Flexible IDF approach with endogenous inputs - Discussion paper

Abstract This study contributes to the development of proxy-variable methods for modelling multiple-input, multiple-output production technologies and provides empirical evidence on the relationship between input-use intensity and economic viability. The proxy-variable framework is used to address the endogeneity of variable inputs. We estimate output growth and decompose it into contributions from quasi-fixed inputs, variable inputs, and productivity change, explicitly accounting for the endogeneity of variable inputs. The study also evaluates the economic effects of selected agrochemical-saving technologies recorded in the Farm Accountancy Data Network (FADN), specifically organic farming and precision agriculture. The analysis provides empirical evidence to inform the parametrization of these technologies in terms of their production characteristics. In addition, it examines the role of contract work as a mechanism for the adoption and diffusion of new technologies within the production process. The contribution is threefold. First, the study extends the proxy-variable literature by incorporating a flexible representation of a multiple-input, multiple-output production process, enabling consistent estimation of production technology and productivity in the presence of endogenous inputs. It develops an operational framework for identifying and estimating a translog input distance function specified with three outputs, three variable inputs, and three quasi-fixed inputs. Second, it advances the multiple-output proxy-variable approach by explicitly addressing the treatment of productivity and efficiency, thereby contributing to bridging the gap between proxy-variable methods and stochastic frontier analysis. Third, it provides new empirical evidence on productivity dynamics and the role of capacity constraints in shaping short-run production responses across European farms, with particular emphasis on agrochemical inputs. Further information can be acquired in deliverable 3.2. Citation Čechura, L., Žáková Kroupová, Z., Vacek, J., & Kumbhakar, S. C. (2026). Flexible IDF approach with endogenous inputs - Discussion paper (Version v01). BrightSpace Horizon Europe project GA Nr. 101060075. https://doi.org/10.5281/zenodo.19663128----------------- Funding acknowledgement Funded by the European Union. Grant Agreement No. 101060075. Views and opinions expressed are those of the authors only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the granting authority can be held responsible for them. Legal notice This document was produced under the terms and conditions of Grant Agreement No. 101060075 for the European Commission. It does not necessary reflect the view of the European Union and in no way anticipates the Commission’s future policy in this area. The European Commission is not liable for any consequence stemming from the reuse of this publication. © BrightSpace, 2026 The reuse of this document is authorised under a Creative Commons Attribution 4.0 International (CCBY 4.0) licence (https://creativecommons.org/licenses/by/4.0/). This means that reuse is allowed provided appropriate credit is given and any changes are indicated. For any use or reproduction of elements that are not owned by the BrightSpace consortium, permission may need to be sought directly from the respective right holders. Project information BrightSpace Horizon Europe project Grant Agreement No. 101060075 https://cordis.europa.eu/project/id/101060075 CALL: Innovative governance, environmental observations and digital solutions in support of the Green Deal WORK PROGRAMME Topic ID: HORIZON-CL6-2021-GOVERNANCE-01-12 EU agriculture within a safe and just operating space and planetary boundaries BrightSpace Project coordination: Wageningen Economic Research, The Hague, NL Contact: brightspace.wser@wur.nl | Website: www.brightspace-project.eu Project duration: 1 November 2022 – 31 October 2027.