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This article focuses on the demand system of French farmers concerning pesticides uses. We estimate the demand elasticities of herbicides, insecticides and fungicides with respect to pesticide expenditure, and considering crop differentiation. Then we compare two indexes that are used in agronomic literature to measure the intensity of pesticides uses. We retain a Linear Approximated Almost Ideal Demand System (LA/AIDS) specification. A Full-Information Maximum Likelihood estimation procedure is used for dealing with the problem of censored dependent variable. We consider two cross-sections observed in 2001 and 2006 covering pesticides uses of three crops. We confirm the previous results of the literature that farmers response to price variation is very low, with higher prices response in 2006 than in 2001. Moreover, we find that conditional herbicides expenditure elasticities are often higher than insecticides expenditure elasticities, but lower than those of fungicides. We find higher own-price elasticities for herbicides and fungicides than for insecticides, which is the less used. Finally, application dose seems statistically better to explain herbicides decision, whereas treatment frequency index appears better for insecticides and fungicides. However, most of elasticities are closed for dose and treatment frequency index.

This analysis shows that multivariate generalizations to the classical Heckman (1976 and 1979) two-step estimator that account for cross-equation correlation and use the inverse Mills ratio as a correction-term are consistent only if certain restrictions apply to the true error-covariance structure.We derive an alternative class of generalizations to the classical Heckman two-step approach that conditions on the entire selection pattern rather than the selection of particular equations and, therefore, uses modified correction-terms. This class of estimators is shown to be consistent. In addition, Monte-Carlo results illustrate that these estimators display a smaller mean square prediction error.