IDEAS home Printed from https://ideas.repec.org/p/pen/papers/14-045.html
   My bibliography  Save this paper

Using Invalid Instruments on Purpose: Focused Moment Selection and Averaging for GMM, Second Version

Author

Listed:
  • Francis J. DiTraglia

    () (Department of Economics, University of Pennsylvania)

Abstract

In finite samples, the use of a slightly endogenous but highly relevant instrument can reduce mean-squared error (MSE). Building on this observation, I propose a moment selection criterion for GMM in which moment conditions are chosen based on the MSE of their associated estimators rather than their validity: the focused moment selection criterion (FMSC). I then show how the framework used to derive the FMSC can address the problem of inference post-moment selection. Treating post-selection estimators as a special case of moment-averaging, in which estimators based on different moment sets are given data-dependent weights, I propose a simulation-based procedure to construct valid confidence intervals for a variety of formal and informal moment-selection and averaging procedures. Both the FMSC and confidence interval procedure perform well in simulations. I conclude with an empirical example examining the effect of instrument selection on the estimated relationship between malaria transmission and income.

Suggested Citation

  • Francis J. DiTraglia, 2011. "Using Invalid Instruments on Purpose: Focused Moment Selection and Averaging for GMM, Second Version," PIER Working Paper Archive 14-045, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 09 Dec 2014.
  • Handle: RePEc:pen:papers:14-045
    as

    Download full text from publisher

    File URL: https://economics.sas.upenn.edu/sites/default/files/filevault/14-045.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Matei Demetrescu & Uwe Hassler & Vladimir Kuzin, 2011. "Pitfalls of post-model-selection testing: experimental quantification," Empirical Economics, Springer, vol. 40(2), pages 359-372, April.
    2. Daron Acemoglu & Simon Johnson & James A. Robinson, 2001. "The Colonial Origins of Comparative Development: An Empirical Investigation," American Economic Review, American Economic Association, vol. 91(5), pages 1369-1401, December.
    3. Dani Rodrik & Arvind Subramanian & Francesco Trebbi, 2004. "Institutions Rule: The Primacy of Institutions Over Geography and Integration in Economic Development," Journal of Economic Growth, Springer, vol. 9(2), pages 131-165, June.
    4. Eddelbuettel, Dirk & Sanderson, Conrad, 2014. "RcppArmadillo: Accelerating R with high-performance C++ linear algebra," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1054-1063.
    5. Gerda Claeskens & Christophe Croux & Johan Van Kerckhoven, 2006. "Variable Selection for Logistic Regression Using a Prediction-Focused Information Criterion," Biometrics, The International Biometric Society, vol. 62(4), pages 972-979, December.
    6. Hong, Han & Preston, Bruce & Shum, Matthew, 2003. "Generalized Empirical Likelihood Based Model Selection Criteria For Moment Condition Models," Econometric Theory, Cambridge University Press, vol. 19(06), pages 923-943, December.
    7. Donald, Stephen G & Newey, Whitney K, 2001. "Choosing the Number of Instruments," Econometrica, Econometric Society, vol. 69(5), pages 1161-1191, September.
    8. Xiao, Zhiguo, 2010. "The weighted method of moments approach for moment condition models," Economics Letters, Elsevier, vol. 107(2), pages 183-186, May.
    9. Guido Kuersteiner & Ryo Okui, 2010. "Constructing Optimal Instruments by First-Stage Prediction Averaging," Econometrica, Econometric Society, vol. 78(2), pages 697-718, March.
    10. Kai Carstensen & Erich Gundlach, 2006. "The Primacy of Institutions Reconsidered: Direct Income Effects of Malaria Prevalence," World Bank Economic Review, World Bank Group, vol. 20(3), pages 309-339.
    11. Aart Kraay, 2012. "Instrumental variables regressions with uncertain exclusion restrictions: a Bayesian approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(1), pages 108-128, January.
    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. Kabaila, Paul & Leeb, Hannes, 2006. "On the Large-Sample Minimal Coverage Probability of Confidence Intervals After Model Selection," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 619-629, June.
    14. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(02), pages 241-257, June.
    15. Yuhong Yang, 2005. "Can the strengths of AIC and BIC be shared? A conflict between model indentification and regression estimation," Biometrika, Biometrika Trust, vol. 92(4), pages 937-950, December.
    16. Leeb, Hannes & Potscher, Benedikt M., 2008. "Sparse estimators and the oracle property, or the return of Hodges' estimator," Journal of Econometrics, Elsevier, vol. 142(1), pages 201-211, January.
    17. Xu Cheng & Zhipeng Liao, 2011. "Select the Valid and Relevant Moments: An Information-Based LASSO for GMM with Many Moments, Second Version," PIER Working Paper Archive 13-062, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 21 Oct 2013.
    18. repec:eee:econom:v:200:y:2017:i:1:p:17-35 is not listed on IDEAS
    19. Judge, George G. & Mittelhammer, Ron C., 2007. "Estimation and inference in the case of competing sets of estimating equations," Journal of Econometrics, Elsevier, vol. 138(2), pages 513-531, June.
    20. Leeb, Hannes & P tscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(01), pages 21-59, February.
    21. Claeskens, Gerda & Hjort, Nils Lid, 2008. "Minimizing Average Risk In Regression Models," Econometric Theory, Cambridge University Press, vol. 24(02), pages 493-527, April.
    22. Timothy G. Conley & Christian B. Hansen & Peter E. Rossi, 2012. "Plausibly Exogenous," The Review of Economics and Statistics, MIT Press, vol. 94(1), pages 260-272, February.
    23. 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.
    24. Berkowitz, Daniel & Caner, Mehmet & Fang, Ying, 2012. "The validity of instruments revisited," Journal of Econometrics, Elsevier, vol. 166(2), pages 255-266.
    25. Donald W. K. Andrews, 1999. "Consistent Moment Selection Procedures for Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 67(3), pages 543-564, May.
    26. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2009. "Choosing instrumental variables in conditional moment restriction models," Journal of Econometrics, Elsevier, vol. 152(1), pages 28-36, September.
    27. Easterly, William & Levine, Ross, 2003. "Tropics, germs, and crops: how endowments influence economic development," Journal of Monetary Economics, Elsevier, vol. 50(1), pages 3-39, January.
    28. Kabaila, Paul, 1998. "Valid Confidence Intervals In Regression After Variable Selection," Econometric Theory, Cambridge University Press, vol. 14(04), pages 463-482, August.
    29. 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.
    30. Liao, Zhipeng, 2013. "Adaptive Gmm Shrinkage Estimation With Consistent Moment Selection," Econometric Theory, Cambridge University Press, vol. 29(05), pages 857-904, October.
    31. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, vol. 29(3), pages 229-256, September.
    32. Xu Cheng & Zhipeng Liao & Ruoyao Shi, 2013. "Uniform Asymptotic Risk of Averaging GMM Estimator Robust to Misspecification, Second Version," PIER Working Paper Archive 15-017, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 25 Mar 2015.
    33. Andrews, Donald W. K. & Lu, Biao, 2001. "Consistent model and moment selection procedures for GMM estimation with application to dynamic panel data models," Journal of Econometrics, Elsevier, vol. 101(1), pages 123-164, March.
    34. Guggenberger, Patrik, 2010. "The Impact Of A Hausman Pretest On The Asymptotic Size Of A Hypothesis Test," Econometric Theory, Cambridge University Press, vol. 26(02), pages 369-382, April.
    35. Jeffrey D. Sachs, 2003. "Institutions Don't Rule: Direct Effects of Geography on Per Capita Income," NBER Working Papers 9490, National Bureau of Economic Research, Inc.
    36. Schorfheide, Frank, 2005. "VAR forecasting under misspecification," Journal of Econometrics, Elsevier, vol. 128(1), pages 99-136, September.
    37. Patrik Guggenberger & Gitanjali Kumar, 2012. "On the size distortion of tests after an overidentifying restrictions pretest," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(7), pages 1138-1160, November.
    38. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(03), pages 458-467, December.
    39. McCloskey, Adam, 2017. "Bonferroni-based size-correction for nonstandard testing problems," Journal of Econometrics, Elsevier, vol. 200(1), pages 17-35.
    40. Eddelbuettel, Dirk & Francois, Romain, 2011. "Rcpp: Seamless R and C++ Integration," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i08).
    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. Hansen, Bruce E., 2016. "Efficient shrinkage in parametric models," Journal of Econometrics, Elsevier, vol. 190(1), pages 115-132.
    2. repec:taf:emetrv:v:36:y:2017:i:6-9:p:840-852 is not listed on IDEAS
    3. Xu Cheng & Zhipeng Liao & Ruoyao Shi, 2013. "Uniform Asymptotic Risk of Averaging GMM Estimator Robust to Misspecification, Second Version," PIER Working Paper Archive 15-017, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 25 Mar 2015.

    More about this item

    Keywords

    Moment selection; GMM estimation; Model averaging; Focused Information Criterion; Post-selection estimators;

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

    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:pen:papers:14-045. 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: (Administrator) or (Rebekah McClure). General contact details of provider: http://edirc.repec.org/data/deupaus.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.