Regional input-output with endogenous internal and external network flows

Regional I-O analysis has a long history, including seminal works by Chenery (1953) and Leontief and Strout (1963), with the latter analysis seen as a disaggregation of the Leontief-Strout (L-S) approach. Other significant contributors include Isard et al. (1960), Polenske (1980), Hewings (1985), Miller and Blair (1985) and Oosterhaven (1988). An overview is provided in Roy (2004a). As more and more regional survey data became available, such analysis was approached with more confidence. In fact, regional I-O has become one of the most widely practiced techniques in the field of regional science. Before proceeding further, we need to clarify the terminology. For this, we turn to Isard et al. (1998). The first class of regional model which they define is the interregional model where both the flows and the I-O coefficients have four indices, that is, the flow of sector i into sector j from region r to region s. As it is extremely difficult to implement a full interregional model, most developments have concentrated on devising multi-regional models with less stringent data requirements. Although the dimensionality of these approaches reduces from four to three, different indices are absorbed in the flows compared to the I-O coefficients. The flows relate to the total flow of sector i as input to all other sectors between regions r and s, with the aggregation over destination sectors j. These flows are more likely to be available within freight statistics. The I-O coefficients relate to the amount of the sector i product being supplied as intermediate inputs to sector j in region s per unit of output of sector j in region s, aggregated over the different regions r which supply the inputs. It is precisely this different nature of the aggregation of the flows versus that over the I-O coefficients which creates the main challenge to development of sound multiregional methods.