Semiparametric single-index panel data models with cross-sectional dependence

Abstract

a b s t r a c tIn this paper, we consider a semiparametric single-index panel data model with cross-sectional dependence and stationarity. Meanwhile, we allow fixed effects to be correlated with the regressors to capture unobservable heterogeneity. Under a general spatial error dependence structure, we then establish some consistent closed-form estimates for both the unknown parameters and the link function for the case where both cross-sectional dimension (N) and temporal dimension (T ) go to infinity. Rates of convergence and asymptotic normality are established for the proposed estimates. Our experience suggests that the proposed estimation method is simple and thus attractive for finite-sample studies and empirical implementations. Moreover, both the finite-sample performance and the empirical applications show that the proposed estimation method works well when the cross-sectional dependence exists in the data set.

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

“…The nonlinearity of g o can also be clearly seen from Figure 3, which plots the estimated cost function (the solid line) together its 95% confidence intervals (the dashed lines) on [1.6, 2.3]. To further compare the performance of these three models, we follow Dong et al (2015) and Dong et al (2016) to compute mean squared error (MSE) for each of the three models using MSE =…”

“…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)).…”

Series estimation for single‐index models under constraints

“…In order to establish a consistent closed-form estimate for θ 0 through (6), we explore the idea of double series expansion alluded to in Dong, Gao & Peng (2015) for the general single-index modelling of cross-sectional data. We first define an ordering relationship with respect to p in (6).…”

“…Then the proof is complete. The detailed proof of this lemma has been given in Dong, Gao & Peng (2015), thus omitted.…”

“…To the best of our knowledge, however, limited studies are available for series-based estimation for single-index models. The existing literature includes Yu & Ruppert (2002), and Ma & Song (2015) for using spline estimation to investigate the cross sectional single-index models, Dong, Gao & Peng (2015) and Dong, Gao & Tjøstheim (2016) for employing Hermite polynomials to study single-index models in panel data and non-stationary time series models, respectively.…”