Control Functions and Simultaneous Equations Methods
探讨控制函数方法在联立方程系统中的适用性，指出其在非线性非加性模型中需要强额外限制，并回顾替代方法及不当使用导致的偏差。
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.