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In this paper we analyze nonparametric dynamic panel data models with interactive fixed effects, where the predetermined regressors enter the models nonparametrically and the common factors enter the models linearly but with individual specific factor loadings. We consider the issues of estimation and specification testing when both the cross-sectional dimension and the time dimension are large. We propose sieve estimation for the nonparametric function by extending Bai’s (2009) principal component analysis (PCA) to our nonparametric framework. Based on the asymptotic expansion of the Gaussian quasi-log-likelihood function, we derive the convergence rate for the sieve estimator and establish its asymptotic normality. The sources of asymptotic biases are discussed and a bias-corrected estimator is provided. We also propose a consistent specification test for the linearity of the functional form by comparing the linear and sieve estimators. We establish the asymptotic distributions of the test statistic under both the null hypothesis and a sequence of Pitman local alternatives. A bootstrap procedure is proposed to obtain the bootstrap p-values and its asymptotic validity is justified. Monte Carlo simulations are conducted to investigate the finite sample performance of our estimator and test. We apply our method to an economic growth data set to study the relationship between capital accumulation and real GDP growth rate.


Common factors; Cross section dependence; Interactive fixed effects; Linearity; Nonparametric dynamic panel; Sieve method; Specification test



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Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

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