We propose a shape-constrained production function estimator starting from the method described in Kumbhakar, Park, Simar, Tsionas 2006 (KPST).
We maximize the loglikelihood of a local linear estimator at each observation. We estimate the parameters for the noise and inefficiency distributions that are potentially heteroscedasticity.
The challenge to imposing shape constraints, such as monotonicity and concavity, is we need to jointly esitmate the maximum likelihood function for all observations while imposing the constraints. This is on-going research with Kevin Layer.