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Interregional price linkages of fossil-energy and food sectors: evidence from an international input–output analysis using the GTAP database

Abstract

This study examined the impacts of price changes in fossil-energy resources on food prices across the world. We approached this issue with the input–output (IO) price model, which is suitable for evaluating the price effects due to cost-push (supply driven) processes through transaction linkages of intermediate goods. We employ an international interregional IO table comprising 14 regions and 57 industrial sectors, which is compiled from the global trade analysis project (GTAP) 9 database. The results revealed: (1) interregional price linkages are particularly strong between a wheat-producing region and energy producers in the adjacent regions; and (2) the world oil sector appears to exert the strongest effects on mechanized sectors (wheat, plant fibers and fishing) and regions practicing advanced agriculture (East Asia, the US, and Russia). Furthermore, a comparison with empirical observations suggests that approximately one tenth of observed 2-year price changes in US wheat in 2004–2016 can be explained by the cost-push processes derived from the world oil price changes.

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Fig. 1

Source modified and simplified after Peters et al. (2011). Note The figure shows an example of a 3-region table for simplicity. The shaded blocks indicate the diagonal blocks for intra-regional transactions (\(\varvec{Z}^{{\varvec{rr}}}\) and \(\varvec{y}^{{\varvec{rr}}}\))

Fig. 2
Fig. 3
Fig. 4

Source IEA (2018) and FAO (2019). See text for details

Notes

  1. 1.

    We may sometimes abbreviate the term “fossil energy” to “energy” for simplicity.

  2. 2.

    We use for convenience the term “food” to loosely indicate both edible and non-food agricultural produce or sectors supplying them. Likewise, we use the term “agriculture” to indicate all primary industries including forestry and fisheries (i.e., Sectors No. 1 to 14 in Table 1 presented later).

  3. 3.

    Among these, data of primary inputs and domestic/international taxes and subsidies can also be obtained from the GTAP, but these values are irrelevant in the context of this study.

  4. 4.

    A mathematical derivation of Eq. (6) is provided in “Appendix 1”.

  5. 5.

    One must bear this in mind when referring to Fig. 2 later.

  6. 6.

    Such an assumption somewhat contradicts the essence of Sect. 3.1.1 where regional differences in energy prices are implicitly assumed. However, Sect. 3.1.1 can be regarded as describing a short-term situation in which price elasticity of regional substitution is low, in contrast to this Section.

  7. 7.

    World crude oil price: Average import costs on c.i.f. basis in $US per barrel, which are volume-weighted averages for France, Germany, Italy, Spain, UK, Japan, Canada and USA. Although these values are not producer prices, we assume that they largely represent the trends in world oil market prices. US wheat price: producer prices in the USA extracted from the FAOSTAT database.

  8. 8.

    The existence of the relevant inverse matrix is assumed throughout.

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Acknowledgements

We acknowledge with gratitude that this work was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI 16KT0036.

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Correspondence to Tatsuki Ueda.

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Appendix 1: Mathematical derivation of Eq. (6)

Appendix 1: Mathematical derivation of Eq. (6)

This appendix explains a mathematical derivation for Eq. (6) in the main text, on the basis of Tamamura (2014). Assume an economy with n goods (sectors) and one region for notational simplicity. We set to describe a situation in which the price of the nth good is exogenously increased from \(p_{n}\) to \(p_{n} + \Delta p_{n}\), which induces price increases in the other n − 1 goods in response, via cost-push processes, from \(p_{i}\) to \(p_{i} + \Delta p_{i} (i = 1, \ldots ,n - 1)\).

We begin by partitioning the input coefficient matrix A into four sub-matrices:

$$\varvec{A} = \left[ {\begin{array}{*{20}c} {\varvec{A}_{11} } & {\varvec{A}_{12} } \\ {\varvec{A}_{21} } & {\varvec{A}_{22} } \\ \end{array} } \right],$$
(8)

where

$$\varvec{A}_{11} = \left[ {\begin{array}{*{20}c} {a_{11} } & \cdots & {a_{1,n - 1} } \\ \vdots & \ddots & \vdots \\ {a_{n - 1,1} } & \cdots & {a_{n - 1,n - 1} } \\ \end{array} } \right],\;\varvec{A}_{12} = \left[ {\begin{array}{*{20}c} {a_{1n} } \\ \vdots \\ {a_{n - 1,n} } \\ \end{array} } \right],\;\varvec{A}_{21} = \left[ {\begin{array}{*{20}c} {a_{n1} } & \cdots & {a_{n,n - 1} } \\ \end{array} } \right],\;\varvec{A}_{22} = \left[ {a_{nn} } \right]$$

Notice when A is transposed, the corresponding sub-matrices become:

$$\varvec{A}^{\prime} = \left[ {\begin{array}{*{20}c} {\varvec{A}_{11}^{\prime} } & {\varvec{A}_{21}^{\prime} } \\ {\varvec{A}_{12}^{\prime} } & {\varvec{A}_{22} } \\ \end{array} } \right]$$
(9)

First, using these sub-matrices, we rearrange Eq. (4) with respect to goods 1 to n − 1:

$$\varvec{A}_{11}^{\prime} \varvec{p}_{1} + \varvec{A}_{21}^{\prime} p_{n} + \varvec{v}_{1} = \varvec{p}_{1}$$
(10)

where \(\varvec{p}_{1}\) and \(\varvec{v}_{1}\) are the vectors of price and value-added of goods 1 to n − 1, respectively.

When the price of the nth good is raised, the prices of the other goods are increased in response, as mentioned above, and the economy will reach another price equilibrium:

$$\varvec{A}_{{\text{11}}}^{\prime} \left( {\varvec{p}_{1} + \Delta \varvec{p}_{1} } \right) + \varvec{A}_{21}^{\prime} \left( {p_{n} + \Delta p_{n} } \right) + \varvec{v}_{1} = \varvec{p}_{1} + \Delta \varvec{p}_{1}$$
(11)

Subtracting Eq. (10) from (11) gives:Footnote 8

$$\begin{aligned} \varvec{A}_{11}^{\prime } \Delta \varvec{p}_{1} + \varvec{A}_{21}^{\prime } \Delta p_{n} = \Delta \varvec{p}_{1} \; \Leftrightarrow \hfill \\ \Delta \varvec{p}_{1} = \left( {\varvec{I} - \varvec{A}_{11}^{\prime } } \right)^{ - 1} \varvec{A}_{21}^{\prime } \Delta p_{n} \hfill \\ \end{aligned}$$
(12)

Second, we define the transposed Leontief inverse matrix in four sub-matrices corresponding to Eq. (9):

$$\varvec{B}^{{\prime }} = \left( {\varvec{I} - \varvec{A}^{{\prime }} } \right)^{ - 1} = \left[ {\left( {\varvec{I} - \varvec{A}} \right)^{ - 1} } \right]^{{\prime }} = \left[ {\begin{array}{*{20}c} {\varvec{B}_{11}^{{\prime }} } & {\varvec{B}_{21}^{{\prime }} } \\ {\varvec{B}_{12}^{{\prime }} } & {\varvec{B}_{22} } \\ \end{array} } \right]$$
(13)

where the sub-matrices B11 to B22 are defined in correspondence with A11 to A22 in Eq. (8).

Multiplying \(\left( {\varvec{I} - \varvec{A}^{{\prime }} } \right)\) and \(\varvec{B}^{{\prime }}\) (Eq. 13) gives:

$$\left( {\varvec{I} - \varvec{A}^{{\prime }} } \right)\varvec{B} = \left[ {\begin{array}{*{20}c} {\varvec{I}_{{\varvec{n} - 1}} - \varvec{A}_{11}^{{\prime }} } & { - \varvec{A}_{21}^{{\prime }} } \\ { - \varvec{A}_{12}^{{\prime }} } & {\varvec{I}_{1} - \varvec{A}_{22} } \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {\varvec{B}_{11}^{{\prime }} } & {\varvec{B}_{21}^{{\prime }} } \\ {\varvec{B}_{12}^{{\prime }} } & {\varvec{B}_{22} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {\varvec{I}_{{\varvec{n} - 1}} } & {\varvec{O}_{{\varvec{n} - 1}} } \\ {\varvec{O}_{{\varvec{n} - 1}}^{{\prime }} } & {\varvec{I}_{1} } \\ \end{array} } \right],$$
(14)

where In is the n-dimensional identity matrix and On is the n-dimensional zero vector.

Hence, we have:

$$\begin{aligned} \left( {\varvec{I} - \varvec{A}_{11}^{{\prime }} } \right)\varvec{B}_{21}^{{\prime }} + \left( { - \varvec{A}_{21}^{{\prime }} } \right)\varvec{B}_{22} = \varvec{O}_{{\varvec{n} - 1}} \; \Leftrightarrow \hfill \\ \varvec{B}_{21}^{{\prime }} /b_{nn} = \left( {\varvec{I} - \varvec{A}_{11}^{{\prime }} } \right)^{ - 1} \varvec{A}_{21}^{{\prime }} \hfill \\ \end{aligned}$$
(15)

Finally, inserting Eq. (15) into (12) gives:

$$\Delta \varvec{p}_{1} = \left( {\varvec{B}_{21}^{{\prime }} /b_{nn} } \right)\Delta p_{n}$$
(16)

This proves Eq. (6).

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Ueda, T., Kunimitsu, Y. Interregional price linkages of fossil-energy and food sectors: evidence from an international input–output analysis using the GTAP database. Asia-Pac J Reg Sci 4, 55–72 (2020). https://doi.org/10.1007/s41685-019-00124-9

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Keywords

  • Food price
  • GTAP database
  • International trade
  • Input–output price model
  • Oil price

JEL Classification

  • C67
  • F14
  • Q11
  • Q31
  • Q41