Conventional dual methods ignore production risk. Under production ris
k. estimation of the cost function is complicated even with risk neutr
ality because the observed actual output is not the decision-relevant
expected output. The decision-relevant cost function is not directly o
bserved. An ex ante cost function approach is proposed by embedding th
e dual distance function computation of expected output within the est
imation process. The resulting estimator is consistent and asymptotica
lly efficient. Monte Carlo results indicate that biases and mean squar
ed errors from conventional ex post methods are substantial whereas th
is approach approximates the efficiency of the directly observable cas
e. An empirical application to U.S. agriculture also produces more pla
usible estimates than conventional methods.