Collier, Johnson and Ruggiero (2011) deal with the problem of estimating technical efficiency using regression analysis that allows multiple inputs and outputs. This revives an old problem in the analysis of production. In this note we provide an alternative maximum likelihood estimator that addresses the concerns. A Monte Carlo experiment shows that the technique works well in practice. A test for homotheticity, a critical assumption in Collier, Johnson and Ruggiero (2011) is constructed and its behavior is examined using Monte Carlo simulation and an empirical application to European banking. 
Notes on technical efficiency estimation with multiple inputs and outputs