Bootstrap inference under cross-sectional dependence

In this paper, we introduce a method of generating bootstrap samples with unknown patterns of cross-sectional/spatial dependence, which we call the spatial dependent wild bootstrap. This method is a spatial counterpart to the wild dependent bootstrap of Shao (2010) and generates data by multiplying a vector of independently and identically distributed external variables by the eigendecomposition of a bootstrap kernel. We prove the validity of our method for studentized and unstudentized statistics under a linear array representation of the data. Simulation experiments document the potential for improved inference with our approach. We illustrate our method in a firm-level regression application investigating the relationship between firms' sales growth and the import activity in their local markets using unique firm-level and imports data for Canada.