Abstract
This paper presents a new method for estimating regional trade flows using transportation survey data describing commodity origin–destination flows. Explicit attention is paid to the difference between commodity flows and trade flows that arises from the presence of transhipment points. Observed commodity flows in the transportation survey data are converted to production–consumption trade flows that are consistent with the multi-regional input–output framework. Regional trade flow estimates are then reconciled with regional production and consumption estimates using a mathematical program that aims to make minimal adjustments while imposing known multi-regional input–output accounting identities. It is shown that commodities originating or terminating at a transhipment point should be reassigned to their probable production origins or consumption destinations as long as an unbiased sample of previous observations is available. As the number of observations increases, the prediction error of the production origin or consumption destination decreases exponentially. A real-world case study in the Province of Ontario in Canada demonstrates the feasibility of estimating interregional trade flows from commercial vehicle survey data and shows that the estimated pattern of trade flows is maintained after adjustments are made to satisfy accounting constraints. Therefore, it is possible to create a balanced multi-regional input–output model based on a commercial vehicle survey and the limited supplementary data available at the regional level.
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Notes
See Rose (1995) for a discussion on the relationship between IO and computable general equilibrium (CGE) models.
RAS is not an acronym—the method is named after the right-hand side of an equation. It is also known as “bi-proportional” matrix balancing.
For example, Alward et al. (1998), Lindall et al. (2006), Schwarm et al. (2006), Jackson et al. (2006), and Park et al. (2009) use the Commodity Flow Survey (CFS) from the US Census Bureau and the Bureau of Transportation Statistics (BTS) to estimate trade flows; Al-Battaineh and Kaysi (2005) use the Ministry of Transportation of Ontario (Canada) Commercial Vehicle Survey (CVS) to estimate commodity flows.
Instead of using optimization to estimate trade flows between regions, Al-Battaineh and Kaysi (2005) use optimization to estimate truck flows between regions.
The appendix in supplementary material shows how this objective function can be easily translated into a standard quadratic program in matrix form [\(\min f\left( x \right) =\frac{1}{2}\mathbf{x}^{\mathrm{T}}\mathbf{Hx}+\mathbf{f}^{\mathrm{T}}\mathbf{x}\)].
Canning and Wang (2005) show how imposing accounting relationships (as in step two) will definitely improve, or at least not worsen the initial estimates, since those constraints are identities and must be true for any system of economic regions.
Miller and Blair (2009) discuss how observed national technology is often assumed uniform across regions and the conditions that make this assumption reasonable.
Alternatively, Fig. 3 could be interpreted as commodity flows involving a transhipment point at the origin. In this case, the x-axis contains the number of observations of commodities previously made that enter the transhipment point, and the y-axis contains the error created when predicting the origin of future commodities leaving the transhipment point.
A distribution center serving all regions equally is the worst case scenario because it is the hardest to predict from a sample of observations for the same reason the outcome of a fair coin is harder to predict than the outcome of a biased coin: it is more random.
Make and Use tables for the province of Ontario are also based on NAICS, but both the employment and input–output data make different aggregations of NAICS requiring a correspondence between the classifications as shown in Table A1 in the appendix of supplementary material.
A correspondence was established with Statistics Canada commodity groupings as given in Table A2 in the appendix of supplementary material.
The number of observations in the MTO CVS of commodities originating (or terminating at) distribution centers and truck terminals in Toronto with known consumption destinations (or production origins) is given in Table A3 in the appendix of supplementary material.
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Bachmann, C., Kennedy, C. & Roorda, M.J. Estimating regional trade flows using commercial vehicle survey data. Ann Reg Sci 54, 855–876 (2015). https://doi.org/10.1007/s00168-015-0689-6
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DOI: https://doi.org/10.1007/s00168-015-0689-6