Abstract
This paper studies the estimation of the partially linear panel data models, allowing for cross-sectional dependence through a common factors structure. This semiparametric additive partial linear framework, including both linear and nonlinear additive components, is more flexible compared to linear models, and is preferred to a fully nonparametric regression because of the ‘curse of dimensionality’. The consistency and asymptotic normality of the proposed estimators are established for the case where both cross-sectional dimension and temporal dimension go to infinity. The theoretical findings are further supported for small samples via a Monte Carlo study. The results suggest that the proposed method is robust to a wide variety of data generation processes.
Similar content being viewed by others
References
Pesaran M H, Estimation and inference in large heterogeneous panels with multifactor error structure, Econometrica, 2006, 74: 967–1012.
Kapetanios G, Pesaran M H, and Yamagata T, Panels with nonstationary multifactor error structures, Journal of Econometrics, 2011, 160: 326–348.
Pesaran M H and Tosetti E, Large panels with common factors and spatial correlations, Journal of Econometrics 2011, 161: 182–202.
Chudik A, Pesaran M H, and Tosetti E, Weak and strong cross section dependence and estimation of large panels, Econometrics Journal, 2011, 14: 45–90.
Huang X, Nonparametric estimation in large panels with cross-section dependence, Econometric Reviews, 2013, 32(5–6): 754–777.
Su L and Jin S, Sieve estimation of panel data models with cross section dependence, Journal of Econometrics, 2012, 186(1): 222–244.
Cai Z, Fang Y, and Xu Q, Testing capital asset pricing models using functional-coefficient panel data models with cross-sectional dependence, Journal of Econometrics, 2020, https://doi.org/10.1016/j.jeconom.2020.07.018.
Robinson P M, Root-n consistent semiparametric regression, Econometrica, 1988, 56: 931–954.
Li Q and Ullah A, Estimating partially linear panel data models with one-way error components, Econometric Reviews, 1998, 17(2): 145–166.
Cai Z, Chen L, and Fang Y, Semiparametric estimation of partially vary-coefficient dynamic panel data models, Econometric Reviews, 2015, 34(6–10): 695–719.
Chen J, Gao J, and Li D, Semiparametric trending panel data models with cross-sectional dependence, Journal of Econometrics, 2012, 171: 71–85.
Chen M and Yan J, Unbiased CCE estimator for interactive fixed effects panels, Economics Letters, 2019, 175: 1–4.
Su L and Ullah A, Profile likelihood estimation of partially linear panel data models with fixed effects, Economics Letters, 2006, 92(1): 75–81.
Fan J Q and Huang T, Profile likelihood inferences on semi-parametric varying-coefficient partially linear models, Bernoulli, 2005, 11: 1031–1057.
Fan J Q, Huang T, and Li R Z, Analysis of longitudinal data with semiparametric estimation of covariance function, Journal of the American Statistical Association, 2007, 102(478): 623–641.
Su L and Jin S, Profile quasi-maximum likelihood estimation of partially linear spatial autoregressive models, Journal of Econometrics, 2010, 157(1): 18–23.
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was supported by the National Natural Science Foundation of China under Grant Nos. 71703156, 71988101, and 72073126.
This paper was recommended for publication by Editor CAI Zongwu.
Rights and permissions
About this article
Cite this article
Huang, B., Sun, Y. & Wang, S. Estimation of Partially Linear Panel Data Models with Cross-Sectional Dependence. J Syst Sci Complex 34, 2219–2230 (2021). https://doi.org/10.1007/s11424-021-0122-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11424-021-0122-4