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

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Author Info

  • 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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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Frank Kleibergen, 2000. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Tinbergen Institute Discussion Papers 00-055/4, Tinbergen Institute.
    2. Nelson, C. & Startz, R., 1988. "Some Furthere Results On The Exact Small Sample Properties Of The Instrumental Variable Estimator," Working Papers 88-06, University of Washington, Department of Economics.
    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. Donald W.K. Andrews & Marcelo Moreira & James H. Stock, 2004. "Optimal Invariant Similar Tests for Instrumental Variables Regression," NBER Technical Working Papers 0299, National Bureau of Economic Research, Inc.
    5. 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.
    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. 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.
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    Citations

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    Cited by:
    1. Alessandro Gambini & Alberto Zazzaro, 2010. "Long-Lasting Bank Relationships and Growth of Firms," CESifo Working Paper Series 3106, CESifo Group Munich.
    2. 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.
    3. 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.
    4. Daron Acemoglu & Francisco Gallego & James A. Robinson, 2014. "Institutions, Human Capital and Development," Documentos de Trabajo 449, Instituto de Economia. Pontificia Universidad Católica de Chile..
    5. Mikusheva, Anna, 2010. "Robust confidence sets in the presence of weak instruments," Journal of Econometrics, Elsevier, vol. 157(2), pages 236-247, August.
    6. Vieira, Flávio & MacDonald, Ronald & Damasceno, Aderbal, 2012. "The role of institutions in cross-section income and panel data growth models: A deeper investigation on the weakness and proliferation of instruments," Journal of Comparative Economics, Elsevier, vol. 40(1), pages 127-140.
    7. Rockey, James, 2012. "Reconsidering the fiscal effects of constitutions," European Journal of Political Economy, Elsevier, vol. 28(3), pages 313-323.
    8. Emanuele Millemaci & Ferdinando Ofria, 2014. "Kaldor-Verdoorn's law and increasing returns to scale: A comparison across developed countries," Journal of Economic Studies, Emerald Group Publishing, vol. 41(1), pages 140 - 162, January.
    9. 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.
    10. 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.
    11. 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.
    12. Christopher F Baum, 2006. "An Introduction to Modern Econometrics using Stata," Stata Press books, StataCorp LP, number imeus, April.

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