Partial identification in microeconometrics

我们打算应用一般工具变量（GIV）方法来推导离散结果和离散内生变量的非参数工具变量模型中的平均治疗效应（ATE）和局部平均治疗效应（LATE）。二元结果和离散内生变量的单方程工具变量模型一般不能点识别。在这种情况下，两阶段最小二乘（2SLS）方法通常用于通过指定线性参数限制来确保点识别。2SLS方法的优点是可以在Imbens和Angrist（1994）的限制下，方便地计算局部平均处理效应（LATE）的相合估计。然而，如果我们想估计其他有用的治疗效应参数，如平均治疗效应（ATE）或分位数治疗效应（QTE），我们必须施加一些额外的限制，以保持点识别，这听起来是站不住脚的，例如，假设治疗反应是同质的。我们可以考虑允许部分识别的计量经济学模型，而不是使用不合理的假设来完成点识别的不完整模型。我们可以得到一组观测等价的参数值，并且该组的范围可以足够重要，以获得有价值的信息，而无需进一步限制。在这种情况下，我们可以考虑非参数阈值交叉模型。通过使用Chesher和罗森（2017）提出的一般工具变量（GIV）方法，可以确定平均治疗效应（ATE）。为了应用这种方法，我可以使用英国家庭小组调查和英国人口普查纵向研究的数据集。我想用这些数据来分析犯罪率和高中辍学率。在本研究中，我决定先使用更具限制性的点辨识2SLS模型，再将其与GIV方法的结果进行比较。我们可以发现LATE的2SLS估计位于GIV估计的集合中。我们还可以比较使用不同工具变量的结果。最后，我们还可以通过使用Beschukov等人提出的方法来分析识别集上的推理。（2013 b，2015）和Belloni，Bugni和Beschukov（2018）提出的方法。与传统方法相比，本研究可以为政策相关的微观计量经济学问题提供一个更为保守和稳健的观点。

We intend to apply the general instrument variable (GIV) method to derive the set of both average treatment effect (ATE) and local average treatment effects (LATE) in nonparametric instrumental variable models for discrete outcomes and discrete endogenous variables. Single equation instrumental variable models for binary outcomes and discrete endogenous variables could not be point-identified generally. In this kind of setting, the two stage least squares (2SLS) method is commonly used to secure point-identification by specifying linear parametric restrictions. Theadvantage of 2SLS method is that we can easily compute the consistent estimator for local average treatment effects (LATE) under the restrictions of Imbens and Angrist (1994). However, if we want to estimate other useful treatment effects' parameters such as average treatment effects (ATE) or quantile treatment effects (QTE), we have to put some additional restrictions to maintain point identification which sounds untenable, for example, assuming the treatment response as homogenous. Instead of using unsound assumptions to complete the incomplete models with point identification, we can consider of econometric models that allow for partial identification. We can obtain a set of values for the parameters of interest which are observationally equivalent given the data, and the range of the set may be non-trivial enough to get valuable information without making further restrictions. In this circumstance, we can consider a nonparametric threshold-crossing model. By using the general instrument variable (GIV) method proposed by Chesher and Rosen (2017), the average treatment effects (ATE) can be set-identified. To apply this method, I may use the dataset of the British Household Panel Survey and UK Census Longitudinal Studies. I want to use these datasets to analyse the crime rate and the high school dropout rate. In this research, I decided to first use the more restrictive point identifying 2SLS model, and then compare it with the results of GIV method. We may find the 2SLS estimation of LATE lies in the set of GIV estimation. We can also compare the result of using different instrument variables. Finally, we may also analyse the inference on the identified set by using the method proposed by Chernozhukov et al. (2013b, 2015) and the method proposed by Belloni, Bugni and Chernozhukov (2018). This research could provide a more conservative and robust point of view on policy-related micro-econometrics problems compared to the traditional methods.