Across the state and across the border: Spill-over, feedback, and agglomeration in many-region economies

My paper considers the size of spillover, feedback, and agglomeration processes in many-region economies. I begin by noting the regional development across the Niagara Frontier of the United States-Canadian border which is motivating this research. By the end of the 1980's, with the implementation of the Canada-United States Trade Agreement, it had became apparent that there were significant spillover effects across the Niagara Frontier into Western New York from the Toronto region, and possibly beyond into other parts of the State, to Rochester and even New York City. Such spillover, together with the associated feedback effects, may be considered as a contribution to the process agglomeration, whereby economic activities reinforce each other to promote more rapid economic growth. I summarize the shifting debate over the significance of agglomeration, and then link this discussion to the parallel debate as to the contribution of spill-over and feedback to multipliers in the input-output modeling of single- and multi-region economies, and the need to incorporate better descriptions of the structure of regional economies (such as social accounting, and the flows between contiguous localities). I then formalize a simple three-region model to show how feedback and spill-over vary with the relative size, the geographic configuration of regions, the choice of model closure, including assumptions about spatial interactions as embodied in the supply-pool and gravity models. To illustrate the findings for New York State and the Niagara Frontier I use a many-county input-output model to simulate spill-over and feedback effects across a variety of metropolitan, clustered, hierarchical and remote activities, focussing on the cross-border interactions with Toronto. The results help to identify the circumstances for which it may be necessary to take into account the consequences of feedback and spill-over. The calculation also shows how the interaction between long-range spill-over effects and short-range feedback effects can compound to contribute the overall pattern of agglomeration in a multi-regional economy.