Input/output selection in DEA under expert information, with application to financial markets

Data envelopment analysis (DEA), as generally used, assumes precise knowledge regarding which variables are inputs and outputs; however, in many applications, there exists only partial knowledge. This paper presents a new methodology for selecting input/output variables endogenously to the DEA model in the presence of partial (or expert's) knowledge by employing a reward variable observed exogenous to the operation of the DMUs. The reward is an allocation of a limited resource by an external agency, e.g. capital allocation by a market, based on the perceived internal managerial efficiencies. We present an iterative two-stage optimization model which addresses the benefit of possibly violating the expert information to determine an optimal internal performance evaluation of the DMUs for maximizing its correlation with the reward metric. Theoretical properties of the model are analyzed and statistical significance tests are developed for the marginal value of expert violation. The methodology is applied in Fundamental Analysis of publicly-traded firms, using quarterly financial data, to determine an optimized DEA-based fundamental strength indicator. More than 800 firms covering all major sectors of the US stock market are used in the empirical evaluation of the model. The firms so-screened by the model are used within out-of-sample mean-variance long-portfolio allocation to demonstrate the superiority of the methodology as an investment decision tool.