Spatial scale and product mix economies in U.S. banking with simultaneous spillover regimes

© 2019 Elsevier B.V. The literature on bank scale economies focuses on the familiar type of returns to scale that are internal to the firm. Using a spatial approach, we analyze returns to scale for banks that are made up of external (i.e., spillover) economies. We extend ray-scale economies (RSE), expansion-path scale economies (EPSE) and expansion-path subadditivity (EPSU) to the spatial case. This involves introducing direct and composite and decomposed indirect RSE, EPSE and EPSU. These direct and indirect measures relate to the cost implications for a firm from a change in: (i) the firm's output levels that are, as is standard, under its control; and (ii) the composite/decomposed spillover effect on the firm's output levels, which is primarily, but not entirely, outside its control. We include an application to U.S. banks (1998–2015) that allows a bank to simultaneously belong to a number of spatial networks, which is typically what we observe for firms. For large banks we find constant direct RSE and EPSE, and zero composite indirect RSE and constant composite indirect EPSE. These composite indirect results do not counteract any policy suggestions from the direct RSE and EPSE concerning the debate on whether there should be size caps on very large U.S. banks. The direct RSE and EPSE for large banks suggest that these banks use society's resources efficiently to provide their services. Size caps on very large banks would place downward pressure on these direct RSE and EPSE results, which could lead to large banks using society's resources inefficiently