Nonparametric dynamic panel data models: Kernel estimation and specification testing

Abstract

Motivated by the first differencing method for linear panel data models, we propose a class of iterative local polynomial estimators for nonparametric dynamic panel data models with or without exogeous regressors. The estimators utilize the additive structure of the first-differenced model, the fact that the two additive components have the same functional form, and the unknown function of interest is implicitly defined as a solution of a Fredholm integral equation of the second kind. We establish the uniform consistency and asymptotic normality of the estimators. We also propose a consistent test for the correct specification of linearity in typical dynamic panel data models based on the L 2 distance of our nonparametric estimates and the parametric estimates under the linear restriction. We derive the asymptotic distributions of the test statistic under the null hypothesis and a sequence of Pitman local alternatives, and prove its consistency against global alternatives.Simulations suggest that the proposed estimators and tests perform well in finite samples. We apply our new methods to study the relation between economic growth, initial economic condition and capital accumulation and find the nonlinear relation between economic growth and initial economic condition.

Specification Test for Panel Data Models with Interactive Fixed Effects

“…Solow (1956) argues there is no association between the two and Jones (1995) confirms the point empirically. The endogenous growth model predicts a positive relation and the argument is reinforced by Bond, Leblebicioglu and Schiantarelli (2010)'s Su and Lu (2012). Su and Lu (2012) use a short panel data with N = 71 and T = 4 which only allows for additive fixed effects as in traditional panel data models.…”

“…The endogenous growth model predicts a positive relation and the argument is reinforced by Bond, Leblebicioglu and Schiantarelli (2010)'s Su and Lu (2012). Su and Lu (2012) use a short panel data with N = 71 and T = 4 which only allows for additive fixed effects as in traditional panel data models. Our model incorporates cross section dependence and allows for interactive fixed effects using large dimensional panel dataset.…”

Specification test for panel data models with interactive fixed effects

“…Jin and Su (2013) construct a nonparametric test for poolability in nonparametric regression models with IFE. Su and Zhang (2013) extend the PCA estimation of Bai (2009) to nonparametric dynamic panel data models with IFE. Despite the robustness of nonparametric estimates and tests, they are usually subject to slower convergence rates than their parametric counterparts.…”

“…Recently nonparametric panel data models with IFE have started to receive attention; see Freyberger (2012), Su and Jin (2012), Jin and Su (2013), and Su and Zhang (2013). Freyberger (2012) considers identification and sieve estimation of nonparametric panel data models with IFE when  is large and  is fixed.…”

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).…”