A Multicriteria Approach to Model Specification and Estimation

In decision theory, incommensurabilities among conflicting decision criteria are typically handled by multicriteria optimization methods such as Pareto efficiency and mean-variance analysis. In econometrics and statistics, where conflicting model criteria replace conflicting decision criteria, probability assessments are routinely used to transform disparate model discrepancy terms into apparently commensurable quantities. This tactic has both strengths and weaknesses. On the plus side, it permits the construction of a single real-valued measure of theory and data incompatibility in the form of a likelihood function or a posterior probability distribution. On the minus side, the amalgamation of conceptually distinct model discrepancy terms into a single real-valued incompatibility measure can make it difficult to untangle the true source of any diagnosed model specification problem. This paper discusses recent theoretical and empirical work on a multicriteria ``flexible least squares'' (FLS) approach to model specification and estimation. The basic FLS objective is to determine the ``cost-efficient frontier,'' that is, the set of estimates that are minimally incompatible with a specified set of model criteria. The relation of this work to previous work in econometrics, statistics, and systems science is also clarified.