2006. "A Remark On Bimodality And Weak Instrumentation In Structural Equation Estimation," Econometric Theory, Cambridge University Press, vol. 22(5), pages 947-960, October.

    More about this item

    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:taf:emetrv:v:36:y:2017:i:6-9:p:818-839. See general information about how to correct material in RePEc.

    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: the person in charge (email available below). General contact details of provider: http://www.tandfonline.com/LECR20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.