Econometric Modeling of Input-Driven Output Risk through a Versatile CES Production Function

The conventional functional form of the Constant-Elasticity-of-Substitution (CES) production function is a general nesting number other forms functions. Examples such functions include Leontief, Cobb–Douglas, and linear Nevertheless, CES specification still restrictive in multiple aspects. One example fact that marginal effect increasing input use always has to be increase variability output quantity by construction this function. This paper proposes generalized variant allows for various effects on probability distribution output. Failure allow possible input–output risk structure indeed one limitations limitation may result false inferences about input-driven risk. In light this, present solution problem. First, it shown familiar formulation suffers from very structural assumptions regarding considerations, restrictions lead biased inefficient estimates Following theme Just Pope’s approach, CES-based production-function overcomes shortcoming original introduced, three-stage Nonlinear Least-Squares (NLS) estimation procedure proposed presented. To illustrate approaches paper, two empirical applications irrigation fertilizer response using famous Hexem–Heady experimental dataset are provided. Finally, implications modeling risks discussed.