In this paper, we study a random-coefficients model for a binary outcome. We allow for the possibility that some or even all of the explanatory variables are arbitrarily correlated with the random coefficients, thus permitting endogeneity. We assume the existence of observed instrumental variables Z that are jointly independent with the random coefficients, although we place no structure on the joint determination of the endogenous variable X and instruments Z, as would be required for a control function approach. The model fits within the spectrum of generalized instrumental variable models, and we thus apply identification results from our previous studies of such models to the present context, demonstrating their use. Specifically, we characterize the identified set for the distribution of random coefficients in the binary response model with endogeneity via a collection of conditional moment inequalities, and we investigate the structure of these sets by way of numerical illustration.

中文翻译：

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二进制结果的工具变量随机系数模型。

在本文中，我们研究了二进制结果的随机系数模型。我们考虑了某些或什至所有解释变量与随机系数任意相关的可能性，从而允许内生性。尽管我们没有像控制函数方法那样对内生变量X和工具Z进行联合确定，但我们假定存在与随机系数共同独立的观测工具变量Z。该模型符合广义工具变量模型的范围，因此，我们将对此类模型的先前研究得出的识别结果应用于当前环境，从而证明了它们的使用。具体来说，