Stephen Cooke (p)

Maureen Lankhuizen

A Leontief multiplier—the step up that makes exports (X) equal output (Q)—typifies a simple idea clothed in complex calculations. For a single sector economy, it equals one plus the ratio of domestic to imported inputs. In a multi-sector model, the multiplier equals this ratio but only after the cofactors have taken full account of which sectors are responsible for which intermediate transactions.
Cofactors represent the extraordinary accounting of output used as inputs to produce other outputs. Cofactors can be calculated as signed minor determinants of a transpose matrix, cross products, exterior products, or as power series approximations. The parallax among them creates the opportunity to understand this process of accounting and reallocating. Because cofactor measure the share of shares within all possible supply chains among sectors, the results can be remarkably tangled.
The difference between a Leontief output matrix that embodies cofactor information and a diagonal matrix of exports equals a new intermediate inputs matrix ( ). The inputs of reflect the reallocated inputs to each sector by derived demand both direct and indirect. In the presence of this reallocation, each sector’s multiplier equals one plus the ratio of to their respective exports, where exports equal imports by sector.
Miller and Blair (2009) describe a measure of contribution in which the off-diagonal multipliers are deleted entirely. By contrast, Ritz and Spaulding’s (1975) contribution method involves normalizing the columns of the multiplier matrix by its principal diagonal elements. Both the Miller and Blair and Ritz and Spaulding methods are special cases of the more general Waters et al. approach.

Maureen Lankhuizen (p)

Stephen Cooke

Statistical information on freight transport does not adequately capture developments in practice. This paper applies a Bayesian framework to integrate statistics on regional freight transport with data on regional trade. The resulting data describe freight transport in the Netherlands at the NUTS 3 regional level by NSTR commodity groups, and by type of flow. We distinguish intraregional transport, regional exports and imports, international exports and imports, and regional transit. The contribution of this paper is that conditions driving regional transport flows are reflected more clearly in the data. The results show the relative importance of logistic processes in regional transport in the Netherlands. Similarly, specific regional production patterns are also reflected in the data. The results enable better monitoring of developments in freight transport.