Imposing Monotonicity in Stochastic Frontier Models: An Iterative Nonlinear Least Squares Procedure

Despite its importance, the monotonicity condition is typically overlooked in stochastic frontier analysis. This article illustrates a straightforward approach for the estimation of monotonic stochastic frontier models incorporating exogenous inefficiency effects. An iterative estimation algorithm based on nonlinear least squares is developed and the behavior of the proposed procedure is investigated through a set of Monte Carlo experiments. The simulation results suggest that imposing monotonicity may enhance the efficiency analysis in small samples and in presence of small signal-to-noise ratios. We find that, in these cases, the proposed algorithm performs similarly to the monotone Henningsen and Henning (2009) three-step procedure. Our results also highlight that the translog functional form is not able to naturally ensure monotonicity in presence of small sample sizes, especially when the model is not correctly specified. An application based on FADN agricultural data illustrates the usefulness of the proposed algorithm.