Regions may share factors of production, too: Implementation of topologies within the World Trade Model

ABSTRACT

The World Trade Model (WTM), which incorporates input - output data and minimizes global factor costs subject to satisfying demands while being constrained by each region's factor endowments, is one of models based on the principle of comparative advantage. These factor endowments are not necessarily fixed in each region as traditionally posed in most theories, but rather can or de facto be shared across regions. We highlight the importance of this feature for economic modeling, and then introduce an extension for the integration of topological rules into WTM to facilitate the sharing of factors with directionality (one-way or two-way) across regions. A series of numerical examples illustrating a range of sharing scenarios is demonstrated to facilitate an examination of this extension's features. Finally, we discuss the most interesting cases in which this topology can be used, as well as the additional challenges or implementations that can be derived from this work.

KEYWORDS:

• World Trade Model
• Factors of production sharing
• Input – output
• International trade
• Globalization

JEL:

• Codes: C67
• D57
• F1
• F2
• F6
• R15

Acknowledgements

The authors greatly thank the interesting comments and suggestions made by the reviewers and Editors, which in our view notably helped improving the article. Their research is also possible thanks to the Spanish Ministry of Science, Innovation and Universities, through PID2019-106822RB-I00 and PID2022- 140010OB-I00; and the Government of Aragon through S40_20R and S40_23R (CREDENAT) group financing.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 It emphasizes that in a pure ‘Ricardian' understanding, instead of having a single row of factor uses of a type, technologies (e.g., with different qualities of land) do not compete for being chosen over others. Instead, the best technologies are utilized first until they deplete the resources, followed by other technologies. This leads to two different possibilities of defining factors in which different qualities compete among technologies (defined as a vector) or not (defined as a diagonalized vector) in the WTM.

2 Beginning with articles by (Jones, 1971; Samuelson, 1971a, 1971b), a number of writers have returned to an older tradition, traceable in the works of Marshall, Ohlin himself, and Harrod, which assumes that, in the short run at least, capital goods are sector-specific. In the light of this tradition, the Heckscher-Ohlin-Samuelson model is seen as describing positions of long-run equilibrium only (Neary, 1978). This last cited work deals with cases in which the assumption of sector-specific capital leads to more intuitively plausible results than the assumption of intersectoral capital mobility. Also, we can argue that the expansion capacity of an economy cannot grow immediately, but it cannot be denied that financial capital may freely flow depending on financial regulations. Today capital flows much faster, although with some limits in a year (for example, foreign capital investment does not occur with a quick decision), via financial credit, shares of businesses, etc. An obvious example of this is the movement of capital across countries and into developing markets, which created political and structural risks in regions losing their capital. In order to model realistically, it is imperative to provide some endowments for capital for the regions while simultaneously allowing for sharing of capital among the regions, rather than having to choose for relatively arbitrarily large numbers of ‘slack' for the endowments to account for possible inflows in each region.

3 Calculating the unemployment rate in Spain and several other countries during the years of economic slowdown, or "crisis," was also "tricky" because many long-term unemployed – typically the elderly – were no longer looking for work, and similarly, many young people extended their student lives due to a pessimistic economic outlook, reducing the productive population while increasing the inactive.

4 Ultimately the question is whether at least 100% of $f_v^i$ must be usable in some region. If this is not allowed, it is de facto a reduction of the available endowment $f_v^i$. We note, however, that this may create challenges when ‘isolated' regions exist (not involved in the factor sharing), so one suggestion could be to better tend to work with $M_{i,j,v}=1$for $i=j$, properly defining the endowments ${\mathbf{f}}_i=\left(f_v^i\right)$ first, in accordance with the nature of the scenarios that are studied (as it typically has been done in WTM/RCOT studies). This relates to Note 7 on the cases of disjoint subsets of regions requiring additional constraints.

5 With this, we are recognizing the possibility of disjoint subsets of regions which require factor (i.e. ‘mass') conservation conditions for each block of regions. An example is a four-region case like the following: $\left[\begin{array}{cccc}1& 0.25& 0& 0\\ 0& 0.5& 0.5& 0\\ 0& 0.5& 1& 0\\ 0& 0& 0& 0.75\end{array}\right]$

In this case, addition to Equations 14 and 15, it would be reasonable to require: ${\mathbf{F}}_1{\mathbf{x}}_1+{\mathbf{F}}_2{\mathbf{x}}_2+{\mathbf{F}}_3{\mathbf{x}}_3\le {\mathbf{f}}_1+{\mathbf{f}}_2+{\mathbf{f}}_3$.

6 A benefit-of-trade rent may be required to induce some regions to export, even though their production for exports is beneficial for the world as a whole. With the emergence of both kinds of rents, prices of goods will rise to values that may exceed no-trade prices, at least the no-trade prices of the producing regions (see Duchin, 2005).

7 In the case of WTM, this idea for a future study was originally suggested by Dilekli et al. (2018), where low-cost producing regions of electricity would run out of water due to their intensive water use (via the once-through cooling technology).

8 For example, shared endowments can be introduced for "employment availability', allowing partial or full sharing to represent partial or full free movement of people, e.g. among different explicitly represented regions within a country, or among countries (e.g. Liechtenstein-Germany, or Belgium-The Netherlands; US-Canada, etc.).

Additional information

Funding

This work was supported by Gobierno de Aragón (S40_20R and S40_23R for the CREDENAT group) and Ministerio de Ciencia e Innovación (grant numbers PID2019-106822RB-I00 and PID2022- 140010OB-I00).