Series Estimation under Cross-sectional Dependence

This paper develops an asymptotic theory of the series estimation under general crosssectional dependence and heterogeneity, covering both nonparametric and semiparametric estimates. A uniform rate of consistency, asymptotic normality and sufficient conditions for the √ n rate of convergence are established. A new data-driven studentization that dispenses with the need for "distance measures", as required by the spatial HAC estimation, is introduced and leads to asymptotically correct inference. Conditions imposed on dependence are carefully formulated to accommodate various cross-sectional settings plausible in economic applications and readily apply to panel and time series data. Strong, as well as weak dependence are covered, filling the current gap in the theoretical literature, and conditional heteroscedasticity is allowed. A finite sample Monte Carlo study indicates a highly satisfactory performance of the estimation and testing procedures. Applying the methods of the paper to two illustrative examples reveals some subtle yet interesting differences in results, compared to that under the assumption of independence. JEL Classifications: C13; C14; C21