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Calibrating and Applying Random-Utility-Based Multiregional Input–Output Models for Real-World Applications

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Abstract

Random-utility-based multiregional input–output (RUBMRIO) models are used to study the impact of changes in transport networks or spatial economies on interregional or international trade patterns. These models rely on elastic prices algorithms to estimate trade flows. According to the literature, two different RUBMRIO elastic prices algorithms exist: an original algorithm that was the subject of theoretical investigation, and a modified algorithm that has been commonly used in practice. The original algorithm measures prices and acquisition costs in dollars, whereas the modified algorithm measures prices and acquisition costs in units of utility. By deriving the equivalence conditions of these algorithms, it is proven that the modified algorithm is only equivalent to the original algorithm under very restrictive conditions: first, initial sector prices must be the same in each region; second, cost parameters must be the same for all industries; and third, no other variables can be introduced into the original trade coefficient model specification. In a numerical example, the modified algorithm results in a mean absolute percentage error of 56% for trade flow values. Due to these restrictions, it is recommended that future studies adopt the approach of determining initial RUBMRIO prices endogenously before calibration, which are shown be solved directly from a system of linear equations, and applying the original RUBMRIO elastic prices algorithm (measuring prices in dollars).

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Notes

  1. Dollars are used as monetary units throughout this paper. They can be substituted for any other monetary unit.

  2. Leontief (1936) describes his work as an attempt to construct a “Tableau Economique” or Economic Table, first proposed by French economist François Quesnay.

  3. Namely that trade flows need only be characterized by a sector and an origin-destination pair, whereas IRIO models additionally require trade flows to be specified to a destination sector (for use).

  4. Zhao and Kockelman (2004) equivalently specify a dispersion parameter (λi), where \( {\lambda}_i{V}_i^{rs}={b}_i^r+{d}_i^{rs} \). However, in real-world applications, a dispersion or scale parameter is not separately identifiable; rather, coefficients (βi) are estimated (which are implicitly scaled by the scale parameter). See section 3.2 in Train (2009) for further details.

  5. The representative utility function presented in (10) is in its most basic form; in real-world applications, other variables are often added, which are discussed in the concluding section.

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  1. Department of Civil and Environmental Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada

    Chris Bachmann

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Bachmann, C. Calibrating and Applying Random-Utility-Based Multiregional Input–Output Models for Real-World Applications. Netw Spat Econ 19, 219–242 (2019). https://doi.org/10.1007/s11067-019-9444-3

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