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Control Functions and Simultaneous Equations Methods

Authors: Richard Blundell , Dennis Kristensen and Rosa Matzkin
Date: 01 May 2013
Type: Journal article, American Economic Review: Papers and Proceedings,
DOI: 10.1257/aer.103.3.563


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. Download full version

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