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LM-BIC Model Selection in Semiparametric Models

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  • Ivan Korolev

Abstract

This paper studies model selection in semiparametric econometric models. It develops a consistent series-based model selection procedure based on a Bayesian Information Criterion (BIC) type criterion to select between several classes of models. The procedure selects a model by minimizing the semiparametric Lagrange Multiplier (LM) type test statistic from Korolev (2018) but additionally rewards simpler models. The paper also develops consistent upward testing (UT) and downward testing (DT) procedures based on the semiparametric LM type specification test. The proposed semiparametric LM-BIC and UT procedures demonstrate good performance in simulations. To illustrate the use of these semiparametric model selection procedures, I apply them to the parametric and semiparametric gasoline demand specifications from Yatchew and No (2001). The LM-BIC procedure selects the semiparametric specification that is nonparametric in age but parametric in all other variables, which is in line with the conclusions in Yatchew and No (2001). The results of the UT and DT procedures heavily depend on the choice of tuning parameters and assumptions about the model errors.

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  • Ivan Korolev, 2018. "LM-BIC Model Selection in Semiparametric Models," Papers 1811.10676, arXiv.org.
    • Handle: RePEc:arx:papers:1811.10676
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Ivan Korolev, 2018. "A Consistent Heteroskedasticity Robust LM Type Specification Test for Semiparametric Models," Papers 1810.07620, arXiv.org, revised Nov 2019.
    3. Hong, Han & Preston, Bruce & Shum, Matthew, 2003. "Generalized Empirical Likelihood–Based Model Selection Criteria For Moment Condition Models," Econometric Theory, Cambridge University Press, vol. 19(6), pages 923-943, December.
    4. Hausman, Jerry A & Newey, Whitney K, 1995. "Nonparametric Estimation of Exact Consumers Surplus and Deadweight Loss," Econometrica, Econometric Society, vol. 63(6), pages 1445-1476, November.
    5. Caner, Mehmet, 2009. "Lasso-Type Gmm Estimator," Econometric Theory, Cambridge University Press, vol. 25(1), pages 270-290, February.
    6. Donald W. K. Andrews, 1999. "Consistent Moment Selection Procedures for Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 67(3), pages 543-564, May.
    7. Liao, Zhipeng, 2013. "Adaptive Gmm Shrinkage Estimation With Consistent Moment Selection," Econometric Theory, Cambridge University Press, vol. 29(5), pages 857-904, October.
    8. Lian, Heng, 2014. "Semiparametric Bayesian information criterion for model selection in ultra-high dimensional additive models," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 304-310.
    9. Andrews, Donald W. K. & Lu, Biao, 2001. "Consistent model and moment selection procedures for GMM estimation with application to dynamic panel data models," Journal of Econometrics, Elsevier, vol. 101(1), pages 123-164, March.
    10. Adonis Yatchew & Joungyeo Angela No, 2001. "Household Gasoline Demand in Canada," Econometrica, Econometric Society, vol. 69(6), pages 1697-1709, November.
    11. Richard Schmalensee & Thomas M. Stoker, 1999. "Household Gasoline Demand in the United States," Econometrica, Econometric Society, vol. 67(3), pages 645-662, May.
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    Cited by:

    1. Ivan Korolev, 2018. "A Consistent Heteroskedasticity Robust LM Type Specification Test for Semiparametric Models," Papers 1810.07620, arXiv.org, revised Nov 2019.

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