Abstract
In this paper, we consider a partially linear panel data model with cross-sectional dependence and non-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 unknown function for the case where N and T go jointly to infinity. Rates of convergence and asymptotic normality results are established for the proposed estimators. 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.
Highlights
Nonlinear and nonstationary time series models have received considerable attention during the last thirty years
The Balassa–Samuelson model implies that countries with a relatively low ratio of tradables to nontradables productivity will have a depreciated real exchange rate, which can be evaluated by calculating the gap between a purchasing power parity (PPP)–based U.S dollar exchange rate and the nominal U.S dollar exchange rate
For the partially linear panel data model (5.3), our comparisons based on the in sample mean squared errors (In–MSE) and rolling out sample mean squared errors (Out–MSE) suggest using k = 6 as the truncation parameter
Summary
Nonlinear and nonstationary time series models have received considerable attention during the last thirty years. (2011) extend the linear panel data models considered by Bai (2009) and Pesaran (2006) by allowing the factors ( often known as macro shocks in some basic economic concepts) to follow nonstationary time series processes. One of our aims is to provide some new asymptotic theory for panel data models with the presence of integrated processes when N and T diverge jointly. The detailed discussion will be seen in the rest of this paper Another crucial finding is that the joint divergence of (N, T ) → (∞, ∞) makes the asymptotic theory drastically different from that of the integrated time series case. G(w)dw and similar notation applies to multiple integration
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