Advances in Econometrics for Treatment Effect Bounds, Time-Varying-Parameter Nonstationary/Stationary Autoregressive Models, and Identification-Robust Inference

这个研究项目包括五个不同的主题。第一种方法是在具有两个连续或离散的潜在结果变量、一个二元治疗变量和一个独立于潜在结果的二元工具变量（IV）的模型中，为平均治疗效果（ATE）开发新的治疗效果界限。由于治疗效果的异质性，ATE未被确定。该研究首先考虑治疗效果分布为二元的情况，开发了利用独立性条件和IV限制的ATE边界。对于任意治疗效果分布，边界都成立。该界显式依赖于IV估计量的概率极限，且形式简单，有利于推理。所施加的假设并不比目前文献中考虑的假设更强或更弱。结果适用于经济学中的治疗效果分析和不完全依从性的医学随机试验分析。第二部分发展确定性时变自回归（AR）模型，该模型可能表现出（局部）非平稳性或平稳性以及两者之间的平滑过渡。PI考虑在时域内通过非参数平滑对参数进行估计。减少时变参数引起的偏差的标准方法在（局部）非平稳情况下失效。因此，需要引入新的减少偏置的方法。另一个需要解决的重要问题是局部平滑估计器初始条件的内生特性，这些初始条件由AR系数和的时变路径决定。PI分析了评估、测试、CS构建和预测的方法。他还开发了时变参数存在的测试。这项研究将提供一个有用的新的时间序列模型，允许时变的非平稳性/平稳性。第三，他开发了对矩条件模型的弱识别和识别失败具有鲁棒性的推理方法。现有的几种方法采用条件似然比型（CLR）检验和CS，将Moreira（2003）的CLR检验推广到线性IV回归模型。当参数的维数大于等于2时，现有的程序(i)不一定具有正确的渐近大小（ii）不减小到Moreira？在已知具有最佳功率特性的线性IV模型中进行CLR测试。PI引入了新的clr类型的程序，这些程序没有这些缺陷。最后两个研究领域是在弱辨识或缺乏辨识的条件下，对无限多条件矩非线性函数的不等式限制所定义的部分辨识模型的推理和拉格朗日乘子检验。本研究为社会科学数据的统计分析开发了新的方法。该项目将有利于社会，因为它将提高用于各种重要问题的数据分析的质量。这些方法将对经济政策分析有用，但也将用于分析具有类似统计特征的数据的医学和工程研究人员。

This research project includes five different topics. The first develops new treatment effect bounds for the average treatment effect (ATE) in models with two continuous or discrete potential outcome variables, a binary treatment variable, and a binary instrumental variable (IV) that is independent of the potential outcomes. The ATE is not identified due to treatment effect heterogeneity. The research develops bounds on ATE that exploit the independence condition and an IV restriction by first considering the case where the treatment effect distribution is binary. The bounds hold for arbitrary treatment effect distributions. The bounds depend explicitly on the probability limit of the IV estimator and are of a simple form, which is conducive to inference. The assumptions imposed are neither stronger nor weaker than those currently considered in the literature. The results are applicable to treatment effect analysis in economics and to the analysis of medical randomized trials with incomplete compliance.The second portion develops deterministically time-varying autoregressive (AR) models that may exhibit (local) nonstationarity or stationarity and smooth transitions between the two. The PI considers estimation of the parameters by nonparametric smoothing in the time domain. Standard methods of reducing bias due to the time-varying parameters fail in the (locally) nonstationary case. Hence, new bias reduction methods will need to be introduced. Another important issue to be addressed is the endogenous character of the initial conditions for the local smoothing estimator, which are determined by the time-varying path of the sum of the AR coefficients. The PI analyzes methods for estimation, testing, CS construction, and forecasting. He also develops tests for the presence of time-varying parameters. This research will provide a useful new time series model that allows for time-varying nonstationarity/stationarity.Third, he develops inference methods that are robust to weak identification and identification failure in moment condition models. Several existing methods employ conditional likelihood ratio-type (CLR) tests and CS's that generalize the CLR test of Moreira (2003) for the linear IV regression model. Existing procedures (i) do not necessarily have correct asymptotic size when the dimension of the parameter is two or greater and (ii) do not reduce to Moreira?s CLR test in the linear IV model, which is known to have optimal power properties. The PI introduces new CLR-type procedures that do not have these deficiencies.The last two areas of research are on inference in partially-identified models that are defined by inequality restrictions on nonlinear functions of infinitely-many conditional moments and Lagrange multiplier tests under weak identification or lack of identification. This research develops new methods for the statistical analysis of social science data. The project will benefit society because it will improve the quality of data analysis used for a variety of important questions. These methods will be useful for economic policy analysis but will also be used by medical and engineering researchers who analyze data with similar statistical features.