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A Consistent Nonparametric Bootstrap Test of Exogeneity

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  • Lee, Jinhyun

Abstract

This paper proposes a novel way of testing exogeneity of an explanatory variable without any parametric assumptions in the presence of a "conditional" instrumental variable. A testable implication is derived that if an explanatory variable is endogenous, the conditional distribution of the outcome given the endogenous variable is not independent of its instrumental variable(s). The test rejects the null hypothesis with probability one if the explanatory variable is endogenous and it detects alternatives converging to the null at a rate n..1=2:We propose a consistent nonparametric bootstrap test to implement this testable implication. We show that the proposed bootstrap test can be asymptotically justi.ed in the sense that it produces asymptotically correct size under the null of exogeneity, and it has unit power asymptotically. Our nonparametric test can be applied to the cases in which the outcome is generated by an additively non-separable structural relation or in which the outcome is discrete, which has not been studied in the literature.

Suggested Citation

  • Lee, Jinhyun, 2013. "A Consistent Nonparametric Bootstrap Test of Exogeneity," SIRE Discussion Papers 2013-95, Scottish Institute for Research in Economics (SIRE).
    • Handle: RePEc:edn:sirdps:512
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    File URL: http://hdl.handle.net/10943/512
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    References listed on IDEAS

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    1. Wu, De-Min, 1973. "Alternative Tests of Independence Between Stochastic Regressors and Disturbances," Econometrica, Econometric Society, vol. 41(4), pages 733-750, July.
    2. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    3. Lavergne, Pascal & Vuong, Quang H, 1996. "Nonparametric Selection of Regressors: The Nonnested Case," Econometrica, Econometric Society, vol. 64(1), pages 207-219, January.
    4. Donald W. K. Andrews, 1997. "A Conditional Kolmogorov Test," Econometrica, Econometric Society, vol. 65(5), pages 1097-1128, September.
    5. Angrist, Joshua D, 1990. "Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records," American Economic Review, American Economic Association, vol. 80(3), pages 313-336, June.
    6. Chesher, Andrew, 1985. "Score tests for zero covariances in recursive linear models for grouped or censored data," Journal of Econometrics, Elsevier, vol. 28(3), pages 291-305, June.
    7. Jinyong Hahn & Geert Ridder, 2011. "Conditional Moment Restrictions and Triangular Simultaneous Equations," The Review of Economics and Statistics, MIT Press, vol. 93(2), pages 683-689, May.
    8. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-890, July.
    9. Richard Blundell & Joel L. Horowitz, 2007. "A Non-Parametric Test of Exogeneity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(4), pages 1035-1058.
    10. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-1458, November.
    11. P. Lavergne & Q.H. Vuong, 1996. "Nonparametric selection of regressors : the nonnested case [[Sélection non paramétrique de régresseurs : le cas de régressions non emboîtées]]," Post-Print hal-02689500, HAL.
    12. Lewbel, Arthur, 1995. "Consistent nonparametric hypothesis tests with an application to Slutsky symmetry," Journal of Econometrics, Elsevier, vol. 67(2), pages 379-401, June.
    13. Rivers, Douglas & Vuong, Quang H., 1988. "Limited information estimators and exogeneity tests for simultaneous probit models," Journal of Econometrics, Elsevier, vol. 39(3), pages 347-366, November.
    14. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, September.
    15. Angrist, Joshua D, 1990. "Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records: Errata," American Economic Review, American Economic Association, vol. 80(5), pages 1284-1286, December.
    16. Chen, Xiaohong & Fan, Yanqin, 1999. "Consistent hypothesis testing in semiparametric and nonparametric models for econometric time series," Journal of Econometrics, Elsevier, vol. 91(2), pages 373-401, August.
    17. Richard W. Blundell & Richard J. Smith, 1989. "Estimation in a Class of Simultaneous Equation Limited Dependent Variable Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(1), pages 37-57.
    18. Ait-Sahalia, Yacine & Bickel, Peter J. & Stoker, Thomas M., 2001. "Goodness-of-fit tests for kernel regression with an application to option implied volatilities," Journal of Econometrics, Elsevier, vol. 105(2), pages 363-412, December.
    19. Grogger, Jeffrey, 1990. "A simple test for exogeneity in probit, logit, and poisson regression models," Economics Letters, Elsevier, vol. 33(4), pages 329-332, August.
    20. Abadie A., 2002. "Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 284-292, March.
    21. Trevor S. Breusch, 1986. "Hypothesis Testing in Unidentified Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 635-651.
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