Non Parametric 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