Semiparametric trending panel data models with cross-sectional dependence

Abstract

a b s t r a c tA semiparametric fixed effects model is introduced to describe the nonlinear trending phenomenon in panel data analysis and it allows for the cross-sectional dependence in both the regressors and the residuals. A pooled semiparametric profile likelihood dummy variable approach based on the firststage local linear fitting is developed to estimate both the parameter vector and the nonlinear time trend function. As both the time series length T and the cross-sectional size N tend to infinity, the resulting estimator of the parameter vector is asymptotically normal with a root-(NT ) convergence rate.Meanwhile, the asymptotic distribution for the nonparametric estimator of the trend function is also established with a root-(NTh) convergence rate. Two simulated examples are provided to illustrate the finite sample performance of the proposed method. In addition, the proposed model and estimation method are applied to a CPI data set as well as an input-output data set.

Semiparametric Single-Index Panel Data Models with Interactive Fixed Effects: Theory and Practice

“…Due to the presence of the factor structure, the leading term √ kη N T is much slower than k(N T ) −1 , which is a result commonly found in traditional nonparametric panel data models without interactive fixed effects (e.g., Chen et al (2012b) and Dong et al (2015)). The term O P (k −r/2 ) represents the rate of convergence of truncation residual and is quite standard in the literature (e.g., Newey (1997)).…”

“…For the case of cross-sectional or time series data, previous studies have examined the choices of optimal bandwidth and truncation parameter (e.g., Gao et al (2002), Li and Racine (2010) and Li et al (2013)) for nonparametric and varying-coefficient models. For the case of panel data, even the choice of optimal bandwidth (or truncation parameter) alone remains unresolved (see, for example, Sun et al (2009), Su andJin (2012) and Chen et al (2012b)); let alone simultaneous choice of optimal truncation parameter and the number of factors. For single-index panel data models with interactive fixed effects, simultaneous choice of k and m is even more daunting, and thus we will leave it for future work.…”

Partially linear single index models for repeated measurements

“…The pioneering work in this context can be traced back to Severini and Staniswalis (1994), followed by a series of efforts, such as Chen et al (2012); Chen and Jin (2006); Fan and Li (2004); He et al (2005); Carroll (2001, 2006); and Su and Ullah (2006). All of these works focus on the case in which the models either contain one nonparametric component or a summand of nonparametric functions.…”

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

“…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).…”

“…In recent years, many researchers have come up with new ideas to exploit the rich information contained in large panels. The assumption of large dimensional panel is extremely useful in exploring stochastic trends (Phillips and Moon, 1999;Bai et al, 2009) or deterministic trends (Robinson, 2011;Chen et al, 2012b) in econometric analysis of panel data.…”