A follow-up note on the plausibility of the Leontief and Ghosh closed models

ABSTRACT

Herein we consider Leontief and Ghosh models that partly endogenize both part of final demand and part of value-added. We use Osterhaven's [(2012) Adding Supply-driven Consumption Makes the Ghosh Model Even More Implausible. Economic Systems Research, 24, 101–111] numerical three-sector example to show that anomalies of the sort he finds for a Ghosh closed model can also be found in the closed version of a Leontief model. By assuming, as Oosterhaven did, that aggregate exogenous resources are fixed, we obtain mirror results to his in a Ghosh setting, albeit in the more-traditional Leontief instance. Such numerical anomalies for the three-sector case turn out to be generic to both partially closed models for any 2×2 input–output model. A proof for the general n×n case remains to be uncovered.

KEYWORDS:

• Demand-driven model
• supply-driven model
• closed linear models

Acknowledgments

Support from the projects ECO2016-75204P (first author), and MICINN-ECO2017-83534P (second author) is gratefully acknowledged. We are also grateful to a referee, the editors Bart Los and Michael Lahr, and to the participants of the Santiago de Compostela IO Network meeting of 2018 for their comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 In short, all sectors must share the same ratio of consumption demand to output for Leontief’s model, or domestic value-added to output for Ghosh’s model.

2 The notational convention is that if y represents a column vector then y′ is a row vector of that same quantity.

3 See Leontief (1936, 1941, 1953) for a description of the closed model.

4 Leontief (1986) concludes that we cannot truly close static models, hence the need for some exogenous driving force such as investment, government demand or net exports.

5 In fact, Manresa and Sancho (2013) formally demonstrate in a 2×2 linear model that these types of regularities are generic in the equilibrium solution of the two closed models.

Additional information

Funding

This work was supported by the Ministerio de Economía y Competitividad: [Grant Number ECO2016-75204P, ECO2017-83534P].