Abstract
A 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 semiparametric profile likelihood approach based on the first-stage local linear fitting is developed to estimate both the parameter vector and the time trend function. As both the time series length T and the cross-sectional size N tend to infinity simultaneously, the resulting semiparametric estimator of the parameter vector is asymptotically normal with an optimal rate of convergence. Meanwhile, an asymptotic distribution for the estimate of the nonlinear time trend function is also established with also an optimal rate of convergence. Two simulated examples are provided to illustrate the finite sample behavior of the proposed estimation method. In addition, the proposed model and estimation method is applied to the analysis of two sets of real data.
Highlights
Modeling time series with trend functions has attracted an increasing interest in recent years
In order to take into account existing information and contribution from a set of explanatory variables, this paper proposes extending the nonparametric model by Robinson (2008) to a semiparametric partially linear panel data model with cross–sectional dependence
If we model the trend by a linear function as in (5.8), the estimated trend resulting from the ordinary least squares (OLS) would be 2.7689 − 0.0119t, which indicates a decrease in the per-worker output from 1960 to 1987
Summary
Modeling time series with trend functions has attracted an increasing interest in recent years. Li, Chen and Gao (2010) extend the work of Cai (2007) in a trending time–varying coefficient time series model to a panel data time–varying coefficient model In such existing studies, the residuals are assumed to be cross–sectionally independent. In order to take into account existing information and contribution from a set of explanatory variables, this paper proposes extending the nonparametric model by Robinson (2008) to a semiparametric partially linear panel data model with cross–sectional dependence. In our discussion, both the residuals and explanatory variables are allowed to be cross–sectionally dependent. The mathematical proofs of the main results are relegated to Appendices A and B
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