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Tests and confidence sets with correct size when instruments are potentially weak

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  • Anna Mikusheva

    (Harvard University)

  • Brian P. Poi

    ()
    (StataCorp)

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    Abstract

    We consider inference in the linear regression model with one endoge- nous variable and potentially weak instruments. We construct confidence sets for the coefficient on the endogenous variable by inverting the Anderson-Rubin, Lagrange multiplier, and conditional likelihood-ratio tests. Our confidence sets have correct coverage probabilities even when the instruments are weak. We propose a numerically simple algorithm for finding these confidence sets, and we present a Stata command that supersedes the one presented in Moreira and Poi (Stata Journal 3: 57–70). Copyright 2006 by StataCorp LP.

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    Bibliographic Info

    Article provided by StataCorp LP in its journal Stata Journal.

    Volume (Year): 6 (2006)
    Issue (Month): 3 (September)
    Pages: 335-347

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    Handle: RePEc:tsj:stataj:v:6:y:2006:i:3:p:335-347

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    Related research

    Keywords: condivreg; instrumental variables; weak instruments; confidence set; similar test;

    References

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    1. Andrews, Donald W.K. & Moreira, Marcelo J. & Stock, James H., 2007. "Performance of conditional Wald tests in IV regression with weak instruments," Journal of Econometrics, Elsevier, vol. 139(1), pages 116-132, July.
    2. 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.
    3. Marcelo J. Moreira & Brian P. Poi, 2003. "Implementing Tests with Correct Size in the Simultaneous Equation Model," Harvard Institute of Economic Research Working Papers 1993, Harvard - Institute of Economic Research.
    4. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
    5. Nelson, Charles R & Startz, Richard, 1990. "Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 58(4), pages 967-76, July.
    6. 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 518-29, October.
    7. Moreira, Marcelo J., 2009. "Tests with correct size when instruments can be arbitrarily weak," Journal of Econometrics, Elsevier, vol. 152(2), pages 131-140, October.
    8. Donald W.K. Andrews & Marcelo J. Moreira & James H. Stock, 2004. "Optimal Invariant Similar Tests for Instrumental Variables Regression," Cowles Foundation Discussion Papers 1476, Cowles Foundation for Research in Economics, Yale University.
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    Cited by:
    1. Carlo Altomonte & Tommaso Aquilante & Gábor Békés & Gianmarco I. P. Ottaviano, 2014. "Internationalization and Innovation of Firms: Evidence and Policy," CEP Special Papers 032, Centre for Economic Performance, LSE.
    2. Christopher F Baum & Mark E. Schaffer & Steven Stillman, 2007. "Enhanced routines for instrumental variables/GMM estimation and testing," Boston College Working Papers in Economics 667, Boston College Department of Economics, revised 05 Sep 2007.
    3. Emanuele Millemaci & Ferdinando Ofria, 2012. "Kaldor-Verdoorn's Law and Increasing Returns to Scale: A Comparison Across Developed Countries," Working Papers 2012.92, Fondazione Eni Enrico Mattei.
    4. Jason M. Fletcher, 2010. "Social interactions and smoking: evidence using multiple student cohorts, instrumental variables, and school fixed effects," Health Economics, John Wiley & Sons, Ltd., vol. 19(4), pages 466-484.
    5. Rockey, James, 2012. "Reconsidering the fiscal effects of constitutions," European Journal of Political Economy, Elsevier, vol. 28(3), pages 313-323.
    6. MacDonald, Ronald & Vieira, Flávio & Damasceno, Aderbal, 2010. "The Role of Institutions in Cross-Section Income and Panel Data Growth Models: A Deeper Investigation on the Weakness and Proliferation of Instruments," SIRE Discussion Papers 2010-50, Scottish Institute for Research in Economics (SIRE).
    7. Daron Acemoglu & Francisco Gallego & James A. Robinson, 2014. "Institutions, Human Capital and Development," NBER Working Papers 19933, National Bureau of Economic Research, Inc.
    8. Mikusheva, Anna, 2013. "Survey on statistical inferences in weakly-identified instrumental variable models," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 29(1), pages 117-131.
    9. Alessandro Gambini & Alberto Zazzaro, 2010. "Long-Lasting Bank Relationships and Growth of Firms," CESifo Working Paper Series 3106, CESifo Group Munich.
    10. Mikusheva, Anna, 2010. "Robust confidence sets in the presence of weak instruments," Journal of Econometrics, Elsevier, vol. 157(2), pages 236-247, August.
    11. Christopher F Baum, 2006. "An Introduction to Modern Econometrics using Stata," Stata Press books, StataCorp LP, number imeus, March.
    12. Austin Nichols, 2007. "Review of An Introduction to Modern Econometrics Using Stata by Baum," Stata Journal, StataCorp LP, vol. 7(1), pages 131-136, February.

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