A methodology to study price-quantity interactions in input–output modeling: an application to NextGenerationEU funds

Abstract

The standard input–output (IO) model consists of two distinct and self-contained modules that describe the underlying factors governing quantities and prices. However, these modules operate independently, existing in separated spheres where prices do not influence quantities and quantities do not affect prices. This limitation restricts the standard model's ability to evaluate market dynamics that involve simultaneous changes in both quantities and prices. To overcome this limitation, we introduce an extended version of the traditional IO price and quantity models, combining them into a unified ‘price-quantity’ model that establishes connections between the two IO modules. We apply this integrated IO model to evaluate the impact of NextGenerationEU funds on the Spanish economy utilizing input–output and national accounts data for 2016.

KEYWORDS:

• Price-quantity feedback
• expanded IO models
• impact evaluation

JEL CLASSIFICATIONS:

• C67
• D57
• E37

Acknowledgments

Earlier versions of this paper were presented at the first Workshop on Environmental Economics and Policy in Granada, Spain, and at the 29th International IO conference in Alguer, Italy. We are grateful for the comments and suggestions provided by the participants. We also extend our appreciation to the referees and the Editor, professor Yasuhide Okuyama, for their constructive feedback and recommendations to improve this work, especially regarding the presentation of the model in Section 2. It goes without saying that any remaining errors or limitations are our sole responsibility.

Disclosure statement

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

Notes

1 See also the rest of contributions in the monographic issue of Economic Systems Research, volume 3, number 1.

2 The nonnegative invertibility of matrix (I-A) is always guaranteed for matrices A built from empirical input-output data. Nikaido (1972), chapter 3, provides the theoretical justification.

3 INE is the Spanish National Institute of Statistics. It depends on the Ministry of Economic Affairs.

4 See the explanations in Miller and Blair (2022), chapter 2, for input-output data and Cardenete et al. (2017), chapter 6, for an extension to Social Accounting Matrix data.

5 See also https://commission.europa.eu/strategy-and-policy/recovery-plan-europe_en for details on the stimulus packages and https://planderecuperacion.gob.es/ejecucion for information about the implementation plan in Spain.

6 Billions in US units, or milliards in UK terminology. In our calculations, we deflate this figure to 2016 prices to ensure compatibility with the model database. The deflated level amounts to about 143 thousand of millions of Euros.

7 Varian (1992), chapter 9, explains the interplay of the two income effects.

8 If we denote by d the vector of injected funds, the reported results in the Appendix for the open Leontief model correspond to the change in gross output evaluated by (I−A)⁻¹·d.

Additional information

Funding

The first and second authors thank the support of the Climamodel-SEJ511 project funded by PAIDI, Junta de Andalucía. The third author thanks the support of Research Project PID2020-116771GB-100 from the Ministry of Science of Spain as well as the support of the Severo Ochoa Program for Centers of excellence in R&D grant CEX2019-00915-S to the Barcelona School of Economics.