Matching points: Supplementing instruments with covariates in triangular models
针对离散内生变量且工具变量取值较少的经济模型，提出一种通过匹配协变量与工具变量对来恢复阶条件、实现结果函数点识别的方法，并给出估计量。适用于教育回报和Head Start项目选择等实证场景。
Models with a discrete endogenous variable and an instrument that takes on fewer values are common in economics. This paper presents a new method that matches pairs of covariates and instruments to restore the order condition in this scenario and to achieve point-identification of the outcome function. The outcome function must be monotonic in a scalar disturbance, but it can be nonseparable. The first stage for the discrete endogenous variable needs to have a multi-index structure but allows for multidimensional heterogeneity. This paper also provides estimators of the outcome function. Two empirical examples of the return to education and of selection into Head Start illustrate the usefulness and limitations of the method. © 2023 Elsevier B.V.