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Abstract There has been considerable interest in estimations of input effects on the probability distribution of output. Most empirical and theoretical analyses utilize multiplicative stochastic specifications which are analyzed and found unduly restrictive, particularly since inputs that marginally reduce risk are not allowed. A more general stochastic specification is proposed, free of these a priori restrictions. The proposed functional form estimation is discussed and demonstrated with nitrogen‐response data and common log‐linear production functions. Though nitrogen is risk‐increasing, the marginal variance contribution is smaller when compared to estimates based upon multiplicative specification. Finally, stochastic specification error effects are analyzed.
Just et al. (Tue,) studied this question.