Christophe Gouel (PSAE-INRAE) avec Alain Carpentier (SMART-INRAE), Fabienne Femenia (SMART-INRAE), Obafémi Philippe Koutchadé (SMART-INRAE) et David Laborde (FAO)
This paper compares three tractable specifications of acreage choice for agricultural equilibrium models: (i) constant elasticity of transformation (CET), as commonly used in CGE models; (ii) heterogeneous land with Fréchet-distributed yields, inspired by quantitative trade theory; and (iii) multinomial logit, derived from entropy regularization and convex management costs. Within a unified production environment, we derive land allocation, production responses, and supply elasticities, and clarify microfoundations, calibration, and empirical restrictions. A key result shows that, when calibrated on identical benchmark shares and elasticities, CET and Fréchet specifications yield identical counterfactual production responses but differ in their implications for physical acreage: the Fréchet approach preserves area balance, whereas CET generally allocates efficient land rather than hectares. We show, however, that the Fréchet mechanism imposes severe restrictions, including implausibly large acreage elasticities and negative yield-composition effects far larger than those found in the limited comparable evidence. We then estimate a nested multinomial logit model on French farm-accounting panel data, obtain acreage elasticities consistent with the literature, and use these estimates to calibrate nested logit, CET, and Fréchet specifications to match the same local output responses. Counterfactual simulations show that matching local supply elasticities is not sufficient: away from the benchmark, the Fréchet selection mechanism can generate implausibly large acreage reallocations and yield declines, while the nested logit separates acreage and intensification responses more transparently. The analysis bridges CGE, quantitative trade, positive mathematical programming, and econometric acreage models, and guides calibration choices when physical land accounting and credible yield responses matter.