The main objective of the paper is to present a general framework for
estimating production frontier models with panel data. A sample of fir
ms i = 1, ..., N is observed on several time periods t = 1, ...T. In t
his framework, nonparametric stochastic models for the frontier will b
e analyzed. The usual parametric formulations of the literature are vi
ewed as particular cases and the convergence of the obtained estimator
s in this general framework are investigated. Special attention is dev
oted to the role of N and of T on the speeds of convergence of the obt
ained estimators. First, a very general model is investigated. In this
model almost no restriction is imposed on the structure of the model
or of the inefficiencies. This model is estimable from a nonparametric
point of view but needs large values of T and of N to obtain reliable
estimates of the individual production funct ions and estimates of th
e frontier function. Then more specific nonparametric firm effect mode
ls are presented. In these cases, only NT must be large to estimate th
e common production function; but again both large N and T are needed
for estimating individual efficiencies and for estimating the frontier
. The methods are illustrated through a numerical example with real da
ta.