S3RI Seminar - A Rank-Reduced Functional Coefficient Panel Data Model, by Jia Chen (York) Seminar

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We consider estimation of a functional coefficient panel data model with serial correlation. In order to achieve dimension reduction and improve estimation efficiency, we introduce a novel semiparametric estimation procedure. This semiparametric method imposes a rank-reduced structure on the model's functional coefficients and employs a Cholesky decomposition of the serial covariance matrices. By using the Cholesky decomposition, we are able to obtain a transformation of the original model, which is free from serial correlation. By applying a standard semiparametric method to the transformed model, more efficient estimates of the coefficient functions can be obtained. Under some regularity conditions, we derive the asymptotic distribution for the proposed semiparametric estimators and show their efficiency gains when the serial covariance matrices are correctly specified. Hence, to avoid misspecification of the serial covariance matrices and ensure efficiency improvement, we propose approaches to consistently estimate the Cholesky decomposition for both balanced and unbalanced panel data. Numerical studies including Monte Carlo experiments and an empirical application show that the developed semiparametric method works reasonably well in finite samples.