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

Author

Listed:
  • Anna Mikusheva

    (Harvard University)

  • Brian P. Poi

    () (StataCorp)

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.

Suggested Citation

  • Anna Mikusheva & Brian P. Poi, 2006. "Tests and confidence sets with correct size when instruments are potentially weak," Stata Journal, StataCorp LP, vol. 6(3), pages 335-347, September.
  • Handle: RePEc:tsj:stataj:v:6:y:2006:i:3:p:335-347
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    References listed on IDEAS

    as
    1. Marcelo J. Moreira & Brian P. Poi, 2003. "Implementing tests with correct size in the simultaneous equations model," Stata Journal, StataCorp LP, vol. 3(1), pages 57-70, March.
    2. 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 967-976, July.
    3. 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 518-529, October.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
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    Cited by:

    1. Rockey, James, 2012. "Reconsidering the fiscal effects of constitutions," European Journal of Political Economy, Elsevier, vol. 28(3), pages 313-323.
    2. 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.
    3. Aguirre, Alvaro, 2016. "The risk of civil conflicts as a determinant of political institutions," European Journal of Political Economy, Elsevier, vol. 42(C), pages 36-59.
    4. Chowdhury, Shyamal & Krause, Annabelle & Zimmermann, Klaus F, 2015. "Arsenic Contamination of Drinking Water and Mental Health," CEPR Discussion Papers 10978, C.E.P.R. Discussion Papers.
    5. Carlo Altomonte & Tommaso Aquilante & Gábor Békés & Gianmarco I.P. Ottaviano, 2013. "Internationalization and innovation of firms: evidence and policy," Economic Policy, CEPR;CES;MSH, vol. 28(76), pages 663-700, October.
    6. Bakaki Zorzeta, 2016. "Fossil Fuel Rents: Who Initiates International Crises?," Peace Economics, Peace Science, and Public Policy, De Gruyter, vol. 22(2), pages 173-190, April.
    7. 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.
    8. Klaus Friesenbichler & Michael Peneder, 2016. "Innovation, competition and productivity," The Economics of Transition, The European Bank for Reconstruction and Development, vol. 24(3), pages 535-580, July.
    9. Alessandro Gambini & Alberto Zazzaro, 2013. "Long-lasting bank relationships and growth of firms," Small Business Economics, Springer, vol. 40(4), pages 977-1007, May.
    10. Christopher F Baum, 2006. "An Introduction to Modern Econometrics using Stata," Stata Press books, StataCorp LP, number imeus, April.
    11. González Felipe, 2013. "Can Land Reform Avoid a Left Turn? Evidence from Chile after the Cuban Revolution," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 13(1), pages 31-72, April.
    12. Liu, Gordon G. & Xue, Xindong & Yu, Chenxi & Wang, Yafeng, 2016. "How does social capital matter to the health status of older adults? Evidence from the China Health and Retirement Longitudinal Survey," Economics & Human Biology, Elsevier, vol. 22(C), pages 177-189.
    13. 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.
    14. Böhme, Marcus H. & Persian, Ruth & Stöhr, Tobias, 2015. "Alone but better off? Adult child migration and health of elderly parents in Moldova," Journal of Health Economics, Elsevier, vol. 39(C), pages 211-227.
    15. 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.
    16. Daron Acemoglu & Francisco A. Gallego & James A. Robinson, 2014. "Institutions, Human Capital, and Development ," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 875-912, August.
    17. Austin Nichols, 2007. "Causal inference with observational data," Stata Journal, StataCorp LP, vol. 7(4), pages 507-541, December.
    18. repec:bla:manchs:v:85:y:2017:i:5:p:601-633 is not listed on IDEAS
    19. 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.
    20. Christopher F Baum & Mark E. Schaffer & Steven Stillman, 2007. "Enhanced routines for instrumental variables/GMM estimation and testing," CERT Discussion Papers 0706, Centre for Economic Reform and Transformation, Heriot Watt University.
    21. Mikusheva, Anna, 2010. "Robust confidence sets in the presence of weak instruments," Journal of Econometrics, Elsevier, vol. 157(2), pages 236-247, August.
    22. Klaus S. Friesenbichler & Michael Peneder, 2016. "Innovation, Competition and Productivity. Firm Level Evidence for Eastern Europe and Central Asia," WIFO Working Papers 516, WIFO.

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