This paper proposes a new strategy for the identification of the marginal effects of an endogenous multivalued variable (which can be continuous, or a vector) in a model with an Instrumental Variable (IV) of lower dimension, which may even be a single binary variable, and multiple controls. Despite the failure of the classical order condition, we show that identification may be achieved by exploiting heterogeneity of the “first stage” in the controls through a new rank condition that we term covariance completeness. The identification strategy justifies the use of interactions between instruments and controls as additional exogenous variables and can be straightforwardly implemented by parametric, semiparametric, and nonparametric two-stage least squares estimators, following the same generic algorithm. Monte Carlo simulations show that the estimators have excellent performance in moderate sample sizes. Finally, we apply our methods to the problem of estimating the effect of air quality on house prices, based on Chay and Greenstone (2005, Journal of Political Economy 113, 376–424). All methods are implemented in a companion Stata software package.

中文翻译：

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用单一仪器识别多种边际效应

本文提出了一种新策略，用于识别具有低维工具变量 (IV) 甚至可能是单个二元变量的模型中的内生多值变量（可以是连续的或向量）的边际效应, 和多个控件。尽管经典顺序条件失败了，但我们表明，可以通过我们称之为的新等级条件利用控制中“第一阶段”的异质性来实现识别协方差完备性. 识别策略证明了使用仪器和控制之间的交互作为额外的外生变量是合理的，并且可以通过参数、半参数和非参数两阶段最小二乘估计器直接实现，遵循相同的通用算​​法。蒙特卡罗模拟表明，估计器在中等样本量下具有出色的性能。最后，我们根据 Chay 和 Greenstone (2005,政治经济学杂志113, 376–424)。所有方法都在配套的 Stata 软件包中实现。