Control Functions and Simultaneous Equations Methods. - Blundell, Richard; Kristensen, Dennis; Matzkin, Rosa L (American Economic Review, 2013)
The control function approach is a convenient method of estimation in simultaneous equation systems. This requires that the system can be expressed in triangular form with variables satisfying a conditional mean independence restriction. Linear simultaneous models with additive errors can always be expressed in this form. However, in nonlinear nonadditive simultaneous systems, conditional independence requires a strong additional restriction known as control function separability. We argue that nonadditive models are a key characteristic of simultaneous models of economic behavior with unobserved heterogeneity. We review alternative 'system' approaches and document the biases that occur when the control function approach is used inappropriately.