An extension of the hypothetical extraction method: endogenous consumption and the armington treatment of imports

Abstract

The hypothetical extraction method (HEM) is the tool of choice for identifying underlying economic interdependencies. It provides critical information to policymakers regarding the strategic role of different sectors. However, the standard implementation of the HEM does not include the impact that falls on the price structure as a result of the substitution between domestic and imported products that takes place after the extraction of a sector or industry, in this case. We propose to overcome this limitation by extending the HEM using an Armington-Leontief model with endogenous consumption. Unlike the perfect substitution assumption typical of the standard HEM, the Armington assumption with endogenous consumption implies that the shift from domestic inputs to imports affects the cost functions. Therefore, both quantities and prices become endogenous in the ‘post-extraction' equilibrium. We also argue that HEM indicators should be expanded beyond the typical output-related indicators, i.e. value-added, employment, or pollutant levels, so that summary indices of the type more commonly used in economics, such as welfare indicators, are used. We implement this novel approach using the latest input–output data for Spain in 2016.

KEYWORDS:

• Armington assumption
• hypothetical extractions
• endogenous consumption
• cost functions

JELCODES:

• C63; C67; D57; D58

Acknowledgements

We are grateful to the comments of seminar participants in the 9th SHAIO 2022 meetings in Aveiro and to the valuable suggestions for improvement of the two referees and the editor of the journal.

Disclosure statement

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

Notes

1 We refer to Guerra and Sancho (2010) and Dietzenbacher and Lahr (2013) for details on modelling gradual extractions.

2 See, for instance, Temurshoev (2010) and Temurshoev and Oosterhaven (2014) for a wider definition of supply-side HEM indicators such as value-added, employment, etc.

3 In microeconomics terminology, the elasticity of substitution goes to infinity.

4 As a rule, we will also use the following notation throughout. Symbol x will represent a scalar, x a column vector, x′ a row vector and X a matrix. When necessary, the diagonal matrix version of a vector x will be denoted as $\hat{\mathbf{x}}$.

5 This property refers to the maximal eigenvalue of A+B−$\widehat{\text{μ}}$ being less than 1.

6 See Guerra and Sancho (2018) and Sancho (2019) for details.

7 See Emonts-Holly et al. (2021) for a discussion of the different alternatives to deal with this "closing" issue within the activity analysis perspective.

8 Steenge and Serrano (2012) link the wage rate to final demand per unit of labour or, as defined by the authors ‘national income per head'. This allows the evaluation of income distribution effects within the IO framework.

9 See Table A1 in the Annex for the complete description of the sectorial breakdown included in the total symmetric Spanish IO table for 2016.

10 This situation was raised by one of the referees during the review process.

Additional information

Funding

We gratefully acknowledge the support from grant PID2020-116771GB-100 funded by MCIN/AEI/10.13039/501100011033. The first author also thanks the support from projects PAIDI2020-P20.00691 awarded by the Regional Government of Andalusia and B-SEJ-544-UGR20 FEDER2014-2020. The second author also thanks the support of the Severo Ochoa Program for Centres of Excellence in R&D grant CEX2019-00915-S to the Barcelona School of Economics.