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

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  • Francis DiTraglia

    () (Department of Economics, University of Pennsylvania)

Abstract

Infinite 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 DiTraglia, 2011. "Using Invalid Instruments on Purpose: Focused Moment Selection and Averaging for GMM, Second Version," PIER Working Paper Archive 15-027, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 10 Aug 2015.
  • Handle: RePEc:pen:papers:15-027
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    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. 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.
    3. 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.
    4. 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.
    5. Donald, Stephen G & Newey, Whitney K, 2001. "Choosing the Number of Instruments," Econometrica, Econometric Society, vol. 69(5), pages 1161-1191, September.
    6. Xiao, Zhiguo, 2010. "The weighted method of moments approach for moment condition models," Economics Letters, Elsevier, vol. 107(2), pages 183-186, May.
    7. Guido Kuersteiner & Ryo Okui, 2010. "Constructing Optimal Instruments by First-Stage Prediction Averaging," Econometrica, Econometric Society, vol. 78(2), pages 697-718, March.
    8. 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.
    9. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(2), pages 241-257, June.
    10. 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.
    11. 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.
    12. Berkowitz, Daniel & Caner, Mehmet & Fang, Ying, 2008. "Are "Nearly Exogenous Instruments" reliable?," Economics Letters, Elsevier, vol. 101(1), pages 20-23, October.
    13. 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.
    14. McCloskey, Adam, 2017. "Bonferroni-based size-correction for nonstandard testing problems," Journal of Econometrics, Elsevier, vol. 200(1), pages 17-35.
    15. Leeb, Hannes & Pötscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(1), pages 21-59, February.
    16. Guggenberger, Patrik, 2012. "On The Asymptotic Size Distortion Of Tests When Instruments Locally Violate The Exogeneity Assumption," Econometric Theory, Cambridge University Press, vol. 28(2), pages 387-421, April.
    17. 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.
    18. 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.
    19. Kabaila, Paul, 1998. "Valid Confidence Intervals In Regression After Variable Selection," Econometric Theory, Cambridge University Press, vol. 14(4), pages 463-482, August.
    20. 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.
    21. Liao, Zhipeng, 2013. "Adaptive Gmm Shrinkage Estimation With Consistent Moment Selection," Econometric Theory, Cambridge University Press, vol. 29(5), pages 857-904, October.
    22. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, vol. 29(3), pages 229-256, September.
    23. 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.
    24. Schorfheide, Frank, 2005. "VAR forecasting under misspecification," Journal of Econometrics, Elsevier, vol. 128(1), pages 99-136, September.
    25. 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.
    26. 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.
    27. Eddelbuettel, Dirk & Francois, Romain, 2011. "Rcpp: Seamless R and C++ Integration," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i08).
    28. 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(6), pages 923-943, December.
    29. 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.
    30. 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.
    31. 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.
    32. Caner, Mehmet, 2014. "Near exogeneity and weak identification in generalized empirical likelihood estimators: Many moment asymptotics," Journal of Econometrics, Elsevier, vol. 182(2), pages 247-268.
    33. 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.
    34. Claeskens, Gerda & Hjort, Nils Lid, 2008. "Minimizing Average Risk In Regression Models," Econometric Theory, Cambridge University Press, vol. 24(2), pages 493-527, April.
    35. Berkowitz, Daniel & Caner, Mehmet & Fang, Ying, 2012. "The validity of instruments revisited," Journal of Econometrics, Elsevier, vol. 166(2), pages 255-266.
    36. 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.
    37. 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.
    38. Guggenberger, Patrik, 2010. "The Impact Of A Hausman Pretest On The Asymptotic Size Of A Hypothesis Test," Econometric Theory, Cambridge University Press, vol. 26(2), pages 369-382, April.
    39. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(3), pages 458-467, December.
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    More about this item

    Keywords

    Moment selection; GMM estimation; Model averaging; Focused Information Criterion; Post-selection estimators;
    All these keywords.

    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

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