American Economic Review: Vol. 103 No. 3 (May 2013)


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Control Functions and Simultaneous Equations Methods

Article Citation

Blundell, Richard, Dennis Kristensen, and Rosa L. Matzkin. 2013. "Control Functions and Simultaneous Equations Methods." American Economic Review, 103(3): 563-69.

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.

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Blundell, Richard (U College London and IFS, London)
Kristensen, Dennis (U College London and IFS, London)
Matzkin, Rosa L. (UCLA)

JEL Classifications

C26: Single Equation Models: Single Variables: Instrumental Variables (IV) Estimation
C36: Multiple or Simultaneous Equation Models: Instrumental Variables (IV) Estimation

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