Estimation in Partially Linear Single-Index Panel Data Models With Fixed Effects

Abstract

In this paper, we consider semiparametric estimation in a partially linear singleindex panel data model with fixed effects. Without taking the difference explicitly, we propose using a semiparametric minimum average variance estimation (SMAVE) based on a dummy-variable method to remove the fixed effects and obtain consistent estimators for both the parameters and the unknown link function. As both the cross section size and the time series length tend to infinity, we not only establish an

Non- and Semi-Parametric Panel Data Models: A Selective Review

“…Choosing any d-dimensional vector β and p-dimensional vector θ with θ = 1 and first nonzero element being positive and following the above iterations, we can obtain initial estimators of β 0 and θ 0 , which is shown to be weakly consistent by Chen et al (2013b). Such initial estimators of β 0 and θ 0 are denoted β and θ, respectively.…”

“…In this section, we will review extensions of these models to the panel data case: single-index panel data models with heterogeneous link functions (Chen et al, 2013a) and partially linear single-index panel data models with fixed effects (Chen et al, 2013b).…”

“…To solve the minimization problem (3.7), Chen et al (2013b) propose the following iterative procedure:…”

“…To address such issues, some more flexible nonlinear modelling frameworks, and nonparametric and semiparametric estimation methodologies have been introduced in recent years by allowing the panel data "speak for themselves". (2006,2010), Wu and Zhang (2006), Li and Racine (2007), Cai and Li (2008), Henderson et al (2008), Mammen et al (2009), Li et al (2011a), Chen et al (2012aChen et al ( , 2012bChen et al ( , 2013aChen et al ( , 2013b, Su and Lu (2013).…”

Partially linear single index models for repeated measurements

“…The PLSiM as a natural extension allows discrete explanatory variables to be modeled in the linear part. See Carroll et al (1997); Chen et al (2013); Liang and Wang (2005); for studies and applications of PLSiM.…”