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Nonparametric estimation of fixed effects panel data varying coefficient models

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  • Rodriguez-Poo, Juan M.
  • Soberón, Alexandra

Abstract

In this paper, we consider the nonparametric estimation of a varying coefficient fixed effect panel data model. The estimator is based in a within (un-smoothed) transformation of the regression model and then a local linear regression is applied to estimate the unknown varying coefficient functions. It turns out that the standard use of this technique produces a non-negligible asymptotic bias. In order to avoid it, a high dimensional kernel weight is introduced in the estimation procedure. As a consequence, the asymptotic bias is removed but the variance is enlarged, and therefore the estimator shows a very slow rate of convergence. In order to achieve the optimal rate, we propose a one-step backfitting algorithm. The resulting two-step estimator is shown to be asymptotically normal and its rate of convergence is optimal within its class of smoothness functions. It is also oracle efficient. Further, this estimator is compared both theoretically and by Monte-Carlo simulation against other estimators that are based in a within (smoothed) transformation of the regression model. More precisely the profile least-squares estimator proposed in this context in Sun et al. (2009). It turns out that the smoothness in the transformation enlarges the bias and it makes the estimator more difficult to analyze from the statistical point of view. However, the first step estimator, as expected, shows a bad performance when compared against both the two step backfitting algorithm and the profile least-squares estimator.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:133:y:2015:i:c:p:95-122
    DOI: 10.1016/j.jmva.2014.09.008
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    References listed on IDEAS

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    1. Cai, Zongwu & Li, Qi, 2008. "Nonparametric Estimation Of Varying Coefficient Dynamic Panel Data Models," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1321-1342, October.
    2. Martins-Filho, Carlos & Yao, Feng, 2009. "Nonparametric regression estimation with general parametric error covariance," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 309-333, March.
    3. You, Jinhong & Zhou, Xian & Zhou, Yong, 2010. "Statistical inference for panel data semiparametric partially linear regression models with heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1079-1101, May.
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    5. Henderson, Daniel J. & Carroll, Raymond J. & Li, Qi, 2008. "Nonparametric estimation and testing of fixed effects panel data models," Journal of Econometrics, Elsevier, vol. 144(1), pages 257-275, May.
    6. Mammen, Enno & Støve, Bård & Tjøstheim, Dag, 2009. "Nonparametric Additive Models For Panels Of Time Series," Econometric Theory, Cambridge University Press, vol. 25(2), pages 442-481, April.
    7. Haibo Zhou & Jinhong You & Bin Zhou, 2010. "Statistical inference for fixed-effects partially linear regression models with errors in variables," Statistical Papers, Springer, vol. 51(3), pages 629-650, September.
    8. Kusum Mundra, 2005. "Nonparametric Slope Estimators for Fixed-Effect Panel Data," Econometrics 0502008, University Library of Munich, Germany.
    9. 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.
    10. Elias Masry, 1996. "Multivariate Local Polynomial Regression For Time Series:Uniform Strong Consistency And Rates," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(6), pages 571-599, November.
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    12. Juan M. Rodriguez‐Poo & Alexandra Soberon, 2014. "Direct semi‐parametric estimation of fixed effects panel data varying coefficient models," Econometrics Journal, Royal Economic Society, vol. 17(1), pages 107-138, February.
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    Cited by:

    1. Sanying Feng & Tiejun Tong & Sung Nok Chiu, 2023. "Statistical Inference for Partially Linear Varying Coefficient Spatial Autoregressive Panel Data Model," Mathematics, MDPI, vol. 11(22), pages 1-19, November.
    2. Arteaga-Molina, Luis A. & Rodríguez-Poo, Juan M., 2019. "Empirical likelihood based inference for a categorical varying-coefficient panel data model with fixed effects," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 110-124.
    3. 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.
    4. Halder, Shaymal C. & Malikov, Emir, 2020. "Smoothed LSDV estimation of functional-coefficient panel data models with two-way fixed effects," Economics Letters, Elsevier, vol. 192(C).
    5. Phillips, Peter C.B. & Wang, Ying, 2022. "Functional coefficient panel modeling with communal smoothing covariates," Journal of Econometrics, Elsevier, vol. 227(2), pages 371-407.
    6. Feng, Sanying & He, Wenqi & Li, Feng, 2020. "Model detection and estimation for varying coefficient panel data models with fixed effects," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).

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    More about this item

    Keywords

    Varying coefficient models; Fixed effects; Panel data; Local linear regression; Oracle efficient estimator; Within estimator; Profile least squares estimator;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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