Nonparametric instrumental variables estimation for efficiency frontier

The paper investigates endogeneity issues in nonparametric frontier models. It considers a nonseparable model for a cost function C=φ(Y,U) where C and Y are the cost and the output, U is uniform in [0,1] and φ is increasing with respect to U. The cost frontier corresponds to U=0 and U can be interpreted as a normalized level of inefficiency. The endogeneity issue arises when Y is dependent of U. For identification and estimation, we use a nonparametric instrumental variables estimator of the model for fixed value U=α, and obtain an estimate of the α-quantile cost frontier φ(Y,α). This involves the solution of a non linear integral equation. If the true frontier φ(Y,0) is wanted, it is then estimated by estimating the bias correction φ(Y,0)−φ(Y,α) under additional regularity conditions. The procedure is illustrated through a simulated sample and with an empirical application to the efficiency of post offices.