Title: "Applicability of Control Function Separability as a Condition for Feasible Control Function Estimation of Simultaneous Equations Models"
Abstract: An existing condition, called control function separability, characterizing the feasibility of control function estimation of nonparametric systems of simultaneous equations with scalar disturbances, developed by Blundell and Matzkin, 2014, is shown to be equivalent to a triangular representation condition. An alternative characterization of control function separability in terms of model structural derivatives is given. Necessary and almost necessary conditions are developed, showing that control function separability is restrictive to the point of effectively requiring two additional structural monotonicity conditions, symmetry in the inverse structural equations in the main dependent variable, and a control function that is linear in the structural disturbances. It is further shown how these conditions can be used easily to rule out control function separability, and thus to rule out the feasibility of the control function approach.