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Specification testing for conditional moment restrictions under local identification failure

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  • Prosper Dovonon
  • Nikolay Gospodinov

Abstract

In this paper, we study the asymptotic behavior of specification tests in conditional moment restriction models under first‐order local identification failure with dependent data. More specifically, we obtain conditions under which the conventional specification test for conditional moment restrictions retains its standard normal limit when first‐order local identification fails but global identification is still attainable. In the process, we derive some novel intermediate results that include extending the first‐ and second‐order local identification framework to models defined by conditional moment restrictions, establishing the rate of convergence of the GMM estimator and characterizing the asymptotic representation for degenerate U‐statistics under strong mixing dependence. Importantly, the specification test is robust to first‐order local identification failure regardless of the number of directions in which the Jacobian of the conditional moment restrictions is degenerate and remains valid even if the model is first‐order identified.

Suggested Citation

  • Prosper Dovonon & Nikolay Gospodinov, 2024. "Specification testing for conditional moment restrictions under local identification failure," Quantitative Economics, Econometric Society, vol. 15(3), pages 849-891, July.
    • Handle: RePEc:wly:quante:v:15:y:2024:i:3:p:849-891
    DOI: 10.3982/QE2242
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    References listed on IDEAS

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    1. Manuel A. Domínguez & Ignacio N. Lobato, 2004. "Consistent Estimation of Models Defined by Conditional Moment Restrictions," Econometrica, Econometric Society, vol. 72(5), pages 1601-1615, September.
    2. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    3. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, vol. 59(2), pages 307-345, March.
    4. Hansen, Lars Peter, 2013. "Uncertainty Outside and Inside Economic Models," Nobel Prize in Economics documents 2013-7, Nobel Prize Committee.
    5. Matias D. Cattaneo & Michael Jansson & Whitney K. Newey, 2018. "Inference in Linear Regression Models with Many Covariates and Heteroscedasticity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1350-1361, July.
    6. Scott Joslin & Kenneth J. Singleton & Haoxiang Zhu, 2011. "A New Perspective on Gaussian Dynamic Term Structure Models," The Review of Financial Studies, Society for Financial Studies, vol. 24(3), pages 926-970.
    7. Gallant, A. Ronald, 1981. "On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form," Journal of Econometrics, Elsevier, vol. 15(2), pages 211-245, February.
    8. Lee, Ji Hyung & Liao, Zhipeng, 2018. "On Standard Inference For Gmm With Local Identification Failure Of Known Forms," Econometric Theory, Cambridge University Press, vol. 34(4), pages 790-814, August.
    9. Lee, Lung-Fei & Chesher, Andrew, 1986. "Specification testing when score test statistics are identically zero," Journal of Econometrics, Elsevier, vol. 31(2), pages 121-149, March.
    10. Prosper Dovonon & Alastair Hall, 2018. "The Asymptotic Properties of GMM and Indirect Inference under Second-order Identification," CIRANO Working Papers 2018s-37, CIRANO.
    11. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(6), pages 797-834, December.
    12. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 369-380, October.
    13. Richard K. Crump & Nikolay Gospodinov, 2022. "On the Factor Structure of Bond Returns," Econometrica, Econometric Society, vol. 90(1), pages 295-314, January.
    14. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-1458, November.
    15. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, September.
    16. Prosper Dovonon & Eric Renault, 2013. "Testing for Common Conditionally Heteroskedastic Factors," Econometrica, Econometric Society, vol. 81(6), pages 2561-2586, November.
    17. Engle, Robert F. & Ng, Victor K. & Rothschild, Michael, 1990. "Asset pricing with a factor-arch covariance structure : Empirical estimates for treasury bills," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 213-237.
    18. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 393-395, October.
    19. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2003. "Empirical likelihood estimation and consistent tests with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 117(1), pages 55-93, November.
    20. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
    21. Tae Kim & Zhi-Ming Luo & Chiho Kim, 2011. "The central limit theorem for degenerate variable -statistics under dependence," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 683-699.
    22. Sentana, Enrique & Fiorentini, Gabriele, 2001. "Identification, estimation and testing of conditionally heteroskedastic factor models," Journal of Econometrics, Elsevier, vol. 102(2), pages 143-164, June.
    23. Dovonon, Prosper & Hall, Alastair R., 2018. "The asymptotic properties of GMM and indirect inference under second-order identification," Journal of Econometrics, Elsevier, vol. 205(1), pages 76-111.
    24. Potscher, Benedikt M & Prucha, Ingmar R, 1989. "A Uniform Law of Large Numbers for Dependent and Heterogeneous Data Processes," Econometrica, Econometric Society, vol. 57(3), pages 675-683, May.
    25. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    26. de Jong, R.M. & Bierens, H.J., 1994. "On the Limit Behavior of a Chi-Square Type Test if the Number of Conditional Moments Tested Approaches Infinity," Econometric Theory, Cambridge University Press, vol. 10(1), pages 70-90, March.
    27. Domowitz, Ian & White, Halbert, 1982. "Misspecified models with dependent observations," Journal of Econometrics, Elsevier, vol. 20(1), pages 35-58, October.
    28. King, Mervyn & Sentana, Enrique & Wadhwani, Sushil, 1994. "Volatility and Links between National Stock Markets," Econometrica, Econometric Society, vol. 62(4), pages 901-933, July.
    29. Lars Peter Hansen, 2014. "Nobel Lecture: Uncertainty Outside and Inside Economic Models," Journal of Political Economy, University of Chicago Press, vol. 122(5), pages 945-987.
    30. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(1), pages 17-39, February.
    31. Francq, Christian & Zakoïan, Jean-Michel, 2006. "Mixing Properties Of A General Class Of Garch(1,1) Models Without Moment Assumptions On The Observed Process," Econometric Theory, Cambridge University Press, vol. 22(5), pages 815-834, October.
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