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Specification test for panel data models with interactive fixed effects. (English) Zbl 1331.62485
Summary: In this paper, we propose a consistent nonparametric test for linearity in a large dimensional panel data model with interactive fixed effects. Both lagged dependent variables and conditional heteroskedasticity of unknown form are allowed in the model. We estimate the model under the null hypothesis of linearity to obtain the restricted residuals which are then used to construct the test statistic. We show that after being appropriately centered and standardized, the test statistic is asymptotically normally distributed under both the null hypothesis and a sequence of Pitman local alternatives by using the concept of conditional strong mixing that was recently introduced by B. L. S. Prakasa Rao [Ann. Inst. Stat. Math. 61, No. 2, 441–460 (2009; Zbl 1314.60054)]. To improve the finite sample performance, we propose a bootstrap procedure to obtain the bootstrap \(p\)-value. A small set of Monte Carlo simulations illustrates that our test performs well in finite samples. An application to an economic growth panel dataset indicates significant nonlinear relationships between economic growth, initial income level and capital accumulation.

MSC:
62P20 Applications of statistics to economics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
62E20 Asymptotic distribution theory in statistics
91B62 Economic growth models
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