Estimation of a rank-reduced functional-coefficient panel data model with serial correlation

We consider estimation of a functional-coefficient panel data model. This model is useful for modeling time varying and cross-sectionally heterogeneous relationships between economic variables. We allow for serial correlation and heteroscedasticity in the model. When the number of explanatory variables is large, we impose a rank-reduced structure on the model’s functional coefficients to reduce the number of functions to be estimated and thus improve estimation efficiency. To adjust for serial correlation and further improve estimation efficiency, we use a Cholesky decomposition on the serial covariance matrices to produce a transformation of the original panel data model. By applying the standard semiparametric profile least squares 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 developed semiparametric estimators and show their efficiency improvement under correct specification of the serial covariance matrices. To attain this efficiency gain when the serial covariance structure is unknown, we propose approaches to consistently estimate the lower triangular matrix in the Cholesky decomposition for balanced panel data, and the serial covariance matrices for unbalanced panel data. Numerical studies, including Monte Carlo experiments and an empirical application to economic growth data, show that the developed semiparametric method works reasonably well in finite samples.