A Comparison of Multivariate Logit and Translog Models for Energy and Nonenergy Input Cost Share Analysis

With the advent of the translogarithmic (translog) cost function has come greater interest in estimating systems of input share equations (Christensen and Greene, 1976; Berndt and Wood, 1975). A distinguishing feature of the translog cost function is that optimal input shares are linear in parameters. The linearity arises from the second-order approximation and facilitates estimation of the share system. Linearity, however may result in negative fitted shares if error terms are assumed to be additive and normally distributed. Woodland (1979) demonstrated that maximum likelihood estimators with an underlying Dirichlet distribution constrain fitted shares to be inside the zero-one interval for the sample. However, it is possible to obtain shares outside the zero-one interval when the model is used for forecasting. Moreover, there is no theoretical reason why input shares should be monotonic in input prices. If a third-order Taylor series expansion is assumed, the monotonicity restriction can be relaxed, but such an assumption sacrifices the principle of parametric parsimony (Fuss et al., 1978).