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Nonparametric dynamic panel data models: Kernel estimation and specification testing

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  • Su, Liangjun
  • Lu, Xun

Abstract

Motivated by the first-differencing method for linear panel data models, we propose a class of iterative local polynomial estimators for nonparametric dynamic panel data models with or without exogenous regressors. The estimators utilize the additive structure of the first-differenced model—the fact that the two additive components have the same functional form, and the unknown function of interest is implicitly defined as a solution of a Fredholm integral equation of the second kind. We establish the uniform consistency and asymptotic normality of the estimators. We also propose a consistent test for the correct specification of linearity in typical dynamic panel data models based on the L2 distance of our nonparametric estimates and the parametric estimates under the linear restriction. We derive the asymptotic distributions of the test statistic under the null hypothesis and a sequence of Pitman local alternatives, and prove its consistency against global alternatives. Simulations suggest that the proposed estimators and tests perform well for finite samples. We apply our new method to study the relationships among economic growth, the initial economic condition and capital accumulation, and find a significant nonlinear relation between economic growth and the initial economic condition.

Suggested Citation

  • Su, Liangjun & Lu, Xun, 2013. "Nonparametric dynamic panel data models: Kernel estimation and specification testing," Journal of Econometrics, Elsevier, vol. 176(2), pages 112-133.
  • Handle: RePEc:eee:econom:v:176:y:2013:i:2:p:112-133
    DOI: 10.1016/j.jeconom.2013.04.020
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    References listed on IDEAS

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    Cited by:

    1. Su, Liangjun & Jin, Sainan & Zhang, Yonghui, 2015. "Specification test for panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 186(1), pages 222-244.
    2. Rodriguez-Poo, Juan M. & Soberón, Alexandra, 2015. "Nonparametric estimation of fixed effects panel data varying coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 95-122.
    3. Christopher F. Parmeter & Jeffrey S. Racine, 2018. "Nonparametric Estimation and Inference for Panel Data Models," Department of Economics Working Papers 2018-02, McMaster University.
    4. Li, Cong & Liang, Zhongwen, 2015. "Asymptotics for nonparametric and semiparametric fixed effects panel models," Journal of Econometrics, Elsevier, vol. 185(2), pages 420-434.
    5. Sainan Jin & Liangjun Su & Yonghui Zhang, 2015. "Nonparametric testing for anomaly effects in empirical asset pricing models," Empirical Economics, Springer, vol. 48(1), pages 9-36, February.
    6. Green, Carl & Long, Wei & Hsiao, Cheng, 2015. "Testing error serial correlation in fixed effects nonparametric panel data models," Journal of Econometrics, Elsevier, vol. 188(2), pages 466-473.
    7. Juan Rodriguez-Poo & Alexandra Soberón, 2015. "Differencing techniques in semi-parametric panel data varying coefficient models with fixed effects: a Monte Carlo study," Computational Statistics, Springer, vol. 30(3), pages 885-906, September.
    8. repec:eee:csdana:v:116:y:2017:i:c:p:79-105 is not listed on IDEAS
    9. repec:kap:enreec:v:69:y:2018:i:1:d:10.1007_s10640-016-0071-x is not listed on IDEAS
    10. Li, Hongjun & Li, Qi & Liu, Ruixuan, 2016. "Consistent model specification tests based on k-nearest-neighbor estimation method," Journal of Econometrics, Elsevier, vol. 194(1), pages 187-202.

    More about this item

    Keywords

    Additive models; Dynamic panel data models; Fredholm integral equation; Iterative estimator; Linearity; Local polynomial regression; Specification test;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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