Sensitivity Analysis of Arbitrarily Identified Simultaneous-Equation Models

Abstract

Current sociological theory often leads to underidentified simultaneous-equation models, some of which are "identified" by arbitrary specification. This paper applies the term sensitivity analysis to methods for exploring how numerical parameter estimates depend upon the identifying assumptions in such models. Three ad hoc sensitivity analysis methods are identified that have been used in the literature: (1) estimation under alternative specifications, (2) trying out a range of numerical values of underidentified parameters, and (3) the use of algebraic inequalities to obtain bounds on sample estimates of parameters. Mathematical programming is introduced here as a fourth method generalizing the last procedure and is then applied to a specific numerical example.