Tracing VARDI coefficients: a proposal

ABSTRACT

We propose a new approach for tracing the so-called ‘value-added-(re)distribution-important coefficients’ (in short the VARDI coefficients) in a world input–output model. From the perspective of a selected group of economies, VARDI coefficients may be defined as those elements in world input–output matrix in the case of which a small change in their levels leads to the maximization of a share of this group of economies in value added in global value chains. Due to the rapid development of the World Input Output Database, this approach may be easily applied in empirical research to different groups of countries and sectors in world IO models. In an illustrative empirical case study, we use the new approach in order to answer a question regarding what the main directions of the future macroeconomic policy of the U.S. could be in order to ensure the maximization of the country’s share in global value added.

KEYWORDS:

• World input–output data
• global value chains
• nonlinear optimization

Acknowledgements

We thank the Editors, Michael Lahr and Bart Los, and anonymous referees for their valuable comments on earlier versions of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Łukasz Lach http://orcid.org/0000-0001-8599-1162

Notes

1 The list of available methods and models used to trace ICs in IO models is rather extensive. These approaches differ in terms of defining the ICs and formulating respective methodological suggestions. Since the development of Sherman and Morrison’s (1950) fundamental formula for estimating the effects on the inverse matrix of a change in an element of the original matrix several studies have aimed to extend and modify this initial proposition (comp. e.g. shortcut methods for estimating final-demand multipliers (Phibbs and Holsman, 1980, 1983; Katz, 1983; Jensen and Hewings, 1985), ‘hybrid’ techniques in regional input-output modelling (Phibbs and Holsman, 1982), methods of estimating a technology matrix from a domestic transactions matrix and a row vector of imports into each sector (Parikh and Edwards, 1977), cell-correction variant of RAS (this is referred to as ‘CRAS’; for details see Oosterhaven and Escobedo-Cardenoso, 2011), methods of estimation of regional input-output tables using cross-regional methods (Jiang et al., 2012), proposals built upon the concept of the so-called ‘field of influence’ (Hewings et al., 1988; Sonis and Hewings, 1992; Tarancón et al., 2008), the concept of the so-called ‘fundamental economic structure’ (West, 2000; Thakur, 2008), among others). Excellent reviews of previous methods used in the context of tracing ICs in IO models may be found in Lahr (1993) and Miller and Blair (2009).

2 As emphasized by Lahr (2001) and Tarancón et al. (2008) such a generalization is especially important in several major IO applications, especially identifying key sectors, as well as identifying sectors as targets of further enhancement with primary data (this could expedite the work of national statistical bureaus).

3 For a general concept of the proof see, e.g. Timmer et al. (2013).

4 Note, that the policy to change elements in the subarea S₃ seems to be a difficult one as, on the one hand, a particular country-group must promote exports, but also production in their importing country-groups must be involved. Thus, one may have increasing exports and yet also decreasing elements in S₃ if foreign imports rise faster than domestic exports. These remarks, on the margin, illustrate general problems of practical implementation of suggestions resulting from mathematical models.

5 Note that the interpretation of the division into subareas S₁, S₂, S₃, and S₄ presented in Figure 1 is valid not only for matrix ${\mathbf{A}}_t$ but also the square matrices ${\mathbf{A}}_t^{\mathbf{E}}$, ${\mathbf{E}}_t$ and ${\mathbf{E}}_t^{\ast }$.

6 Details on the motivation behind the particular choice of groups of countries and sectors in the illustrative example are provided in the appendix at the end of this paper.

7 For details see http://www.neos-server.org.

8 Recall that ${\mathbf{E}}_t^{\ast }$ denotes the part of the global solution to the Nonlinear optimization problem.

9 In comparison to the data presented in Table 2 the changes in IO coefficients reported in the remaining export-promotion-related IO subtables turned out to be less essential. Therefore, these results are presented and discussed in the online Appendix.

10 Since the magnitudes of changes in the import-substitution-related IO subtables turned out to be of much smaller size compared to the changes presented in Tables 2 and 3 we decided to provide these results only in the online Appendix (see Tables A4–A8).

11 The proposed approach seems to be especially useful in terms of short-term policymaking as IO coefficients are in general stable for short time horizons (Carter, 1970; Gurgul and Lach, 2016a). Thus, the conclusions drawn from the most recent modified global IO table (i.e. the 2014 IO table) may seem as potentially helpful for more effective policymaking in the nearest future.

12 For similar reasons we also use one scale for all subareas in the region S₃ (growth of IO coefficients).

13 Detailed results of this additional simulation are available from the authors upon request.

14 In particular, one of the potentially interesting modifications of the initial model could take into account a strategy of substituting imported inputs by domestically produced inputs under the assumption of fixed technical input coefficients.

15 One of the potential problems with interpretation of the empirical findings presented in the paper is the issue of aggregation bias that may turn to be quite noticeable for highly aggregated data (Kymn, 1990). However, the empirical example presented in the paper serves mainly for general illustrative purposes. Thus, we decided to use a small-scale aggregated model just to indicate what the new methodology may help to discover and explore. Instead, using disaggregated WIOD data results in IO tables with around 6 million elements which seem to be too big to be discussed in detail in a single paper aimed mainly at presenting a new method with a clear illustrative example.

16 This idea seems particularly important in the case of large developing economies that would like to move away from processing trade, which basically includes assembly types of work. The latter is labour intensive, and triggers participation in GVC because of low wages. In consequence, such countries do not seem as interested in increasing their value added per se as they are in increasing the non-wage part of the value added (i.e. the operating surplus). Taking this remark into account, in the online Appendix we provide general insights into the methodology of tracing the so-called ‘operating-surplus-important coefficients’ in the framework of semi-closed IO models (in the online Appendix this particular variant of the Nonlinear optimization problem is referred to as ‘OS-modified Nonlinear optimization problem’).

1 Using non-aggregated WIOD data seems an interesting direction for future empirical studies. Such detailed analyses may help answer many specific questions, as the WIOD IO tables give access to very detailed data (each global IO table contains around six million coefficients).

2 For example, De Backer and Miroudot (2013) summarize the views of OECD on this subject and suggest grouping economies according to their level of export/import exposure, which tends to be higher for smaller countries than for larger countries. Alternatively, Timmer et al. (2015) assign countries according to their geography and examine the regions of the EU, East Asia, NAFTA and others.

3 Country classification is based on WIOD 2016 Release. The group EU contains all 28 member states of the European Union (including United Kingdom). The group Remaining countries contains all countries listed in WIOD except for the members of the groups U.S., China, Mexico, Canada, Japan and EU.

4 For example, examining separately those manufacturing sectors in the case of which the share of the U.S. in global value added is the largest relatively (e.g., car manufacturing or chemical products) or the smallest (e.g., textile and leather products) could help to answer an interesting question regarding whether or not one could expect the increase in the OVAS the U.S. to be mainly caused by activity in those manufacturing sectors in which the US economy already plays a dominant role.

Additional information

Funding

Financial support for this paper from National Science Centre of Poland (Research Grant no. DEC-2015/19/B/HS4/00088) is gratefully acknowledged.