Variable Inputs Allocation among Crops: A Time-Varying Random Parameters Approach[Allocation d'intrants variables entre les cultures : Une approche de paramètres aléatoires variant dans le temps]

In this paper, we propose an approach to allocate input uses among crops produced by farmers, based on panel data that includes input use aggregated at the farm-level. Our proposed approach simultaneously allows for (i) controlling for observed and unobserved farm heterogeneity, (ii) accounting for the potential dependence of input uses on acreage decisions, and (iii) ensuring consistent values of input use estimates. These are significant issues commonly faced in the estimation of input allocation equations. The approach is based on a model of input allocation derived from accounting identities, where unobserved input uses per crop are treated as time-varying random parameters. We estimate our model on a sample of French farms' accounting data, by relying on an extension of the Stochastic Approximation of Expectation Maximization algorithm. Our results show good performance of our approach in accurately allocating input uses among crops, for the crops the most frequently produced in our data sample in particular.