主 题：Deep Neural Network Empowered Two-stage Regression with a Non-linear First Stage (含有非线性第一阶段的深度神经网络增强回归)
报告人：陈涛 博士
时 间：2023年12月21日 14:00
地 点：崇仁楼110会议室
中文简介：在使用两阶段最小二乘回归进行因果推断时，工具变量（IVs）与内生解释变量之间的真实关系大多是未知的。因此，使用线性的第一阶段——一个参数化的第一阶段——进行传统建模并不能保证正确地确定这种关系。这种错误规定可能会削弱模型的识别能力，并随后导致不可靠的推断。在本文中，我们在两阶段回归模型中加入深度神经网络（DNNs），以帮助在第一阶段恢复IVs 与内生解释变量之间的真实关系。我们推导了基于多项式激活函数的DNN 估计器的大样本性质。然后，我们构建了一个用于弱识别的广义第一阶段F检验，并证明了这种检验的有效性，为使用这种基于DNN 的方法提供了指导原则。
英文简介：In causal inference with two-stage least squares regression, the true relationship between the instrumental variables (IVs) and the endogenous explanatory variables is mostly unknown. Hence, traditional modelling using a linear first stage – or, more generally, a parametric first stage – is not guaranteed to correctly specify this relationship. Such misspecification may weaken the model identification and lead to unreliable inference subsequently. In this paper, we incorporate deep neural networks (DNNs) in a two-stage regression model to help recover the true relationship between the IVs and the endogenous explanatory variables in the first stage. We derive the large sample properties of a DNN-based estimator formulated on the polynomial activation functions. Then we construct a generalized first-stage F-test for weak identification and justify the test validity, which provides a guideline for the use of this DNN-based method.