Uncovering spatial productivity centers using asymmetric bidirectional spillovers

The principal contribution of this paper is to present the first method to sift through a large number of firms in an industry to uncover which firms act as large spatial total factor productivity (TFP) growth centers. We define a large spatial TFP growth center as a firm that is a large net generator of spatial TFP growth spillovers, i.e., it is a source of large TFP growth spill-outs to other firms vis-à-vis the size of the TFP growth spill-ins that permeate to the firm from other firms. We use this definition because, other things being equal, firms would want to locate near a firm that is a net generator of TFP growth spillovers. In the process of presenting the above method we make three further contributions, two of which are methodological and the other relates to our application. First, rather than follow the literature on spatial frontier modeling by considering spatial interaction between firms in a single network, we introduce a more sophisticated model that is able to account for spatial interaction in multiple networks. Second, we obtain bidirectional spatial TFP growth decompositions by complementing a unidirectional decomposition in the literature, where the spillover components are spill-ins to a firm, with a decomposition that includes spill-out components. Third, from a spatial revenue frontier for U.S. banks (1998–2015), we find a number of cases where banks that represent large spatial TFP growth centers have branches that cluster together, while in several states we find no such clusters.