This paper considers a stochastic frontier production function which h
as additive, heteroscedastic error structure. The model allows for neg
ative or positive marginal production risks of inputs, as originally p
roposed by Just and Pope (1978). The technical efficiencies of individ
ual firms in the sample are a function of the levels of the input vari
ables in the stochastic frontier, in addition to the technical ineffic
iency effects. These are two features of the model which are not exhib
ited by the commonly used stochastic frontiers with multiplicative err
or structures, An empirical application is presented using cross-secti
onal data on Ethiopian peasant farmers. The null hypothesis of no tech
nical inefficiencies of production among these farmers is accepted. Fu
rther, the flexible risk models do not fit the data on peasant farmers
as well as the traditional stochastic frontier model with multiplicat
ive error structure.