Estimating multiple-input- multiple-output production functions with an analysis of credit unions

In this article, we develop a methodology to estimate production functions characterized by multiple inputs and multiple outputs. Aggregate output is estimated assuming a piecewise-linear production possibility set and by measuring distance to the boundary using nonparametric techniques. The parameters of the production function are then estimated in a second-stage using Ordinary Least Squares (OLS). The primary advantage of this approach is the ability to measure the output aggregate nonparametrically. The approach developed in this article is applied to estimate credit union production. An alternative approach developed by Vinod (1968) specifies an extended Cobb-Douglas equation and estimates the parameters using canonical correlation. Our new approach is compared to Vinod's canonical correlation approach.