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Direct semi‐parametric estimation of fixed effects panel data varying coefficient models

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  • Juan M. Rodriguez‐Poo
  • Alexandra Soberon

Abstract

In this paper, we present a new technique to estimate varying coefficient models of unknown form in a panel data framework where individual effects are arbitrarily correlated with the explanatory variables in an unknown way. The estimator is based on first differences and then a local linear regression is applied to estimate the unknown coefficients. To avoid a non‐negligible asymptotic bias, we need to introduce a higher‐dimensional kernel weight. This enables us to remove the bias at the price of enlarging the variance term and, hence, achieving a slower rate of convergence. To overcome this problem, we propose a one‐step backfitting algorithm that enables the resulting estimator to achieve optimal rates of convergence for this type of problem. It also exhibits the so‐called oracle efficiency property. We also obtain the asymptotic distribution. Because the estimation procedure depends on the choice of a bandwidth matrix, we also provide a method to compute this matrix empirically. The Monte Carlo results indicate the good performance of the estimator in finite samples.

Suggested Citation

  • 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.
  • Handle: RePEc:wly:emjrnl:v:17:y:2014:i:1:p:107-138
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    File URL: http://hdl.handle.net/10.1111/ectj.12022
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    Cited by:

    1. Feng, Guohua & Gao, Jiti & Peng, Bin & Zhang, Xiaohui, 2017. "A varying-coefficient panel data model with fixed effects: Theory and an application to US commercial banks," Journal of Econometrics, Elsevier, vol. 196(1), pages 68-82.
    2. Hu, Xuemei, 2017. "Semi-parametric inference for semi-varying coefficient panel data model with individual effects," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 262-281.
    3. 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.
    4. Price, Sarah & Zhang, Xiaohui & Spencer, Anne, 2020. "Measuring the impact of national guidelines: What methods can be used to uncover time-varying effects for healthcare evaluations?," Social Science & Medicine, Elsevier, vol. 258(C).
    5. Zhang, Shangfeng & Zhang, Chaojie & Su, Zitian & Zhu, Mengyue & Ren, Huiru, 2023. "New structural economic growth model and labor income share," Journal of Business Research, Elsevier, vol. 160(C).
    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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